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Probing the genetic basis of gene expression variation through Bayesian analysis of allelic imbalance and transcriptome studies of oil palm interspecies hybrids

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Probing the genetic basis of gene expression variation through Bayesian analysis of allelic imbalance and transcriptome studies of oil palm interspecies hybrids

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Content Copyright 2021 Katrina Sherbina

Probing the Genetic Basis of Gene Expression Variation Through Bayesian Analysis of Allelic
Imbalance and Transcriptome Studies of Oil Palm Interspecies Hybrids

by

Katrina Sherbina

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(Computational Biology and Bioinformatics)

August 2021

ii

Acknowledgments
It takes a village to pursue a Ph.D. and I am so thankful to all the individuals in “my
village” that have mentored and supported me along the way. First and foremost, I would like to
thank my advisor Sergey V. Nuzhdin for his advising, encouragement, patience, and enthusiasm
for research and mentorship that made it possible for me to get this far. I will forever be grateful
for the wonderful people across the world that Sergey has introduced me to from whom I have
learned so much. Thank you to Ngoot-Chin Ting, Rajinder Singh, and all our collaborators in the
Malaysian Palm Oil Board for the opportunity to contribute to vital efforts to improve oil palm
breeding. I am very thankful for working with Lauren M. McIntrye, Fabio Marroni, and Luis
Novelo who have graciously and unwearyingly advised me not only on the allelic - León
imbalance project but also on other aspects of my dissertation. Thank you to my other
as committee members Paul D. Thomas and Liang Chen who have provided invaluable insight
early as my qualifying exams.
I am grateful to have had the privilege to work with past and current members of the
Nuzhdin lab. Thank you to Peter L. Chang, Wendy Vu, and all my former officemates Junsong
Zhao, Yerbol Kurmangaliyev, Asif Zubair, Hossein Asgharian, Vasantika Suryawanshi, and
Christopher Conow for your conversations on research and life and making me excited to come
into the office. I will cherish not only the work we did but the friendships fostered and all the
milestones we celebrated together.
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I would also like to thank my family, friends, and fiancé for their unwavering support and
believing in me when I had my doubts. I am forever indebted to my parents for instilling in me
my work ethic and always encouraging me to pursue my academic goals no matter how hard it
would be or how long it would take. Finally, thank you to my fiancé for being my rock through
the challenges of graduate school and helping me work through and prepare for various
milestones in my career.

iv

Table of Contents
Acknowledgments........................................................................................................................... ii
List of Tables ................................................................................................................................. vi
List of Figures ............................................................................................................................... vii
Abstract .......................................................................................................................................... ix
Chapter 1: Introduction ....................................................................................................................1
1.1. From QTL to genetical genomics .......................................................................1
1.2. eQTL and ASE measure different aspects of gene expression regulation .........3
1.3. Overview of subsequent chapters .......................................................................6
Chapter 2: Expression of fatty acid and triacylglycerol synthesis genes in interspecific hybrids
of oil palm ........................................................................................................................................9
2.1. Introduction ........................................................................................................9
2.2. Materials and Methods .....................................................................................12
2.2.1. Palm materials ...........................................................................................12
2.2.2. Oil palm mesocarp RNA extraction ..........................................................13
2.2.3. Library preparation and transcriptome sequencing ...................................14
2.2.4. RNA-seq data analysis ..............................................................................14
2.2.5. Differential expression analysis ................................................................16
2.2.6. Quantitative real-time PCR (qRT-PCR) ...................................................16
2.3. Results ..............................................................................................................18
2.3.1. Gene functional annotation .......................................................................18
2.3.2. Expression of genes related to FA and TAG biosynthetic processes ........20
2.3.3. DEGs in different genetic backgrounds across early and late
developmental stages .............................................................................................24
2.3.4. Evaluation of the QTL-linked DEGs using qRT-PCR ..............................28
2.4. Discussion .........................................................................................................32
2.5. Data Availability...............................................................................................38
2.6. Author contributions .........................................................................................38
Chapter 3: Identification and Functional Characterization of Misexpressed Genes in Elaeis
guineensis and oleifera Interspecies Hybrids ................................................................................39
3.1. Introduction ......................................................................................................39
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3.2. Materials and Methods .....................................................................................42
3.3.1. Identification of orthologous genes and GO annotation ...........................42
3.3.2. Acquiring publicly available RNA-seq data on oil palm mesocarp gene
expression ..............................................................................................................43
3.3.3. RNA-seq data processing ..........................................................................43
3.3.4. Identification of misexpressed genes ........................................................44
3.3.5. GO enrichment of co-expressed clusters of misregulated genes ...............44
3.3.6. Genotyping using RNA-seq data ...............................................................45
3.3.7. Detecting significant differences in expression between genotypes .........46
3.3. Results ..............................................................................................................47
3.3.1. Detection of misexpressed genes in BC1 genotypes .................................47
3.3.2. Functional characterization of modules of misexpressed genes ...............53
3.3.3. Significant differences in expression of misexpressed genes between
homozygous and heterozygous samples ................................................................57
3.4. Discussion .........................................................................................................61
3.5. Acknowledgement of Collaborators .................................................................64
Chapter 4: Power Calculator for Detecting AI Using Hierarchical Bayesian Model ....................65
4.1. Introduction ......................................................................................................65
4.2. Methods ............................................................................................................68
4.2.1. Model description ......................................................................................68
4.2.2. Simulations ................................................................................................70
4.2.3. Computing type I error and power ............................................................73
4.3. Results ..............................................................................................................74
4.4. Discussion .........................................................................................................84
4.5. Availability of materials and methods ..............................................................86
4.6. Acknowledgement of Collaborators .................................................................87
Chapter 5: Discussion ...................................................................................................................88
References ......................................................................................................................................91
Appendix A ..................................................................................................................................120
Appendix B ..................................................................................................................................121
Appendix C ..................................................................................................................................123

vi

List of Tables
Table 2.1. Functional annotation of 43,920 potential genes (141,513 putative isoforms) against
four public databases (From Ting, NC et. al. 2020). .................................................................... 19
Table 2.2. The number of genes with a significant change in expression among the OxG, BC2
(2.6-1) and (2.6-5) populations, mesocarp developmental stages (late and early) and C16.0
content (high and low). ................................................................................................................. 26
Table 2.3. Differentially expressed genes (DEGs) related to synthesis of FA (GO:0006633,
GO:0006636 and GO:0008610) and TAG (GO:0019432) identified by comparing the two
mesocarp developmental stages (late and early) and amongst the OxG, BC2 (2.6-1) and (2.6-
5) populations................................................................................................................................ 27
Table 3.1. As much as almost 70% and 98% of genes misexpressed in at least one BC1 and all
BC1 genotypes, respectively, were expressed in one or more E. oleifera x E. guineensis F1
and backcross 2 (BC2) hybrids from a previously analyzed RNA-seq dataset. ............................ 49
Table 3.2. GO term enrichment across all misexpressed genes. ................................................... 52
Table 3.3. DESeq2 was used to determine whether there was a significant difference in
expression between genotypes for one of 5 genes misexpressed in all BC1 genotypes. .............. 59
Table 3.4. For each one of 5 genes misexpressed in all BC1 genotypes, DESeq2 was used to
determine whether there was a significant difference in expression between genotypes that is
different between early and late developmental stages considered to be up to and after 133
days after pollination (DAP), respectively.. .................................................................................. 60
Table 4.1. The expected number of reads ( 𝜇𝜇 ) aligning better to allele g1 than g2, 𝑥𝑥𝑥𝑥 , 𝑘𝑘 ; better
to allele g2 than g1, 𝑦𝑦𝑥𝑥 , 𝑘𝑘 ; or ambiguously, that is equally well to both alleles, 𝑧𝑧 𝑥𝑥 , 𝑘𝑘 . ................. 69
Supplementary Table C.1. Results for all scenarios under which read counts were simulated
and AI was estimated by Bayesian model. ................................................................................. 124

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List of Figures
Figure 1.1. eQTL versus ASE. ........................................................................................................ 5
Figure 2.1. FPKM expression levels for various genes mapped to the fatty acid biosynthesis
pathway. ........................................................................................................................................ 22
Figure 2.2. RNA-seq data from 24 samples plotted on the first two principal components
indicating the major differences in total gene expression between samples.. .............................. 25
Figure 2.3. Normalized expression profiles of FATB_1 (XLOC_016685) and the isoforms
(TCONS_) quantified by qRT-PCR compared to transcriptomic profiles. .................................. 29
Figure 2.4. Normalized expression profiles of LACS4_1 (XLOC_016055) and the isoforms
(TCONS_) quantified by qRT-PCR compared to transcriptomic profiles. .................................. 31
Figure 3.1. The number of expressed genes in the 30 largest sets of intersection between the
groups of expressed genes in each genotype, that is Elaeis oleifera (EO), (EG), and a BC1
genotype. ....................................................................................................................................... 48
Figure 3.2. The number of misexpressed genes in the 50 largest sets of intersection between
the groups of misexpressed genes in each BC1 genotype denoted by “BC” followed by a
number. ......................................................................................................................................... 50
Figure 3.3. Distribution of expression of misexpressed genes in each BC1 RNA-seq library .... 51
Figure 3.4. Clusters of genetically correlated transcriptional profiles of genes misexpressed in
at least one (A) and in all (B) 21 BC1 genotypes. ......................................................................... 55
Figure 3.5. GO enrichment within each of 14 clusters of genes misexpressed in at least one
BC1. TopGO enrichment was performed for each of the 14 clusters using the weight01 method
and the biological process ontology.. ............................................................................................ 56
Figure 3.6. Comparison of the range of expression in TPM for BC1 samples that are
homozygous for the E. guineensis allele (EG/EG) or heterozygous (EG/EO) for one of the
genes misexpressed in all BC1 populations.. ................................................................................ 58
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Figure 4.1. Read counts are simulated in two conditions independently with a specific number
of simulations, allele specific reads, biological replicates (bioreps), level of allelic imbalance
(AI) θ, and probability of an allele g1 (g2) specific read. ............................................................. 72
Figure 4.2. Type I error is always less than 0.05 across number of simulations, number of
allele specific reads, and magnitude of deviation from the null when testing H1 or H3. ..............75
Figure 4.3. Type I error was less than 0.08 across different numbers of biological replicates
(bioreps) and numbers of allele specific reads (also per biorep). ..................................................77
Figure 4.4. At any given effect size or Δ𝐴𝐴𝐴𝐴 , the power to detect AI in a condition or differing
levels of AI between conditions is consistent across the number of simulations. .........................78
Figure 4.5. The power to detect AI in a condition or differing levels of AI between conditions
increases as the number of allele specific reads per biorep increases but does plateau for higher
effect sizes and Δ𝐴𝐴𝐴𝐴 . ......................................................................................................................79
Figure 4.6. Increasing the number of allele specific reads and, for at least 480 allele specific
reads, increasing the number of biological replicates increases power to detect AI or a
difference in AI between conditions. .............................................................................................80
Figure 4.0.7. Increasing the number of biological replicates increases the power to detect AI
or a difference in AI between conditions. ......................................................................................81
Figure 4.8. The power to detect AI in a condition or differing levels of AI between conditions
increases as the effect sizes or ΔAI increases for higher effect sizes and ΔAI, but does plateau ...83
Supplementary Figure A.1. RNA-seq data from 24 samples plotted on all pairs of the first six
principal components (PC) except for PC 1 and 2. ......................................................................120
Supplementary Figure C.1. For each scenario simulated under H1 null, H2 null, H3 null, we
counted the proportion of simulations where the Bayesian evidence against allelic balance in
condition 1 (H1) is less than 0.05 (A), against allelic balance in condition 2 (H1) is less than
0.05 (B), and against equal levels of AI (H3) is less than 0.05 (C). We generated a matrix of
these proportions where each row (1000 of them) is a simulation and each column is a scenario
and created kernel density plots of the row averages of this matrix. ...........................................169

ix

Abstract
Studying transcriptional variation is important in establishing how genotypic variation
influences variability in complex organismal phenotypes. Insights from such studies are vital to
improving crop breeding and better understanding human health and disease. Here, we present
two transcriptomic studies on a globally important oil crop, oil palm, and interspecific hybrids.
Such studies have previouslly been limited to one oil palm species, Elaeis guineensis. In the first
study, we validate candidate genes from prior QTL studies involved in the regulation of oil
biosynthesis using RNA-seq data from two oil palm hybrid generations that have not previously
been analyzed by this approach. We also find fatty acid and triacylglycerol synthesis genes
differentially expressed between hybrid generations and up-regulated in later versus earlier
stages of mesocarp development. In the second study, we used an independently generated
backcross 1 population to look further into differences in expression between the hybrid and pure
species parent due to how much genomic material the hybrid inherits from either parent. We find
about 3700 genes expressed in at least one backcross 1 genotype but silent in both pure species
parents that are enriched for several biological processes previously implicated in hybrid
dysfunction or vigor. Focusing on five of these genes containing biallelic SNPs, we found three
with increased in expression in samples heterozygous for that gene and, of these, two with this
pattern specific to the later mesocarp developmental stage specific for two. While prior
transcriptomic studies of regulatory incompatibilities find genes expressed in hybrids outside of
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their normal range of expression in parents, we find evidence for a novel type of incompatibility
that leads to expression of genes in hybrids that are normally suppressed in parents.
Measuring allele specific expression (ASE) allows us to identify specific genetic
regulatory mechanisms that govern observed patterns of expression variation. Unequal
expression of two alleles of a gene is referred to as allelic imbalance (AI). While there is
extensive evidence on what factors inflate type I error in AI studies, the literature is lacking in
what affects the power to not only detect AI in a condition (i.e. tissue, life stage, environment)
but differences in AI between conditions. Are more reads or more biological replicates necessary
to boost power to detect differences in AI? I develop software that allows users to simulate read
count data with a previously published Bayesian model of AI with any number of replicates,
reads, and AI and assess type I error and power. Using this software, I present the results of a
simulation study that shows that increasing the number of biological replicates boosts power
more so that increasing coverage without increasing type I error. I argue that these insights will
inform the design of further RNA-seq experiments of oil palm interspecies hybrids balancing the
need for more biological replicates with the challenges of breeding these crops with the goal of
increasing power to study AI of potential candidate genes involved in hybrid incompatibilities
and heterosis.

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Chapter 1
Introduction
1.1. From QTL to genetical genomics
Uncovering the genetic basis of variation in complex traits between individuals and
species has been and continues to be critical for understanding disease etiology (J. Li &
Burmeister, 2005) and evolutionary biology (Anderson et al., 2014) as well as improving crop
breeding (Varshney et al., 2005). One of the long-standing statistical methods employed in this
pursuit is quantitative trait loci (QTL) analysis or mapping. A quantitative trait is a phenotype
exhibiting a continuous range of values in a population and may be influenced by several
polymorphic genes (Kearsey, 1998; Members of the Complex Trait Consortium, 2003). The goal
of QTL analysis is to identify marker loci such that genotypic variation at these loci explains
variation in the quantitative trait of interest (Doerge, 2002; Kearsey, 1998; T. F. C. Mackay et
al., 2009).
Ideally, we would like to pinpoint candidate genes within QTL that cause the phenotypic
variation, but this is challenging when often a QTL encompasses potential thousands of genes.
Even fine mapping alone may not substantially reduce the candidate gene set to a size that can be
feasibly studied further (Kearsey, 1998; Wayne & McIntyre, 2002). To address this challenge,
many have proposed coupling QTL studies with differential expression analysis of genes within
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these loci, a paradigm termed genetical genomics (Jansen, 2001; Doerge, 2002; Wayne &
McIntyre, 2002; J. Li & Burmeister, 2005; T. F. C. Mackay et al., 2009). In so doing, gene
expression is treated as the quantitative trait and the polymorphic marker loci that explain
variation in this trait are called expression QTL (eQTL). This approach has been applied to study
genetic basis of transcriptional variation pertinent to developmental traits, disease, and
environmental responses in many different organisms including flies (Wayne & McIntyre, 2002),
yeast (Brem, 2002), rice (Zhao et al., 2017), soybean (Xu et al., 2013), maize, mice, and humans
(Schadt et al., 2003). Except for Xu et al. (2013), who used quantitative PCR, these studies used
complementary DNA (cDNA) microarrays to profile and quantify all transcripts within a specific
developmental stage or tissue type, referred to as the transcriptome. For non-model organisms
though, there are challenges to using microarrays to study QTL, including the lack of
microarrays designed with sequence probes specific to that organism and high density genetic
maps and pedigree information (Vasemägi & Primmer, 2005). However, it has been suggested
that this may be remedied with the use of several closely related single-species arrays or single
array with probes from multiple species depending on whether the goal is to study intra- or inter-
species gene expression variation (Oshlack et al., 2007).
In the era of next generation sequencing (NGS), the advent of RNA sequencing (RNA-
seq) has advanced the study of the genetic regulation of gene expression variation in both model
and non-model organisms. Several platforms to perform RNA-seq are available with most
currently popular ones involving the following sequence of steps: extraction and purification of
target RNA, fragmentation, conversion to a library of cDNA molecules flanked by adapter
sequences, and subsequent high throughput sequencing (Z. Wang et al., 2009; Van den Berge et
al., 2019). RNA-seq has several improvements over microarrays, including being able to detect a
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wider range of expression, simultaneously quantify and discover previously unknown transcripts,
and detect sequence variants to measure allele specific expression in heterozygous individuals al
without requiring prior sequence information (Z. Wang et al., 2009; Weber, 2015). However,
RNA-sequencing still has some drawbacks in analyzing expression in non-model organisms.
Given that most often RNA-seq short reads are mapped onto a reference transcriptome or
genome, a reference from a related species must be used if one is not available for the non-model
species of interest. However, you risk not being able to map reads if the reference transcriptome
is incomplete, such as when transcript information is lacking for distinct developmental stages or
tissue types, or missing expression of genes that could be in the non-model organism but are
absent in the related species (Weber, 2015; J. W. S. Brown et al., 2017). The challenges to
having complete transcriptomes are already being addressed with development of single-cell
RNA-seq and so called third-generation technologies that can sequence long-read, single
molecules single molecule, long-read sequencing. However, third-generation technologies are
still too costly to achieve deep enough coverage to have sufficient power to quantify gene
expression and assess differential expression. Therefore, we continue to use short-read RNA-seq
to measure the level of gene expression (J. W. S. Brown et al., 2017; Van den Berge et al., 2019).
1.2. eQTL and ASE measure different aspects of gene expression regulation
Gene expression is regulated by cis, trans, and cis by trans interaction effects (Genissel et
al., 2007; Wittkopp et al., 2004; Fear et al., 2016a). Cis regulation is due to polymorphisms (i.e.
SNPs, small indels, transposable element insertion) within the gene region (i.e. promoters,
enhancers, or other noncoding DNA sequences) (Genissel et al., 2007; Buchberger et al., 2019).
Trans effects are a result of modifiers, such as transcription factors, which may not be adjacent to
the gene (Genissel et al., 2007; T. Pastinen, 2004).
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While eQTL are often categorized as cis or trans, it is more appropriate to discuss local
(within some physical distance of the gene) and distant (elsewhere in the genome) eQTLs, each
of which could be a result of cis and/or trans effects (Rockman & Kruglyak, 2006). Thus, a local
eQTL is not necessarily within the regulatory region of the gene. Local regulation may be due to
trans effects, such as a trans-acting regulator in linkage disequilibrium with its target gene or
when the coding sequence of an autoregulatory gene is altered inducing a feedback loop (T.
Pastinen, 2004; Rockman & Kruglyak, 2006). Distant regulation could be the result of a cis x
trans effect, such as when a noncoding DNA element is in close physical contact to the gene it
regulates because of interchromosomal interactions (Rockman & Kruglyak, 2006).
While eQTL studies identify polymorphic loci common to a population that affect overall
gene expression, allele specific expression (ASE) is quantified within each individual by
measuring the expression of each allele at heterozygous sites within coding regions. ASE can
then identify allelic imbalance (AI), which occurs when two alleles within a diploid are not
expressed equally (Wittkopp et al., 2004). The trans and environmental effects on expression of
alleles are assumed to be the same between two alleles when ASE is measured within the same
sample (i.e. tissue, cellular environment) (Tomi Pastinen, 2010). Thus, while an eQTL is
evidence for cis regulation, differences in AI within the same tissue or cellular environment
between individuals of a population is indicative of cis regulatory variation.

5

Figure 1.1. Assume you have collected RNA-seq data from a population of four individuals with the portrayed
haplotypes G1, G2, G3, and G4 at a distinct genomic locus. The coding region is denoted by a box with an arrow
pointing toward the direction of transcription. The sequence to the left of the coding region is the non-coding,
regulatory region. (B) There are differences in the total amount of gene expression (total read count) within this
population of four haplotypes, which indicates that the locus is an eQTL. While eQTL analysis is conducted on the
population level, ASE is measured on the individual level. Given that each individual (G1, G2, G3, or G4) has at
least one single nucleotide polymorphism within the coding region, we can determine the proportion of reads that
map better to one or the other allele (A or T), a.k.a. allele specific reads. To improve the power to detect allelic
imbalance (AI), we can also account for the reads that map equally well to both alleles (ambiguous).
eQTL analyses suffer from the same issues previously described with QTL in general.
We want to isolate specific genetic variants within an identified eQTL that affect gene
expression variation, but such fine mapping is challenging given that an eQTL can contain many
variants, not all of which are causal but are linked to the causal variant through linkage
disequilibrium (J. Zou et al., 2019). To improve fine mapping, several approaches have been
suggested to combine eQTL and ASE under the assumption that the causal variant within the
eQTL will have a heterozygosity pattern that coincides with differences in AI between
individuals (Liang et al., 2021; Y. Liu et al., 2020; Sun, 2012; van de Geijn et al., 2015; J. Zou et
al., 2019). However, the result of eQTL and AI are not always concordant (Findley et al., 2021;
Skelly et al., 2011). It has recently been shown that large-scale eQTL mapping studies using
GTEx, GEUVADIS, and I2QTL data have missed as much as half of the causal variants
6

identified by ASE depending on the tissue type analyzed (Findley et al., 2021). This suggests that
this fine mapping approach may still miss causal variants.
1.3. Overview of subsequent chapters
In the next two chapters, I discuss our work studying gene expression variation using
RNA-sequencing of several generations of interspecies hybrids of a globally important crop, oil
palm. As much as 40% of the vegetable oil harvested globally comes from oil palm even though
only 10% of land worldwide used to cultivate oil crops is used to grow oil palm (Qaim et al.,
2020). The oil palm belongs to the genus Elaeis which consists of two species estimated to have
diverged 51 million years ago: Elaeis guineensis originating from West Africa and Elaeis
oleifera from South America. These two species vary significantly in the types of oils produced
in the mesocarp, which is the middle layer of the pericarp of the fruit, with that of E. oleifera
containing more oleic and linoleic acids and less palmitic and other saturated fatty acids in
comparison to E. guineensis (Sambanthamurthi et al., 2000). While E. oleifera has several
desirable traits, such as a higher ratio of unsaturated to saturated fatty acids, lower height and
resistance to disease, E. guineensis has a higher oil yield making it more commercially viable
(Singh et al., 2013). Research is ongoing to see whether it is feasible to create oil palm
interspecies hybrids by conventional breeding techniques that exhibit favorable traits from both
pure species parents.
The second chapter is a reproduction of our published (N. Ting et al., 2020) analysis of
significant differences in gene expression between F1 and BC2 hybrids of E. guineensis and E.
oleifera. There has been only one other study to the best of our knowledge analyzing the
transcriptome of an oil palm hybrid and it was performed on a different generation cross (Guerin
et al., 2016). It is important to remember that collecting mature fruit bunches to collect mesocarp
7

samples is a challenging task given it takes 3 years for an oil palm to reach maturity and 6-10
years to reach peak productivity (Srestasathiern & Rakwatin, 2014). Our work followed up on
candidate genes implicated in variation in palmitic acid, which is a saturated fatty acid, and
iodine value, a measure of unsaturation, from previous QTL studies. We found several genes
within these QTL regions with statistically significant differences in gene expression between
different hybrid populations and mesocarp developmental stages suggesting a possible gene
regulatory mechanism for variation in these phenotypes.
The third chapter describes observations of gene expression misregulation in oil palm
hybrids using published RNA-sequencing data (Guerin et al., 2016; N. Ting et al., 2020). We
find a significant number of genes that are expressed in the mesocarp of BC1 oil palm hybrids,
but not expressed in the same tissue of either of the pure parent species. Most of these genes are
also expressed in the mesocarp of F1 and BC2 hybrids. These observations indicate an extreme
form of transgressive expression that has not been previously reported to the best of our
knowledge. These misregulated genes seem to be enriched for some biological processes
previously implicated in hybrid dysfunction and heterosis. Furthermore, there is a statistically
significant difference in expression between palms that are homozygous for the E. guineensis
allele and heterozygous for some of the misexpressed genes that is specific to a mesocarp
developmental stage. We propose that this expression misregulation is evidence for a
relationship between hybrid vigor and genetic incompatibilities, the latter which are typically
associated with hybrid dysfunction and not vigor.
Given that previous ASE studies have linked cis regulatory variation to heterosis (Shao et
al., 2019) and hybrid incompatibility (Mugal et al., 2020), it is only natural to consider
measuring ASE in oil palm hybrids to further probe possible regulatory mechanisms for
8

observed gene expression variation. The only ASE study that we are aware of in oil palm is that
of Guerin et al. (2016), who only looked at ASE in seven fatty acid synthesis genes finding no
evidence of AI. This begs the question: what resources do we need to perform a genome-wide
study of ASE in oil palm hybrids?
The fourth chapter details an extensive simulation study to address questions unanswered
in existing literature on what experimental design factors influence the power to detect context-
specific AI. Do you need more biological replicates or sequencing coverage to have sufficient
power to detect a difference in AI between two conditions, which could be different tissue or cell
types or environments? We find that it is more difficult to detect a difference in AI between
conditions than AI within a condition. While Type I error is low across all parameters, the power
varies considerably depending on the number of replicates, sequencing coverage, and true level
of AI within your samples. We advocate thoughtfully weighing the cheaper cost increasing
sequence coverage with few biological replicates against the decrease in statistical power with
having less replicates in comparison to more replicates with increased coverage divided amongst
them.
In the fifth and final chapter, I summarize observations from the previous chapters and
discuss how they apply to measuring ASE in oil palm interspecies hybrids. I highlight the
potential biases in detecting AI given the available reference genomes for the pure species
parents and the need to have sufficient replicates of genotypes of interest to have sufficient
power to detect AI.

9

Chapter 2
Expression of fatty acid and triacylglycerol synthesis genes in interspecific
hybrids of oil palm

Material from: Ting, NC., Sherbina, K., Khoo, JS. et al. Expression of fatty acid and
triacylglycerol synthesis genes in interspecific hybrids of oil palm. Sci Rep 10, 16296 (2020).
https://doi.org/10.1038/s41598-020-73170-5
These authors contributed equally: Ngoot-Chin Ting and Katrina Sherbina.
Unless stated otherwise, please refer to the published paper for Supplementary Figures and
Table.

2.1. Introduction
Currently, palm oil (with kernel oil) is the most important vegetable oil with ~ 75.2
million tons traded globally (Kushairi et al., 2018). In comparison, other major oil crops supplied
only 2.6–54 million tons (USDA, 2017). The traded commodity provides an economic lifeline to
many countries and people in Southeast Asia and Latin America. Oil palm is the subject of
numerous research and development initiatives to further improve oil yield as well as modify its
10

fatty acid composition (FAC). Studies were initiated as early as in the 1970s to decipher the
genetic basis of important economic traits of oil palm (E Barcelos et al., 2002; Billotte et al.,
2001; Ho et al., 2007; Jouannic et al., 2005; Low et al., 2014; Maizura et al., 2006; Purba et al.,
2000; Rajanaidu et al., 2000; Singh et al., 2008, 2009; Montoya et al., 2014; Ong, 2016; N.-C.
Ting et al., 2016). The biosynthesis of fatty acids (FAs) and regulation of triacylglycerol (TAG)
production are of particular interest because of the potential to produce specific feedstocks for a
whole range of industries.
The development of next generation sequencing (NGS) technologies provides the
opportunity for a more in-depth analysis of genes expressed, especially to understand the
genome-wide regulatory mechanisms of oil biosynthesis in oil palm. Large-scale exploitation of
NGS data for studying regulation and transcription of genes that govern FA and TAG synthesis
has been reported for oil palm. (Tranbarger et al., 2011) reconstructed the palm oil biosynthesis
pathway in the mesocarp tissue. They revealed that the plastidial FA synthesis and the
endoplasmic reticulum (ER)-based TAG synthesis are regulated by two distinct transcriptional
programmes. The authors confirmed earlier findings by (Ramli et al., 2008) that FA synthesis
exerts a major control on the synthesis of storage oil. They showed that FA synthesis is most
likely regulated by WRINKLED (WRI1), which encodes an Apetala 2 (AP2) ethylene response
element binding protein family transcription factor (TF). The regulatory role played by WRI1
was further supported by other studies (Bourgis et al., 2011; Dussert et al., 2013; Guerin et al.,
2016; Jin et al., 2017). A bi-genic interaction via WRI1 co-expressed with palmitoyl-acyl carrier
protein (ACP) thioesterase (FATB/PATE) resulted in an increase in total oil produced (Dussert et
al., 2013). The interaction network was further expanded by examining the co-expression of 23
11

genes from the oil palm FA synthesis pathway with other biological processes i.e. glycolysis,
starch metabolism, plastid biogenesis and auxin transportation (Guerin et al., 2016).
Examining differential expression patterns of quantitative trait loci (QTLs) associated
candidate genes and transcripts is an exciting new area for candidate gene validation in plants.
This has provided interesting insights into the regulatory mechanisms of genes influencing
quantitative traits. In chickpea (Cicer arietinum L.) for example, several SNP-containing
candidate genes associated with height were shown to be differentially expressed between tall
and dwarf/semi-dwarf parental lines (Kujur et al., 2016). Similarly, in potato (Solanum
tuberosum L.), a number of genes that were differentially expressed between susceptible and
resistant genotypes were also found in the genomic region associated with resistance to
Phytophthora infestans (late blight) (Muktar et al., 2015). Additionally, in sorghum (Sorghum
bicolor L. Moench), candidate genes regulating nitrogen use efficiency (NUE) were revealed by
the combined use of conventional QTL analysis and differential expression of genes (DEGs) in
samples having contrasting NUE (Gelli et al., 2017). This strategy, to the best of our knowledge,
has not been reported for oil palm although QTL information is available for many important
traits including FAC (Montoya et al., 2013; N.-C. Ting et al., 2016).
To date, almost all publications on transcriptome analysis in oil palm are based on E.
guineensis, the commercially cultivated species in most of the oil palm growing countries. A
second species of South American origin, E. oleifera, has lower yield but interesting
characteristics, such as higher unsaturated oil content, resistance to some diseases, and reduced
height (Edson Barcelos et al., 2015; Rao et al., 1989). As such, interspecific hybrid breeding has
often carried out to introgress the desirable traits from E. oleifera into E. guineensis through F1
(OxG) and repeated backcrossing (BC) (Gomes Junior et al., 2016; Montoya et al., 2014; Soh et
12

al., 2017). However, transcriptome analysis has not been reported for the interspecific OxG
hybrids and, so far, is only available for interspecific backcross-one (BC1) palms (Guerin et al.,
2016). Data for subsequent recurrent backcrossing, such as BC2 and BC3, are also lacking.
Therefore, in the present study, the global expression profiles of FA and TAG related genes
(including their putative isoforms) in OxG and BC2 palms were evaluated. Differentially
expressed genes were also identified in different genetic backgrounds across two developmental
stages as well as between palms with contrasting palmitic acid (C16:0) content. FA-associated
candidate genes, including FATB (/PATE), that were within the confidence intervals of the QTL
previously identified for C16:0 and iodine value (IV, a measure of the degree of unsaturation) of
mesocarp oil (N.-C. Ting et al., 2016) were further evaluated using quantitative real-time PCR
(qRT-PCR). In OxG, these major QTLs which account for up to 69.0% of the phenotypic
variation explained (PVE), were mapped to CHR03 (scaffolds p5_sc00001 and p5_sc00104) of
the current oil palm genome build. Interestingly, the same QTL region was also identified
independently in two interspecific BC2 populations (N.-C. Ting et al., 2016). In addition, we also
discuss the fact that present findings in many aspects either support or have supporting evidence
from the QTL and transcriptome analyses previously carried out for interspecific BC1
populations (Guerin et al., 2016; Montoya et al., 2013).
2.2. Materials and Methods
2.2.1. Palm materials
An interspecific OxG (Colombian E. oleifera, UP1026 x Nigerian E. guineensis, T128)
and two separate BC2 (2.6–1 and 2.6–5) populations from a breeding program at United
Plantations Berhad, Perak, Malaysia were sampled for this study (Supplementary Table S1). The
common BC1 male parent of both the BC2 populations was obtained by crossing the La Mé E.
13

guineensis × Colombian E. oleifera hybrid to a T128 palm. Subsequently, the 2.6–1 and 2.6–5
populations were created by backcrossing the BC1 male parent to an E. guineensis palm obtained
from the cross pollination between T128 and a Serdang pisifera and from the self-pollination of
palm T128, respectively. The FAC data for the OxG and the two BC2 populations was obtained
as previously described15. For each population, two biological replicates with low C16:0 content
(22.2–28.9%) and another two with high C16:0 content (33.1–40.6%) were selected. The
characterization of low- and high-C16:0 content for the hybrid palms was determined based on
the distribution of the C16:0 content in the respective populations. Fruit bunches were harvested
for the four palms in each of the populations at two stages, namely early (up to 17/18 weeks after
anthesis, WAA) and late (after 17/18 WAA) stages of mesocarp development. Individual intact
fruitlets collected from each bunch were mixed and randomly sampled to obtain mesocarp tissue.
The mesocarp was separated from shell and exocarp and immediately frozen in liquid nitrogen
and stored at −80 °C prior to RNA extraction.
2.2.2. Oil palm mesocarp RNA extraction
Total RNA was extracted from the mesocarp tissue using the cetyltrimethylammonium
bromide method in combination with the silica column of RNeasy Plant Mini Kit (QIAGEN,
Germany), as previously reported for Jatropha curcas L
30
. The method was optimized and
modified for oil palm fruit tissues by Ong et al.31. The total RNA was purified using the RNeasy
Mini kit and RNase-free DNase I following the manufacturer’s instructions (QIAGEN,
Germany). The purified total RNA was eluted in 50 ul RNase-free water (QIAGEN, Germany)
and the RNA purity and concentration were measured using a NanoDrop ND-1000 UV–Vis
spectrophotometer (Thermo Fisher Scientific, USA). Total RNA with OD 260/280 and OD
260/230 ratios of ≥ 1.8 and 28S/18S ratios of ≥ 2.0 was acceptable and subjected to further
quality check using the 2100 Bioanalyzer and the RNA 6000 LabChip kit following the
14

manufacturer’s instructions (Agilent Technologies, USA). An RNA integrity number ≥ 7.0
suggests that the sample is suitable for RNA-seq.
2.2.3. Library preparation and transcriptome sequencing
The ERCC spike-in RNA control (Thermo Fisher Scientific, USA) was added to the
purified RNA (2–4 µg) at a concentration around 200 ng/µl to construct 24 libraries. A standard
poly-A enrichment protocol was used for preparing the non-stranded RNA-seq libraries. The
method captures the polyadenylated mRNA by hybridization to poly-T oligos bound to magnetic
beads. The purified mRNA was fragmented and randomly primed to synthesize the double-
stranded cDNAs. Subsequently, the cDNAs were end-repaired and ligated to paired-end adaptors
prior to sequencing. Paired-end RNA-seq was performed using the Illumina HiSeq 4000
sequencing platform (Illumina, USA).
2.2.4. RNA-seq data analysis
The RNA-seq raw sequence data were examined for sequence quality, sequence length
distribution, sequence (A, C, G and T) content ratios, ambiguous base (N) content, sequence
duplication, presence of adaptors and the percentage of GC content using FastQC v0.10.1.
(https://www.bioinformatics.babraham.ac.uk/projects/fastqc/). Consistency and reproducibility
of reads was also examined by comparing these parameters among the samples. Low quality read
filtration was performed using the FastX toolkit v0.0.13.2
(www.hannonlab.cshl.edu/fastx_toolkit). Reads with Phred score < 20, length < 30 bp, and
ambiguous bases and artefacts were discarded from further analysis.
Only good quality paired-reads in each library were mapped to the oil palm EG5.1 genome
build32 using TopHat (https://ccb.jhu.edu/software/tophat/index.shtml) with mostly default
parameters except for minimum intron length (30) and maximum intron length (50,000). The
resulting BAM files of the aligned reads including splicing information were used as input into
15

Cufflinks (https://github.com/cole-trapnell-lab/cufflinks) to assemble all possible transcripts in
each library. The resulting transcript assemblies of the individual samples were then clustered
using Cuffmerge (https://cole-trapnell-lab.github.io/cufflinks/cuffmerge/) to generate a set of
non-redundant transcripts.
Homology-based functional annotation of the non-redundant transcripts was first carried
out by performing sequence similarity search (BLASTX) against the Swiss-Prot/UniProtKB
(https://www.ebi.ac.uk/uniprot) and Reference Sequence database (RefSeq, taxonomy:
Magnoliophyta, https://www.ncbi.nlm.nih.gov/refseq/) using a maximum e-value cut-off at
1.0e−5. Using Blast2GO (https://www.blast2go.com/), the non-redundant transcripts were
further mapped and annotated with Gene Ontology terms (GO,
https://geneontology.org/page/download-ontology) and pathways from Kyoto Encyclopedia of
Genes and Genomes (KEGG, https://www.genome.jp/) databases33,34,35. For the FA related
genes, homology search also included the NCBI BioSystems database
(https://www.ncbi.nlm.nih.gov/biosystems/) and the transcript and protein sequences previously
published for FA genes16,18,19,20,36. However, this targeted gene search did not report
additional genes/transcripts other than those already identified from the annotation pipeline. The
expression profiles were normalized and represented as fragments per kilobase of transcript per
million mapped fragments (FPKM) using Cuffdiff (https://cole-trapnell-
lab.github.io/cufflinks/cuffdiff/).

16

2.2.5. Differential expression analysis
FPKM values output by Cuffdiff were converted to read counts using the formula
𝐹𝐹𝐹𝐹 𝐹𝐹 𝐹𝐹 𝑔𝑔 × 𝑓𝑓𝑓𝑓
𝑔𝑔 × ∑ 𝑟𝑟 𝑔𝑔 𝑔𝑔∈ 𝐺𝐺 1 0
9
, where 𝑓𝑓𝑓𝑓 𝑔𝑔 is the length of gene, 𝑟𝑟 𝑔𝑔 is the number of reads mapped to a gene,
and G is the total set of genes to which reads were mapped. Using the R package DESeq2 1.18.1
(Love et al., 2014), the read counts were normalized by library size and transformed using a
regularized logarithm (rlog) taking into account the experimental design in estimating the
dispersion. The rlog transformed data was used to compute Pearson correlation between all 24
RNA-seq libraries.
Significant changes in expression were determined using DESeq2 for genes with at least
one read count in each of the 24 samples. Briefly, two different generalized linear models (GLM)
with a logarithm link were fitted for each gene. The design matrix used to fit the model consisted
of three factors: (i) population (OxG, 2.6–1 and 2.6–5); (ii) mesocarp developmental stages,
namely early and late development and, (iii) C16:0 content (low- and high-C16:0). The log2 fold-
change (FC) coefficients were estimated using the Wald test and contrasts of the coefficients
were set up to test whether the difference between groups (i.e. levels of a factor) was zero. The
Benjamini and Hochberg procedure (BENJAMINI & HOCHBERG, 1995) was used to control
the false discovery rate at p < 0.01. To focus on genes that not only have a significant change in
expression but effect size, we performed additional tests with the GLM aforementioned for the
null hypothesis that the FC are less than or equal to |1|.
2.2.6. Quantitative real-time PCR (qRT-PCR)
The same stock of the extracted mesocarp RNA (used for RNA-seq) was also used in the
qRT-PCR experiment. Template without reverse transcriptase (NRT) and no-template control
(NTC) were also included to determine the possibility of genomic DNA contamination, presence
17

of primer-dimers or any spurious amplification. The qRT-PCR was performed using
Mastercycler ep realplex (Eppendorf, Germany) and the BioMark HD system (FLUIDIGM,
USA). For the Mastercycler ep realplex system, conversion of total RNA to single-stranded
cDNAs was carried out using the high-capacity cDNA reverse-transcription kit following the
manufacturer’s instructions (Applied Biosystems, USA). Preparation of qRT-PCR masteer
reaction mixtures and the PCR programme used were as described by Chan et al.39.
For both the reference and candidate genes, the qRT-PCR data was analysed using
geNorm 3.4 (Vandesompele et al., 2002). Eight reference genes (Ubiquitin, pOP-EA01332,
Actin, GAPDH, NAD5, Tubulin, GRAS and Cyp2) (Chan et al., 2014; Yeap et al., 2014) were
tested and the results showed that the GAPDH, ACTIN and Cyp2 combination gave the most
satisfactory expression stability (M < 1.5) (Supplementary Figure S3). The primer information is
available in Supplementary Table S3. The selected reference gene set was subsequently used for
normalizing the expression of candidate genes. Mean Ct across three replicates in a sample was
calculated and transformed into the relative expression quantities using formula Q = E(minCt—
sampleCt) where, E = Ex + 1 and minCt is the smallest Ct observed among the tested samples.
For a candidate gene, the term representing relative expression quantities was QGOI whereas,
Qrefij refers to the expression quantities for the selected reference genes. Both the terms were
subsequently used for estimation of normalized expression for a candidate gene,
GOInorm = QGOI/Qrefij. In the case where three reference genes were selected, Qrefij = (Qref1 × Qref2
× Qref3)1/3. Calculation for standard deviations (SD) for each GOInorm was also carried out as
described in the geNorm manual (Vandesompele et al., 2002).
For the BioMark HD system, cDNA stock was prepared using the FLUIDIGM reverse
transcription master mix. Preparation of qRT-PCR master reaction mixtures, preamplification,
18

Delta gene assay and qRT-PCR were carried out by following the manufacturer’s instructions
(FLUIDIGM, USA). Default parameters were used for collecting and analysing the data where
expression values (delta delta Ct, ddCt) were normalized against the same set of reference genes
consisting of GAPDH, ACTIN and Cyp2 (determined when qRT-PCT was performed in the
Mastercycler ep realplex system) and the calibrator (which was the pooled samples). Fold change
of ddCt (ddCtFC) = 2
−ddCt
was also calculated representing the relative changes of gene
expression42. Significance (p < 0.05) of differential expression between low- and high-C16:0
content groups was determined using t-test (SPSS 16.0).
2.3. Results
2.3.1. Gene functional annotation
Total RNA extracted from mesocarp tissue of the 12 interspecific palms harvested at two
stages of fruit development were sequenced using the Illumina HiSeq 4000 sequencing platform
(Illumina, USA). For each sample, the abundance of ERCC transcripts was measured and
normalized to FPKM using the TopHat-Cufflinks pipeline as described in the RNA-seq data
analysis section. The dose response of ERCC spike-in RNA transcripts showed strong
correlation between the sequencing read counts and RNA inputs with an average R2 of 0.9115.
An average of 118 million quality paired-reads were generated after filtration. Approximately
79.0–88.0% of the paired-reads generated were successfully mapped to the EG5.1 genome. A
vast majority of these reads (97.7%) was mapped uniquely and only 2.3% of the reads mapped at
multiple locations on EG5.1 using the mapping criteria applied in this study.

19

Table 2.1. Functional annotation of 43,920 potential genes (141,513 putative isoforms) against four public databases
(From Ting, NC et. al. 2020).
Public database Annotated genes Annotated isoforms Unigene annotation rate (%)
RefSeq 30,657 125,548 88.72
Swiss-Prot 21,380 96,066 67.88
GO* 20,069 90,117 63.68
KEGG** 4059 18,062 12.76

The combined assembly of all 24 samples yielded 43,920 potential genes (with
nomenclature XLOC_) consisting of 141,513 putative isoforms (nomenclature TCONS_). The
putative isoforms were searched for plant sequence homology in several protein databases
including RefSeq, Swiss-Prot and GO. The results showed that 88.7 and 63.7% of the assembled
transcripts were homologous to known proteins in RefSeq and Swiss-Prot, respectively (Table
2.1). The majority of the significant similarities (97,319 transcripts) from the RefSeq BLAST
search was to genes from E. guineensis and 10,878 aligned to date palm (Phoenix dactylifera)
genes. The annotation to GO terms resulted in 160 genes (consisting of 588 putative isoforms)
and 38 genes (202 putative isoforms) assigned to FA (GO:0006633) and TAG (GO:0019432)
biosynthetic processes, respectively. In fact, a larger number of GO terms was found to be
associated with various FA and lipid related biological processes and are listed in Supplementary
Table S2.
In order to understand the possible metabolic and biological functions of these putative
genes, 918 were successfully mapped to 147 metabolic pathways in the KEGG database. A total
of 72 genes consisting 312 putative isoforms from the present study were mapped to the FA
biosynthesis pathway. Transcripts were also assigned to other related pathways involving
metabolic processes of pyruvate, α-linolenic acid (C18:3), linoleic acid (C18:2), biosynthesis of
unsaturated FAs, FA elongation and FA degradation. A number of genes were also mapped to
lipid related pathways such as 168 genes (887 putative isoforms) that were mapped to the
20

glycerolipid metabolic pathway, which includes the TAG formation process. Other than FA and
TAG, genes were also assigned to the glycerolphospholipid, sphingolipid and other lipid related
pathways (Supplementary Figure S1).
2.3.2. Expression of genes related to FA and TAG biosynthetic processes
The transcripts that mapped to the EG5.1 genome build were converted to FPKM.
Transcripts with FPKM = 0 refers to no expression while FPKM > 0 refers to some expression.
However, low FPKM may also be due to technical artefacts and, therefore FPKM expression
values > 0.1 were accepted as being a more reliable threshold. The number of expressed
transcripts with FPKM > 0.1 were consistent across all samples in the validation panel, ranging
from 74,476–81,999 (52.6–57.9%) transcripts in OxG, 73,366–80,919 (51.8–57.2%) in BC2
(2.6–1) and 76,575–82,303 (54.1–58.2%) in BC2 (2.6–5) (Supplementary Figure S2). It was also
consistently observed that the number of expressed transcripts was higher in the earlier mesocarp
developmental stage compared to late stage. In the earlier stage, the average expressed
transcripts observed in OxG, BC2 (2.6–1) and BC2 (2.6–5) were 81,620, 78,027 and 80,651,
respectively. Whereas, a slightly lower number of transcripts 77,986, 77,387 and 78,457 were
observed in the later stage of the three respective crosses.
Compilation of the top-50 highly expressed genes in each sample resulted in a total of 340 genes.
Of these, 110 matched to 535 GO terms, including biosynthesis of FA (GO:0006633)
unsaturated FA (GO:0006636), TAG (GO:0019432), acyl-carrier-protein (GO:0042967), lipid
oxidation (GO:0034440) and transportation (GO:0006869). This suggests that the FA and lipid
related genes were actively expressed during the two ripening stages when the fruits were
sampled.
In relation to the biosynthesis of FAs, major genes encoding enzymes such as acetyl-CoA
carboxylase (ACCase), beta-ketoacyl-ACP synthases (KAS I, II and III), hydroxyacyl-ACP
21

dehydrase (HAD), enoyl-ACP reductase (EAR/ENR); Δ9-stearoyl-ACP desaturase (SAD), ACP
thioesterases mainly FATA and FATB, long-chain acyl-CoA synthetase (LACS) and the WRI1
transcription factor were identified from GO:0006633, GO:0006636 and GO:0008610. One to
five putative paralogous genes (XLOC_) were found for each of these, which in most cases were
located on different chromosomes. A majority of the genes was also found to have multiple
putative isoforms such as XLOC_021657 of WRI1 and XLOC_032515 of EAR1 consisting of up
to ten putative isoforms. The isoforms were expressed at varying levels in the two mesocarp
developmental stages analysed (Figures 1A and B in Ting, NC et. al. 2020). For XLOC_021657
of WRI1, TCONS_00077403 and _00077402 were the two most actively expressed putative
isoforms, detected in most of the later stages of mesocarp development with FPKM values up to
65.67 and 43.31, respectively. In contrast, very low expression was detected for
TCONS_00077397 and _00077401 of the same TF in both stages of fruit development across all
the three genetic backgrounds. Although, TCONS_00077400 had considerably higher expression
of up to 15.15 FPKM, it was only expressed in about 50.0% of the samples in the validation
panel. Other putative isoforms of WRI1 mostly demonstrated either no expression or had low
FPKM compared to TCONS_00077400. Variability in expression of these putative isoforms
could contribute to the multiple roles that WRI1 plays during oil palm fruit development.
The three putative genes (XLOC_027861, _026230 and _040788) identified as SAD
(XP_010926734 and _010927705), which is involved in conversion of C18:0- to C18:1-ACPs,
were the most highly expressed genes among the identified FA synthesis genes throughout the
biosynthesis pathway (Figure 2.1 and please also refer to Figure 1A in published paper). High
FPKM values were observed for XLOC_027861 (TCONS_00099844) ranging from 196.76–
5271.14 and 829.13–8192.63 in the earlier and later stages of mesocarp development,
22

respectively. For another two SAD gene variants, the observed FPKM values in the earlier and
later stages were in the range of 263.73–1575.63 and 256.16–2382.01 for XLOC_026230 and,
39.32–1103.72 and 156.46–1574.87 for XLOC_040788.

Figure 2.1. FPKM expression levels for various genes mapped to the fatty acid biosynthesis pathway as observed in
the early (left panel) and late (right panel) stages of mesocarp development (From Ting, NC et. al. 2020).

The next most highly expressed FA genes were FATA and LACS4. High expression levels
in the later stage of fruit development, ranging from 24.28–227.23 were observed for the putative
gene XLOC_026226 of FATA. For LACS4, six transcript variants were identified of which
XLOC_040339 (TCONS_00136992) and XLOC_024538 (TCONS_00088294) were found to be
abundantly expressed in the later stages of mesocarp development in all three families with
23

FPKM values in the range of 116.24–311.02 and 48.92–126.30, respectively. In comparison, a
lower expression level was observed at the earlier stage of mesocarp development, ranging from
45.88–138.90 (XLOC_040339, TCONS_00136992) and 22.83–61.81 (XLOC_024538,
TCONS_00088294).
For the TAG biosynthetic pathway, putative genes and isoforms encoding enzymes
glycerol-3-phosphate dehydrogenase (GPDH), glycerol-3-phosphate acyltransferase (GPAT),
lysophosphatidic acid acyltransferase (LPAAT), phosphatidic acid phosphatase (PAP),
diacylglycerol:acyl-CoA acyltransferase (DGAT), phosphatidylcholine:diacylglycerol
acyltransferase (PDAT) and delta-12 fatty acid desaturase (FAD2) were also identified and
mapped to various steps of the TAG synthesis and FA modification pathways in ER (Figure 1C
in Ting, NC et. al. 2020). Among these, FAD2 (XLOC_028041) was the most actively expressed
gene with FPKM values ranging from 18.39–566.19 and 44.10–676.13 measured in the earlier
and later stages of mesocarp development, respectively. This ER located desaturase introduces
the second double bond to the PC-bound C18:1 thereby creating C18:2-PC. However, omega-3
fatty acid desaturase (FAD3) which is involved in subsequent desaturation to form C18:3-PC,
was not detected in this GO term. This is not surprising since the mesocarp has about 10.0%
C18:2 and only negligible levels of C18:3. However, a chloroplastic omega-3 fatty acid
desaturase (FAD7/8, XP_010920844) was identified which had high expression levels similar to
FAD2. Chloroplastic omega-3 fatty acid desaturase introduces the third double-bond in the
biosynthesis of C16:3 and C18:3 FAs, which are important membrane constituents. It is also
interesting to note that the FAD2 expression levels were higher than the those of GPAT (< 70
FPKM), LPAAT (< 30 FPKM), PAP (< 25 FPKM) and DGAT (< 21 FPKM) genes that are
involved in the Kennedy pathway. The results concur with evidence presented by Ramli et al.17
24

that FA synthesis exerts a more important effect than the Kennedy pathway in the regulation of
oil synthesis in oil palm. The present study indicates this to be so even in interspecific hybrids
and the backcrosses.
2.3.3. DEGs in different genetic backgrounds across early and late developmental stages
Principal component analysis (PCA) for 43,920 potential genes was performed to visually
explore possible sources of variation in the RNA-seq data and if it drives clustering of the
samples. Generally, the greatest proportion of variance in gene expression was driven by
populations (16.4 %) followed by developmental stage, which accounted for 13.0 % of the total
variance (Figure 2.2). The OxG palms (A1-4) clustered separately from both of the two BC2
populations (B1-4 and C1-4) pointing to different global expression patterns between the
interspecific hybrids and backcrosses. In each population, samples obtained from the late
developmental stage (-RBL/H) also separated well from those at the early developmental stage (-
UBL/H/). Projecting the data onto other principal components did not reveal other sample
characteristics that could be major drivers of the variation in the data (Supplementary Figure
A.1). Therefore, population and mesocarp development were two of the factors included in the
model for DEG analysis.
25

Figure 2.2. RNA-seq data from 24 samples plotted on the first two principal components indicating the major
differences in total gene expression between samples. Mesocarp samples are categorised into early (up to 18/19
WAA) and late (after 18/19 WAA) developmental stages. Samples labelled as A1–4; B1–4 and C1–4 were from
OxG, BC
2
(2.6-1) and BC
2
(2.6-5) populations, respectively. For C16:0 content, “low” (-U/RBL) ranged from 22.2–
28.9 % while “high” (-U/RBH) ranged from 33.1– 40.6 % with respect to the level of C16:0 in mesocarp.

DESeq2 was used to investigate population, developmental stage, and C16:0 content
specific differences in expression of genes with at least one read count per sample, which
reduced the number of potential genes under consideration to 24,496. Differential gene
expression amongst pairs of the three populations, mesocarp developmental stages and C16.0
content was determined using the Wald test. The largest number of DEGs was identified between
developmental stages followed by between pairs of populations and then between high and low
C16:0 content (Table 2.2). By comparing the two mesocarp developmental stages, a total of
6,094 DEGs was identified of which 217 were related to GO terms for biosynthetic, metabolic,
oxidation and transportation processes of FAs, TAGs, lipids, glycerol-3-phosphate and acyl-
26

Table 2.2. The number of genes with a significant change in expression among the OxG, BC
2
(2.6-1) and (2.6-5)
populations, mesocarp developmental stages (late and early) and C16.0 content (high and low). Significant DEGs at
adjusted p-value < 0.01 are presented for up-regulation (FC > 0 and > 1) and down-regulation (FC < 0 and < -1)
(From Ting, NC et. al. 2020).
Contrast H0: log2 fold change (FC) = 0 H0: |log2 fold change (FC)| <= 1
FC > 0 FC < 0 FC > 1 FC < -1
BC2 (2.6-1) vs. OxG 1,919 (7.80 %) 1,852 (7.60 %) 69 (0.28 %) 118 (0.48 %)
BC2 (2.6-5) vs. OxG 637 (2.60 %) 774 (3.20 %) 20 (0.08 %) 81 (0.33 %)
BC2 (2.6-5) vs. BC2 (2.6-1) 352 (1.40 %) 369 (1.50 %) 2 (0.008 %) 5 (0.02 %)
Late vs. early stage 3,120 (13.00 %) 2,974 (12.00 %) 162 (0.66 %) 154 (0.63 %)
High- vs. low-C16.0 14 (0.06 %) 10 (0.04 %) 0 0

carrier-protein. Of these, it is worth noting that 21 DEGs were among the key genes (Figure 1 in
Ting, NC et. al. 2020) involved directly in biosynthesis of FAs (GO:0006633) and TAGs
(GO:0019432). As expected, 19 of these DEGs showed a significantly higher expression ranging
from 0.4–2.36 FC at the later stage compared to early stage of fruit development.
Among the population contrasts, the highest number of genes with significant expression
changes were observed between OxG and BC2 (2.6–1) (3771 DEGs) followed by 1411 DEGs in
OxG vs. BC2 (2.6–5) and 721 DEGs when comparing the two BC2 populations (Table 2.2). The
number of DEGs involved in the FA and TAG biosynthesis pathways was also found
correspondingly reduced from eight to five and one across the three respective contrasts (Table
2.3). There were only 24 DEGs identified between high- vs. low-C16:0 content palms.
Unfortunately, none were found to be involved in FA or TAG biosynthetic activities.

27

DEG
(XLOC_) CHR/Sc Position (bp) FC padj FC padj FC padj FC padj
ACCase_1 6563 CHR12 12,184,042–12,203,276 1.14 0.000185 - - - - - -
KASIII_1 10596 CHR15 19,057,442–19,067,706 1.24 4.82E-05 - - - - - -
KASI_1 4431 CHR10 23,056,853–23,066,783 1.17 0.001629 - - - - - -
KASI_2 16133 CHR03 15,058,145–15,063,433 1.95 0.001751 - - - - - -
KASI_3 17309 CHR03 38,723,675–38,767,004 1.12 0.000542 - - - - - -
KASII_1 3916 CHR10 22,940,770–22,949,844 0.4 0.006365 -0.52 0.006092 -0.76 6.14E-05 - -
SAD_3 27861 CHR08 8,306,193–8,310,109 1.99 1.67E-05 - - - - - -
SAD_4 40788 Sc08824 1,899–2,580 1.76 0.000234 - - - - - -
FATA_1 26226 CHR07 23,339,761–23,350,100 1.69 4.85E-06 -1.36 0.005374 - - - -
FATA_2 27859 CHR08 8,152,030–8,156,099 0.89 0.000361 - - - - - -
FATB_1 16685 CHR03 1,846,010–1,852,083 1.98 0 - - - - - -
WRI1_3 21657 CHR05 39,782,472–39,805,223 2.31 0.003447 - - - - - -
LACS2_2 38609 Sc01482 169,573–173,778 -1.95 9.94E-05 - - - - - -
LACS4_1 16055 CHR03 11,141,682–11,177,588 - - -3.36 0 -1.6 0.000643 1.76 0.00038627
LACS4_2 1175 CHR01 8,875,904–8,916,992 1.88 1.17E-06 - - - - - -
LACS4_3 24538 CHR06 40,749,497–40,760,176 1.08 7.9E-07 - - - - - -
LACS4_5 40338 Sc06230 1,531–7,626 1.46 0.002632 - - - - - -
LACS4_6 40339 Sc06230 1,531–7,626 1.26 1E-08 - - - - - -
LACS9_1 12886 CHR02 24,690,189–24,711,942 -1.57 8.39E-05 - - - - - -
LPAAT1_1 5735 CHR11 19,068,230–19,102,990 - - -0.63 0.007999 - - - -
LPAAT1_2 6920 CHR12 2,630,995–2,662,553 2.36 3.89E-05 - - - - - -
PAP_1 21812 CHR05 47,506,332–47,513,305 - - -0.58 0.009723 - - - -
PAP_2 22518 CHR05 47,506,332–47,513,305 - - -1.11 0.0053 - - - -
DGAT2_1 3845 CHR10 19,704,781–19,710,080 1.12 0.000188 - - - - -
FAD2_1 27483 CHR08 27,389,878–27,394,517 - - - - -1.7 0.009958 - -
FAD2_2 28041 CHR08 27,389,878–27,394,517 - - -2.17 4.57E-05 -2.72 3.2E-07 - -
FAD2_3 32536 Sc00131 551,194–554,932 1.8 2E-08 -1.34 0.001543 -1.3 0.004682 - -
Gene
Corresponding gene position in EG5
build
Late vs. early stage BC2 (2.6-1) vs. OxG BC
2
(2.6-5) vs. OxG BC2 (2.6-5) vs. BC2 (2.6-1)
Table 2.1. Differentially expressed genes (DEGs) related to synthesis of FA (GO:0006633, GO:0006636 and GO:0008610) and TAG (GO:0019432)
identified by comparing the two mesocarp developmental stages (late and early) and amongst the OxG, BC 2 (2.6-1) and (2.6-5) populations. Significant
in expression at adjusted p-value (padj) < 0.01 determined with H 0: log 2 fold change (FC) = 0 (From Ting, NC et. al. 2020).
28

2.3.4. Evaluation of the QTL-linked DEGs using qRT-PCR
Of the 27 DEGs related to FA (GO:0006633) and TAG (GO:0019432) biosynthetic
processes, FATB_1 (XLOC_016685) and LACS4_1 (XLOC_016055) were also previously
located within the QTL confidence regions (ranging from 1.5–11 Mbp on CHR03) associated
with myristic acid (C14:0), C16:0, stearic acid (C18:0), oleic acid (C18:1) and IV (N.-C. Ting et
al., 2016). These genes and their putative isoforms were quantified in the present study using the
OxG and BC2 palms with contrasting C16:0 content.
Expression profiles observed in the qRT-PCR experiment were compared to those
observed for the corresponding genes and isoforms in the transcriptome data. A similar
expression pattern was observed for FATB_1 in which, an obvious increase in expression was
observed at the later stages of mesocarp development compared to the earlier stages (Table 2.3,
Figure 2.3). More specifically, at the later stages of mesocarp development, significant
differential expression (p < 0.05) of FATB_1 was noticeable in specific comparison groups i.e.
A1&2_RBL vs. A3&4_RBH in OxG and B1&2_RBL vs. B3&4_RBH in BC2 (2.6–1). However,
at the earlier fruit developmental stages, only contrasting palms in BC2 (B1&2_UBL vs.
B3&4_UBH and C1&2_UBL vs. C3&4_UBH) demonstrated significant differential expression.
The FATB_1 gene (XLOC_016685) demonstrated a higher level of expression in the BC2 palms
with high C16:0 content in comparison with palms containing low C16:0 content. In OxG,
however, palms with low C16:0 content (A1&2_RBL) showed a relatively higher level of
FATB_1 expression (1.29) than the high C16:0 palms (average expression level in A3&4_RBH
was 0.97). The qRT-PCR data was generally consistent with that observed for the transcriptome
data except for the differential patterns in A1&2_RBL vs. B3&4_RBH which were only
29

observed in the qRT-PCR data (Figure 2.3).

The present study also evaluated expression of the candidate isoforms for FATB_1. Four
putative isoforms were identified and labelled as FATB_1a (TCONS_00060749), _1b
(TCONS_00060752), _1c (TCONS_00060750) and _1d (TCONS_00060751) (Supplementary
Figure S4). By evaluating the expression profiles of individual putative isoforms (in the
transcriptome data), the possibility that the observed combined differential expression of
FATB_1 gene was contributed by the independent isoforms FATB_1b (B1&2_UBL vs.
B3&4_UBH and C1&2_UBL vs. C3&4_UBH), FATB_1c (B1&2_RBL vs. B3&4_RBH) and
FATB_1d (C1&2_UBL vs. C3&4_UBH) was evaluated. Changes in expression profiles were
observed when two (FATB_1cd) to three (FATB_1bcd) of these isoforms were co-amplified with
Figure 2.3. Normalized expression profiles of FATB_1 (XLOC_016685) and the isoforms (TCONS_)
quantified by qRT-PCR (right panel) in comparison with the transcriptomic expression profiles (left panel). The
primers for qRT-PCR were designed to amplify the common exonic regions between isoforms denoted by two
/three letters (From Ting, NC et. al. 2020).

30

a common primer-pair (in qRT-PCR experiment). Distinct primer-pairs that could distinguish all
isoforms were not possible based on the sequence information available. In FATB_1cd,
differential expression was observed in C1&2_UBL vs. C3&4_UBH and the profile was similar
to that of FATB_1b and FATB_1d alone. Interestingly, significant differential expression was
observed for FATB_1cd in the A1&2_RBL vs. A3&4_RBH contrast where neither FATB_1c nor
FATB_1d independently had a similar expression profile. The combined expression of
FATB_1cd was higher in the A3&4_RBH palms relative to A1&2_RBL in OxG and this profile
was in contrast to that observed for FATB_1 at the gene level. Similarly, the profile observed for
FATB_1bcd in B1&2_UBL vs. B3&4_UBH and B1&2_RBL vs. B3&4_RBH was not similar to
that observed for FATB_1cd and FATB_1 (Figure 2.3).
The putative gene LACS4_1 (XLOC_016055) was identified at position 11,141,682–
11,177,588 bp on CHR03. Unlike the other two putative genes of LACS4, XLOC_040339
(located in p5_Sc06230) and XLOC_024538 (located in CHR06) which were measured in tens
to over hundreds of FPKM, XLOC_016055 (LACS4_1) was expressed at a much lower level
with FPKM values of no higher than 3.00 (Figure 2.4). For LACS4_1, a primer-pair labelled as
LACS4_1abcefg was designed to amplify a common exonic region shared among all the putative
isoforms except for LACS4_1d (TCONS_00057559). This was because the entire length of the
LACS4_1d sequence falls outside the range shared by other isoforms (Supplementary Figure S4).
The qRT-PCR result showed significant differential expression between the high- and low-C16:0
palms in OxG at the earlier stages of mesocarp development (A1&2_UBL vs. A3&2_UBH) and
the profile was similar to that demonstrated by LACS4_1 in the transcriptome data. The
transcriptomic profile of LACS4_1 also revealed differential expression between high- and low-
C16:0 palms in BC2 (2.6–1) (B1&2_RBL vs. B3&4_RBH) but the same profile was not
31

observed in LACS4_1abcefg. This discrepancy could be due to exclusion of LACS4_1d which
may be contributing to the differential expression in B1&2_RBL vs. B3&4_RBH. This was
confirmed when the LACS4_1d isoform was evaluated separately using qRT-PCR (Figure 2.4).

Figure 2.4. Normalized expression profiles of LACS4_1 (XLOC_016055) and the isoforms (TCONS_) quantified
by qRT-PCR (right panel) in comparison with the transcriptomic expression profiles (left panel). The primer for
qRT-PCR denoted by two letters (i.e. _bc) was designed to amplify the common exonic region between isoforms
TCONS_00057556 and_00057553 (From Ting, NC et. al. 2020).

For LACS4_1 (XLOC_016055), the expression profile of another individual isoform
LACS4_1b (TCONS_00057556) was also reproducible when evaluated by qRT-PCR although no
significant differential expression was identified. However, a significant differential expression
profile was detected between high- and low-C16:0 palms in BC2 (2.6–5) (C3&4_UBH vs.
C1&2_UBL) when this isoform is co-expressed with isoform LACS4_1c (TCONS_00057553).
32

The average combined expression level of LACS4_1bc in C1&2_UBL was 0.78 whereas it was
3.16 in C3&4_UBH, which corresponds to a FC of 2.0 (Figure 2.4).
The predicted protein sequence of all four isoforms of FATB_1 contained both a
functional N-terminal domain of acyl-ATP thioesterase (Acyl-thio_N, PF12590.8) and the acyl-
ACP thioesterase domain (Acyl-ACP TE, PF01643.17) (Supplementary Figure S5). One of the
isoforms, FATB_1a, had 38 amino acids deleted from Acyl-ACP TE, which could affect the
protein function and may explain the low expression levels observed. With respect to LACS4_1,
truncations were observed at the 5′ site of the AMP-binding domain (PF00501.28) among all the
identified isoforms with the exception of LACS4_1b. However, other regions in the AMP-
binding domain were highly conserved, with LACS4_1d being the only isoform where changes in
a number of amino acids were observed (Supplementary Figure S6). This likely explains the
different genomic location of LAC4_1d from the shared region of the other isoforms
(Supplementary Figure S4). The results suggest that isoforms may be partially functional or may
even be non-functional, providing initial evidence that isoform abundance may be a valid area
for further investigation. Post-translational modification, protein longevity, localisation and
turnover rates may also influence oil synthesis and accumulation.
2.4. Discussion
In many oil producing plants, oil content and the proportion of specific FAs have been
associated with the expression of regulatory genes and TFs (Huang et al., 2016; Lei et al., 2012).
In oil palm, high level expression of a number of key genes in FA and TAG biosynthesis
pathways was also found to be positively correlated with higher oil content in the mesocarp
tissue (Dussert et al., 2013; Guerin et al., 2016; Jin et al., 2017). These findings lay a good
foundation and suggest that the expression profile of FA and TAG synthesis genes has a strong
33

effect on the observed phenotype, which is the FAC. As such, the present study was aimed at
evaluating the expression of these genes, including their putative isoforms and identifying
differential expression patterns between palms with high- and low-C16:0 content, the main
saturated FA in palm oil.
In this study, there was an acceptable reads-mapping rate up to 88.0%. Furthermore,
approximately 98.0% of the mapped reads were unique transcripts although the reference
genome used was an E. guineensis assembly (EG5.1). A high percentage of the ~ 44 K potential
genes was also successfully annotated via RefSeq, Swiss-Prot, GO and the KEGG databases,
which gives further confidence in the quality of generated reads and allows for subsequent
transcriptome profiling. Most of the genes encoding key enzymes involved in both the FA and
TAG synthesis pathways were successfully identified from the main GO terms (GO:0006633,
GO:0006636, GO:0008610 and GO:0019432). Therefore, this study has generated a good
collection of FA and lipid related genes as well as the putative isoforms for a more in-depth
study on specific genes of interest. Only a few genes went undetected such as pyruvate
dehydrogenase (PDH), FAD3 and acyl-CoA:lyso-phosphatidylcholine acyltransferase (LPCAT),
possibly categorized under other GO terms which were not examined in the present study.
Similar to other plant species (Baud et al., 2009), many of the FA genes in oil palm have
been reported to be transcriptionally regulated by WRI1 (Bourgis et al., 2011; Dussert et al.,
2013; Guerin et al., 2016; Jin et al., 2017). WRI1 was one of the key candidate genes present in
the QTL region associated with a number of FAs identified in OxG and BC2 (N.-C. Ting et al.,
2016). The more than twofold higher expression of a WRI1 paralog (XLOC_021657) at the later
stage of mesocarp development in conjunction with the increased expression of most of the FA
and TAG DEGs listed in Table 2.3, supports the regulatory mechanism as mentioned above.
34

Among the FA and TAG genes evaluated, SAD, LACS4, FATA and FAD2 were found to exhibit
extra-high expression levels. (Wong et al., 2014) made a similar observation reporting that these
four genes were among the top six highly expressed genes in the mature mesocarp tissue of E.
guineensis. Interestingly some of these genes namely SAD_2 (XLOC_026230/XP_010926734)
and FATA_1 (XLOC_026226/XP_010926746) located on CHR07, as well as SAD_3
(XLOC_027861/XP_010927705) and SAD_4 (XLOC_040788/XP_010927705) on CHR08, were
also present in previously identified QTL regions associated with various FAC in a BC1 mapping
population25. The CHR07 chromosomal region harbours QTLs associated with C16:1, C18:0,
C18:1, C20:0 and IV. The PVE explained by each of the QTLs ranged from 18.3 to 50.2%
indicating that the genomic region had a moderate to high effect on the traits concerned. The
PVE for C18:0 content was particularly high suggesting that SAD and FATA play a critical role
in regulating FA in the interspecific palms. On CHR08, the QTL was associated with C14:0
where PVE was 10.4%, which indicates that the genomic region has some effect on FAC.
In this study, 12 paralogous genes of SAD, LACS4, FATA and FAD2 appeared to be
significantly differentially expressed both between the two developmental stages as well as when
comparing BC2 to the OxG genetic background (Table 2.2). Eight of these paralogs including
two for SAD, four for LACS4, one for each of FATA and FAD2, showed higher expression levels
at the later stages of mesocarp development with FC ranging from 1.08–1.99. For SAD, this is in
agreement with previous reports on the high desaturase activity of SAD, which facilitates C18:1-
ACP accumulation and plays a crucial role in determining the ratio of saturated to unsaturated
C18 FAs in membranes and storage lipids in the mesocarp (Parveez et al., 2015;
Sambanthamurthi et al., 2000). This higher gene expression coincides with the higher rate of FA
synthesis and oil accumulation as the fruits mature and ripen after 17/18 WAA.
35

In addition, comparison of the BC2 and OxG genetic backgrounds revealed that all the nine FA
(GO:0006633) and TAG (GO:0019432) synthesis DEGs (including LACS4, FATA and FAD2)
showed higher expression levels in OxG compared to BC2. Considering that 50% of the OxG
genome comes from E. oleifera, which has higher unsaturated C18 and lower C16:0 content than
E. guineensis, this suggests a co-regulation system that promotes unsaturated C18 synthesis in
the OxG hybrids compared to BC2 which has more E. guineensis genetic background. FATA
encodes a thioesterase that terminates de novo FA synthesis by catalyzing the hydrolysis of
particularly C18:1-ACP. The higher expression of FATA_1 at later stage of development (during
the oil deposition period) as well as higher expression in OxG hybrids compared to BC2 suggest
oil palm mesocarp FATA acyl-ACP thioesterase is important not only for oil deposition in the
mesocarp but also for the final composition of FAs that are exported from the plastid and enter
the storage lipid pool.
FAD2, localized in the ER, is responsible for the synthesis of C18:2 and drives the
desaturation of C18:1 in the mesocarp. The concordant higher expression of both SAD and FAD2
in OxG hybrids compared to BC2 would facilitate higher accumulation of C18:2 in OxG hybrids.
Free FAs released by FATA and FATB are activated by LACS, which forms an important link
between FA synthesis in the plastid and TAG assembly in the ER. Dussert et al. (2013) reported
that LACS9 and LACS4-1 were both highly expressed in the oil palm mesocarp but, based on co-
expression studies, Guerin et al. (2016) suggested that LACS9 plays the predominant role in the
oil palm mesocarp. The current study, however indicates that LACS4 is more highly expressed,
which was also observed in the oil-accumulating avocado mesocarp (Kilaru et al., 2015). It is
also interesting that in the current study the paralogs of LACS4 were more highly expressed at
the later stage of development coinciding with higher FA and TAG synthesis while LACS9
36

showed higher transcription at the earlier stage of development coinciding with higher membrane
lipid synthesis. In Arabidopsis, it was shown that LACS4 and LACS9 have overlapping
functions and LACS9 is involved in importation of FA into plastid for the biosynthesis of
glycolipids (Jessen et al., 2015). It would be interesting to learn if LACS9 plays a similar role in
lipid trafficking from the ER into the plastid in the oil palm mesocarp for membrane lipid
synthesis given its higher expression at the earlier stage of development. The significantly higher
expression of LACS4 in the OxG hybrids compared to BC2 suggests a more prominent role of
this gene in E. oleifera compared to E. guineensis. The effect of specific genetic backgrounds on
gene expression has also been reported previously where many genes encoding PC-related
enzymes in the FA and TAG synthesis pathways were found to be more abundantly expressed in
the E. guineensis intraspecific hybrids (dura x pisifera) compared to the dura mother palm (Jin et
al., 2017).
Interestingly, FATB_1 (XLOC_016685) and LACS4_1 (XLOC_016055) detected in
multiple comparisons via late vs. early, BC2(2.6–1) vs. OxG, BC2(2.6–5) vs. OxG and BC2(2.6–
5) vs. BC2(2.6–1), were also located in a genomic region associated with a major QTL for FAC

(N.-C. Ting et al., 2016). Consequently, the expression of the two genes was further evaluated
via qRT-PCR. As expected, overall expression profiles revealed by qRT-PCR for the two genes
was similar with those observed in the transcriptomic expression data. Unfortunately, significant
changes in expression for FATB_1 and LACS4_1 were inconsistent across the two different
stages of mesocarp development and genetic backgrounds evaluated. For both the BC2 crosses, it
was observed that FATB_1 was more abundantly expressed in early stages in palms with high
C16:0 content, in comparison with palms containing low C16:0 content. However, at later stages
of mesocarp development, the pattern remained consistent in only one of the BC2 populations.
37

Furthermore, the expression pattern observed in the OxG background was not consistent with
that in the BC2 population, where palms with low C16:0 content demonstrated a higher level of
expression of FATB_1 compared to high C16:0-palms. This again suggests the differential
expression patterns observed are dependent on the genetic background being investigated. In
interspecific hybrid breeding specifically, the expression profile is also likely influenced by the
number of backcrossing cycles carried out for the population.
Another possibility is that the different isoforms of a gene influence the expression
profile observed and even the activity or functionality of the enzyme produced. For this reason, a
number of the putative isoforms for FATB_1 and LACS4_1 was evaluated with qRT-PCR. As
expected, there was variation in expression profiles demonstrated by the individual isoforms,
which clearly suggests their potential contribution towards the final measured expression of a
gene. In some cases, the expression profiles of two or more isoforms were investigated using
single primer-pair encompassing these isoforms. Even in this case, clear differential expression
associated with the various isoforms was evident across the different genetic backgrounds, with
high and low levels of C16:0 content. This suggests that different isoforms are expressed at
different levels during fruit maturation across different genetic backgrounds.
The results from the present study also suggest that differences in expression of the
candidate genes i.e. FATB_1 and LACS4_1, including their isoforms can be generally correlated
with the presence of the QTL interval, as determined using conventional QTL mapping of a
segregating bi-parental family. Further in-depth studies with a large sample size will surely
unravel the role of different isoforms in the FA and oil synthesis regulatory processes and the
genes involved. This study demonstrates that evaluating the expression patterns of candidate
genes (especially their isoforms) within QTL regions revealed by DNA markers can help to
38

better understand the genetic basis of complex traits in plants. Expression profiles of the specific
isoforms of candidate genes like SAD, FATB and LACS4 provide another layer of support for the
association of the markers defining the QTL regions to FAC in oil palm interspecific hybrids and
their backcrosses. However, as pointed out by (Azodi et al., 2020), genomic regions defined by
genetic markers may not capture the entire variation associated with complex traits.
Transcriptome analysis in combination with DNA markers using appropriate statistical models is
probably required to better decipher the molecular mechanism of complex traits (Azodi et al.,
2020), which is an interesting area for future research in oil palm.

2.5. Data Availability
The data have been deposited to BioProject accession number PRJNA606124 in the
NCBI BioProject database.

2.6. Author contributions
Study concept and design: RS*, RS, SM, FM, SN, KS and N-CT. Selection and
collection of samples: RS*, N-CT, KS, KK and ZY. RNA sequencing, data analysis and
interpretation: J-SK, N-CT, KS, PC, P-LC, K-LC and MAAH. N-CT did the analysis with qRT-
PCR. Drafting the manuscript: N-CT and KS. Critical revision and approval of the final
manuscript: all authors.

39

Chapter 3
Identification and Functional Characterization of Misexpressed
Genes in Elaeis guineensis and oleifera Interspecies Hybrids
3.1. Introduction
At the heart of speciation is the progressive accumulation of new species-specific alleles.
While they function well in the genetic background in which they arose, these alleles fail to
interact properly within interspecific hybrids produced in the lab (Morgan et al., 2020; Rhode &
Cruzan, 2005). Such negative interactions have been termed Dobzhansky-Muller
Incompatibilities, or DMI (Gavrilets, 2014; Satokangas et al., 2020). In gene regulatory networks
(GRNs), where heterologous genes may not properly regulate each other in hybrids,
misregulation results in abnormal development (Bomblies & Weigel, 2007; McDaniel et al.,
2008; Lenz et al., 2014; Lu et al., 2020), metabolism (Du et al., 2017), and sterility (Malone et
al., 2007; Good et al., 2010; Brill et al., 2016; Alhazmi et al., 2019).
40

The whole transcriptome consequences of this misregulation have been analyzed
numerous times in hybrids often finding evidence of transgressive expression, or gene expression
in hybrids outside the range of that of the parental species. Typically, the studies focus on genes
expressed at lower levels compared to what is normal in pure parents (Maheshwari & Barbash,
2011; Brill et al., 2016; R. Li et al., 2016; Kerwin & Sweigart, 2020). The preponderance of such
underexpression has numerous explanations, including improper development of reproductive
tissues resulting in strongly diminished expression of reproduction-related genes (Mugal et al.,
2020), or the mispairing of homologous chromosomes due to sequence divergence, where
normal active region pairing is required for full expression (J. Brown & O’Neill, 2010; Fishman
& Sweigart, 2018; M. Liu et al., 2021). However, there have been some studies showing sex-
specific overexpression of genes on the X-chromosome in animal hybrids (Good et al., 2010;
Sanchez-Ramirez et al., 2021).
Hybrids between plants (Zhigunov et al., 2017; Botet & Keurentjes, 2020) and animals
(Gélin et al., 2019; Tan et al., 2020) sometimes exhibit hybrid vigor, or heterosis, by way of
more robust development and accelerated growth rate. While hybrid vigor is extensively
exploited in agriculture to accomplish stronger yields, the mechanistic underpinnings of this
phenomenon are still debated (Goulet et al., 2017; I. Mackay et al., 2021). It is hypothesized that
complementation of deleterious alleles within a hybrid that are fixed in the parents might mask
deleterious mutations thereby enhancing hybrid performance (Vacher & Small, 2019). Another
hypothesis for heterosis is that expression may drift around optimal levels in pure species but
then return closer to the optima in interspecies hybrids (Rosas et al., 2010). Neither of these
hypotheses suggest a connection between hybrid vigor and misexpression.
41

It was hinted that enhanced expression might in fact contribute to hybrid vigor (Luca
Comai, personal communication). Indeed, normal expression regulation might have a
suppressive rather than enhancing nature, particularly in plants where homology-based
microRNA (miRNA) mediated regulation is common (Shen et al., 2017). From this point of
view, it could be hypothesized that hybrid vigor is a consequence of gene overexpression arising
from DMIs that result in the inability of GRNs in hybrids to properly suppress genes as normally
occurs in pure species parents. One could further hypothesize that these DMIs are a result of
divergence between miRNA sequences and their respective gene targets between species thereby
leading to deficiencies in suppression. While not yet supported at the RNA expression level, this
hypothesis is bolstered by a study comparing protein levels between yeast inter- and intra-
specific hybrids (Blein-Nicolas et al., 2015). The authors observed unexpectedly greater
deviation from mean parental protein levels in interspecific F1 hybrids than intraspecific hybrids.
Whether or not these hybrids were also characterized by hybrid vigor has not been reported.
Here, we analyze whole genome expression levels in mesocarp of pure palm oil species
Elaeis guineensis and E. oleifera and their hybrids. While the former pure species produces a
greater quantify of palm oil, the latter yields a higher quality product (N. Ting et al., 2020; M
Ithnin et al., 2021). Interspecies hybrids are bred in the hope of getting the benefits of both pure
species in a hybrid palm (Astorkia et al., 2020). These hybrids are characterized by an
astounding degree of hybrid vigor often growing to have a larger plant canopy than parental
palms, but also suffer from several abnormalities, including high degree of pollen infertility
(Maizura Ithnin et al., 2011). For species that easily hybridize, these palms have been diverged
for a long time, perhaps 51MYA after the vicariance of African and South American populations
(Singh et al., 2013).
42

We hypothesized that GRNs in the Elaeis species group accumulated a remarkable
number of DMIs, resulting in robust patterns of misexpression and strong overexpression in
hybrids. With this hypothesis in mind, we identified genes not expressed in the parental species
that exhibit high transcript levels in F1 and backcross hybrids. Compared with 16,969 normally
expressed genes, we find up to 3,699 genes strongly but erroneously expressed in backcross 1
(BC1) hybrids in a previously published dataset (Guerin et al., 2016). To verify this astounding
observation, we have also asked whether these genes are also observed expressed in
independently derived hybrids (N. Ting et al., 2020). We detect a remarkable concordance
between these genes. We deliver a never reported but strong and repeatable observation
consistent with the hypothesis of gene misexpression, potentially underlying hybrid vigor in oil
palms.
3.2. Materials and Methods
3.3.1. Identification of orthologous genes and GO annotation
Protein sequences and pre-computed pairwise alignments were downloaded from the
OMA database (Altenhoff et al., 2018) for the following species: Arabidopsis thaliana (DB
release: Ensembl Plants 38; TAIR10), Brassica napus (DB release: Darmor-bzh; v5), Gossypium
raimondii (DB release: Ensembl Plants 38; Graimondii2_0), Helianthus annuus (DB release:
Ensembl Plants 39; HanXRQr1.0), Zea mays (DB release: Ensembl Plants 40; AGPv4), Musa
acuminata subsp. malaccensis (DB release: Ensembl Plants 21; MA1; 6-DEC-2013), and
Glycine max (DB release: Ensembl Plants 19; V1.0; 24-JUN-2013). The Phoenix dactylifera
(DPV01, RefSeq assembly accession: GCF_000413155.1) and Elaeis guineensis (EG5, RefSeq
assembly accession: GCF_000442705.1) protein sequences and assembly annotations were
downloaded from RefSeq. A custom script was used to parse the annotations for gene-protein
43

pairs to create a file listing protein that are isoforms from the same gene. Orthologous proteins
were found using OMA Standalone version OMA 2.4.1 (Altenhoff et al., 2019). OMA
Standalone also predicted functions of proteins in both E. guineensis and P. dactylifera by
assigning GO terms to these proteins from proteins within the same OMA group that were
downloaded from the OMA database.
3.3.2. Acquiring publicly available RNA-seq data on oil palm mesocarp gene expression
Fifty-nine RNA-seq libraries totaling 1.41 billion reads from BioProject PRJEB11097
were downloaded from NCBI SRA. Here, we summarize the description of the data from a
previously published analysis of it (Guerin et al., 2016). Four libraries were created from
samples of Elaeis guineensis taken at 100, 120, 140, and 160 days after pollination (DAP).
Another four libraries were created from Elaeis oleifera samples collected at 124, 133, 143, and
152 DAP. The remaining 51 libraries were created from samples taken across 21 genotypes of
backcross 1 (BC1) E. guineensis x E. oleifera hybrids (2-3 replicates per genotype) at 120, 140,
and/or 160 DAP. These genotypes were created by backcrossing a female E. oleifera H833D x
male E. guineensis LM3261D F1 hybrid to a male E. guineensis LM2509D.
Additionally, twenty-four RNA-seq libraries from F1 and BC2 hybrids from our previous
study were re-analyzed here. Please refer to Section 2.2.1 in this dissertation for a full description
these materials.
3.3.3. RNA-seq data processing
Read quality was checked using FASTQC (Andrews, n.d.). Reads were then trimmed
using Trimmomatic ((Bolger et al., 2014)) with the settings ILLUMINACLIP LEADING:3
TRAILING:3 SLIDINGWINDOW:5:20 MINLEN:50 and mapped to the E. guineensis 5.0
reference (EG5, Refseq accession GCF_000442705.1) (Singh et al., 2013) and using STAR
(Dobin et al., 2013). We chose to map all libraries to the EG5 assembly as the current reference
44

genome for E. oleifera is not anchored to chromosomes and is not as well annotated with
genomic features as EG5. Uniquely mapped reads to each E. guineensis gene feature were
counted using featureCounts (Liao et al., 2014).
3.3.4. Identification of misexpressed genes
Genes with zero read counts across all libraries were removed and not considered in any
subsequent analysis. Raw read counts for the remaining genes were converted to transcripts per
million (TPM) to mitigate the bias due to gene length and sequencing depth (Conesa et al.,
2016). The R package zFPKM was used to compute a z-score for the log2(TPM) by fitting and
then mirroring a half Gaussian curve to the right half of the main peak of the distribution of
log2(TPM) (Hart et al., 2013). Per the author’s guidelines, a gene was considered expressed in a
library if its z-score (zTPM) was > -3. Furthermore, a gene was considered expressed in a
genotype (E. guineensis, E. oleifera or one of the hybrid genotype) if it was expressed in all
biological replicates of that genotype. A gene was considered misexpressed in a BC1 genotype if
it was expressed in that genotype but not in either of the pure species parents, E. guineensis and
E. oleifera.
3.3.5. GO enrichment of co-expressed clusters of misregulated genes
Two separate co-expression networks were built using Modulated Modularity Clustering,
or MMC (Stone & Ayroles, 2009): one for the genes misexpressed in every BC1 genotype and
another for all genes misexpressed in at least one BC1 genotype. The input to the program was
the TPM of each gene in each BC1 RNA-seq library. A co-expression network is created with
genes as the nodes and edges representing the Spearman correlation between the transcriptional
profiles of the two genes connected by the edge. Then, MMC jointly finds the graph partition P
and value of a σ that maximizes an objective function, where σ is a parameter that describes the
degree of modularity in the co-expression network. Modularity is a measure of the community
45

structure within a graph. A low value of σ is indicative of a graph with a high degree of
modularity, which occurs when a graph can be partitioned into many modules (or clusters) such
that the nodes within a cluster are much more strongly connected to each other than to nodes in
other parts of the graph. After optimization, genes are partitioned into P modules using a greedy
search that recursively bisects the co-expression network into subgraphs until the modularity
cannot be increased any further.
Using the GO annotation inferred for each gene by OMA, the TopGO package (Alexa et
al., 2006) in R (v. 4.0.2, R Core Team, 2020) was used to determine if any clusters were enriched
for any GO processes. Enrichment was tested with Fisher’s exact test and the default weight01 to
account for the hierarchical structure of GO terms. A cluster was considered enriched for a
specific GO term if the number of genes in that cluster with that annotation is greater than would
be expected given the frequency of that term in the set of genes misexpressed in at least one BC1
genotype. We also tested for GO enrichment within the entire set of misexpressed genes relative
to all genes with TPM ≥ 1 in at least one RNA-seq library.
3.3.6. Genotyping using RNA-seq data
Illumina reads were mapped to the EG5 assembly using BWA MEM 0.7.9a-r786 (H. Li
& Durbin, 2009). Variants were called using the GATK pipeline, which considers indel
realignment and base quality score recalibration, and calls variants across all samples
simultaneously through the UnifiedGenotyper program across uniquely mapped reads. Variants
were filtered using standard hard filtering parameters according to GATK Best Practices
recommendation (DePristo et al., 2011; Auwera et al., 2013):MQ > 36, QD > 24, MQRankSum
< 2. Among these variants, a smaller set was chosen from a set of 507,650 markers previously
identified across the entire range in both E. guineensis and E. oleifera that carried fixed but
different alleles (M Ithnin et al., 2021). Allelic calls in each of the 24 samples were supported by
46

at least 8 reads. Subsequent analyses were based on a set of 14,848 biallelic SNPs with minor
allele frequency of at least 0.05 and with genotypes called in at least 20 individuals.
Only 10 and 36 out of the biallelic SNP sites were detected in the genes misexpressed in
every and misexpressed in at least one BC1 genotype, respectively. A misexpressed gene was
called heterozygous (EG/EO) or containing one allele each from E. oleifera (EO) and E.
guineensis (EG) if it had at least one biallelic SNP. Otherwise, that gene was considered
homozygous for the EG allele.
3.3.7. Detecting significant differences in expression between genotypes
DESeq2 version 1.28.1 (Love et al., 2014) was used to test for significant differential
expression of misexpressed genes. Two generalized linear models (GLM) with a logarithmic link
were independently fit for each gene. The first model included one dependent factor, genotype,
with two levels: EG/EO and EG/EG. The second include one dependent factor that consisted of
as many levels as combinations of genotype and developmental stage. The samples were
classified into one of two developmental stages, namely up to 133 DAP and after 133 DAP,
because some BC1 genotypes did not have a sufficient number of replicates to have sufficient
power to determine differential expression at each of three times (DAP) at which the tissues were
collected. The log2 fold-change (FC) coefficients were estimated using the Wald test and
contrasts of the coefficients were set up to test whether the difference between groups (i.e. levels
of a factor) was zero. While the library size normalization factor and dispersion were estimated
using all genes, the Wald test and contrast of coefficients were done separately for each gene.

47

3.3. Results
3.3.1. Detection of misexpressed genes in BC
1
genotypes
To mitigate the erroneous classification of a gene as expressed due to leaky expression or
sequencing or mapping error, a gene was considered to be expressed in a genotype (i.e. Elaeis
guineensis, Elaeis oleifera, or one of the BC1 genotypes) only if the z-score of its TPM
(henceforth referred to as zTPM) was greater than -3 in every RNA-seq library sequenced for
that genotype (Hart et al., 2013). Given this definition, there were 25,720 genes and pseudogenes
found to be expressed the mesocarp in at least one of the pure species or BC1 genotypes. Of these
genes, almost 70% (16,969) were expressed in all the pure species and hybrids (Figure 3.1). If a
gene was expressed in one of the pure species, then generally it was expressed in both with only
34 and 24 expressed only in E. oleifera and only E. guineensis, respectively. Interestingly, we
find 3,699 genes that are expressed in at least one BC1 genotype but are not expressed (or silent)
in both the pure species parents. We henceforth call these genes “misexpressed”. Further, 821 of
these are misexpressed uniquely in only one of the BC1 genotypes. Notably, there are 42 genes
that are expressed in each of the BC1 genotypes, but neither in E. guineensis nor E. oleifera
(Figure 3.1).

48

Figure 3.1. The number of expressed genes (y-axis of vertical bar graph) in the 30 largest sets of intersection
between the groups of expressed genes in each genotype, that is Elaeis oleifera (EO), Elaeis guineensis (EG), and a
BC
1
genotype denoted by “BC” followed by a number. A gene is considered expressed if it is zTPM > -in all
libraries for that genotype. The matrix beneath the vertical bar graph depicts which group of genotypes (row) share
the set of expressed genes (column and x-axis of vertical bar graph). The number of expressed genes in each
genotype is denoted in the horizontal bar graph in the lower left-hand corner. Approximately 70% of all expressed
genes are expressed in both the pure parents and each BC
1
genotype. Created using UpsetR v1.4.0.

49

Table 3.1. As much as almost 70% and 98% of genes misexpressed in at least one BC
1
and all BC
1
genotypes,
respectively, were expressed in one or more E. oleifera x E. guineensis F1 and backcross 2 (BC
2
) hybrids from a
previously analyzed RNA-seq dataset ((N. Ting et al., 2020). Mesocarp tissue samples were collected from four F1
hybrids (genotypes A1-A4) and two BC
2
populations from different parental crosses (B1-B4 and C1-C4,
respectively). From each individual palm, samples were collected during early mesocarp development (UBL/UBH)
or late mesocarp development (RBL/RBH) for RNA sequencing. Biological replicates were classified as having low
(UBL/RBL) or high (UBH/RBH) palmitic acid content. Columns 2 and 3 are the number (#) and proportion (%),
respectively, of genes misexpressed in at least one BC
1
genotypes that were expressed in a F1 or BC
2
replicate
(Library). Columns 4 and 5 are the number (#) and proportion (%), respectively, of genes misexpressed in all BC
1

genotypes that were expressed in a F1 or BC
2
replicate.
Library
# of genes misexpressed in at
least one BC1 genotypes
%
# of genes misexpressed in all
BC1 genotypes
%
A1_RBL 2490 67.32 40 95.24
A1_UBL 2378 64.29 37 88.10
A2_RBL 1636 44.23 33 78.57
A2_UBL 2472 66.83 35 83.33
A3_RBH 2413 65.23 40 95.24
A3_UBH 2682 72.51 39 92.86
A4_RBH 1823 49.28 35 83.33
A4_UBH 2584 69.86 41 97.62
B1_RBL 2282 61.69 37 88.10
B1_UBL 2765 74.75 40 95.24
B2_RBL 1792 48.45 32 76.19
B2_UBL 1902 51.42 35 83.33
B3_RBH 2018 54.56 32 76.19
B3_UBH 2126 57.47 38 90.48
B4_RBH 2207 59.66 36 85.71
B4_UBH 2372 64.13 41 97.62
C1_RBL 2288 61.85 39 92.86
C1_UBL 2572 69.53 39 92.86
C2_RBL 2262 61.15 37 88.10
C2_UBL 2398 64.83 38 90.48
C3_RBH 2073 56.04 36 85.71
C3_UBH 2040 55.15 39 92.86
C4_RBH 1810 48.93 38 90.48
C4_UBH 1989 53.77 37 88.10

This misexpressed genes are unlikely to be due to a technical artifact. These genes, by
definition, were not only detected above a normalized expression threshold, but also exhibit a
wide range of expression levels in each of the BC1 genotypes (Figure 3.3, top). Anywhere from
50

about 48% -70% and 76%-98% of genes misexpressed in at least one BC1 and all BC1
genotypes, respectively, were found to be expressed in at least one F1 or BC2 populations in
mesocarp tissue (Table 3.1) from a previously published dataset (N. Ting et al., 2020).
Additionally, the genes misexpressed in at least one BC1 genotype are enriched for 27 biological
process GO terms (p-value < 0.05, Table 3.2). Notably, eight of these terms pertain to metabolic
processes involving lipids and fatty acids (GO:0006629; GO:0006633, GO:0006869,
GO:0016042) or sugars (GO:0006012, GO:0005985) and two pertain to reproductive processes
(GO:0007142, GO: 0048236).

Figure 3.2. The number of misexpressed genes (y-axis of vertical bar graph) in the 50 largest sets of intersection
between the groups of misexpressed genes in each BC
1
genotype denoted by “BC” followed by a number. A gene is
considered misexpressed in a BC
1
genotype if it is expressed in that genotype (zTPM > -3 in all libraries for that
genotype) and silent in both the pure species parents E. guineensis and E. oleifera. The matrix beneath the vertical
bar graph depicts which group of BC
1
genotypes (rows) share the set of misexpressed genes (column and x-axis of
vertical bar graph). The number of misexpressed genes in each BC
1
genotype is denoted in the horizontal bar graph
in the lower left-hand corner. Most misexpressed genes are unique to single BC
1
genotypes. Created using UpsetR
v1.4.0.
51

Figure 3.3. Distribution of expression (y-axis) of misexpressed genes in each BC
1
RNA-seq library (x-axis). A gene is considered misexpressed in a BC
1

genotype if it is expressed (zTPM > -3) in all libraries of that genotype but silent in all E. guineensis and E. oleifera libraries. The portion of the RNA-seq library
label prior to the hyphen denotes the BC
1
genotype and the portion after the hyphen the replicate. Note that BC12, BC12a, and BC12b are all libraries of the
BC12 genotype. The width of any section of any of a violin plot is determined by a kernel density fit to the expression values of all genes misexpressed in the
BC
1
genotype library denoted on the x-axis. The bottom plot is the distribution of the misexpressed genes from the top plot that are misexpressed in only one
BC
1
genotype. The number of genes misexpressed in at least that BC
1
genotype (top) or uniquely misexpressed in that BC
1
genotype (bottom) is in parentheses
next to the RNA-seq library name on the x-axis. While most misexpressed genes are unique to a BC
1
genotype, the genes misexpressed only in one BC
1

genotype are not the most highly expressed amongst all misexpressed genes.

52

Table 3.2. GO term enrichment across all misexpressed genes. TopGO enrichment across the 5736 GO terms
associated with genes misexpressed in at least one BC
1
genotype was performed using the weight01 method and the
biological process ontology. The number of misexpressed genes with a given GO term was compared to the
frequency that would be expected given the frequency of the term in the set of genes with TPM ≥ 1 in at least one
RNA-seq library. Annotated refers to the number of GO terms found in the background dataset, Significant refers to
the number of terms and child terms found in the target dataset and Expected refers to the expected number of GO
terms in the target dataset given the distribution of GO terms in the background dataset. GO terms found to be
enriched at the p<0.05 level using Fisher’s exact test are shown.
GO.ID Term Annotated Significant Expected p Value
GO:0030001 metal ion transport 56 17 4.46 7.3E-14
GO:0009691 cytokinin biosynthetic process 13 7 1.04 1.8527E-08
GO:0006629 lipid metabolic process 193 26 15.38 1.0812E-07
GO:0009733 response to auxin 36 1 2.87 2.1208E-07
GO:0006633 fatty acid biosynthetic process 35 8 2.79 4.133E-06
GO:0000160 phosphorelay signal transduction
system
41 7 3.27 0.00012
GO:0002229 defense response to oomycetes 5 3 0.4 0.00021
GO:0006464 cellular protein modification
process
125 10 9.96 0.00026
GO:0009644 response to high light intensity 2 2 0.16 0.00079
GO:0006869 lipid transport 22 4 1.75 0.00299
GO:0007166 cell surface receptor signaling
pathway
11 3 0.88 0.00307
GO:0009734 auxin-activated signaling
pathway
11 3 0.88 0.00307
GO:0045492 xylan biosynthetic process 4 2 0.32 0.00457
GO:0007142 male meiosis II 4 2 0.32 0.00457
GO:0009639 response to red or far red light 13 3 1.04 0.00511
GO:0006012 galactose metabolic process 6 2 0.48 0.011
GO:0007275 multicellular organism
development
39 4 3.11 0.01492
GO:0010256 endomembrane system
organization
7 2 0.56 0.01511
GO:0016042 lipid catabolic process 24 4 1.91 0.01985
GO:0010274 hydrotropism 9 2 0.72 0.02497
GO:0042138 meiotic DNA double-strand
break formation
1 1 0.08 0.02819
GO:0006850 mitochondrial pyruvate
transmembrane transport
1 1 0.08 0.02819
GO:0007076 mitotic chromosome
condensation
1 1 0.08 0.02819
GO:0010024 phytochromobilin biosynthetic
process
1 1 0.08 0.02819
GO:0048236 plant-type sporogenesis 1 1 0.08 0.02819
GO:0000226 microtubule cytoskeleton
organization
24 3 1.91 0.02884
GO:0005985 sucrose metabolic process 12 2 0.96 0.04332

53

Most misexpressed genes are specific to one BC1 genotype. When looking at all possible
nonempty intersections of the sets of misexpressed genes in each BC1 genotype (21 sets in total),
the top 10 largest are those unique to a BC1 genotype except for the set denoting 42 genes
misexpressed in all BC1 genotype (Figure 3.2). Interestingly, these misexpressed genes unique to
a BC1 genotype do not seem to be the most highly expressed of all misexpressed genes (Figure
3.3, bottom) when comparing their range of expression to those misexpressed in possibly more
than one BC1 genotype (Figure 3.3, top).
3.3.2. Functional characterization of modules of misexpressed genes
Modulated modularity clustering, or MMC, ((Stone & Ayroles, 2009) was performed to
identify genetically correlated clusters of genes misexpressed in at least one BC1 genotype.
MMC determines the optimal partitioning of a graph representing all pairwise correlations
between transcribed genes that maximizes modularity such that higher values of this measure
indicate that the graph is characterized by strongly connected clusters, i.e. clusters with a high
average module degree measured as the average absolute correlation amongst all pairs of gene in
that cluster. Maximum overall modularity was achieved with 14 clusters excluding 58 of the
3,699 genes that are misexpressed in at least one of the BC1 genotypes (Figure 3.4a), implying
that these 58 genes were not informative for finding clusters. The clusters are enumerated in
decreasing order of magnitude of average module degree such that cluster 1 consists of genes
with the highest correlated expression. The average module degree ranged from about 0.138 in
cluster 14 to 0.614 in cluster 1. Most of these clusters contained genes misexpressed in more than
one or two BC1 genotypes except for cluster 3 and 4 containing 19 and 15 genes, respectively.
All the genes in cluster 3 were misexpressed in BC3 with only one of those genes also
misexpressed in BC10. Cluster 4 consisted of genes only misexpressed in BC1.
54

GO enrichment analysis was performed for each of the 14 clusters to determine if any of
the clusters consisted of genes involved in the same biological pathways. Neither cluster 4 nor 7
were enriched for any GO biological processes with a p-value < 0.05. This does not seem to be
associated with low intra-cluster connectivity as the average module degree for these clusters are
about 0.471436 and 0.295842, respectively, and clusters with even lower connectivity were
enriched for some GO biological processes. Setting an a priori significance level of 0.05, the
other 12 clusters were each enriched for 2-8 processes except for clusters 2, 3, 8, and 9 which
were enriched only for ribosomal large subunit assembly (GO:0000027), oligopeptide transport
(GO:0006857), RNA modification (GO:0009451), and cell redox homeostasis (GO:0045454),
respectively (Figure 3.5, Supplementary Table B.1). Most clusters were enriched for a distinct
biological process GO term that was not enriched in the other clusters, however, there were
exceptions. Notably, both clusters 11 and 14 both significant enrichment in metal ion transport
(GO:0030001), fatty acid biosynthetic process (GO:0006633), and lipid metabolic process
(GO:0006629) (Figure 3.5, Supplementary Table B.1). Additionally, both clusters 1 and 6 were
enriched for cellular protein modification process (GO:0006464).
MMC was subsequently performed on the set of 42 genes misexpressed in all BC1
genotypes under the hypothesis that this analysis should yield genetic correlations that match
those found amongst these genes when analyzing the larger set of genes misexpressed in at least
one BC1 genotype of which they are a part of. This analysis resulted in three clusters: cluster 1
contains 11 genes, cluster 2 has 9 genes, and the remaining 22 genes form the least intra-
connected cluster 3. (Figure 3.4b) For each of the two clusters with the highest average module
degree, most of the genes clustered into the same module of the correlation graph amongst
overarching set of 3,699 genes misexpressed in at least one BC1 genotype: 7 of the 11 genes in
55

cluster 1 (average module degree = 0.546815) were also found in the cluster with highest average
module degree and 6 of the 9 genes in cluster 2 (average module degree = 0.434910) were found
in cluster 6 of the overarching misexpressed gene set. The 22 genes in cluster 3 (average module
degree = 0.190322) were spread across 5 clusters with average module degrees ranging from
0.138342 to 0.295842.

Figure 3.4. Clusters of genetically correlated transcriptional profiles of genes misexpressed in at least one (A) and in
all (B) 21 BC
1
genotypes. Clusters are formed by recursively bisecting a graph of correlations between all pairs of
transcriptional profiles until the modularity can no longer be increased. Modularity describes community structure
within the graph with higher modularity indicating more clusters that are strongly connected. Modules are ordered
from the top left to the bottom right by decreasing average absolute correlation between all pairs of genes within the
module. (A) 3,641 genes misexpressed in at least one B
C
1 genotype were grouped into 14 clusters. While there were
3,699 such misexpressed genes, 58 were deemed uninformative by the Modulated Modularity Clustering algorithm.
(B) 42 genes misexpressed in all BC
1
genotype were grouped into 3 clusters with 11, 9, and 22 genes in clusters 1, 2,
and 3, respectively.

56

Figure 3.5. GO enrichment within each of 14 clusters of genes misexpressed in at least one BC
1
. TopGO enrichment
was performed for each of the 14 clusters using the weight01 method and the biological process ontology. GO terms
found to be enriched at the p<0.05 level using Fisher’s exact test are shown. Horizontal line is at -log10(0.05).

57

3.3.3. Significant differences in expression of misexpressed genes between homozygous
and heterozygous samples
Only the 42 genes misexpressed in every BC1 genotype were considered when assessing
if the magnitude of misexpression of a gene is dependent upon its allelic composition. The power
to determine significant differences in expression of misexpressed genes in each BC1 genotype
would have been low given that there only two to three biological replicates per genotype. After
calling SNPs using the full RNA-seq dataset and filtering sites with VCFtools, there were only
kept 10 out of a possible 14848 sites retained for further analysis. Given these 10 sites, it was
possible to determine for 5 of the 42 misexpressed genes which BC1 samples were homozygous
(EG/EG) for the E. guineensis allele or heterozygous (EG/EO), i.e. containing both the E
guineensis (EG) and E. oleifera allele (EO), for each of the genes. For each of the 5 genes, there
were anywhere from 6 to 29 samples that were heterozygous for that gene. For each of these
genes, the distribution of expression (in terms of TPM) for that gene in the homozygous samples
and heterozygous samples are plotted side by side in Figure 3.6.
Two of the 5 misexpressed genes (LOC105041160 and LOC105060820) have a
statistically significant difference in expression between genotypes, that is samples homozygous
and heterozygous at that gene (p-value < 0.05, Table 3.3), as determined by DESeq2 fitting a
model with only one factor (i.e. genotype) to each of the genes in DESeq2. While
LOC105041160 encodes an uncharacterized protein, LOC105060820 encodes a LRR receptor-
like serine/threonine-protein kinase FEI 1. These two genes were not in the same cluster either in
the clustering of genes misexpressed in at least one BC1 genotype or misexpressed in every BC1
genotype. Considering the clusters of gene misexpressed in at least one BC1 genotype:
LOC105041160 is in cluster 11, which is enriched for some metabolic pathways involving fatty
acids as previously described, while gene-LOC105060820 is in cluster 6, which is enriched for
58

auxin-activated signaling pathway (GO:0009734), cellular protein modification (GO:0006464),
and microtubule cytoskeleton organization (GO:0000226).

Figure 3.6. Comparison of the range of expression in TPM (y-axis) for BC
1
samples that are homozygous for the E.
guineensis allele (EG/EG) or heterozygous (EG/EO) for one of the genes (denoted in the subplot title) misexpressed
in all BC
1
genotypes. A gene in particular sample was classified as heterozygous (EG/EO), i.e. possessing both the
E. guineensis (EG) and E. oleifera (EO) alleles, if there was at least one site within the gene at which VCFtools
detected an EO allele. Only 5 of the 42 genes misexpressed in each BC
1
genotypes contained any heterozygous sites.

59

Table 3.3. DESeq2 was used to determine whether there was a significant difference in expression between
genotypes for one of 5 genes misexpressed in all BC
1
genotypes. Genotype here means that a sample is homozygous
for the E. guineensis allele (EG/EG) or heterozygous (EG/EO) for a given gene. Only 5 of the 42 genes could be
evaluated after filtering sites by VCFtools. The difference in expression (i.e. log2 fold change) was considered
significant for a gene if it’s p-value < 0.05 assuming the null hypothesis that log
2
fold change = 0. Given this
criteria, LOC105041160 and LOC105060820 have a significant difference in expression between genotypes.
Gene RefSeq Protein Accession EG/EO vs EG/EG
log
2
fold change p-value
LOC105053881 XP_010933514.2 0.004018141 0.991668651
LOC105041160 XP_010916316.1 1.20606428 0.021548898
LOC105047188 XP_010924306.1 0.572233692 0.30304729
LOC105055852 XP_010936160.1 -0.096691035 0.816973375
LOC105060820 XP_010942956.1 2.126559179 2.54E-14

By fitting another model to each gene expression profile in with one factor describing the
combination of genotype and developmental stage, it became evident that whether there is a
significant difference in expression between genotypes for a given gene is dependent upon the
mesocarp developmental stage. While it did not have a significant difference in expression
between genotypes when genotype is the only dependent variable in the model, LOC105047188
does have a significant difference in expression between genotypes in the late developmental
stage (after 133 days after pollination, or DAP) (Table 3.4). This gene is within the cluster with
the highest average module degree when considering both the genes misexpressed in at least one
and in every BC1 genotype, which is enriched for cellular protein modification process (GO:
0006464), mitochondrial pyruvate transmembrane transport (GO:0006850), and
phytochromobilin biosynthetic process (GO:0010024). When incorporating the developmental
stage in the model, the significant difference in expression between genotypes for
LOC105041160 is only evident in the late developmental stage (after 133 DAP), but not in the
early stage (up to 133 DAP) (Table 3.4). Interestingly, the developmental stage does not seem to
affect the statistically significant expression of LOC105060820 between genotypes as the log2
fold change is around 2 for both developmental stages.
60

Table 3.4. For each one of 5 genes misexpressed in all BC1 genotypes, DESeq2 was used to determine whether
there was a significant difference in expression between genotypes that is different between early and late
developmental stages considered to be up to and after 133 days after pollination (DAP), respectively. Genotype here
means that a sample is homozygous for the E. guineensis allele (EG/EG) or heterozygous (EG/EO) for a given gene.
Only 5 of the 42 genes could be evaluated after filtering sites by VCFtools. The difference in expression (i.e. log2
fold change) was considered significant for a gene if it’s p-value < 0.05 assuming the null hypothesis that log
2
fold
change = 0.
EG/EO vs EG/EG
Gene RefSeq Protein
Accession
after 133DAP up to 133DAP
log2FC p-value log2FC p-value
LOC105053881 XP_010933514.2 0.698515 0.123466 -0.54335 0.271001
LOC105041160 XP_010916316.1 1.52584 0.0399782 0.797117 0.292967
LOC105047188 XP_010924306.1 2.04969 0.00198824 -0.136887 0.853141
LOC105055852 XP_010936160.1 0.418069 0.400614 -0.324934 0.575309
LOC105060820 XP_010942956.1 2.31153 3.48433e-10 1.92799 2.20668e-05

The protein coding genes LOC105060820 (XP_010942956.1), LOC105041160
(XP_010916316.1), and LOC105047188 (XP_010924306.1) are each a part of different families
of duplicated genes in E. guineensis where not all of the genes in each family are misexpressed.
Both LOC105060820 and LOC105041160 are each related to a single other E. guineensis gene
by duplication but neither of these other duplicated genes are misexpressed in any of the BC1
genotypes. However, both are found in the sets of genes we find expressed in both E. guineensis
and E. oleifera. The LOC105047188 is part of a family of 4 paralogous genes within E.
guineensis encoding chlorophyll a-b binding proteins of LHCII type 1. Two of the genes in this
family, LOC105032174 and LOC105048687 are not misexpressed in any BC1 genotype, but we
find that the former is expressed in both pure species parents while the latter is expressed in E.
guineensis but not E. oleifera. the other two protein-coding genes LOC105041013
(XP_010916097) and LOC105047188 are misexpressed but in different sets of BC1 genotypes:
the former is misexpressed in only BC23 while the latter is misexpressed in every BC1 genotype.
These two genes are also in different clusters of misexpressed genes with LOC105041013 being
in cluster 6 of misexpressed genes in at least one BC1 genotype.
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3.4. Discussion
There is ample evidence in the literature of interspecies hybrids exhibiting a level of gene
expression outside the range of their pure species parents, also called transgressive expression
(Renaut et al., 2009; Gomes & Civetta, 2015; Zhang et al., 2019; Go & Civetta, 2020; Glombik
et al., 2020; McGirr & Martin, 2020; Sanchez-Ramirez et al., 2021). To the best of our
knowledge, this work is the first to show an extreme version of transgressive expression wherein
BC1 hybrids of E. guineensis and E. oleifera express genes in mesocarp that do not seem to be
expressed at all in same tissue type in either one of the parental species. This phenomenon does
not seem to be a technical artifact as we observed that the misexpressed genes exhibit a sizeable
range of expression levels even after normalization.
We find that genes misexpressed in oil palm interspecies hybrids are enriched for
biological processes that have been implicated in previous studies of hybrid sterility. It has been
shown that sterile male potato hybrids exhibit abnormalities in male meiosis I and II (Larrosa et
al., 2011) and we found that the latter process is enriched among genes misexpressed in at least
one BC1 genotype, in particular in co-expressed cluster (14) of 1,325 misexpressed genes in at
least one BC1 genotype. This supports the fact that oil palm interspecies hybrids often have a
high degree of pollen infertility (Maizura Ithnin et al., 2011). None of the genes misexpressed in
every BC1 genotype were annotated with this function, suggesting that any relationship between
misexpression and potential deficiencies in male meiosis II may not be present in all genotypes.
Another process enriched in all misexpressed genes in comparison to all normally expressed
genes is meiotic DNA double-strand break formation (GO:0042138). A link between DNA
double-strand break formation and sterility has been shown in intersubspecific mice by way of
allelic incompatibilities in Prdm9, which facilitates programed DNA double-strand breaks
62

induced by the SPO11 protein In fact, programmed DNA double-strand breaks (Mukaj et al.,
2020).
Several of the enriched GO terms pertain to processes related heterosis. The GO term
defense response to oomycetes (GO:0002229), which pertains to reactions triggered to guard a
cell against oomycetes (a fungus-like microorganism), is enriched in a cluster (11) of 986
misexpressed genes in at least one BC1 genotype. It would be interesting to test if some BC1
genotypes do in fact exhibit better defense against these fungus-like microorganisms, particularly
as certain grapevine hybrids are less susceptible to the some strains of the oomycete Plasmopara
viticola than others (Toffolatti et al., 2012). Several metabolic and biosynthetic processes
involving lipids and fatty acids were enriched not only in misexpressed genes in comparison to
normally expressed genes but also in two co-expression clusters (11 and 14). This is line with
observations that some BC1 and BC2 genotypes have 10-26% more oil yield in comparison to
commercial oil palm varieties (Maizura Ithnin et al., 2011). The enrichment of GO biological
processes implicated in hybrid incompatibilities and heterosis within misexpressed genes
suggests a possible relationship between these two phenomena. However, this is only indirect
evidence. This should be corroborated with more direct evidence, such as looking further into if
any “speciation genes”, which are genes that have been shown to contribute to speciation, are
misexpressed in oil palm hybrids (Mack & Nachman, 2017).
Misexpressed genes seem to be genotype specific. Not only do we find that misexpressed
genes are specific to certain BC1 genotypes, but we also show the expression of some
misexpressed genes is significantly different between homozygous E. guineensis and
heterozygous palms. Further, these significant differences in expression are specific to
developmental stage. Indeed, both LOC105041160 and LOC105047188 had a statistically
63

significant difference in expression between homozygous and heterozygous palms in the late
developmental stage, but not the early one.
We also show evidence of paralog-specific misexpression. Both LOC105060820 and
LOC105041160 are differentially expressed between homozygous and heterozygous genotypes
but neither of their paralogs are misexpressed. Also, LOC105047188 is part of a family of four
genes duplicated within E. guineensis and only one other gene in that family is misexpressed,
namely LOC105041013 which, unlike the former, is only misexpressed in BC23. There is ample
evidence in the literature of considerably different expression patterns between paralogous genes
and we see evidence of this in the current study (Fishman & Sweigart, 2018; Glombik et al.,
2020). Namely, the genes LOC105053544, LOC105046836, and LOC105032174 are all
expressed in both pure species parents, but they are each paralogous to a gene in E. guineensis
that is misexpressed. The relationship between the genes LOC105047188 and LOC105048687 is
unlike the previous relationships mentioned in that former is misexpressed in all BC1 genotypes
and the latter is expressed in E. guineensis but silent in E. oleifera. In the long run, paralogous
genes may diverge in function such that each retains a different subset of the ancestral gene’s
function (a.k.a. subfuctionalization) or one copy may acquire a novel function (a.k.a.
neofunctionalization) (Glombik et al., 2020). The paralogous genes found here differing in
whether they misexpressed, or arguably “newly” expressed, in all BC1 genotypes or normally
expressed in the pure parent species are not an example of either subfuctionalization or
neofunctionalizaion as expression was measured only in the mesocarp tissue. To test these
hypotheses about sub- or neo-functionalization, we would need to assay gene expression in other
tissues of E. guineensis, E. oleifera, and their hybrids and see if some genes that are expressed in
the mesocarp of E. guineensis and E. oleifera are expressed in other tissue types in the hybrids.
64

3.5. Acknowledgement of Collaborators
Peter L. Chang performed the variant identification. Luke Genutis wrote custom scripts to
perform the GO enrichment and determine the genotype of the misexpressed genes. Sergey V.
Nuzhdin contributed critical insights and was instrumental to writing the introduction.

65

Chapter 4
Power Calculator for Detecting AI Using Hierarchical Bayesian
Model
4.1. Introduction
Gene expression in a diploid individual is the result of the combined expression of both
alleles. Allele Specific Expression (ASE) is the amount of mRNA transcribed at each allele. The
two alleles of a diploid individual can show significantly different expression, a condition termed
allelic imbalance (AI) (Wittkopp et al., 2004). AI is a result of genetic variation in regulation in
cis (e.g. promoters, enhancers, and other noncoding sequences), trans (e.g. transcription factors)
or resulting from cis by trans interactions (Fear et al., 2016a; Genissel et al., 2007; R. M. Graze
et al., 2012; Rita M. Graze et al., 2009; Miller et al., 2021; Wittkopp et al., 2004; F. Zou et al.,
2014). AI has been observed as a consequence of imprinting (Baran et al., 2015; Crowley et al.,
2015; Gregg et al., 2010) and nonsense mediated decay (Rivas et al., 2015) and has also been
shown to contribute to heterosis (Shao et al., 2019) and hybrid incompatibility (Mugal et al.,
2020). The extent of AI in human tissues can give information on the impact of heterozygous
mutations on the expression of the mutated allele in healthy (Kukurba et al., 2014) or cancerous
human tissues (Mayba et al., 2014). By comparing patients and controls, AI of TGFBR1 has
66

been associated with an increased risk of colorectal cancer (Valle et al., 2008). Also, loss of
heterozygosity can be detected using AI (Z. Liu et al., 2018; Tuch et al., 2010).
Comparing AI between conditions or tissues can provide new insights into the
mechanisms of gene expression regulation (Baran et al., 2015; Castel et al., 2020; Fear et al.,
2016a; Guo et al., 2008; L. León-Novelo et al., 2018a; Springer & Stupar, 2007; The GTEx
Consortium et al., 2015; Tukiainen et al., 2017). AI is thought to vary in different human (Castel
et al., 2020), mouse (Campbell et al., 2008; Pinter et al., 2015), sheep (Salavati et al., 2019), cow
(Chamberlain et al., 2015), and flycatcher (M. Wang et al., 2017a) tissues, thus suggesting an
environmental impact on gene regulation. A study on monozygotic twins identified genes with
differences in AI (da Silva Francisco Junior et al., 2019). Identifying variation in AI between
tissues leads to hypotheses about gene regulation mechanisms that explain tissue dependent
allelic expression (Cowles et al., 2002; Rivas et al., 2015; Tukiainen et al., 2017). Comparison of
allele specific expression between reciprocal crosses has been used to elucidate parent of origin
effects in mice and maize (Babak et al., 2015; Gregg et al., 2010; Springer & Stupar, 2007; F.
Zou et al., 2014). The comparisons can include external treatments. For example, in rice,
researchers compared AI across different tissues and different light cycle conditions identifying
several genes in which levels of AI were affected by the tissue/light conditions (Shao et al.,
2019).
Most often, these comparisons of AI between conditions are heuristic without a formal
statistical test. However, statistical comparisons have been made to assess heterogeneity of AI
between mated and virgin Drosophila female head tissue (L. León-Novelo et al., 2018a),
different human tissues types within an individual (Pirinen et al., 2015; Rivas et al., 2015;
Tukiainen et al., 2017), and subpopulations of cells in different developmental stages (Choi et
67

al., 2019). Statistical tests have also been performed to assess whether cis effects differ among
alleles in a population (Miller et al., 2021) or in parent of origin effects in mice (F. Zou et al.,
2014). Some of these approaches employ Bayesian hierarchical models, which have the benefit
of being able to estimate numerous parameters and incorporate various forms of data in order to
do so (Pirinen et al., 2015; Choi et al., 2019). In particular, Bayesian models can incorporate
priors to better and more flexibly estimate overdispersion in read count data (Turro et al., 2011;
M. Wang et al., 2017a) and control for bias in detecting AI when one allele maps better to the
reference due to DNA sequence or technical bias (Skelly et al., 2011; Turro et al., 2011; R. M.
Graze et al., 2012; L. G. León-Novelo et al., 2014; L. León-Novelo et al., 2018a). In contrast to
frequentist approaches, these models can treat the total number of reads as a random rather than
fixed variable thereby improving the power to detect AI by accounting for variance due to
random sampling of the mRNA pool during RNA sequencing (R. M. Graze et al., 2012; L. G.
León-Novelo et al., 2014).
Type I error in AI studies has been well explored and is known to be high, particularly
when failing to account for map bias (Degner et al., 2009), using the binomial test (Castel et al.,
2015; L. G. León-Novelo et al., 2014; Skelly et al., 2011; van de Geijn et al., 2015; M. Wang et
al., 2017a; F. Zou et al., 2014). It has also been shown that the power to detect AI is affected by
the level of total gene expression and not only the number of reads that map allele specifically
(L. León-Novelo et al., 2018a; M. Wang et al., 2017a). What is currently absent from the
literature is an understanding of the power for studies of AI and, in particular, what the best
allocation of resources is for boosting power for detection of AI when the hypothesis of interest
is a comparison of AI between conditions. What is more important: more reads or more
replicates? Is there a minimum number of replicates needed? A minimum number of reads? As
68

the read numbers per sample possible are exploding with the capacity of the new technologies,
and the per sample preparations are dramatically lower than a decade ago, it is time to determine
the necessary size and scope of such studies to control type I and type II error. It is common
practice to assess power of association studies (Hong & Park, 2012; Sham & Purcell, 2014), but
no software is currently available for assessing power for detecting differences in AI between
conditions.
To address this need, we present here the package BayesASE_power. It consists of tools
to simulate RNA-seq read counts under a previously published Bayesian model of AI (L. León-
Novelo et al., 2018a; Miller et al., 2021) with any number of replicates, reads, and levels of AI. It
aggregates the results across multiple simulated datasets to easily evaluate and compare Type I
error and power in detecting AI within and differences in AI between conditions. We perform an
extensive simulation study to show how BayesASE_power can help plan experiments to achieve
the desired power in detecting AI within a condition and interactions of AI between conditions.
4.2. Methods
4.2.1. Model description
We summarize here the basic features of the hierarchical Bayesian model used for
detection of AI in any condition and for comparing levels of AI between any two conditions,
which has been described earlier (L. León-Novelo et al., 2018a) and implemented in the package
BayesASE (Miller et al., 2021). Let g1 and g2 be the two alleles of a diploid individual,
respectively. For each gene or gene region, condition i and biological replicate (biorep) k, 𝑥𝑥 𝑖𝑖 , 𝑘𝑘
and 𝑦𝑦 𝑖𝑖 , 𝑘𝑘 are the number of reads that map align better (or unambiguously) to allele g1 and g2,
respectively, while 𝑧𝑧 𝑖𝑖 , 𝑘𝑘 is the number of reads that map equally well (or ambiguously) to both
alleles (Table 4.1).
69

One important parameter in determining AI is the ability to correctly assign reads to an
allele given that the read originated from that allele. We express this as the quantity 𝑟𝑟 𝑖𝑖 , 𝑔𝑔 1
( 𝑟𝑟 𝑖𝑖 , 𝑔𝑔 2
),
which is the probability of a read aligning to allele g1 (g2) given that it came from that allele.
Low values of these probabilities correspond to a high degree of ambiguously mapped reads,
which occurs when there is little sequence divergence between the two alleles.
Table 4.1. The expected number of reads ( 𝜇𝜇 ) aligning better to allele g1 than g2, 𝑥𝑥 𝑖𝑖 ,𝑘𝑘 ; better to allele g2 than g1,
𝑦𝑦 𝑖𝑖 ,𝑘𝑘 ; or ambiguously, that is equally well to both alleles, 𝑧𝑧 𝑖𝑖 ,𝑘𝑘 .
𝒙𝒙 𝒊𝒊 , 𝒌𝒌 𝒚𝒚 𝒊𝒊 , 𝒌𝒌 𝒛𝒛 𝒊𝒊 , 𝒌𝒌
( 𝟏𝟏 𝜶𝜶 𝒊𝒊 ⁄ ) 𝜷𝜷 𝒊𝒊 , 𝒌𝒌 𝒓𝒓 𝒊𝒊 , 𝒈𝒈 𝟏𝟏 𝛼𝛼 𝑖𝑖 𝛽𝛽 𝑖𝑖 , 𝑘𝑘 𝑟𝑟 𝑖𝑖 , 𝑔𝑔 1
[(1 − 𝑟𝑟 𝑖𝑖 , 𝑔𝑔 1
) 𝛼𝛼 𝑖𝑖 ⁄ + (1 − 𝑟𝑟 𝑖𝑖 , 𝑔𝑔 2
) 𝛼𝛼 𝑖𝑖 ] 𝛽𝛽 𝑖𝑖 , 𝑘𝑘

AI in condition i is measured by the parameter 𝜃𝜃 𝑖𝑖 , representing the proportion of reads
originating from the allele g1, which that can be written as follows:
𝜃𝜃 𝑖𝑖 =
𝔼𝔼 (𝑥𝑥 𝑖𝑖 , 𝑘𝑘 𝑟𝑟 𝑖𝑖 , 𝑔𝑔 1
) ⁄
𝔼𝔼 (𝑥𝑥 𝑖𝑖 , 𝑘𝑘 𝑟𝑟 𝑖𝑖 , 𝑔𝑔 1
+ 𝑦𝑦 𝑖𝑖 , 𝑘𝑘 𝑟𝑟 𝑖𝑖 , 𝑔𝑔 2
⁄ ) ⁄
=
1/𝛼𝛼 𝑖𝑖 𝛼𝛼 𝑖𝑖 + 1/𝛼𝛼 𝑖𝑖
Notably, when 𝜃𝜃 𝑖𝑖 is close to 0, we have one extreme case of AI with all the reads originating
from g2. When 𝜃𝜃 𝑖𝑖 = 0.5, we have perfect allelic balance with 50% of the reads from each allele.
With 𝜃𝜃 𝑖𝑖 = 1, we are in the opposite direction of extreme AI with all the reads originating from
g1. 𝜃𝜃 𝑖𝑖 is a function of 𝛼𝛼 𝑖𝑖 , which is also a measure of AI representing the ratio of reads mapping
to g1 over the reads mapping to g2. Consequently, 𝛼𝛼 𝑖𝑖 may vary from zero, when all reads map to
g2, to infinity, when all reads map to g1. In the case of allelic balance, 𝛼𝛼 𝑖𝑖 = 1.
The model also allows incorporating biological variability across conditions and
replicates via the variable 𝛽𝛽 𝑖𝑖 , 𝑘𝑘 . The ideal case is 𝛽𝛽 𝑖𝑖 , 𝑘𝑘 = 1 for all bioreps, which indicates that each
biorep has the same variance.
The full model for the read counts assumes that they follow a negative binomial
distribution: 𝑥𝑥 𝑖𝑖 , 𝑘𝑘 , 𝑦𝑦 𝑖𝑖 , 𝑘𝑘 , 𝑧𝑧 𝑖𝑖 , 𝑘𝑘 ~ 𝑁𝑁𝑁𝑁 (𝑚𝑚 𝑚𝑚 𝑚𝑚𝑚𝑚 = 𝜇𝜇 , 𝑑𝑑 𝑥𝑥 𝑑𝑑𝑑𝑑 𝑚𝑚𝑟𝑟 𝑑𝑑 𝑥𝑥 𝑑𝑑 𝑚𝑚 = 𝜙𝜙 ). Previous studies have shown that
70

a negative binomial distribution accounts for more variance, or overdispersion, in read counts for
biological replicates than would be expected for technical replicates, which can instead be
modeled by a Poisson distribution (Robinson & Smyth, 2007; Anders & Huber, 2010). While
the dispersion is common to all read counts 𝑥𝑥 𝑖𝑖 , 𝑘𝑘 , 𝑦𝑦 𝑖𝑖 , 𝑘𝑘 , and 𝑧𝑧 𝑖𝑖 , 𝑘𝑘 , the expected values are defined
separately for ambiguously and unambiguously mapped reads as previously described (Table
4.1). Please refer to L. León-Novelo et al., 2018a for the full description of the prior distributions
on the model parameters.
4.2.2. Simulations
Given the ability of BayesASE to independently test AI in two conditions and
simultaneously test for a difference in AI between conditions, the following null hypotheses are
defined:
1. Allelic balance in condition 1, i.e. null H1: 𝜃𝜃 1
= 0.5 or equivalently 𝛼𝛼 1
= 1.
2. Allelic balance in condition 2, i.e. null H2: 𝜃𝜃 2
= 0.5 or equivalently 𝛼𝛼 2
= 1.
3. Level of AI is the same in both conditions, i.e. null H3: 𝜃𝜃 1
= 𝜃𝜃 2
or equivalently 𝛼𝛼 1
= 𝛼𝛼 2
.
To test these hypotheses, three scenarios are defined (Figure 4.1):
1. H1, H2 and H3 are satisfied
2. H1 is satisfied, H2 and H3 are violated
3. H1 and H2 are violated, H3 is satisfied
Read counts were simulated under various scenarios assuming a negative binomial model
with a dispersion of 0.02 and the mean (μ) defined for 𝑥𝑥 𝑖𝑖 , 𝑘𝑘 , 𝑦𝑦 𝑖𝑖 , 𝑘𝑘 , and 𝑧𝑧 𝑖𝑖 , 𝑘𝑘 as shown in Table 4.1.
The full list of the simulation parameters is shown in (Supplementary Table C.1).
In the following results, the simulations were designed varying 𝜃𝜃 1
and 𝜃𝜃 2
from 0.25 to
0.75 with step 0.05, corresponding to varying 𝛼𝛼 1
and 𝛼𝛼 2
from 0.57735 to 1.73205. Previous work
71

has shown that the results for 𝜃𝜃 𝑖𝑖
> 0.5 ( 𝛼𝛼 𝑖𝑖 < 1) are symmetric to those for 𝜃𝜃 𝑖𝑖 > 0.5 ( 𝛼𝛼 𝑖𝑖 < 1) (L.
León-Novelo et al., 2018a) so we focus here on the former set of 𝜃𝜃 𝑖𝑖 values.
𝑟𝑟 𝑖𝑖 , 𝑔𝑔 1
and 𝑟𝑟 𝑖𝑖 , 𝑔𝑔 2
were simulated to vary between 0.2 and 0.8 with step 0.05. Low values
represent low discrimination ability (high sequence similarity) between alleles, while high values
represent high discrimination ability (low sequence similarity). The same probability of an allele
specific read rg1 (rg2) is used in simulating the read counts and fitting the model to the data
because misspecification of bias has already been addressed in a previous paper (L. León-Novelo
et al., 2018a).
The number of bioreps was set to 3 for most simulations. When investigating the effect of
varying number of bioreps on type I and type II error, the number of replicates was varied
between 3 and 12.
The total number of allele specific (or informative) reads was varied from 12 to 480,000.
This is the sum of the reads that map unambiguously in the simulation. Informative reads were
equally distributed across bioreps. The coverage is a function number (#) of allele specific reads
and the probability of an allele specific reads. Thus, the coverage per biological replicate is
𝑡𝑡 𝑑𝑑 𝑡𝑡 𝑚𝑚 𝑓𝑓 𝑐𝑐 𝑑𝑑 𝑐𝑐 𝑚𝑚 𝑟𝑟 𝑚𝑚 𝑐𝑐 𝑚𝑚 𝑑𝑑 𝑚𝑚𝑟𝑟 𝑏𝑏 𝑥𝑥𝑑𝑑 𝑓𝑓 𝑑𝑑 𝑐𝑐𝑥𝑥𝑐𝑐𝑚𝑚𝑓𝑓 𝑟𝑟 𝑚𝑚𝑑𝑑 𝑓𝑓𝑥𝑥 𝑐𝑐𝑚𝑚 𝑡𝑡𝑚𝑚 = �
# 𝑎𝑎 𝑓𝑓 𝑓𝑓 𝑎𝑎𝑓𝑓 𝑎𝑎 𝑠𝑠𝑠𝑠 𝑎𝑎 𝑠𝑠 𝑖𝑖 𝑓𝑓 𝑖𝑖 𝑠𝑠 𝑟𝑟 𝑎𝑎𝑎𝑎 𝑟𝑟 𝑠𝑠 # 𝑏𝑏𝑖𝑖 𝑏𝑏 𝑟𝑟 𝑎𝑎𝑠𝑠 𝑠𝑠 𝑎𝑎 𝑎𝑎 𝑔𝑔 (𝑟𝑟 𝑖𝑖 ,𝑔𝑔1
, 𝑟𝑟 𝑖𝑖 ,𝑔𝑔 2
) � � 2 �
For simplicity, all simulations were run under the “ideal case” assuming 𝛽𝛽 𝑖𝑖 , 𝑘𝑘 = 1 for all
conditions and replicates.
72

Figure 4.1. Read counts are simulated in two conditions (ex. liver and kidney tissue) independently with a specific number of simulations, allele specific
reads, biological replicates (bioreps), level of allelic imbalance (AI) θ, and probability of an allele g1 (g2) specific read. The number of allele specific reads
is the sum of unambiguously mapped reads in the experiment. Biological replicates in an experiment are samples from the same condition. In this example,
there are k biological replicates, 12 × k allele specific reads, 3 reads in every biorep that map equally well to both alleles (denoted by grey lines), and the
probability of an allele specific read is r
i,g1
= r
i,g2
= 0.8. The Type I error or power in rejecting allelic balance in condition 1 (or 2) is determined by
simulating that condition under allelic balance, i.e. H1 (or H2) null when θ
1
=0.5 (or θ
2
=0.5), or allelic imbalance, i.e. H1 (or H2) not null such as when
θ
1
=0.55 (or θ
2
=0.55), respectively. The Type I error in rejecting equal levels of AI between the two conditions (H3 null) can be determined with two cases:
allelic balance in both conditions, i.e. θ
1
= θ
2
=0.5 or equal levels of AI, ex. θ
1
= θ
2
=0.55. The power to reject equal levels of AI between two conditions is
assessed by simulations of allelic balance in one condition (H1 null) and allelic imbalance in the second (H2 not null), e.x. θ
1
=0.5 and θ
2
=0.5.
73

4.2.3. Computing type I error and power
Type I error is defined as the proportion of simulations for which the Bayesian evidence
against allelic balance or equal levels of AI is less than 0.05 when simulations were performed
under the null hypothesis. Three different null hypotheses are possible, as shown in Figure 4.1,
and described previously. Hypothesis H1 and H2 are null when 𝜃𝜃 1
= 0.5 and 𝜃𝜃 2
= 0.5,
respectively. H3 is null when 𝜃𝜃 1
= 𝜃𝜃 2
. It is important to note that H3 can be null even when both
H1 and H2 are not null if both conditions are simulated with the same level of AI.
The power to detect AI within a condition or a difference in AI between conditions is the
proportion of simulations for which the Bayesian evidence against allelic balance or equal levels
of AI is less than or equal to 0.05 when simulations were performed under the not null
hypothesis. Within a condition, the H1 (or H2) hypothesis is not null when 𝜃𝜃 1
≠ 0.5 (or 𝜃𝜃 2
≠
0.5). When comparing AI between conditions, the H3 hypothesis is not null when one condition
is simulated with allelic balance ( 𝜃𝜃 1
= 0.5) and the other with allelic imbalance ( 𝜃𝜃 2
≠ 0.5).
We compare Type I error and power between different magnitudes of deviation from the
null, which are measured as Δ𝐴𝐴𝐴𝐴 . We define 𝜃𝜃 0
= 0.5 and specify Δ𝐴𝐴𝐴𝐴 for each one of the
previously described hypotheses:
• To test for a deviation from allelic balance in condition 1, i.e. test for
H1 , Δ𝐴𝐴𝐴𝐴
1
=
| 𝜃𝜃 1
− 𝜃𝜃 0
|
𝜃𝜃 0
. Thus, when 𝜃𝜃 1
= 0.5, Δ𝐴𝐴𝐴𝐴
1
= 0.
• Analogously, to test for a deviation from allelic balance in condition 2, i.e. test
for H2, Δ𝐴𝐴𝐴𝐴
2
=
| 𝜃𝜃 2
− 𝜃𝜃 0
|
𝜃𝜃 0
for H2.
74

• To test for equality of levels of AI between two conditions, i.e. test for H3, we
define the relative deviation of the level of AI in condition 2 from that of 1: Δ𝐴𝐴𝐴𝐴
3

=
| 𝜃𝜃 2
− 𝜃𝜃 1
|
𝜃𝜃 1
. Thus, when 𝜃𝜃 1
= 𝜃𝜃 2
, Δ𝐴𝐴𝐴𝐴
3
= 0.
4.3. Results
Since both are tests for allelic balance in a single condition, we refer to the test for either
H1 or H2 as H1 in the following results for ease of visualization. Figure 4.2 shows variation in
type I error as a function of one of the previously defined simulation parameters. In all panels,
we varied both Δ 𝐴𝐴𝐴𝐴
1
and Δ 𝐴𝐴𝐴𝐴
3
from 0 to 0.3 with a step of 0.1 to test for H1 (panels a, c, and e)
and H3 (panels b, d, and f), respectively. To test for Type I error in rejecting null H1, 𝜃𝜃 1
= 0.5
and 𝜃𝜃 2
varied from 0.5 to 0.65 with a step of 0.05. To test for rejecting null H3, 𝜃𝜃 1
and 𝜃𝜃 2
were
both set to 0.5, 0.55, 0.6, or 0.65.
In particular, Figure 4.2a-b shows the type I error when varying the number of
simulations (x-axis) for different values of Δ𝐴𝐴𝐴𝐴 . The number of replicates was fixed at three and
the number of informative reads was fixed at 2,400 (i.e. 800 per replicate). The type I error is
never above 0.05 and, when the number of simulated features is 5,000 or higher, it is consistently
around 0.04 testing for either H1 or H3. In all the three panels, the probability of correctly
assigning a read was fixed to ri,g1 = ri,g2 = 0.8.
Figure 4.2c-d shows type I error as a function of informative reads per biological
replicate at different magnitudes of Δ 𝐴𝐴𝐴𝐴 . The number of biological replicates is fixed at 3 and the
number of simulations at 1000. Type I error is always lower than 0.05. However, type I error
increases as the number of informative reads increases due to the lack of power associated with
low numbers of informative reads.
75

Figure 4.2. Type I error is always less than 0.05 across number of simulations, number of allele specific reads, and
magnitude of deviation from the null when testing H1 or H3. (a-b) The x-axis is the number of simulations to obtain
a read count dataset. The number (#) of allele specific reads was set to 2400, there were 3 bioreps, and the
probability of an allele specific read was set to r
i,g1
= r
i,g2
= 0.8. Either Δ 𝐴𝐴 𝐴𝐴 1
or Δ 𝐴𝐴 𝐴𝐴 3
was varied from 0.5 to 0.65 by a
step of 0.05 to test for H3 or H1, respectively. (c-d) The x-axis is the number (#) of allele specific reads per
biological replicate (biorep). There were 1000 simulations and the probability of an allele specific read was set to
r
i,g1
= r
i,g2
= 0.8. H1 and H3 were evaluated as for the simulations in a-b. (Bottom Left) H3 was evaluated using
simulations of each of two conditions under the same 𝜃𝜃 ≠ 0.5. For H3, the effect size is the relative deviation from
allelic balance in either of the two conditions =
| 𝜃𝜃 − 𝜃𝜃 0
|
𝜃𝜃 0
, where 𝜃𝜃 0
= 0.5. In evaluating H1, the relative difference in
the levels of allelic imbalance Δ 𝐴𝐴 𝐴𝐴 was computed where the second condition was simulated under the not null
hypothesis. (e-f) The x axis is the deviation from the null hypothesis of allelic balance in a condition Δ 𝐴𝐴 𝐴𝐴 1
or of
equal levels of AI between conditions Δ 𝐴𝐴 𝐴𝐴 3
. Δ 𝐴𝐴 𝐴𝐴 3
was varied to test for H1 while Δ 𝐴𝐴 𝐴𝐴 1
was varied to test for H3.
There were 1000 simulations and the probability of an allele specific read was set to r
i,g1
= r
i,g2
= 0.8.
76

Figure 4.2e-f shows the variation of type I error as a function of variations in Δ𝐴𝐴𝐴𝐴 . The
number of simulated features was fixed to 1,000 and the number of biological replicates was
fixed to 3. Three different amounts of informative reads were simulated, namely, 96, 240, 480,
2400, and 24000. Type I error increased as the number of allele specific reads increased but was
always below 0.05.
In Figure 4.3, we show variations in type I error as a function of the number of replicates,
assuming different numbers of informative reads. In the two top panels (a and b), we simulated
eight different values of the total number of informative reads (120 to 6,400) ranging from a
minimum of 10 reads per biological replicates (120 reads in total, for 12 replicates), to 2,1333.3
reads per biological replicates (6,400 in 3 replicates). The number of simulated features was
fixed at 1000 and the probability of correctly assigning a read was fixed to ri,g1 = ri,g2 = 0.8. Δ𝐴𝐴𝐴𝐴
was set to zero in both panels. We show results for type I error in rejecting H1 and H3 in panels a
and b, respectively. Type I error in most of the scenarios is below the 0.05 threshold and always
below 0.08. As expected, type I error is higher at a higher number of informative reads. For any
given number of total informative reads, type I error slightly increases as the number of
replicates increases.
In the lower panels (c and d), we simulated four different numbers of informative reads
per replicate (40, 80, 160 and 320). The number of simulated features was fixed at 1,000 and the
probability of correctly assigning a read was fixed to ri,g1 = ri,g2 = 0.8. Δ 𝐴𝐴𝐴𝐴 was set to zero in both
panels. Again, type I error for rejecting H1 (Figure 4.3c) and for rejecting H3 (Figure 4.3d) was
below 0.05 for most scenarios and was never above 0.08. As expected, increases in the number
of replicates and in coverage per replicate led to an increase of type I error.
77

Figure 4.3. H1 and H3 refer to simulations under the null hypothesis of allelic balance within a condition and equal
levels of AI between the two conditions, respectively. The Type I Error (y-axis) is computed as the proportion of
simulations for which the Bayesian evidence against allelic balance within a condition or against equal levels of AI
between conditions is < 0.05. The x-axis is the number of biological replicates (bioreps) that were simulated. The
number (#) of allele specific reads is the sum of the reads that map unambiguously to an allele in the experiment.
This number divided by the number of bioreps is the number (#) of allele specific reads per bioreps. 𝛥𝛥 𝐴𝐴 𝐴𝐴 is the
relative difference in the levels of allelic imbalance between the two conditions: 𝛥𝛥 𝐴𝐴 𝐴𝐴 =
| 𝜃𝜃 2
− 𝜃𝜃 1
|
𝜃𝜃 1
. The probability of an
allele specific read was set to r
i,g1
= r
i,g2
= 0.8 and 1000 simulations were done. Type I error was less than 0.08 across
different numbers of biological replicates (bioreps) and numbers of allele specific reads (also per biorep).

We show in Figure 4.4 power for detecting AI as a function of the number of simulations
under different deviations from the null hypothesis ( Δ𝐴𝐴𝐴𝐴 ). The number of replicates was fixed to
three, the total number of informative reads was fixed to 500, and the probability of correctly
assigning a read was fixed to ri,g1 = ri,g2 = 0.8. The number of simulations does not affect power.
The magnitude of deviation from the null on the contrary has a strong effect on power. When
78

Δ𝐴𝐴𝐴𝐴
1
>= 0.2, power is greater than 80%. Power for rejecting H3 is slightly lower than that for
rejecting H1, especially for moderate deviations from the null. When Δ𝐴𝐴𝐴𝐴
3
=0.2, power is
approximately 60%. This observation is in agreement with what we observed in previous work
(L. León-Novelo et al., 2018a).

Figure 4.4. H1 and H3 refer to simulations under the not null hypothesis of allelic imbalance within a condition and
unequal levels of AI between the two conditions, respectively. The x-axis is the number of simulations that were
done to obtain a read count dataset. The power (y-axis) is computed as the proportion of simulations for which the
Bayesian evidence against allelic balance within a condition or against equal levels of AI between conditions is <
0.05. For testing for both H1 and H3, deviations from the null were varied from 0.1 to 0.3 with a step of 0.1. The
number (#) of allele specific reads was set to 2400 and the probability of an allele specific read was set to r
i,g1
= r
i,g2
= 0.8. At any given effect size or Δ 𝐴𝐴 𝐴𝐴 , the power to detect AI in a condition or differing levels of AI between
conditions is consistent across the number of simulations.

79

Figure 4.5. H1 and H3 refer to simulations under the not null hypothesis of allelic imbalance within a condition and
unequal levels of AI between the two conditions, respectively. The x-axis is the number (#) of allele specific reads
per biological replicate (biorep). The power (y-axis) is computed as the proportion of simulations for which the
Bayesian evidence against allelic balance within a condition or against equal levels of AI between conditions is <
0.05. For testing for both H1 and H3, deviations from the null were varied from 0.1 to 0.3 with a step of 0.1. There
were 1000 simulations, 3 biological replicates (bioreps) and the probability of an allele specific read was set to r
i,g1
=
r
i,g2
= 0.8. The power to detect AI in a condition or differing levels of AI between conditions increases as the
number of allele specific reads per biorep increases but does plateau for higher effect sizes and Δ 𝐴𝐴 𝐴𝐴 .

Figure 4.5 reports power as a function of the number of informative reads per replicate
with a fixed number of three replicates, 1,000 simulated features and the probability of correctly
assigning a read was set to ri,g1 = ri,g2 = 0.8. Power for rejecting H1 (panel a) and H3 (panel b) is
affected by size of the deviation from the null and by the number of informative reads. When the
deviation from the null is small, power may remain low even for high informative coverage,
while for larger deviations ( Δ𝐴𝐴𝐴𝐴 =0.3) power is above 80% with 60 informative reads per
replicate (H1) or 300 informative reads per replicate (H3).

80

Figure 4.6. H1 and H3 refer to simulations under the not null hypothesis of allelic imbalance within a condition and
unequal levels of AI between the two conditions, respectively. For evaluating H1, the x-axis is the effect size, which
(continued from previous page) is relative deviation from allelic balance in a condition =
| 𝜃𝜃 − 𝜃𝜃 0
|
𝜃𝜃 0
, where 𝜃𝜃 0
= 0.5.
For evaluating H3, the x-axis is the relative difference in levels of AI between two conditions Δ 𝐴𝐴 𝐴𝐴 =
| 𝜃𝜃 2
− 𝜃𝜃 1
|
𝜃𝜃 1
where
the first condition was simulated under the null hypothesis and the second under the not null hypothesis 𝜃𝜃 ≠ 0.5.
The power (y-axis) is computed as the proportion of simulations for which the Bayesian evidence against allelic
balance within a condition or against equal levels of AI between conditions is < 0.05. There were 1000 simulations
and the probability of an allele specific read was set to r
i,g1
= r
i,g2
= 0.8. Simulations were performed for 3, 4, 5, 6, 8,
and 12 biological replicates (bioreps, x-axis) for various numbers (#) of allele specific reads. Increasing the number
of allele specific reads and, for at least 480 allele specific reads, increasing the number of biological replicates
increases power to detect AI or a difference in AI between conditions.
81

Figure 4.0.7. H1 and H3 refer to simulations under the not null hypothesis of allelic imbalance within a condition
and unequal levels of AI between the two conditions, respectively. For evaluating H1, the x-axis is the effect size,
which is the relative deviation from allelic balance in a condition =
| 𝜃𝜃 − 𝜃𝜃 0
|
𝜃𝜃 0
, where 𝜃𝜃 0
= 0.5. For evaluating H3, the
x-axis is the relative difference in levels of AI between two conditions Δ 𝐴𝐴 𝐴𝐴 =
| 𝜃𝜃 2
− 𝜃𝜃 1
|
𝜃𝜃 1
where the first condition
simulated under the null hypothesis and the second under the not null hypothesis 𝜃𝜃 ≠ 0.5. The power (y-axis) is
computed as the proportion of simulations for which the Bayesian evidence against allelic balance within a
condition or against equal levels of AI between conditions is < 0.05. There were 1000 simulations and the
probability of an allele specific read was set to r
i,g1
= r
i,g2
= 0.8. Simulations were performed for 3, 4, 5, 6, 8, and 12
biological replicates (bioreps, x-axis) for various number (#) of allele specific reads per biological replicate
82

(bioreps). Increasing the number of biological replicates increases the power to detect AI or a difference in AI
between conditions.

Figure 4.6 shows how power varies as a function of the number of biological replicates,
under various numbers of informative reads, and for different deviations from the null. The
number of simulated features was set to 1000 and the probability of correctly assigning a read
was set to ri,g1 = ri,g2 = 0.8. Panels a and b show power for Δ𝐴𝐴𝐴𝐴 = 0.1. Power for such a small
deviation from the null is fairly low under most conditions. H1 can be rejected with power >
80% only when the total number of reads is at least 2,400, provided that the number of replicates
is at least 12. Power for rejecting H3 is even lower, and never reaches 80%. For Δ𝐴𝐴𝐴𝐴 = 0.2
(panels c and d) power is already sensibly higher. With 960 informative reads, H1 can be
rejected with power > 80% even with 3 biological replicates. H3 can also be rejected with power
> 80% with 960 informative reads provided that they are equally distributed across at least 8
replicates. When Δ𝐴𝐴𝐴𝐴 = 0.3 (panels e-f), power is further increased and it approaches 100%
under several scenarios.
Figure 4.7 shows variation in power as a function of the number of biological replicates,
under different numbers of informative reads per replicate and for different deviations from the
null hypothesis. The number of simulated features was set to 1000 and the probability of
correctly assigning a read was set to ri,g1 = ri,g2 = 0.8. Panels a and b show power for Δ𝐴𝐴𝐴𝐴 = 0.1.
In this scenario, power of 80% is only achieved for rejecting H1 if 12 replicates are available
with 320 informative reads per replicate. Rejection of H3 under this small deviation is always
lower than 80%. For Δ𝐴𝐴𝐴𝐴 = 0.2 (panels c and d), several scenarios achieve a power > 80% for
rejecting H1, such as 320 informative reads per replicate with 3 replicates and 80 informative
reads per replicate with 6 replicates. H3 is also rejected with power > 80% in some instances,
83

such as 160 informative reads per replicates with 8 replicates and 80 informative reads with 12
replicates. Finally, when Δ𝐴𝐴𝐴𝐴 = 0.3 power is high: most simulated scenarios have power near
100% of rejecting H1, and several scenarios have power >80% of rejecting H3. For example,
with 320 informative reads per replicate, 3 replicates are sufficient to give > 80% power for
rejecting H3.
Figure 4.8 shows power as a function of Δ𝐴𝐴𝐴𝐴 under different numbers of informative
reads with 3 biological replicates and 1,000 simulations. Panel a shows power in rejecting H1.
When Δ 𝐴𝐴𝐴𝐴 is 0.5 (i.e. one allele is expressed 50% less than the other one), power is approaching
100% even when the total number of informative reads is as low as 96, which corresponds to 32
informative reads per biological replicate. For Δ𝐴𝐴𝐴𝐴 = 0.3, power is > 80% when the total number
of informative reads >= 240.

Figure 4.8. H1 and H3 refer to simulations under the not null hypothesis of allelic imbalance within a condition and
unequal levels of AI between the two conditions, respectively. For evaluating H1, the x-axis is the effect size, which
is the relative deviation from allelic balance in either of the two conditions =
| 𝜃𝜃 − 𝜃𝜃 0
|
𝜃𝜃 0
, where 𝜃𝜃 0
= 0.5. For evaluating
H3, the x-axis is the relative difference in levels of AI between two conditions 𝛥𝛥 𝐴𝐴 𝐴𝐴 =
| 𝜃𝜃 2
− 𝜃𝜃 1
|
𝜃𝜃 1
where the first
condition simulated under the null hypothesis and the second under the not null hypothesis 𝜃𝜃 ≠ 0.5. The power (y-
axis) is computed as the proportion of simulations for which the Bayesian evidence against allelic balance within a
condition or against equal levels of AI between conditions is < 0.05. There were 1000 features and the probability
of an allele specific read was set to r
i,g1
= r
i,g2
= 0.8. The power to detect AI in a condition or differing levels of AI
between conditions increases as the effect sizes or 𝛥𝛥 𝐴𝐴 𝐴𝐴 increases for higher effect sizes and 𝛥𝛥 𝐴𝐴 𝐴𝐴 , but does plateau.
84

As observed in previous plots, the power in rejecting H3 is lower. When Δ𝐴𝐴𝐴𝐴 = 0.3,
power is < 80% when using in total 240 informative reads. Higher numbers of informative reads
result in substantial increases of power, although differences in power when using 480, 2400, or
24000 total informative reads are negligible.

4.4. Discussion
We present here results of an extensive simulation study to quantify type I error and
power in detecting allelic imbalance using the model implemented in the BayesASE pipeline
(Miller et al., 2021). Type I error was below the nominal value of 0.05 for most simulated
scenarios and was less than 0.08. Type I error values higher than 0.05 were observed for extreme
numbers of allele-specific reads and bioreps, which in our simulations correspond to greater than
or equal to 4800 informative reads with at least 4 bioreps.
Power and type I error were both affected by the number of informative reads. However,
type I error rarely exceeded the nominal value of 5% even for very high numbers of informative
reads (Figure 4.3), while increasing the number of informative reads substantially increased
power (Figure 4.5). These observations are in agreement with simulations performed using the
previous version of this model (L. León-Novelo et al., 2018b) and with previous work focusing
on the increase of power as a function of coverage (Edsgärd et al., 2016; Fontanillas et al., 2010).
The size of the deviation from the null has been shown to affect power with stronger
deviations eliciting higher power (M. Wang et al., 2017b). Our results confirm this observation
showing that a deviation from the null of Δ𝐴𝐴𝐴𝐴 = 0.3 was enough to elicit a power > 80% in most
scenarios, while a high number of replicates and/or high number of informative reads are needed
85

to achieve high power with small imbalance (Figure 4.7, Figure 4.8). The use of several
replicates and of high coverage is also recommended based on the analysis of type I error, which
revealed that type I error is around 5% even for a high number of replicates and informative
reads. When Δ𝐴𝐴𝐴𝐴 is 0.1, the size of the allelic imbalance is small, and the power is generally very
low. Only when the number of allele-specific reads per replicate is 320 and the number of
replicates is high does the power exceed 50%.
The maximum level of imbalance that we simulated was Δ𝐴𝐴𝐴𝐴 =0.3, which is still a
moderate imbalance. When testing Δ 𝐴𝐴𝐴𝐴
0
, this corresponds to 𝜃𝜃 1
=0.65. In this condition, power is
already high under several scenarios. For example, power for rejecting H1 exceeded 80% already
when simulating 80 allele-specific reads per replicate and three replicates, and it approached
100% when increasing the number of reads and/or the number of replicates (Figure 4.7). Power
for rejecting H3 showed similar patterns but was usually lower. When Δ𝐴𝐴𝐴𝐴 =0.3, rejection of H3
reached a power greater than 80% with three replicates only when at least 320 allele-specific
reads were available.
An important advancement of the model used in the present study is the possibility of
testing for difference of AI between conditions, also referred to as rejection of hypothesis H3.
Preliminary analysis has shown that power for rejecting H3 is lower than for detecting AI in a
single sample (Fear et al., 2016b; L. León-Novelo et al., 2018b), and this is confirmed in most
scenarios investigated in the present study. Levels of type I error were comparable for tests of the
H1/H2 and H3 hypotheses, while power for H1/H2 was higher than power for rejection of H3.
There are a couple of limitations to the current simulation study. Ideally, we want to
simulate read counts for n genes or randomly segregated regions of the genome with different
variances. For computational efficiency, the current implementation simulates read counts for
86

one gene n times. We conducted a meta-analysis to see if aggregating the results across multiple
scenarios could be used as a proxy for simulating read counts for n genes. However, we find that
the Type I error is inflated in this approach (Appendix C, Supplementary Figure 1). At present,
BayesASE_power is designed to take estimates of AI in the format output by the Python package
BayesASE. The software would need to be altered to be used with other Bayesian analyses of AI,
such as TreCASE (F. Zou et al., 2014), which has been shown to estimate ASE effects that are
concordant with those of BayesASE (Miller et al., 2021).
A question of interest for planning experimental work is given any total sequencing depth
Dtot, assuming that Dtot represents reads that can be assigned to either allele (i.e. informative), is
the power for detecting AI influenced by the number of replicates across which the total
coverage is spread? Previous studies suggested that a coverage of a few hundred reads were
sufficient to accurately estimate the extent of AI in one sample (Fontanillas et al., 2010; Main et
al., 2009). In agreement with such observations, our results show that under most scenarios, the
optimal approach in terms of power is to divide the total number of reads across several
biological replicates both for detecting AI in one sample and for detecting difference in AI
between samples (Figure 4.6). This, of course, must be balanced against the fact that preparing
several (let us say L) independent libraries, each one accounting for Dtot/L allele specific reads, is
more expensive than obtaining the Dtot reads with a single library.
4.5. Availability of materials and methods
This study was performed using programs written in Python and R that are freely
available on GitHub: https://github.com/McIntyre-Lab/BayesASE_power.
87

4.6. Acknowledgement of Collaborators
This work is being prepared for submission with the following agreed upon authors’ list
amongst all collaborators: Katrina Sherbina, Luis G. Leon Novelo (University of Texas School
of Public Health), Sergey V. Nuzhdin, Lauren M. McInytre (University of Florida), and Fabio
Marroni (Università di Udine). All authors contributed to the study design. Katrina Sherbina
performed all simulations and analysis. Katrina Sherbina and Fabio Marroni drafted the
manuscript and Lauren M. McInytre contributed critical revisions.

88

Chapter 5
Discussion
Given the crop’s global agronomic importance, we have a vested interest in optimizing
breeding strategies to create oil palm interspecies hybrids with healthier fatty acid content and
increased disease resistance without sacrificing oil yield. This depends on understanding how
both molecular and organismal phenotypic variation is influenced by genetic variation within the
two oil palm species, Elaeis guineensis and Elaeis oleifera, and their interspecific hybrids and
backcrosses. Toward improving this understand, I have detailed two transcriptomic studies in
Chapters 2 and 3 in oil palm hybrids, which to date are few given the considerable time it takes
for oil palm to mature and achieve peak productivity (Srestasathiern & Rakwatin, 2014). In
Chapter 1, we corroborate prior studies identifying QTL associated with fatty acid traits by
finding some genes within these QTL have a statistically significant differences in expression
between different hybrid generation crosses and mesocarp developmental stages and that these
differences vary across isoforms of these genes. In Chapter 2, we find evidence of gene
expression misregulation that is unlikely due to leaky expression or technical artifacts as some
genes we find misexpressed in BC1 populations (recall these are not expressed in either pure
89

species parent) are expressed in F1 and BC2 hybrids and are related to biological processes
implicated in hybrid dysfunction and vigor. We hypothesize that this misexpression indicates a
relationship between both Dobzhansky-Mueller incompatibilities (DMI) and hybrid vigor.
Namely, sequence divergence between transcription regulators (such as miRNA) and their target
genes result in DMI within gene regulatory networks that result in the expression of genes
usually suppressed in pure species parents. While this work is a promising start, we are likely
missing sources of genetic variation underlying complex oil palm traits due to previously
described deficiencies of fine-mapping QTL using expression data and additional restrictions due
to sample size.
Allele specific expression (ASE) analyses are a promising future direction to uncovering
more causal genomic variants underlying traits of interest in oil palm. Indeed, previous ASE
studies have linked allelic imbalance to both heterosis (Shao et al., 2019) and hybrid
incompatibility (Mugal et al., 2020). However, biases inherent in the choice of read mapping and
statistical model for AI are well-documented. While there have been significant improvements in
model development to account for these biases (Skelly et al., 2011; Turro et al., 2011; Mayba et
al., 2014; L. G. León-Novelo et al., 2014; van de Geijn et al., 2015; Pirinen et al., 2015; L. León-
Novelo et al., 2018; Choi et al., 2019 to name a few), what has been missing from the literature is
understanding of power to not only detect AI but differences in AI between conditions and, in
particular, how best to allocate resources to boost power. In response, Chapter 4 details an
extensive simulation study of how varying experimental design parameters, such as the number
of biological replicates and sequencing coverage, affects the Type I error and power in detecting
AI within and difference in AI between conditions. We find that power is substantially boosted
when total coverage in an RNA-seq experiment is divided amongst several biological replicates.
90

Our recommendations in Chapter 4 have important implications for studying ASE in oil
palm given the nature of currently available transcriptomic data. We have come across only one
attempt to assay ASE in an oil palm hybrid generation (Guerin et al., 2016). For 7 fatty acid
synthesis genes for which BC1 samples were heterozygous, the authors compared the average
percentage of expression of the E. guineensis allele between BC1 samples that are homozygous
or heterozygous for the WRI1-1 gene and found no significant differences in allelic expression
except for the MAT gene (Guerin et al., 2016). To address possible biases in their analysis, they
compared read count data for only 44 lipid genes mapped either to an E. guineensis or E. oleifera
publicly available reference and did not find any mapping biases. However, this is not an
exhaustive analysis of potential genome-wide biases. Prior studies inform us that we can almost
eliminate such potential biases with the use of genotype-specific references (Skelly et al., 2011;
Turro et al., 2011; R. M. Graze et al., 2012; Fear et al., 2016a) and DNA controls (R. M. Graze et
al., 2012; Rita M. Graze et al., 2009; Wittkopp et al., 2004). Even if we use a Bayesian model of
AI, such as the one previously developed (L. León-Novelo et al., 2018a) and used for the
simulation study in Chapter 4, there remains the challenge of insufficient biological replication
for any of the genotypes analyzed in either Chapters 2 or 3. Considering the simulation results
presented in Chapter 4, any study of ASE in the current oil palm hybrid data would be
underpowered with only 2-4 biological replicates per hybrid generation and unlikely to detect
any level of AI other than one that is extreme. We hope that in the future to be able to obtain
sufficient data based on experimental design recommendations from Chapter 4 such that we will
have sufficient power to look at cis regulatory variation in oil palm hybrids to better understand
heterosis and hybrid incompatibilities.

91

References
Alexa, A., Rahnenfuhrer, J., & Lengauer, T. (2006). Improved scoring of functional groups from
gene expression data by decorrelating GO graph structure. Bioinformatics, 22(13), 1600–
1607. https://doi.org/10.1093/bioinformatics/btl140
Alhazmi, D., Fudyk, S., & Civetta, A. (2019). Testes Proteases Expression and Hybrid Male
Sterility Between Subspecies of Drosophila pseudoobscura. G3-GENES GENOMES
GENETICS, 9(4), 1065–1074. https://doi.org/10.1534/g3.119.300580
Altenhoff, A. M., Glover, N. M., Train, C.-M., Kaleb, K., Warwick Vesztrocy, A., Dylus, D.,
de Farias, T. M., Zile, K., Stevenson, C., Long, J., Redestig, H., Gonnet, G. H., &
Dessimoz, C. (2018). The OMA orthology database in 2018: Retrieving evolutionary
relationships among all domains of life through richer web and programmatic interfaces.
Nucleic Acids Research, 46(D1), D477–D485. https://doi.org/10.1093/nar/gkx1019
Altenhoff, A. M., Levy, J., Zarowiecki, M., Tomiczek, B., Warwick Vesztrocy, A., Dalquen, D.
A., Müller, S., Telford, M. J., Glover, N. M., Dylus, D., & Dessimoz, C. (2019). OMA
standalone: Orthology inference among public and custom genomes and transcriptomes.
Genome Research, 29(7), 1152–1163. https://doi.org/10.1101/gr.243212.118
Anders, S., & Huber, W. (2010). Differential expression analysis for sequence count data.
Genome Biology, 11(10), R106. https://doi.org/10.1186/gb-2010-11-10-r106
Anderson, J. T., Wagner, M. R., Rushworth, C. A., Prasad, K. V. S. K., & Mitchell-Olds, T.
(2014). The evolution of quantitative traits in complex environments. Heredity, 112(1),
4–12. https://doi.org/10.1038/hdy.2013.33
92

Andrews, S. (n.d.). FastQC: a quality control tool for high throughput sequence data.
http://www.bioinformatics.babraham.ac.uk/projects/fastqc
Astorkia, M., Hernandez, M., Bocs, S., Ponce, K., Leon, O., Morales, S., Quezada, N., Orellana,
F., Wendra, F., Sembiring, Z., Asmono, D., & Ritter, E. (2020). Detection of significant
SNP associated with production and oil quality traits in interspecific oil palm hybrids
using RARSeq. PLANT SCIENCE, 291. https://doi.org/10.1016/j.plantsci.2019.110366
Auwera, G. A., Carneiro, M. O., Hartl, C., Poplin, R., del Angel, G., Levy‐Moonshine, A.,
Jordan, T., Shakir, K., Roazen, D., Thibault, J., Banks, E., Garimella, K. V., Altshuler,
D., Gabriel, S., & DePristo, M. A. (2013). From FastQ Data to High‐Confidence Variant
Calls: The Genome Analysis Toolkit Best Practices Pipeline. Current Protocols in
Bioinformatics, 43(1). https://doi.org/10.1002/0471250953.bi1110s43
Azodi, C. B., Pardo, J., VanBuren, R., de los Campos, G., & Shiu, S.-H. (2020). Transcriptome-
Based Prediction of Complex Traits in Maize([OPEN]). PLANT CELL, 32(1), 139–151.
https://doi.org/10.1105/tpc.19.00332
Babak, T., DeVeale, B., Tsang, E. K., Zhou, Y., Li, X., Smith, K. S., Kukurba, K. R., Zhang, R.,
Li, J. B., van der Kooy, D., Montgomery, S. B., & Fraser, H. B. (2015). Genetic conflict
reflected in tissue-specific maps of genomic imprinting in human and mouse. Nature
Genetics, 47(5), 544–549. https://doi.org/10.1038/ng.3274
Baran, Y., Subramaniam, M., Biton, A., Tukiainen, T., Tsang, E. K., Rivas, M. A., Pirinen, M.,
Gutierrez-Arcelus, M., Smith, K. S., Kukurba, K. R., Zhang, R., Eng, C., Torgerson, D.
G., Urbanek, C., the GTEx Consortium, Li, J. B., Rodriguez-Santana, J. R., Burchard, E.
G., Seibold, M. A., … Lappalainen, T. (2015). The landscape of genomic imprinting
93

across diverse adult human tissues. Genome Research, 25(7), 927–936.
https://doi.org/10.1101/gr.192278.115
Barcelos, E, Amblard, P., Berthaud, J., & Seguin, M. (2002). Genetic diversity and relationship
in American and African oil palm as revealed by RFLP and AFLP molecular markers.
PESQUISA AGROPECUARIA BRASILEIRA, 37(8), 1105–1114.
https://doi.org/10.1590/S0100-204X2002000800008
Barcelos, Edson, Rios, S. de A., Cunha, R. N. V., Lopes, R., Motoike, S. Y., Babiychuk, E.,
Skirycz, A., & Kushnir, S. (2015). Oil palm natural diversity and the potential for yield
improvement. FRONTIERS IN PLANT SCIENCE, 6.
https://doi.org/10.3389/fpls.2015.00190
Baud, S., Wuilleme, S., To, A., Rochat, C., & Lepiniec, L. (2009). Role of WRINKLED1 in the
transcriptional regulation of glycolytic and fatty acid biosynthetic genes in Arabidopsis.
PLANT JOURNAL, 60(6), 933–947. https://doi.org/10.1111/j.1365-313X.2009.04011.x
BENJAMINI, Y., & HOCHBERG, Y. (1995). CONTROLLING THE FALSE DISCOVERY
RATE - A PRACTICAL AND POWERFUL APPROACH TO MULTIPLE TESTING.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL
METHODOLOGY, 57(1), 289–300. https://doi.org/10.1111/j.2517-6161.1995.tb02031.x
Billotte, N., Risterucci, A., Barcelos, E., Noyer, J., Amblard, P., & Baurens, F. (2001).
Development, characterisation, and across-taxa utility of oil palm (Elaeis guineensis
Jacq.) microsatellite markers. GENOME, 44(3), 413–425. https://doi.org/10.1139/g01-
017
Blein-Nicolas, M., Albertin, W., Da Silva, T., Valot, B., Balliau, T., Masneuf-Pomarede, I., Bely,
M., Marullo, P., Sicard, D., Dillmann, C., De Vienne, D., & Zivy, M. (2015). A Systems
94

Approach to Elucidate Heterosis of Protein Abundances in Yeast. MOLECULAR &
CELLULAR PROTEOMICS, 14(8), 2056–2071.
https://doi.org/10.1074/mcp.M115.048058
Bolger, A. M., Lohse, M., & Usadel, B. (2014). Trimmomatic: A flexible trimmer for Illumina
sequence data. Bioinformatics, 30(15), 2114–2120.
https://doi.org/10.1093/bioinformatics/btu170
Bomblies, K., & Weigel, D. (2007). Hybrid necrosis: Autoimmunity as a potential gene-flow
barrier in plant species. Nature Reviews Genetics, 8(5), 382–393.
https://doi.org/10.1038/nrg2082
Botet, R., & Keurentjes, J. (2020). The Role of Transcriptional Regulation in Hybrid Vigor.
FRONTIERS IN PLANT SCIENCE, 11. https://doi.org/10.3389/fpls.2020.00410
Bourgis, F., Kilaru, A., Cao, X., Ngando-Ebongue, G.-F., Drira, N., Ohlrogge, J. B., & Arondel,
V. (2011). Comparative transcriptome and metabolite analysis of oil palm and date palm
mesocarp that differ dramatically in carbon partitioning. PROCEEDINGS OF THE
NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA,
108(30), 12527–12532. https://doi.org/10.1073/pnas.1106502108
Brem, R. B. (2002). Genetic Dissection of Transcriptional Regulation in Budding Yeast. Science,
296(5568), 752–755. https://doi.org/10.1126/science.1069516
Brill, E., Kang, L., Michalak, K., Michalak, P., & Price, D. (2016). Hybrid sterility and evolution
in Hawaiian Drosophila: Differential gene and allele-specific expression analysis of
backcross males. HEREDITY, 117(2), 100–108. https://doi.org/10.1038/hdy.2016.31
Brown, J., & O’Neill, R. (2010). Chromosomes, Conflict, and Epigenetics: Chromosomal
Speciation Revisited. In A. Chakravarti & E. Green (Eds.), ANNUAL REVIEW OF
95

GENOMICS AND HUMAN GENETICS, VOL 11 (WOS:000282662200013; Vol. 11, pp.
291–316). https://doi.org/10.1146/annurev-genom-082509-141554
Brown, J. W. S., Calixto, C. P. G., & Zhang, R. (2017). High‐quality reference transcript datasets
hold the key to transcript‐specific RNA‐sequencing analysis in plants. New Phytologist,
213(2), 525–530. https://doi.org/10.1111/nph.14208
Buchberger, Reis, Lu, & Posnien. (2019). Cloudy with a Chance of Insights: Context Dependent
Gene Regulation and Implications for Evolutionary Studies. Genes, 10(7), 492.
https://doi.org/10.3390/genes10070492
Campbell, C. D., Kirby, A., Nemesh, J., Daly, M. J., & Hirschhorn, J. N. (2008). A survey of
allelic imbalance in F1 mice. Genome Research, 18(4), 555–563.
https://doi.org/10.1101/gr.068692.107
Castel, S. E., Aguet, F., Mohammadi, P., Aguet, F., Anand, S., Ardlie, K. G., Gabriel, S., Getz,
G. A., Graubert, A., Hadley, K., Handsaker, R. E., Huang, K. H., Kashin, S., Li, X.,
MacArthur, D. G., Meier, S. R., Nedzel, J. L., Nguyen, D. T., Segrè, A. V., …
Consortium, Gte. (2020). A vast resource of allelic expression data spanning human
tissues. Genome Biology, 21(1), 234. https://doi.org/10.1186/s13059-020-02122-z
Castel, S. E., Levy-Moonshine, A., Mohammadi, P., Banks, E., & Lappalainen, T. (2015). Tools
and best practices for data processing in allelic expression analysis. Genome Biology,
16(1), 195. https://doi.org/10.1186/s13059-015-0762-6
Chamberlain, A. J., Vander Jagt, C. J., Hayes, B. J., Khansefid, M., Marett, L. C., Millen, C. A.,
Nguyen, T. T. T., & Goddard, M. E. (2015). Extensive variation between tissues in allele
specific expression in an outbred mammal. BMC Genomics, 16(1), 993.
https://doi.org/10.1186/s12864-015-2174-0
96

Chan, P.-L., Rose, R. J., Murad, A. M. A., Zainal, Z., Low, E.-T. L., Ooi, L. C.-L., Ooi, S.-E.,
Yahya, S., & Singh, R. (2014). Evaluation of Reference Genes for Quantitative Real-
Time PCR in Oil Palm Elite Planting Materials Propagated by Tissue Culture. PLOS
ONE, 9(6). https://doi.org/10.1371/journal.pone.0099774
Choi, K., Raghupathy, N., & Churchill, G. A. (2019). A Bayesian mixture model for the analysis
of allelic expression in single cells. Nature Communications, 10(1), 5188.
https://doi.org/10.1038/s41467-019-13099-0
Conesa, A., Madrigal, P., Tarazona, S., Gomez-Cabrero, D., Cervera, A., McPherson, A.,
Szcześniak, M. W., Gaffney, D. J., Elo, L. L., Zhang, X., & Mortazavi, A. (2016). A
survey of best practices for RNA-seq data analysis. Genome Biology, 17(1), 13.
https://doi.org/10.1186/s13059-016-0881-8
Cowles, C. R., Hirschhorn, J. N., Altshuler, D., & Lander, E. S. (2002). Detection of regulatory
variation in mouse genes. Nature Genetics, 32(3), 432–437.
https://doi.org/10.1038/ng992
Crowley, J. J., Zhabotynsky, V., Sun, W., Huang, S., Pakatci, I. K., Kim, Y., Wang, J. R.,
Morgan, A. P., Calaway, J. D., Aylor, D. L., Yun, Z., Bell, T. A., Buus, R. J., Calaway,
M. E., Didion, J. P., Gooch, T. J., Hansen, S. D., Robinson, N. N., Shaw, G. D., …
Pardo-Manuel de Villena, F. (2015). Analyses of allele-specific gene expression in highly
divergent mouse crosses identifies pervasive allelic imbalance. Nature Genetics, 47(4),
353–360. https://doi.org/10.1038/ng.3222
da Silva Francisco Junior, R., dos Santos Ferreira, C., Santos e Silva, J. C., Terra Machado, D.,
Côrtes Martins, Y., Ramos, V., Simões Carnivali, G., Garcia, A. B., & Medina-Acosta, E.
97

(2019). Pervasive Inter-Individual Variation in Allele-Specific Expression in
Monozygotic Twins. Frontiers in Genetics, 10. https://doi.org/10.3389/fgene.2019.01178
Degner, J. F., Marioni, J. C., Pai, A. A., Pickrell, J. K., Nkadori, E., Gilad, Y., & Pritchard, J. K.
(2009). Effect of read-mapping biases on detecting allele-specific expression from RNA-
sequencing data. Bioinformatics, 25(24), 3207–3212.
https://doi.org/10.1093/bioinformatics/btp579
DePristo, M. A., Banks, E., Poplin, R., Garimella, K. V., Maguire, J. R., Hartl, C., Philippakis,
A. A., del Angel, G., Rivas, M. A., Hanna, M., McKenna, A., Fennell, T. J., Kernytsky,
A. M., Sivachenko, A. Y., Cibulskis, K., Gabriel, S. B., Altshuler, D., & Daly, M. J.
(2011). A framework for variation discovery and genotyping using next-generation DNA
sequencing data. Nature Genetics, 43(5), 491–498. https://doi.org/10.1038/ng.806
Dobin, A., Davis, C. A., Schlesinger, F., Drenkow, J., Zaleski, C., Jha, S., Batut, P., Chaisson,
M., & Gingeras, T. R. (2013). STAR: Ultrafast universal RNA-seq aligner.
Bioinformatics, 29(1), 15–21. https://doi.org/10.1093/bioinformatics/bts635
Doerge, R. W. (2002). Mapping and analysis of quantitative trait loci in experimental
populations. Nature Reviews Genetics, 3(1), 43–52. https://doi.org/10.1038/nrg703
Du, S. N. N., Khajali, F., Dawson, N. J., & Scott, G. R. (2017). Hybridization increases
mitochondrial production of reactive oxygen species in sunfish: MITOCHONDRIAL
FUNCTION IN SUNFISH HYBRIDS. Evolution, 71(6), 1643–1652.
https://doi.org/10.1111/evo.13254
Dussert, S., Guerin, C., Andersson, M., Joet, T., Tranbarger, T. J., Pizot, M., Sarah, G., Omore,
A., Durand-Gasselin, T., & Morcillo, F. (2013). Comparative Transcriptome Analysis of
Three Oil Palm Fruit and Seed Tissues That Differ in Oil Content and Fatty Acid
98

Composition. PLANT PHYSIOLOGY, 162(3), 1337–1358.
https://doi.org/10.1104/pp.113.220525
Edsgärd, D., Iglesias, M. J., Reilly, S.-J., Hamsten, A., Tornvall, P., Odeberg, J., &
Emanuelsson, O. (2016). GeneiASE: Detection of condition-dependent and static allele-
specific expression from RNA-seq data without haplotype information. Scientific
Reports, 6(1), 21134. https://doi.org/10.1038/srep21134
Fear, J. M., León-Novelo, L. G., Morse, A. M., Gerken, A. R., Van Lehmann, K., Tower, J.,
Nuzhdin, S. V., & McIntyre, L. M. (2016a). Buffering of Genetic Regulatory Networks
in Drosophila melanogaster. Genetics, 203(3), 1177–1190.
https://doi.org/10.1534/genetics.116.188797
Fear, J. M., León-Novelo, L. G., Morse, A. M., Gerken, A. R., Van Lehmann, K., Tower, J.,
Nuzhdin, S. V., & McIntyre, L. M. (2016b). Buffering of Genetic Regulatory Networks
in Drosophila melanogaster. Genetics, 203(3), 1177–1190.
https://doi.org/10.1534/genetics.116.188797
Findley, A. S., Monziani, A., Richards, A. L., Rhodes, K., Ward, M. C., Kalita, C. A., Alazizi,
A., Pazokitoroudi, A., Sankararaman, S., Wen, X., Lanfear, D. E., Pique-Regi, R., Gilad,
Y., & Luca, F. (2021). Functional dynamic genetic effects on gene regulation are specific
to particular cell types and environmental conditions. ELife, 10, e67077.
https://doi.org/10.7554/eLife.67077
Fishman, L., & Sweigart, A. (2018). When Two Rights Make a Wrong: The Evolutionary
Genetics of Plant Hybrid Incompatibilities. In S. Merchant (Ed.), ANNUAL REVIEW OF
PLANT BIOLOGY, VOL 69 (WOS:000433067800026; Vol. 69, pp. 707–731).
https://doi.org/10.1146/annurev-arplant-042817-040113
99

Fontanillas, P., Landry, C. R., Wittkopp, P. J., Russ, C., Gruber, J. D., Nusbaum, C., & Hartl, D.
L. (2010). Key considerations for measuring allelic expression on a genomic scale using
high-throughput sequencing. Molecular Ecology, 19 Suppl 1, 212–227.
https://doi.org/10.1111/j.1365-294X.2010.04472.x
Gavrilets, S. (2014). Models of Speciation: Where Are We Now? Journal of Heredity, 105(S1),
743–755. https://doi.org/10.1093/jhered/esu045
Gélin, U., Keller, M., de Beaupuis, V., Nowak, R., Lévy, F., & Locatelli, Y. (2019). Impact of
hybridization between sika and red deer on phenotypic traits of the newborn and mother–
young relationships. Animal Behaviour, 158, 65–75.
https://doi.org/10.1016/j.anbehav.2019.09.016
Gelli, M., Konda, A. R., Liu, K., Zhang, C., Clemente, T. E., Holding, D. R., & Dweikat, I. M.
(2017). Validation of QTL mapping and transcriptome profiling for identification of
candidate genes associated with nitrogen stress tolerance in sorghum. BMC PLANT
BIOLOGY, 17. https://doi.org/10.1186/s12870-017-1064-9
Genissel, A., McIntyre, L. M., Wayne, M. L., & Nuzhdin, S. V. (2007). Cis and Trans
Regulatory Effects Contribute to Natural Variation in Transcriptome of Drosophila
melanogaster. Molecular Biology and Evolution, 25(1), 101–110.
https://doi.org/10.1093/molbev/msm247
Glombik, M., Bacovsky, V., Hobza, R., & Kopecky, D. (2020). Competition of Parental
Genomes in Plant Hybrids. FRONTIERS IN PLANT SCIENCE, 11.
https://doi.org/10.3389/fpls.2020.00200
Gomes Junior, R. A., Lopes, R., Vieira da Cunha, R. N., de Abreu Pina, A. J., Quaresma, C. E.,
Santos, R. R., & Vilela de Resende, M. D. (2016). Bunch yield of interspecific hybrids of
100

American oil palm with oil palm in the juvenile phase. CROP BREEDING AND
APPLIED BIOTECHNOLOGY, 16(2), 86–94. https://doi.org/10.1590/1984-
70332016v16n2a14
Good, J. M., Giger, T., Dean, M. D., & Nachman, M. W. (2010). Widespread Over-Expression
of the X Chromosome in Sterile F1 Hybrid Mice. PLoS Genetics, 6(9), e1001148.
https://doi.org/10.1371/journal.pgen.1001148
Goulet, B., Roda, F., & Hopkins, R. (2017). Hybridization in Plants: Old Ideas, New Techniques.
PLANT PHYSIOLOGY, 173(1), 65–78. https://doi.org/10.1104/pp.16.01340
Graze, R. M., Novelo, L. L., Amin, V., Fear, J. M., Casella, G., Nuzhdin, S. V., & McIntyre, L.
M. (2012). Allelic Imbalance in Drosophila Hybrid Heads: Exons, Isoforms, and
Evolution. Molecular Biology and Evolution, 29(6), 1521–1532.
https://doi.org/10.1093/molbev/msr318
Graze, Rita M., McIntyre, L. M., Main, B. J., Wayne, M. L., & Nuzhdin, S. V. (2009).
Regulatory Divergence in Drosophila melanogaster and D. simulans , a Genomewide
Analysis of Allele-Specific Expression. Genetics, 183(2), 547–561.
https://doi.org/10.1534/genetics.109.105957
Gregg, C., Zhang, J., Weissbourd, B., Luo, S., Schroth, G. P., Haig, D., & Dulac, C. (2010).
High-Resolution Analysis of Parent-of-Origin Allelic Expression in the Mouse Brain.
Science, 329(5992), 643–648. https://doi.org/10.1126/science.1190830
Guerin, C., Joët, T., Serret, J., Lashermes, P., Vaissayre, V., Agbessi, M. D. T., Beulé, T.,
Severac, D., Amblard, P., Tregear, J., Durand‐Gasselin, T., Morcillo, F., & Dussert, S.
(2016). Gene coexpression network analysis of oil biosynthesis in an interspecific
101

backcross of oil palm. The Plant Journal, 87(5), 423–441.
https://doi.org/10.1111/tpj.13208
Guo, M., Yang, S., Rupe, M., Hu, B., Bickel, D. R., Arthur, L., & Smith, O. (2008). Genome-
wide allele-specific expression analysis using Massively Parallel Signature Sequencing
(MPSS
TM
) Reveals cis- and trans-effects on gene expression in maize hybrid meristem
tissue. Plant Molecular Biology, 66(5), 551–563. https://doi.org/10.1007/s11103-008-
9290-z
Hart, T., Komori, H., LaMere, S., Podshivalova, K., & Salomon, D. R. (2013). Finding the active
genes in deep RNA-seq gene expression studies. BMC Genomics, 14(1), 778.
https://doi.org/10.1186/1471-2164-14-778
Ho, C.-L., Kwan, Y.-Y., Choi, M.-C., Tee, S.-S., Ng, W.-H., Lim, K.-A., Lee, Y.-P., Ooi, S.-E.,
Lee, W.-W., Tee, J.-M., Tan, S.-H., Kulaveerasingam, H., Alwee, S. S. R. S., &
Abdullah, M. O. (2007). Analysis and functional annotation of expressed sequence tags
(ESTs) from multiple tissues of oil palm (Elaeis guineensis Jacq.). BMC GENOMICS, 8.
https://doi.org/10.1186/1471-2164-8-381
Hong, E. P., & Park, J. W. (2012). Sample Size and Statistical Power Calculation in Genetic
Association Studies. Genomics & Informatics, 10(2), 117–122.
https://doi.org/10.5808/GI.2012.10.2.117
Huang, J., Zhang, T., Zhang, Q., Chen, M., Wang, Z., Zheng, B., Xia, G., Yang, X., Huang, C.,
& Huang, Y. (2016). The mechanism of high contents of oil and oleic acid revealed by
transcriptomic and lipidomic analysis during embryogenesis in Carya cathayensis Sarg.
BMC GENOMICS, 17. https://doi.org/10.1186/s12864-016-2434-7
102

Ithnin, M, Vu, W., Shin, M., Suryawanshi, V., Sherbina, K., Zolkafli, S., Serdari, N., Amiruddin,
M., Abdullah, N., Mustaffa, S., Marjuni, M., Nookiah, R., Kushairi, A., Marjoram, P.,
Nuzhdin, S., Chang, P., & Singh, R. (2021). Genomic diversity and genome-wide
association analysis related to yield and fatty acid composition of wild American oil
palm. PLANT SCIENCE, 304. https://doi.org/10.1016/j.plantsci.2020.110731
Ithnin, Maizura, Singh, R., & Din, A. K. (2011). Elaeis. In Wild Crop Relatives: Genomic and
Breeding Resources Plantation and Ornamental Crops (1st ed., pp. 113–124). Springer
Berlin Heidelberg. https://doi.org/10.1007/978-3-642-21201-7
Jansen, R. (2001). Genetical genomics: The added value from segregation. Trends in Genetics,
17(7), 388–391. https://doi.org/10.1016/S0168-9525(01)02310-1
Jessen, D., Roth, C., Wiermer, M., & Fulda, M. (2015). Two Activities of Long-Chain Acyl-
Coenzyme A Synthetase Are Involved in Lipid Trafficking between the Endoplasmic
Reticulum and the Plastid in Arabidopsis. PLANT PHYSIOLOGY, 167(2), 351-U575.
https://doi.org/10.1104/pp.114.250365
Jin, J., Sun, Y., Qu, J., Syah, R., Lim, C.-H., Alfiko, Y., Rahman, N., Suwanto, A., Yue, G.,
Wong, L., Chua, N.-H., & Ye, J. (2017). Transcriptome and functional analysis reveals
hybrid vigor for oil biosynthesis in oil palm. SCIENTIFIC REPORTS, 7.
https://doi.org/10.1038/s41598-017-00438-8
Jouannic, S., Argout, X., Lechauve, F., Fizames, C., Borgel, A., Morcillo, F., Aberlenc-Bertossi,
F., Duval, Y., & Tregear, J. (2005). Analysis of expressed sequence tags from oil palm
(Elaeis guineensis). FEBS LETTERS, 579(12), 2709–2714.
https://doi.org/10.1016/j.febslet.2005.03.093
103

Kearsey, M. J. (1998). The principles of QTL analysis (a minimal mathematics approach).
Journal of Experimental Botany, 49(327), 1619–1623.
Kerwin, R., & Sweigart, A. (2020). Rampant Misexpression in a Mimulus (Monkeyflower)
Introgression Line Caused by Hybrid Sterility, Not Regulatory Divergence.
MOLECULAR BIOLOGY AND EVOLUTION, 37(7), 2084–2098.
https://doi.org/10.1093/molbev/msaa071
Kilaru, A., Cao, X., Dabbs, P. B., Sung, H.-J., Rahman, M. M., Thrower, N., Zynda, G.,
Podicheti, R., Ibarra-Laclette, E., Herrera-Estrella, L., Mockaitis, K., & Ohlrogge, J. B.
(2015). Oil biosynthesis in a basal angiosperm: Transcriptome analysis of Persea
Americana mesocarp. BMC PLANT BIOLOGY, 15. https://doi.org/10.1186/s12870-015-
0586-2
Kujur, A., Upadhyaya, H. D., Bajaj, D., Gowda, C. L. L., Sharma, S., Tyagi, A. K., & Parida, S.
K. (2016). Identification of candidate genes and natural allelic variants for QTLs
governing plant height in chickpea. SCIENTIFIC REPORTS, 6.
https://doi.org/10.1038/srep27968
Kukurba, K. R., Zhang, R., Li, X., Smith, K. S., Knowles, D. A., Tan, M. H., Piskol, R., Lek, M.,
Snyder, M., MacArthur, D. G., Li, J. B., & Montgomery, S. B. (2014). Allelic Expression
of Deleterious Protein-Coding Variants across Human Tissues. PLOS Genetics, 10(5),
e1004304. https://doi.org/10.1371/journal.pgen.1004304
Kushairi, A., Loh, S. K., Azman, I., Hishamuddin, E., Ong-Abdullah, M., Izuddin, Z. B. M. N.,
Razmah, G., Sundram, S., & Parveez, G. K. A. (2018). OIL PALM ECONOMIC
PERFORMANCE IN MALAYSIA AND R&D PROGRESS IN 2017. JOURNAL OF
OIL PALM RESEARCH, 30(2), 163–195. https://doi.org/10.21894/jopr.2018.0030
104

Lei, A., Chen, H., Shen, G., Hu, Z., Chen, L., & Wang, J. (2012). Expression of fatty acid
synthesis genes and fatty acid accumulation in Haematococcus pluvialis under different
stressors. BIOTECHNOLOGY FOR BIOFUELS, 5. https://doi.org/10.1186/1754-6834-5-
18
Lenz, D., Riles, L., & Fay, J. (2014). Heterochronic Meiotic Misexpression in an Interspecific
Yeast Hybrid. MOLECULAR BIOLOGY AND EVOLUTION, 31(6), 1333–1342.
https://doi.org/10.1093/molbev/msu098
León-Novelo, L. G., McIntyre, L. M., Fear, J. M., & Graze, R. M. (2014). A flexible Bayesian
method for detecting allelic imbalance in RNA-seq data. BMC Genomics, 15, 920.
https://doi.org/10.1186/1471-2164-15-920
León-Novelo, L., Gerken, A. R., Graze, R. M., McIntyre, L. M., & Marroni, F. (2018a). Direct
Testing for Allele-Specific Expression Differences Between Conditions. G3: Genes,
Genomes, Genetics, 8(2), 447–460. https://doi.org/10.1534/g3.117.300139
León-Novelo, L., Gerken, A. R., Graze, R. M., McIntyre, L. M., & Marroni, F. (2018b). Direct
Testing for Allele-Specific Expression Differences Between Conditions. G3: Genes,
Genomes, Genetics, 8(2), 447–460. https://doi.org/10.1534/g3.117.300139
Li, H., & Durbin, R. (2009). Fast and accurate short read alignment with Burrows-Wheeler
transform. Bioinformatics, 25(14), 1754–1760.
https://doi.org/10.1093/bioinformatics/btp324
Li, J., & Burmeister, M. (2005). Genetical genomics: Combining genetics with gene expression
analysis. Human Molecular Genetics, 14(suppl_2), R163–R169.
https://doi.org/10.1093/hmg/ddi267
105

Li, R., Ren, X., Bi, Y., Ho, V. W. S., Hsieh, C.-L., Young, A., Zhang, Z., Lin, T., Zhao, Y.,
Miao, L., Sarkies, P., & Zhao, Z. (2016). Specific down-regulation of spermatogenesis
genes targeted by 22G RNAs in hybrid sterile males associated with an X-Chromosome
introgression. Genome Research, 26(9), 1219–1232.
https://doi.org/10.1101/gr.204479.116
Liang, Y., Aguet, F., Barbeira, A. N., Ardlie, K., & Im, H. K. (2021). A scalable unified
framework of total and allele-specific counts for cis-QTL, fine-mapping, and prediction.
Nature Communications, 12(1), 1424. https://doi.org/10.1038/s41467-021-21592-8
Liao, Y., Smyth, G. K., & Shi, W. (2014). featureCounts: An efficient general purpose program
for assigning sequence reads to genomic features. Bioinformatics, 30(7), 923–930.
https://doi.org/10.1093/bioinformatics/btt656
Liu, M., Tseng, S., Chen, T., & Chung, M. (2021). Visualizing Meiotic Chromosome Pairing and
Segregation in Interspecific Hybrids of Rice by Genomic in situ Hybridization. RICE
SCIENCE, 28(1), 69–80. https://doi.org/10.1016/j.rsci.2020.11.008
Liu, Y., Li, C., Shen, S., Chen, X., Szlachta, K., Edmonson, M. N., Shao, Y., Ma, X., Hyle, J.,
Wright, S., Ju, B., Rusch, M. C., Liu, Y., Li, B., Macias, M., Tian, L., Easton, J., Qian,
M., Yang, J. J., … Zhang, J. (2020). Discovery of regulatory noncoding variants in
individual cancer genomes by using cis-X. Nature Genetics, 52(8), 811–818.
https://doi.org/10.1038/s41588-020-0659-5
Liu, Z., Dong, X., & Li, Y. (2018). A Genome-Wide Study of Allele-Specific Expression in
Colorectal Cancer. Frontiers in Genetics, 9, 570.
https://doi.org/10.3389/fgene.2018.00570
106

Love, M. I., Huber, W., & Anders, S. (2014). Moderated estimation of fold change and
dispersion for RNA-seq data with DESeq2. Genome Biology, 15(12), 550.
https://doi.org/10.1186/s13059-014-0550-8
Low, E.-T. L., Rosli, R., Jayanthi, N., Mohd-Amin, A. H., Azizi, N., Chan, K.-L., Maqbool, N.
J., Maclean, P., Brauning, R., McCulloch, A., Moraga, R., Ong-Abdullah, M., & Singh,
R. (2014). Analyses of Hypomethylated Oil Palm Gene Space. PLOS ONE, 9(1).
https://doi.org/10.1371/journal.pone.0086728
Lu, Y., Sandoval, A., Voss, S., Lai, Z., Kneitz, S., Boswell, W., Boswell, M., Savage, M.,
Walter, C., Warren, W., Schartl, M., & Walter, R. (2020). Oncogenic allelic interaction in
Xiphophorus highlights hybrid incompatibility. Proceedings of the National Academy of
Sciences, 117(47), 29786–29794. https://doi.org/10.1073/pnas.2010133117
Mackay, I., Cockram, J., Howell, P., & Powell, W. (2021). Understanding the classics: The
unifying concepts of transgressive segregation, inbreeding depression and heterosis and
their central relevance for crop breeding. PLANT BIOTECHNOLOGY JOURNAL, 19(1),
26–34. https://doi.org/10.1111/pbi.13481
Mackay, T. F. C., Stone, E. A., & Ayroles, J. F. (2009). The genetics of quantitative traits:
Challenges and prospects. Nature Reviews Genetics, 10(8), 565–577.
https://doi.org/10.1038/nrg2612
Maheshwari, S., & Barbash, D. (2011). The Genetics of Hybrid Incompatibilities. In B. Bassler,
M. Lichten, & G. Schupbach (Eds.), ANNUAL REVIEW OF GENETICS, VOL 45
(WOS:000299299600015; Vol. 45, pp. 331–355). https://doi.org/10.1146/annurev-genet-
110410-132514
107

Main, B. J., Bickel, R. D., McIntyre, L. M., Graze, R. M., Calabrese, P. P., & Nuzhdin, S. V.
(2009). Allele-specific expression assays using Solexa. BMC Genomics, 10(1), 422.
https://doi.org/10.1186/1471-2164-10-422
Maizura, I., Rajanaidu, N., Zakri, A., & Cheah, S. (2006). Assessment of genetic diversity in oil
palm (Elaeis guineensis Jacq.) using Restriction Fragment Length Polymorphism
(RFLP). GENETIC RESOURCES AND CROP EVOLUTION, 53(1), 187–195.
https://doi.org/10.1007/s10722-004-4004-0
Malone, J. H., Chrzanowski, T. H., & Michalak, P. (2007). Sterility and Gene Expression in
Hybrid Males of Xenopus laevis and X. muelleri. PLoS ONE, 2(8), e781.
https://doi.org/10.1371/journal.pone.0000781
Mayba, O., Gilbert, H. N., Liu, J., Haverty, P. M., Jhunjhunwala, S., Jiang, Z., Watanabe, C., &
Zhang, Z. (2014). MBASED: allele-specific expression detection in cancer tissues and
cell lines. Genome Biology, 15(8), 405. https://doi.org/10.1186/s13059-014-0405-3
McDaniel, S. F., Willis, J. H., & Shaw, A. J. (2008). The Genetic Basis of Developmental
Abnormalities in Interpopulation Hybrids of the Moss Ceratodon purpureus. Genetics,
179(3), 1425–1435. https://doi.org/10.1534/genetics.107.086314
Members of the Complex Trait Consortium. (2003). The nature and identification of quantitative
trait loci: A community’s view. Nature Reviews Genetics, 4(11), 911–916.
https://doi.org/10.1038/nrg1206
Miller, B. R., Morse, A. M., Borgert, J. E., Liu, Z., Sinclair, K., Gamble, G., Zou, F., Newman, J.
R. B., León-Novelo, L. G., Marroni, F., & McIntyre, L. M. (2021). Testcrosses are an
efficient strategy for identifying cis -regulatory variation: Bayesian analysis of allele-
108

specific expression (BayesASE). G3 Genes|Genomes|Genetics, jkab096.
https://doi.org/10.1093/g3journal/jkab096
Montoya, C., Cochard, B., Flori, A., Cros, D., Lopes, R., Cuellar, T., Espeout, S., Syaputra, I.,
Villeneuve, P., Pina, M., Ritter, E., Leroy, T., & Billotte, N. (2014). Genetic Architecture
of Palm Oil Fatty Acid Composition in Cultivated Oil Palm (Elaeis guineensis Jacq.)
Compared to Its Wild Relative E. oleifera (HBK) Cortes. PLOS ONE, 9(5).
https://doi.org/10.1371/journal.pone.0095412
Montoya, C., Lopes, R., Flori, A., Cros, D., Cuellar, T., Summo, M., Espeout, S., Rivallan, R.,
Risterucci, A.-M., Bittencourt, D., Zambrano, J. R., Alarcon G, W. H., Villeneuve, P.,
Pina, M., Nouy, B., Amblard, P., Ritter, E., Leroy, T., & Billotte, N. (2013). Quantitative
trait loci (QTLs) analysis of palm oil fatty acid composition in an interspecific pseudo-
backcross from Elaeis oleifera (HBK) Cort,s and oil palm (Elaeis guineensis Jacq.).
TREE GENETICS & GENOMES, 9(5), 1207–1225. https://doi.org/10.1007/s11295-013-
0629-5
Morgan, K., Harr, B., White, M., Payseur, B., & Turner, L. (2020). Disrupted Gene Networks in
Subfertile Hybrid House Mice. MOLECULAR BIOLOGY AND EVOLUTION, 37(6),
1547–1562. https://doi.org/10.1093/molbev/msaa002
Mugal, C. F., Wang, M., Backström, N., Wheatcroft, D., Ålund, M., Sémon, M., McFarlane, S.
E., Dutoit, L., Qvarnström, A., & Ellegren, H. (2020). Tissue-specific patterns of
regulatory changes underlying gene expression differences among Ficedula flycatchers
and their naturally occurring F1 hybrids. Genome Research.
https://doi.org/10.1101/gr.254508.119
109

Muktar, M. S., Luebeck, J., Strahwald, J., & Gebhardt, C. (2015). Selection and validation of
potato candidate genes for maturity corrected resistance to Phytophthora infestans based
on differential expression combined with SNP association and linkage mapping.
FRONTIERS IN GENETICS, 6. https://doi.org/10.3389/fgene.2015.00294
Ong, P.-W. (2016, August 6). Construction of genetic linkage map for oil palm using single
nucleotide polymorphism (SNP) markers identified via genotyping-by-sequencing (GBS).
PAG Asia Conference, Singapore.
Oshlack, A., Chabot, A. E., Smyth, G. K., & Gilad, Y. (2007). Using DNA microarrays to study
gene expression in closely related species. Bioinformatics, 23(10), 1235–1242.
https://doi.org/10.1093/bioinformatics/btm111
Parveez, G. K. A., Rasid, O. A., Masani, M. Y. A., & Sambanthamurthi, R. (2015).
Biotechnology of oil palm: Strategies towards manipulation of lipid content and
composition. PLANT CELL REPORTS, 34(4, SI), 533–543.
https://doi.org/10.1007/s00299-014-1722-4
Pastinen, T. (2004). Cis-Acting Regulatory Variation in the Human Genome. Science,
306(5696), 647–650. https://doi.org/10.1126/science.1101659
Pastinen, Tomi. (2010). Genome-wide allele-specific analysis: Insights into regulatory variation.
Nature Reviews Genetics, 11(8), 533–538. https://doi.org/10.1038/nrg2815
Pinter, S. F., Colognori, D., Beliveau, B. J., Sadreyev, R. I., Payer, B., Yildirim, E., Wu, C., &
Lee, J. T. (2015). Allelic Imbalance Is a Prevalent and Tissue-Specific Feature of the
Mouse Transcriptome. Genetics, 200(2), 537–549.
https://doi.org/10.1534/genetics.115.176263
110

Pirinen, M., Lappalainen, T., Zaitlen, N. A., GTEx Consortium, Dermitzakis, E. T., Donnelly, P.,
McCarthy, M. I., & Rivas, M. A. (2015). Assessing allele-specific expression across
multiple tissues from RNA-seq read data. Bioinformatics, 31(15), 2497–2504.
https://doi.org/10.1093/bioinformatics/btv074
Purba, A., Noyer, J., Baudouin, L., Perrier, X., Hamon, S., & Lagoda, P. (2000). A new aspect of
genetic diversity of Indonesian oil palm (Elaeis guineensis Jacq.) revealed by isoenzyme
and AFLP markers and its consequences for breeding. THEORETICAL AND APPLIED
GENETICS, 101(5–6), 956–961. https://doi.org/10.1007/s001220051567
Qaim, M., Sibhatu, K. T., Siregar, H., & Grass, I. (2020). Environmental, Economic, and Social
Consequences of the Oil Palm Boom. Annual Review of Resource Economics, 12(1),
321–344. https://doi.org/10.1146/annurev-resource-110119-024922
Rajanaidu, N., Kushairi, A., Rafii, M., Mohd, D. A., Maizura, I., Jalani, B., & others. (2000). Oil
palm breeding and genetic resources. Advances in Oil Palm Research, Vol. 1, 171–237.
Ramli, U. S., Mohamad, A. R., Ibrahim, K., Zamri, S. N., & Tahir, N. I. M. (2008).
QUANTITATIVE ANALYSIS OF FLUX CONTROL OVER LIPID BIOSYNTHESIS
IN OIL PALM (Elaeis guineensis) MESOCARP. JOURNAL OF OIL PALM
RESEARCH, SI, 69–76.
Rao, V., Chin, C., Rajanaidu, N., & others. (1989). Biology and performance of Surinam Elaeis
oleifera (HBK) Cortes. Elaeis, 1(32), 109–118.
Rhode, J., & Cruzan, M. (2005). Contributions of heterosis and epistasis to hybrid fitness.
AMERICAN NATURALIST, 166(5), E124–E139. https://doi.org/10.1086/491798
Rivas, M. A., Pirinen, M., Conrad, D. F., Lek, M., Tsang, E. K., Karczewski, K. J., Maller, J. B.,
Kukurba, K. R., DeLuca, D., Fromer, M., Ferreira, P. G., Smith, K. S., Zhang, R., Zhao,
111

F., Banks, E., Poplin, R., Ruderfer, D., Purcell, S. M., Tukiainen, T., … MacArthur, D.
G. (2015). Impact of predicted protein-truncating genetic variants on the human
transcriptome. Science (New York, N.Y.), 348(6235), 666–669.
https://doi.org/10.1126/science.1261877
Robinson, M. D., & Smyth, G. K. (2007). Moderated statistical tests for assessing differences in
tag abundance. Bioinformatics, 23(21), 2881–2887.
https://doi.org/10.1093/bioinformatics/btm453
Rockman, M. V., & Kruglyak, L. (2006). Genetics of global gene expression. Nature Reviews
Genetics, 7(11), 862–872. https://doi.org/10.1038/nrg1964
Rosas, U., Barton, N., Copsey, L., de Reuille, P., & Coen, E. (2010). Cryptic Variation between
Species and the Basis of Hybrid Performance. PLOS BIOLOGY, 8(7).
https://doi.org/10.1371/journal.pbio.1000429
Salavati, M., Bush, S. J., Palma-Vera, S., McCulloch, M. E. B., Hume, D. A., & Clark, E. L.
(2019). Elimination of Reference Mapping Bias Reveals Robust Immune Related Allele-
Specific Expression in Crossbred Sheep. Frontiers in Genetics, 10.
https://doi.org/10.3389/fgene.2019.00863
Sambanthamurthi, R., Sundram, K., & Tan, Y. (2000). Chemistry and biochemistry of palm oil.
PROGRESS IN LIPID RESEARCH, 39(6), 507–558. https://doi.org/10.1016/S0163-
7827(00)00015-1
Sanchez-Ramirez, S., Weiss, J., Thomas, C., & Cutter, A. (2021). Widespread misregulation of
inter-species hybrid transcriptomes due to sex-specific and sex-chromosome regulatory
evolution. PLOS GENETICS, 17(3). https://doi.org/10.1371/journal.pgen.1009409
112

Satokangas, I., Martin, S., Helantera, H., Saramaki, J., & Kulmuni, J. (2020). Multi-locus
interactions and the build-up of reproductive isolation. PHILOSOPHICAL
TRANSACTIONS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 375(1806).
https://doi.org/10.1098/rstb.2019.0543
Schadt, E. E., Monks, S. A., Drake, T. A., Lusis, A. J., Che, N., Colinayo, V., Ruff, T. G.,
Milligan, S. B., Lamb, J. R., Cavet, G., Linsley, P. S., Mao, M., Stoughton, R. B., &
Friend, S. H. (2003). Genetics of gene expression surveyed in maize, mouse and man.
Nature, 422(6929), 297–302. https://doi.org/10.1038/nature01434
Sham, P. C., & Purcell, S. M. (2014). Statistical power and significance testing in large-scale
genetic studies. Nature Reviews Genetics, 15(5), 335–346.
https://doi.org/10.1038/nrg3706
Shao, L., Xing, F., Xu, C., Zhang, Q., Che, J., Wang, X., Song, J., Li, X., Xiao, J., Chen, L.-L.,
Ouyang, Y., & Zhang, Q. (2019). Patterns of genome-wide allele-specific expression in
hybrid rice and the implications on the genetic basis of heterosis. Proceedings of the
National Academy of Sciences, 116(12), 5653–5658.
https://doi.org/10.1073/pnas.1820513116
Shen, Y., Sun, S., Hua, S., Shen, E., Ye, C., Cai, D., Timko, M., Zhu, Q., & Fan, L. (2017).
Analysis of transcriptional and epigenetic changes in hybrid vigor of allopolyploid
Brassica napus uncovers key roles for small RNAs. PLANT JOURNAL, 91(5), 874–893.
https://doi.org/10.1111/tpj.13605
Singh, R., Ong-Abdullah, M., Low, E.-T. L., Manaf, M. A. A., Rosli, R., Nookiah, R., Ooi, L.
C.-L., Ooi, S., Chan, K.-L., Halim, M. A., Azizi, N., Nagappan, J., Bacher, B., Lakey, N.,
Smith, S. W., He, D., Hogan, M., Budiman, M. A., Lee, E. K., … Sambanthamurthi, R.
113

(2013). Oil palm genome sequence reveals divergence of interfertile species in Old and
New worlds. Nature, 500(7462), 335–339. https://doi.org/10.1038/nature12309
Singh, R., Tan, S. G., Panandam, J. M., Rahman, R. A., Ooi, L. C. L., Low, E.-T. L., Sharma,
M., Jansen, J., & Cheah, S.-C. (2009). Mapping quantitative trait loci (QTLs) for fatty
acid composition in an interspecific cross of oil palm. BMC PLANT BIOLOGY, 9.
https://doi.org/10.1186/1471-2229-9-114
Singh, R., Zaki, N. M., Ting, N.-C., Rosli, R., Tan, S.-G., Low, E.-T. L., Ithnin, M., & Cheah, S.-
C. (2008). Exploiting an oil palm EST database for the development of gene-derived SSR
markers and their exploitation for assessment of genetic diversity. BIOLOGIA, 63(2),
227–235. https://doi.org/10.2478/s11756-008-0041-z
Skelly, D. A., Johansson, M., Madeoy, J., Wakefield, J., & Akey, J. M. (2011). A powerful and
flexible statistical framework for testing hypotheses of allele-specific gene expression
from RNA-seq data. Genome Research, 21(10), 1728–1737.
https://doi.org/10.1101/gr.119784.110
Soh, A. C., Mayes, S., Roberts, J., Barcelos, E., Amblard, P., Alvarado, A., Alvarado, J. H.,
Escobar, R., Sritharan, K., Subramaniam, M., & others. (2017). Elaeis oleifera$\times$
Elaeis guineensis Interspecific Hybrid Improvement. In Oil Palm Breeding (pp. 283–
296). CRC Press.
Springer, N. M., & Stupar, R. M. (2007). Allele-specific expression patterns reveal biases and
embryo-specific parent-of-origin effects in hybrid maize. The Plant Cell, 19(8), 2391–
2402. https://doi.org/10.1105/tpc.107.052258
114

Srestasathiern, P., & Rakwatin, P. (2014). Oil Palm Tree Detection with High Resolution Multi-
Spectral Satellite Imagery. Remote Sensing, 6(10), 9749–9774.
https://doi.org/10.3390/rs6109749
Stone, E. A., & Ayroles, J. F. (2009). Modulated Modularity Clustering as an Exploratory Tool
for Functional Genomic Inference. PLoS Genetics, 5(5), e1000479.
https://doi.org/10.1371/journal.pgen.1000479
Sun, W. (2012). A statistical framework for eQTL mapping using RNA-seq data. Biometrics,
68(1), 1–11.
Tan, K., Liu, H., Ye, T., Ma, H., Li, S., & Zheng, H. (2020). Growth, survival and lipid
composition of Crassostrea gigas, C. angulata and their reciprocal hybrids cultured in
southern China. AQUACULTURE, 516.
https://doi.org/10.1016/j.aquaculture.2019.734524
The GTEx Consortium, Ardlie, K. G., Deluca, D. S., Segre, A. V., Sullivan, T. J., Young, T. R.,
Gelfand, E. T., Trowbridge, C. A., Maller, J. B., Tukiainen, T., Lek, M., Ward, L. D.,
Kheradpour, P., Iriarte, B., Meng, Y., Palmer, C. D., Esko, T., Winckler, W., Hirschhorn,
J. N., … Dermitzakis, E. T. (2015). The Genotype-Tissue Expression (GTEx) pilot
analysis: Multitissue gene regulation in humans. Science, 348(6235), 648–660.
https://doi.org/10.1126/science.1262110
Ting, N., Sherbina, K., Khoo, J., Kamaruddin, K., Chan, P., Chan, K., Ab Halim, M., Sritharan,
K., Yaakub, Z., Mayes, S., Massawe, F., Chang, P., Nuzhdin, S., Sambanthamurthi, R., &
Singh, R. (2020). Expression of fatty acid and triacylglycerol synthesis genes in
interspecific hybrids of oil palm. SCIENTIFIC REPORTS, 10(1).
https://doi.org/10.1038/s41598-020-73170-5
115

Ting, N.-C., Yaakub, Z., Kamaruddin, K., Mayes, S., Massawe, F., Sambanthamurthi, R., Jansen,
J., Low, L. E. T., Ithnin, M., Kushairi, A., Arulandoo, X., Rosli, R., Chan, K.-L.,
Amiruddin, N., Sritharan, K., Lim, C. C., Nookiah, R., Amiruddin, M. D., & Singh, R.
(2016). Fine-mapping and cross-validation of QTLs linked to fatty acid composition in
multiple independent interspecific crosses of oil palm. BMC GENOMICS, 17.
https://doi.org/10.1186/s12864-016-2607-4
Tranbarger, T. J., Dussert, S., Joet, T., Argout, X., Summo, M., Champion, A., Cros, D., Omore,
A., Nouy, B., & Morcillo, F. (2011). Regulatory Mechanisms Underlying Oil Palm Fruit
Mesocarp Maturation, Ripening, and Functional Specialization in Lipid and Carotenoid
Metabolism. PLANT PHYSIOLOGY, 156(2), 564–584.
https://doi.org/10.1104/pp.111.175141
Tuch, B. B., Laborde, R. R., Xu, X., Gu, J., Chung, C. B., Monighetti, C. K., Stanley, S. J.,
Olsen, K. D., Kasperbauer, J. L., Moore, E. J., Broomer, A. J., Tan, R., Brzoska, P. M.,
Muller, M. W., Siddiqui, A. S., Asmann, Y. W., Sun, Y., Kuersten, S., Barker, M. A., …
Smith, D. I. (2010). Tumor Transcriptome Sequencing Reveals Allelic Expression
Imbalances Associated with Copy Number Alterations. PLoS ONE, 5(2), e9317.
https://doi.org/10.1371/journal.pone.0009317
Tukiainen, T., Villani, A.-C., Yen, A., Rivas, M. A., Marshall, J. L., Satija, R., Aguirre, M.,
Gauthier, L., Fleharty, M., Kirby, A., Cummings, B. B., Castel, S. E., Karczewski, K. J.,
Aguet, F., Byrnes, A., Lappalainen, T., Regev, A., Ardlie, K. G., Hacohen, N., &
MacArthur, D. G. (2017). Landscape of X chromosome inactivation across human
tissues. Nature, 550(7675), 244–248. https://doi.org/10.1038/nature24265
116

Turro, E., Su, S.-Y., Gonçalves, Â., Coin, L. J., Richardson, S., & Lewin, A. (2011). Haplotype
and isoform specific expression estimation using multi-mapping RNA-seq reads. Genome
Biology, 12(2), R13. https://doi.org/10.1186/gb-2011-12-2-r13
USDA. (2017). Oil crops yearbook, world vegetable oils supply and distribution, 2012/13–
2016/17. https://www.ers.usda.gov/data-products/oil-crops-yearbook/oil-crops-
yearbook/#Vegetableoils and animal fats
Vacher, M., & Small, I. (2019). Simulation of heterosis in a genome-scale metabolic network
provides mechanistic explanations for increased biomass production rates in hybrid
plants. NPJ SYSTEMS BIOLOGY AND APPLICATIONS, 5.
https://doi.org/10.1038/s41540-019-0101-8
van de Geijn, B., McVicker, G., Gilad, Y., & Pritchard, J. K. (2015). WASP: Allele-specific
software for robust molecular quantitative trait locus discovery. Nature Methods, 12(11),
1061–1063. https://doi.org/10.1038/nmeth.3582
Van den Berge, K., Hembach, K. M., Soneson, C., Tiberi, S., Clement, L., Love, M. I., Patro, R.,
& Robinson, M. D. (2019). RNA Sequencing Data: Hitchhiker’s Guide to Expression
Analysis. Annual Review of Biomedical Data Science, 2(1), 139–173.
https://doi.org/10.1146/annurev-biodatasci-072018-021255
Vandesompele, J., De Preter, K., Pattyn, F., Poppe, B., Van Roy, N., De Paepe, A., & Speleman,
F. (2002). Accurate normalization of real-time quantitative RT-PCR data by geometric
averaging of multiple internal control genes. GENOME BIOLOGY, 3(7).
https://doi.org/10.1186/gb-2002-3-7-research0034
117

Varshney, R., Graner, A., & Sorrells, M. (2005). Genomics-assisted breeding for crop
improvement. Trends in Plant Science, 10(12), 621–630.
https://doi.org/10.1016/j.tplants.2005.10.004
Vasemägi, A., & Primmer, C. R. (2005). Challenges for identifying functionally important
genetic variation: The promise of combining complementary research strategies:
ANALYSIS OF FUNCTIONAL GENETIC VARIATION: CHALLENGES and
PROMISES. Molecular Ecology, 14(12), 3623–3642. https://doi.org/10.1111/j.1365-
294X.2005.02690.x
Wang, M., Uebbing, S., & Ellegren, H. (2017a). Bayesian Inference of Allele-Specific Gene
Expression Indicates Abundant Cis-Regulatory Variation in Natural Flycatcher
Populations. Genome Biology and Evolution, 9(5), 1266–1279.
https://doi.org/10.1093/gbe/evx080
Wang, M., Uebbing, S., & Ellegren, H. (2017b). Bayesian Inference of Allele-Specific Gene
Expression Indicates Abundant Cis-Regulatory Variation in Natural Flycatcher
Populations. Genome Biology and Evolution, 9(5), 1266–1279.
https://doi.org/10.1093/gbe/evx080
Wang, Z., Gerstein, M., & Snyder, M. (2009). RNA-Seq: A revolutionary tool for
transcriptomics. Nature Reviews Genetics, 10(1), 57–63. https://doi.org/10.1038/nrg2484
Wayne, M. L., & McIntyre, L. M. (2002). Combining mapping and arraying: An approach to
candidate gene identification. Proceedings of the National Academy of Sciences, 99(23),
14903–14906. https://doi.org/10.1073/pnas.222549199
Weber, A. P. M. (2015). Discovering new biology through RNA-Seq. Plant Physiology,
pp.01081.2015. https://doi.org/10.1104/pp.15.01081
118

Wittkopp, P. J., Haerum, B. K., & Clark, A. G. (2004). Evolutionary changes in cis and trans
gene regulation. Nature, 430(6995), 85–88. https://doi.org/10.1038/nature02698
Wong, Y. C., Kwong, Q. B., Lee, H. L., Ong, C. K., Mayes, S., Chew, F. T., Appleton, D. R., &
Kulaveerasingam, H. (2014). Expression comparison of Oil biosynthesis genes in Oil
palm mesocarp tissue using custom array. Microarrays, 3(4), 263–281.
Xu, X., Zeng, L., Tao, Y., Vuong, T., Wan, J., Boerma, R., Noe, J., Li, Z., Finnerty, S., Pathan,
S. M., Shannon, J. G., & Nguyen, H. T. (2013). Pinpointing genes underlying the
quantitative trait loci for root-knot nematode resistance in palaeopolyploid soybean by
whole genome resequencing. Proceedings of the National Academy of Sciences, 110(33),
13469–13474. https://doi.org/10.1073/pnas.1222368110
Yeap, W.-C., Loo, J. M., Wong, Y. C., & Kulaveerasingam, H. (2014). Evaluation of suitable
reference genes for qRT-PCR gene expression normalization in reproductive, vegetative
tissues and during fruit development in oil palm. PLANT CELL TISSUE AND ORGAN
CULTURE, 116(1), 55–66. https://doi.org/10.1007/s11240-013-0382-3
Zhao, J., Zhang, S., Dong, J., Yang, T., Mao, X., Liu, Q., Wang, X., & Liu, B. (2017). A novel
functional gene associated with cold tolerance at the seedling stage in rice. Plant
Biotechnology Journal, 15(9), 1141–1148. https://doi.org/10.1111/pbi.12704
Zhigunov, A., Ulianich, P., Lebedeva, M., Chang, P., Nuzhdin, S., & Potokina, E. (2017).
Development of F1 hybrid population and the high-density linkage map for European
aspen (Populus tremula L.) using RADseq technology. BMC PLANT BIOLOGY, 17.
https://doi.org/10.1186/s12870-017-1127-y
Zou, F., Sun, W., Crowley, J. J., Zhabotynsky, V., Sullivan, P. F., & Pardo-Manuel de Villena, F.
(2014). A novel statistical approach for jointly analyzing RNA-Seq data from F1
119

reciprocal crosses and inbred lines. Genetics, 197(1), 389–399.
https://doi.org/10.1534/genetics.113.160119
Zou, J., Hormozdiari, F., Jew, B., Castel, S. E., Lappalainen, T., Ernst, J., Sul, J. H., & Eskin, E.
(2019). Leveraging allelic imbalance to refine fine-mapping for eQTL studies. PLOS
Genetics, 15(12), e1008481. https://doi.org/10.1371/journal.pgen.1008481

120

Appendix A

Supplementary Figure A.1. RNA-seq data from 24 samples plotted on all pairs of the first six principal
components (PC) except for PC 1 and 2 which were plotted in Figure 2.2. Mesocarp samples are categorised into
early (up to 18/19 WAA) and late (after 18/19 WAA) developmental stages. Samples labelled as A1–4; B1–4 and
C1–4 were from OxG, BC2 (2.6-1) and BC2 (2.6-5) populations, respectively. For C16:0 content, “low” (L) ranged
from 22.2– 28.9 % while “high” (H) ranged from 33.1– 40.6 % with respect to the level of C16:0 in mesocarp.

121

Appendix B
Supplementary Table B.1. GO term enrichment for each of the 14 clusters of genes misexpressed in at least one
BC
1
genotype. Clusters were determined using Modulated Modularity Clustering and enrichment was determined
using TopGO. The cluster number is in the “mod” column and average module degree is the average absolute
correlation between all pairs of genes in the cluster. Annotated refers to the number of GO terms found in the
background dataset, Significant refers to the number of terms and child terms found in the target dataset and
Expected refers to the expected number of GO terms in the target dataset given the distribution of GO terms in the
background dataset.
mod
average
module
degree GO.ID Term Annotated Significant Expected p-value
1 0.614177848 GO:0006464
cellular protein
modification
process 10 3 1.05 0.00059
1 0.614177848 GO:0006850
mitochondrial
pyruvate
transmembrane
transport 1 1 0.1 0.01965
1 0.614177848 GO:0010024
phytochromobilin
biosynthetic
process 1 1 0.1 0.01965
2 0.506503138 GO:0000027
ribosomal large
subunit assembly 1 1 0.01 0.0022
3 0.502396352 GO:0006857
oligopeptide
transport 2 1 0.01 0.0044
5 0.407818537 GO:0006081
cellular aldehyde
metabolic
process 1 1 0.03 0.0131
5 0.407818537 GO:0006869 lipid transport 4 2 0.13 0.00085
5 0.407818537 GO:0009639
response to red or
far red light 3 1 0.1 0.03887
5 0.407818537 GO:0006694
steroid
biosynthetic
process 1 1 0.03 0.0131
6 0.39324316 GO:0009734
auxin-activated
signaling
pathway 3 2 0.69 0.0144
6 0.39324316 GO:0006464
cellular protein
modification
process 10 6 2.31 0.0076
122

6 0.39324316 GO:0000226
microtubule
cytoskeleton
organization 3 2 0.69 0.0144
8 0.259651452 GO:0009451
RNA
modification 1 1 0 0.0022
9 0.219531635 GO:0045454
cell redox
homeostasis 2 1 0.01 0.0044
10 0.215968147 GO:0006457 protein folding 2 1 0.05 0.013
10 0.215968147 GO:0005985
sucrose
metabolic
process 2 1 0.05 0.013
11 0.170955821 GO:0002229
defense response
to oomycetes 3 2 0.87 0.0278
11 0.170955821 GO:0006633
fatty acid
biosynthetic
process 8 4 2.32 0.0046
11 0.170955821 GO:0006629
lipid metabolic
process 26 9 7.55 0.0241
11 0.170955821 GO:0030001
metal ion
transport 17 9 4.94 0.0000064
11 0.170955821 GO:0000160
phosphorelay
signal
transduction
system 7 3 2.03 0.0249
11 0.170955821 GO:0009644
response to high
light intensity 2 2 0.58 0.0099
12 0.169180974 GO:0060918 auxin transport 1 1 0.01 0.0066
12 0.169180974 GO:0051604
protein
maturation 1 1 0.01 0.0066
13 0.154906579 GO:0006952 defense response 4 1 0.1 0.0346
13 0.154906579 GO:0006783
heme
biosynthetic
process 1 1 0.02 0.0087
14 0.138342144 GO:0007166
cell surface
receptor
signaling
pathway 3 2 0.78 0.0379
14 0.138342144 GO:0009691
cytokinin
biosynthetic
process 7 5 1.82 0.00033
14 0.138342144 GO:0006633
fatty acid
biosynthetic
process 8 4 2.08 0.00847
14 0.138342144 GO:0016042
lipid catabolic
process 4 3 1.04 0.00571
14 0.138342144 GO:0006629
lipid metabolic
process 26 11 6.76 0.03831
14 0.138342144 GO:0007142 male meiosis II 2 2 0.52 0.01367
14 0.138342144 GO:0030001
metal ion
transport 17 7 4.42 0.00165
14 0.138342144 GO:0009733 response to auxin 11 4 2.86 0.03039

123

Appendix C

This appendix contains all the supplementary tables and figures referenced in Chapter 4:
Power Calculator for Detecting AI Using Hierarchical Bayesian Model.

nsimul r_g1 r_g2 coverage/rep nbioreps
num asr
per biorep
num asr theta1 theta2 alpha1 alpha2
prop H1
LE05
prop H2
LE05
prop H3
LE05
1000 0.2 0.2 10 3 4 12 0.9 0.9 0.3333333 0.3333333 0.785 0.767 0.001
1000 0.2 0.2 10 3 4 12 0.75 0.75 0.5773503 0.5773503 0.116 0.116 0
1000 0.2 0.2 10 3 4 12 0.25 0.25 1.7320508 1.7320508 0.117 0.102 0.002
1000 0.2 0.2 10 3 4 12 0.1 0.1 3 3 0.808 0.782 0.006
1000 0.2 0.2 10 3 4 12 0.75 0.75 0.5773503 0.5773503 0.119 0.119 0.002
1000 0.2 0.2 10 3 4 12 0.25 0.25 1.7320508 1.7320508 0.11 0.105 0.001
1000 0.2 0.2 10 3 4 12 0.5 0.9 1 0.3333333 0.001 0.835 0.423
1000 0.2 0.2 10 3 4 12 0.5 0.75 1 0.5773503 0.001 0.137 0.032
1000 0.2 0.2 10 3 4 12 0.5 0.25 1 1.7320508 0.001 0.121 0.039
1000 0.2 0.2 10 3 4 12 0.5 0.1 1 3 0.001 0.853 0.421
1000 0.2 0.2 10 3 4 12 0.5 0.75 1 0.5773503 0.002 0.136 0.033
1000 0.2 0.2 10 3 4 12 0.5 0.25 1 1.7320508 0.001 0.12 0.039
1000 0.2 0.2 10 3 4 12 0.5 0.5 1 1 0.002 0.001 0
1000 0.2 0.5 10 3 7 21 0.9 0.9 0.3333333 0.3333333 0.994 0.993 0.002
1000 0.5 0.2 10 3 7 21 0.9 0.9 0.3333333 0.3333333 0.972 0.973 0.003
1000 0.2 0.5 10 3 7 21 0.75 0.75 0.5773503 0.5773503 0.454 0.418 0.006
1000 0.5 0.2 10 3 7 21 0.75 0.75 0.5773503 0.5773503 0.369 0.415 0.006
1000 0.2 0.5 10 3 7 21 0.25 0.25 1.7320508 1.7320508 0.39 0.364 0.003
1000 0.5 0.2 10 3 7 21 0.25 0.25 1.7320508 1.7320508 0.437 0.434 0.003
1000 0.2 0.5 10 3 7 21 0.1 0.1 3 3 0.975 0.98 0.003
1000 0.5 0.2 10 3 7 21 0.1 0.1 3 3 0.981 0.982 0.003
1000 0.2 0.5 10 3 7 21 0.75 0.75 0.5773503 0.5773503 0.453 0.43 0.005
Supplementary Table C.1. Results for all scenarios under which read counts were simulated and AI was estimated by Bayesian model. "nsimul" is the
number of simulations performed. "r_g1" and "r_g2" refer to the probability that a read aligns to allele g1 or g2, respectively, given it came from that
allele. "coverage/rep" is the sequencing coverage per biological replicate. "nbioreps" is the number of biological replicates. "num asr" ("num asr per
biorep") is the number of allele specific reads (per biological replicate). "theta1" and "theta2" are the level of allelic imbalance in simulated in
condition 1 and 2, respectively. "alpha1" and "alpha2" are another measure of the level of allelic imbalance simulated in condition 1 and 2,
respectively. "prop H1 LE05", "prop H2 LE05", and "prop H3 LE05" refer to the proportion of simulations for which the null hypothesis H1, H2, and
H3, respetively, was rejected at a significance level of 0.05.
124
1000 0.5 0.2 10 3 7 21 0.75 0.75 0.5773503 0.5773503 0.37 0.418 0.008
1000 0.2 0.5 10 3 7 21 0.25 0.25 1.7320508 1.7320508 0.396 0.378 0.004
1000 0.5 0.2 10 3 7 21 0.25 0.25 1.7320508 1.7320508 0.444 0.428 0.002
1000 0.2 0.5 10 3 7 21 0.5 0.9 1 0.3333333 0.002 1 0.899
1000 0.5 0.2 10 3 7 21 0.5 0.9 1 0.3333333 0.002 0.985 0.742
1000 0.2 0.5 10 3 7 21 0.5 0.75 1 0.5773503 0.004 0.471 0.201
1000 0.5 0.2 10 3 7 21 0.5 0.75 1 0.5773503 0.005 0.388 0.139
1000 0.2 0.5 10 3 7 21 0.5 0.25 1 1.7320508 0.004 0.422 0.166
1000 0.5 0.2 10 3 7 21 0.5 0.25 1 1.7320508 0.004 0.458 0.207
1000 0.2 0.5 10 3 7 21 0.5 0.1 1 3 0.002 0.986 0.762
1000 0.5 0.2 10 3 7 21 0.5 0.1 1 3 0.002 0.995 0.896
1000 0.2 0.5 10 3 7 21 0.5 0.75 1 0.5773503 0.003 0.476 0.203
1000 0.5 0.2 10 3 7 21 0.5 0.75 1 0.5773503 0.005 0.399 0.142
1000 0.2 0.5 10 3 7 21 0.5 0.25 1 1.7320508 0.006 0.413 0.169
1000 0.5 0.2 10 3 7 21 0.5 0.25 1 1.7320508 0.004 0.453 0.215
1000 0.2 0.5 10 3 7 21 0.5 0.5 1 1 0.006 0.005 0.004
1000 0.5 0.2 10 3 7 21 0.5 0.5 1 1 0.005 0.009 0.006
1000 0.2 0.8 10 3 10 30 0.9 0.9 0.3333333 0.3333333 0.988 0.985 0
1000 0.5 0.5 10 3 10 30 0.9 0.9 0.3333333 0.3333333 0.998 0.999 0.004
1000 0.8 0.2 10 3 10 30 0.9 0.9 0.3333333 0.3333333 0.999 0.998 0.004
1000 0.2 0.8 10 3 10 30 0.75 0.75 0.5773503 0.5773503 0.787 0.805 0.013
1000 0.5 0.5 10 3 10 30 0.75 0.75 0.5773503 0.5773503 0.604 0.603 0.009
1000 0.8 0.2 10 3 10 30 0.75 0.75 0.5773503 0.5773503 0.713 0.737 0.007
1000 0.2 0.8 10 3 10 30 0.25 0.25 1.7320508 1.7320508 0.737 0.725 0.004
1000 0.5 0.5 10 3 10 30 0.25 0.25 1.7320508 1.7320508 0.592 0.581 0.006
1000 0.8 0.2 10 3 10 30 0.25 0.25 1.7320508 1.7320508 0.79 0.786 0.009
1000 0.2 0.8 10 3 10 30 0.1 0.1 3 3 1 1 0.002
1000 0.5 0.5 10 3 10 30 0.1 0.1 3 3 0.999 0.995 0.003
1000 0.8 0.2 10 3 10 30 0.1 0.1 3 3 0.987 0.988 0.002
1000 0.2 0.8 10 3 10 30 0.75 0.75 0.5773503 0.5773503 0.786 0.8 0.013
1000 0.5 0.5 10 3 10 30 0.75 0.75 0.5773503 0.5773503 0.597 0.603 0.006
1000 0.8 0.2 10 3 10 30 0.75 0.75 0.5773503 0.5773503 0.719 0.74 0.008
125
1000 0.2 0.8 10 3 10 30 0.25 0.25 1.7320508 1.7320508 0.74 0.731 0.005
1000 0.5 0.5 10 3 10 30 0.25 0.25 1.7320508 1.7320508 0.594 0.582 0.007
1000 0.8 0.2 10 3 10 30 0.25 0.25 1.7320508 1.7320508 0.79 0.79 0.007
1000 0.2 0.8 10 3 10 30 0.5 0.9 1 0.3333333 0.007 1 0.988
1000 0.5 0.5 10 3 10 30 0.5 0.9 1 0.3333333 0.005 0.999 0.95
1000 0.8 0.2 10 3 10 30 0.5 0.9 1 0.3333333 0.006 1 0.936
1000 0.2 0.8 10 3 10 30 0.5 0.75 1 0.5773503 0.009 0.795 0.477
1000 0.5 0.5 10 3 10 30 0.5 0.75 1 0.5773503 0.007 0.618 0.278
1000 0.8 0.2 10 3 10 30 0.5 0.75 1 0.5773503 0.007 0.728 0.353
1000 0.2 0.8 10 3 10 30 0.5 0.25 1 1.7320508 0.009 0.768 0.347
1000 0.5 0.5 10 3 10 30 0.5 0.25 1 1.7320508 0.006 0.612 0.298
1000 0.8 0.2 10 3 10 30 0.5 0.25 1 1.7320508 0.008 0.801 0.432
1000 0.2 0.8 10 3 10 30 0.5 0.1 1 3 0.008 1 0.944
1000 0.5 0.5 10 3 10 30 0.5 0.1 1 3 0.004 1 0.944
1000 0.8 0.2 10 3 10 30 0.5 0.1 1 3 0.003 1 0.991
1000 0.2 0.8 10 3 10 30 0.5 0.75 1 0.5773503 0.009 0.8 0.47
1000 0.5 0.5 10 3 10 30 0.5 0.75 1 0.5773503 0.008 0.618 0.279
1000 0.8 0.2 10 3 10 30 0.5 0.75 1 0.5773503 0.006 0.725 0.358
1000 0.2 0.8 10 3 10 30 0.5 0.25 1 1.7320508 0.01 0.772 0.358
1000 0.5 0.5 10 3 10 30 0.5 0.25 1 1.7320508 0.007 0.608 0.298
1000 0.8 0.2 10 3 10 30 0.5 0.25 1 1.7320508 0.006 0.798 0.429
1000 0.2 0.8 10 3 10 30 0.5 0.5 1 1 0.014 0.011 0.009
1000 0.5 0.5 10 3 10 30 0.5 0.5 1 1 0.005 0.009 0.008
1000 0.8 0.2 10 3 10 30 0.5 0.5 1 1 0.009 0.011 0.012
1000 0.5 0.8 10 3 13 39 0.9 0.9 0.3333333 0.3333333 0.997 0.997 0.001
1000 0.8 0.5 10 3 13 39 0.9 0.9 0.3333333 0.3333333 0.998 0.998 0.002
1000 0.5 0.8 10 3 13 39 0.75 0.75 0.5773503 0.5773503 0.813 0.825 0.002
1000 0.8 0.5 10 3 13 39 0.75 0.75 0.5773503 0.5773503 0.804 0.783 0.009
1000 0.5 0.8 10 3 13 39 0.25 0.25 1.7320508 1.7320508 0.791 0.802 0.006
1000 0.8 0.5 10 3 13 39 0.25 0.25 1.7320508 1.7320508 0.822 0.809 0.007
1000 0.5 0.8 10 3 13 39 0.1 0.1 3 3 0.997 0.998 0.001
1000 0.8 0.5 10 3 13 39 0.1 0.1 3 3 0.998 0.995 0.006
126
1000 0.5 0.8 10 3 13 39 0.75 0.75 0.5773503 0.5773503 0.822 0.827 0.003
1000 0.8 0.5 10 3 13 39 0.75 0.75 0.5773503 0.5773503 0.803 0.788 0.008
1000 0.5 0.8 10 3 13 39 0.25 0.25 1.7320508 1.7320508 0.79 0.802 0.007
1000 0.8 0.5 10 3 13 39 0.25 0.25 1.7320508 1.7320508 0.822 0.812 0.012
1000 0.5 0.8 10 3 13 39 0.5 0.9 1 0.3333333 0.008 1 0.99
1000 0.8 0.5 10 3 13 39 0.5 0.9 1 0.3333333 0.007 1 0.973
1000 0.5 0.8 10 3 13 39 0.5 0.75 1 0.5773503 0.015 0.827 0.497
1000 0.8 0.5 10 3 13 39 0.5 0.75 1 0.5773503 0.012 0.819 0.414
1000 0.5 0.8 10 3 13 39 0.5 0.25 1 1.7320508 0.014 0.807 0.432
1000 0.8 0.5 10 3 13 39 0.5 0.25 1 1.7320508 0.01 0.843 0.489
1000 0.5 0.8 10 3 13 39 0.5 0.1 1 3 0.008 1 0.976
1000 0.8 0.5 10 3 13 39 0.5 0.1 1 3 0.01 1 0.995
1000 0.5 0.8 10 3 13 39 0.5 0.75 1 0.5773503 0.014 0.834 0.5
1000 0.8 0.5 10 3 13 39 0.5 0.75 1 0.5773503 0.013 0.815 0.404
1000 0.5 0.8 10 3 13 39 0.5 0.25 1 1.7320508 0.015 0.803 0.43
1000 0.8 0.5 10 3 13 39 0.5 0.25 1 1.7320508 0.011 0.842 0.491
1000 0.5 0.8 10 3 13 39 0.5 0.5 1 1 0.014 0.016 0.013
1000 0.8 0.5 10 3 13 39 0.5 0.5 1 1 0.014 0.012 0.008
1000 0.8 0.8 10 3 16 48 0.9 0.9 0.3333333 0.3333333 0.993 0.994 0.001
1000 0.8 0.8 10 3 16 48 0.75 0.75 0.5773503 0.5773503 0.837 0.848 0.009
1000 0.8 0.8 10 3 16 48 0.25 0.25 1.7320508 1.7320508 0.851 0.845 0.007
1000 0.8 0.8 10 3 16 48 0.1 0.1 3 3 0.997 0.997 0
1000 0.8 0.8 10 3 16 48 0.7 0.7 0.6546537 0.6546537 0.568 0.588 0.009
1000 0.8 0.8 10 3 16 48 0.65 0.65 0.7337994 0.7337994 0.289 0.294 0.011
1000 0.8 0.8 10 3 16 48 0.6 0.6 0.8164966 0.8164966 0.116 0.115 0.014
1000 0.8 0.8 10 3 16 48 0.55 0.55 0.904534 0.904534 0.044 0.043 0.018
1000 0.8 0.8 10 3 16 48 0.45 0.45 1.1055416 1.1055416 0.033 0.037 0.017
1000 0.8 0.8 10 3 16 48 0.4 0.4 1.2247449 1.2247449 0.119 0.107 0.011
1000 0.8 0.8 10 3 16 48 0.35 0.35 1.3627703 1.3627703 0.28 0.298 0.016
1000 0.8 0.8 10 3 16 48 0.3 0.3 1.5275252 1.5275252 0.602 0.602 0.007
1000 0.8 0.8 10 3 16 48 0.75 0.75 0.5773503 0.5773503 0.84 0.847 0.011
1000 0.8 0.8 10 3 16 48 0.25 0.25 1.7320508 1.7320508 0.847 0.841 0.007
127
1000 0.8 0.8 10 3 16 48 0.5 0.9 1 0.3333333 0.007 1 0.992
1000 0.8 0.8 10 3 16 48 0.5 0.75 1 0.5773503 0.008 0.85 0.514
1000 0.8 0.8 10 3 16 48 0.5 0.25 1 1.7320508 0.01 0.868 0.487
1000 0.8 0.8 10 3 16 48 0.5 0.1 1 3 0.006 1 0.996
1000 0.8 0.8 10 3 16 48 0.5 0.75 1 0.5773503 0.007 0.842 0.502
1000 0.8 0.8 10 3 16 48 0.5 0.7 1 0.6546537 0.009 0.587 0.291
1000 0.8 0.8 10 3 16 48 0.5 0.65 1 0.7337994 0.007 0.299 0.143
1000 0.8 0.8 10 3 16 48 0.5 0.6 1 0.8164966 0.007 0.119 0.062
1000 0.8 0.8 10 3 16 48 0.5 0.55 1 0.904534 0.009 0.045 0.03
1000 0.8 0.8 10 3 16 48 0.5 0.45 1 1.1055416 0.01 0.028 0.017
1000 0.8 0.8 10 3 16 48 0.5 0.4 1 1.2247449 0.009 0.126 0.059
1000 0.8 0.8 10 3 16 48 0.5 0.35 1 1.3627703 0.008 0.279 0.124
1000 0.8 0.8 10 3 16 48 0.5 0.3 1 1.5275252 0.01 0.605 0.274
1000 0.8 0.8 10 3 16 48 0.5 0.25 1 1.7320508 0.01 0.867 0.493
1000 0.8 0.8 10 3 16 48 0.5 0.5 1 1 0.009 0.017 0.018
10000 0.8 0.8 8.333333333 6 13.333333 80 0.5 0.65 1 0.7337994 0.0238 0.6359 0.3297
10000 0.8 0.8 8.333333333 6 13.333333 80 0.5 0.6 1 0.8164966 0.0243 0.2867 0.1462
10000 0.8 0.8 8.333333333 6 13.333333 80 0.5 0.5 1 1 0.024 0.0241 0.0229
1000 0.8 0.8 17 3 26.666667 80 0.5 0.65 1 0.7337994 0.01 0.543 0.247
1000 0.8 0.8 17 3 26.666667 80 0.5 0.6 1 0.8164966 0.008 0.254 0.094
1000 0.8 0.8 17 3 26.666667 80 0.5 0.55 1 0.904534 0.009 0.056 0.031
1000 0.8 0.8 17 3 26.666667 80 0.5 0.5 1 1 0.009 0.014 0.012
10000 0.8 0.8 12.5 4 20 80 0.5 0.65 1 0.7337994 0.0191 0.5853 0.298
10000 0.8 0.8 12.5 4 20 80 0.5 0.6 1 0.8164966 0.0199 0.2567 0.1247
10000 0.8 0.8 12.5 4 20 80 0.5 0.5 1 1 0.0192 0.0214 0.0212
1000 0.8 0.8 13 4 20 80 0.5 0.65 1 0.7337994 0.019 0.579 0.294
1000 0.8 0.8 13 4 20 80 0.5 0.6 1 0.8164966 0.022 0.274 0.122
1000 0.8 0.8 13 4 20 80 0.5 0.55 1 0.904534 0.023 0.072 0.041
1000 0.8 0.8 13 4 20 80 0.5 0.5 1 1 0.026 0.017 0.026
1000 0.8 0.8 10 5 16 80 0.5 0.65 1 0.7337994 0.023 0.59 0.298
1000 0.8 0.8 10 5 16 80 0.5 0.6 1 0.8164966 0.023 0.294 0.145
1000 0.8 0.8 10 5 16 80 0.5 0.55 1 0.904534 0.023 0.075 0.048
128
1000 0.8 0.8 10 5 16 80 0.5 0.5 1 1 0.023 0.017 0.016
10000 0.8 0.8 10 5 16 80 0.5 0.65 1 0.7337994 0.0226 0.603 0.3151
10000 0.8 0.8 10 5 16 80 0.5 0.6 1 0.8164966 0.0232 0.2698 0.1376
10000 0.8 0.8 10 5 16 80 0.5 0.5 1 1 0.023 0.0231 0.0213
1000 0.8 0.8 8 6 13.333333 80 0.5 0.65 1 0.7337994 0.019 0.596 0.308
1000 0.8 0.8 8 6 13.333333 80 0.5 0.6 1 0.8164966 0.022 0.266 0.145
1000 0.8 0.8 8 6 13.333333 80 0.5 0.55 1 0.904534 0.02 0.073 0.049
1000 0.8 0.8 8 6 13.333333 80 0.5 0.5 1 1 0.021 0.019 0.025
1000 0.8 0.8 6 8 10 80 0.5 0.65 1 0.7337994 0.024 0.632 0.326
1000 0.8 0.8 6 8 10 80 0.5 0.6 1 0.8164966 0.026 0.293 0.146
1000 0.8 0.8 6 8 10 80 0.5 0.55 1 0.904534 0.026 0.07 0.048
1000 0.8 0.8 6 8 10 80 0.5 0.5 1 1 0.024 0.021 0.029
10000 0.8 0.8 6.25 8 10 80 0.5 0.65 1 0.7337994 0.0264 0.6645 0.3557
10000 0.8 0.8 6.25 8 10 80 0.5 0.6 1 0.8164966 0.0264 0.3019 0.1531
10000 0.8 0.8 6.25 8 10 80 0.5 0.5 1 1 0.0255 0.0279 0.0269
1000 0.8 0.8 4 12 6.6666667 80 0.5 0.65 1 0.7337994 0.032 0.673 0.361
1000 0.8 0.8 4 12 6.6666667 80 0.5 0.6 1 0.8164966 0.031 0.318 0.151
1000 0.8 0.8 4 12 6.6666667 80 0.5 0.5 1 1 0.031 0.029 0.024
1000 0.8 0.8 4 12 6.6666667 80 0.5 0.55 1 0.904534 0.033 0.083 0.053
10000 0.8 0.8 4.166666667 12 6.6666667 80 0.5 0.65 1 0.7337994 0.0259 0.6796 0.3745
10000 0.8 0.8 4.166666667 12 6.6666667 80 0.5 0.6 1 0.8164966 0.0256 0.3271 0.1678
10000 0.8 0.8 4.166666667 12 6.6666667 80 0.5 0.5 1 1 0.0268 0.0263 0.0289
10000 0.8 0.8 16.66666667 3 26.666667 80 0.5 0.65 1 0.7337994 0.0176 0.54 0.2602
10000 0.8 0.8 16.66666667 3 26.666667 80 0.5 0.6 1 0.8164966 0.0191 0.2212 0.1067
10000 0.8 0.8 16.66666667 3 26.666667 80 0.5 0.5 1 1 0.0195 0.0182 0.0181
1000 0.8 0.8 20 3 32 96 0.75 0.75 0.5773503 0.5773503 0.992 0.984 0.008
1000 0.8 0.8 20 3 32 96 0.7 0.7 0.6546537 0.6546537 0.901 0.9 0.017
1000 0.8 0.8 20 3 32 96 0.65 0.65 0.7337994 0.7337994 0.642 0.609 0.023
1000 0.8 0.8 20 3 32 96 0.6 0.6 0.8164966 0.8164966 0.275 0.262 0.019
1000 0.8 0.8 20 3 32 96 0.55 0.55 0.904534 0.904534 0.08 0.082 0.021
1000 0.8 0.8 20 3 32 96 0.45 0.45 1.1055416 1.1055416 0.072 0.07 0.016
1000 0.8 0.8 20 3 32 96 0.4 0.4 1.2247449 1.2247449 0.283 0.279 0.023
129
1000 0.8 0.8 20 3 32 96 0.35 0.35 1.3627703 1.3627703 0.642 0.622 0.024
1000 0.8 0.8 20 3 32 96 0.3 0.3 1.5275252 1.5275252 0.887 0.884 0.011
1000 0.8 0.8 20 3 32 96 0.25 0.25 1.7320508 1.7320508 0.988 0.988 0.016
1000 0.8 0.8 20 3 32 96 0.5 0.75 1 0.5773503 0.008 0.995 0.866
1000 0.8 0.8 20 3 32 96 0.5 0.7 1 0.6546537 0.01 0.911 0.578
1000 0.8 0.8 20 3 32 96 0.5 0.65 1 0.7337994 0.012 0.638 0.307
1000 0.8 0.8 20 3 32 96 0.5 0.6 1 0.8164966 0.011 0.275 0.146
1000 0.8 0.8 20 3 32 96 0.5 0.55 1 0.904534 0.011 0.079 0.044
1000 0.8 0.8 20 3 32 96 0.5 0.45 1 1.1055416 0.012 0.07 0.039
1000 0.8 0.8 20 3 32 96 0.5 0.4 1 1.2247449 0.013 0.282 0.125
1000 0.8 0.8 20 3 32 96 0.5 0.35 1 1.3627703 0.011 0.64 0.318
1000 0.8 0.8 20 3 32 96 0.5 0.3 1 1.5275252 0.012 0.887 0.551
1000 0.8 0.8 20 3 32 96 0.5 0.25 1 1.7320508 0.01 0.991 0.841
1000 0.8 0.8 20 3 32 96 0.5 0.5 1 1 0.013 0.014 0.014
1000 0.8 0.8 25 3 40 120 0.5 0.65 1 0.7337994 0.015 0.687 0.384
1000 0.8 0.8 25 3 40 120 0.5 0.6 1 0.8164966 0.016 0.368 0.172
1000 0.8 0.8 25 3 40 120 0.5 0.55 1 0.904534 0.017 0.079 0.055
1000 0.8 0.8 25 3 40 120 0.5 0.5 1 1 0.017 0.019 0.017
10000 0.8 0.8 25 3 40 120 0.5 0.65 1 0.7337994 0.0231 0.7099 0.385
10000 0.8 0.8 25 3 40 120 0.5 0.6 1 0.8164966 0.0245 0.3339 0.1673
10000 0.8 0.8 25 3 40 120 0.5 0.65 1 0.7337994 0.0181 0.7141 0.3839
10000 0.8 0.8 25 3 40 120 0.5 0.6 1 0.8164966 0.0196 0.3379 0.16
10000 0.8 0.8 25 3 40 120 0.5 0.5 1 1 0.0232 0.0193 0.023
10000 0.8 0.8 25 3 40 120 0.5 0.5 1 1 0.0194 0.0226 0.0239
1000 0.2 0.2 100 3 40 120 0.9 0.9 0.3333333 0.3333333 1 1 0.005
1000 0.2 0.2 100 3 40 120 0.75 0.75 0.5773503 0.5773503 0.997 0.998 0.014
1000 0.2 0.2 100 3 40 120 0.25 0.25 1.7320508 1.7320508 0.997 0.995 0.02
1000 0.2 0.2 100 3 40 120 0.1 0.1 3 3 1 1 0.009
1000 0.2 0.2 100 3 40 120 0.75 0.75 0.5773503 0.5773503 0.997 0.998 0.018
1000 0.2 0.2 100 3 40 120 0.25 0.25 1.7320508 1.7320508 0.997 0.995 0.018
1000 0.2 0.2 100 3 40 120 0.5 0.7 1 0.6546537 0.038 0.949 0.696
1000 0.2 0.2 100 3 40 120 0.5 0.65 1 0.7337994 0.032 0.759 0.429
130
1000 0.2 0.2 100 3 40 120 0.5 0.6 1 0.8164966 0.039 0.367 0.193
1000 0.2 0.2 100 3 40 120 0.5 0.9 1 0.3333333 0.016 1 1
1000 0.2 0.2 100 3 40 120 0.5 0.75 1 0.5773503 0.025 0.997 0.922
1000 0.2 0.2 100 3 40 120 0.5 0.25 1 1.7320508 0.023 0.998 0.908
1000 0.2 0.2 100 3 40 120 0.5 0.1 1 3 0.015 1 1
1000 0.2 0.2 100 3 40 120 0.5 0.75 1 0.5773503 0.025 0.998 0.922
1000 0.2 0.2 100 3 40 120 0.5 0.25 1 1.7320508 0.023 0.997 0.905
1000 0.2 0.2 100 3 40 120 0.5 0.5 1 1 0.024 0.03 0.029
10000 0.8 0.8 18.75 4 30 120 0.5 0.65 1 0.7337994 0.024 0.7647 0.4372
10000 0.8 0.8 18.75 4 30 120 0.5 0.6 1 0.8164966 0.0245 0.3739 0.1895
10000 0.8 0.8 18.75 4 30 120 0.5 0.5 1 1 0.0237 0.0252 0.027
1000 0.8 0.8 19 4 30 120 0.5 0.65 1 0.7337994 0.023 0.749 0.43
1000 0.8 0.8 19 4 30 120 0.5 0.6 1 0.8164966 0.022 0.385 0.187
1000 0.8 0.8 19 4 30 120 0.5 0.55 1 0.904534 0.022 0.104 0.066
1000 0.8 0.8 19 4 30 120 0.5 0.5 1 1 0.022 0.028 0.022
1000 0.8 0.8 15 5 24 120 0.5 0.65 1 0.7337994 0.03 0.798 0.452
1000 0.8 0.8 15 5 24 120 0.5 0.6 1 0.8164966 0.028 0.394 0.207
1000 0.8 0.8 15 5 24 120 0.5 0.55 1 0.904534 0.029 0.102 0.071
1000 0.8 0.8 15 5 24 120 0.5 0.5 1 1 0.026 0.031 0.024
10000 0.8 0.8 15 5 24 120 0.5 0.65 1 0.7337994 0.0263 0.7924 0.47
10000 0.8 0.8 15 5 24 120 0.5 0.6 1 0.8164966 0.025 0.4161 0.2082
10000 0.8 0.8 15 5 24 120 0.5 0.5 1 1 0.0257 0.0259 0.0281
10000 0.8 0.8 12.5 6 20 120 0.5 0.65 1 0.7337994 0.0266 0.8129 0.4908
10000 0.8 0.8 12.5 6 20 120 0.5 0.6 1 0.8164966 0.0265 0.4351 0.2183
10000 0.8 0.8 12.5 6 20 120 0.5 0.5 1 1 0.0269 0.0293 0.028
1000 0.8 0.8 13 6 20 120 0.5 0.65 1 0.7337994 0.034 0.824 0.49
1000 0.8 0.8 13 6 20 120 0.5 0.6 1 0.8164966 0.033 0.413 0.221
1000 0.8 0.8 13 6 20 120 0.5 0.55 1 0.904534 0.031 0.11 0.061
1000 0.8 0.8 13 6 20 120 0.5 0.5 1 1 0.033 0.035 0.039
1000 0.8 0.8 9 8 15 120 0.5 0.65 1 0.7337994 0.042 0.827 0.489
1000 0.8 0.8 9 8 15 120 0.5 0.6 1 0.8164966 0.043 0.471 0.232
1000 0.8 0.8 9 8 15 120 0.5 0.55 1 0.904534 0.047 0.128 0.071
131
1000 0.8 0.8 9 8 15 120 0.5 0.5 1 1 0.043 0.023 0.032
10000 0.8 0.8 9.375 8 15 120 0.5 0.65 1 0.7337994 0.0279 0.8359 0.5249
10000 0.8 0.8 9.375 8 15 120 0.5 0.6 1 0.8164966 0.0288 0.458 0.2354
10000 0.8 0.8 9.375 8 15 120 0.5 0.5 1 1 0.0283 0.0311 0.0278
1000 0.8 0.8 6 12 10 120 0.5 0.65 1 0.7337994 0.033 0.834 0.516
1000 0.8 0.8 6 12 10 120 0.5 0.6 1 0.8164966 0.036 0.467 0.253
1000 0.8 0.8 6 12 10 120 0.5 0.5 1 1 0.033 0.026 0.039
1000 0.8 0.8 6 12 10 120 0.5 0.55 1 0.904534 0.033 0.121 0.082
10000 0.8 0.8 6.25 12 10 120 0.5 0.65 1 0.7337994 0.029 0.8611 0.5443
10000 0.8 0.8 6.25 12 10 120 0.5 0.6 1 0.8164966 0.0285 0.4859 0.2508
10000 0.8 0.8 6.25 12 10 120 0.5 0.5 1 1 0.0281 0.0307 0.0304
1000 0.8 0.8 30 3 48 144 0.75 0.75 0.5773503 0.5773503 1 0.998 0.016
1000 0.8 0.8 30 3 48 144 0.7 0.7 0.6546537 0.6546537 0.975 0.968 0.024
1000 0.8 0.8 30 3 48 144 0.65 0.65 0.7337994 0.7337994 0.758 0.788 0.016
1000 0.8 0.8 30 3 48 144 0.6 0.6 0.8164966 0.8164966 0.393 0.386 0.022
1000 0.8 0.8 30 3 48 144 0.55 0.55 0.904534 0.904534 0.083 0.104 0.03
1000 0.8 0.8 30 3 48 144 0.45 0.45 1.1055416 1.1055416 0.091 0.099 0.015
1000 0.8 0.8 30 3 48 144 0.4 0.4 1.2247449 1.2247449 0.398 0.394 0.031
1000 0.8 0.8 30 3 48 144 0.35 0.35 1.3627703 1.3627703 0.771 0.765 0.017
1000 0.8 0.8 30 3 48 144 0.3 0.3 1.5275252 1.5275252 0.97 0.973 0.018
1000 0.8 0.8 30 3 48 144 0.25 0.25 1.7320508 1.7320508 0.999 1 0.017
1000 0.8 0.8 30 3 48 144 0.5 0.75 1 0.5773503 0.03 1 0.926
1000 0.8 0.8 30 3 48 144 0.5 0.7 1 0.6546537 0.031 0.972 0.749
1000 0.8 0.8 30 3 48 144 0.5 0.65 1 0.7337994 0.033 0.759 0.427
1000 0.8 0.8 30 3 48 144 0.5 0.6 1 0.8164966 0.03 0.405 0.216
1000 0.8 0.8 30 3 48 144 0.5 0.55 1 0.904534 0.032 0.085 0.059
1000 0.8 0.8 30 3 48 144 0.5 0.45 1 1.1055416 0.029 0.099 0.057
1000 0.8 0.8 30 3 48 144 0.5 0.4 1 1.2247449 0.028 0.399 0.192
1000 0.8 0.8 30 3 48 144 0.5 0.35 1 1.3627703 0.027 0.765 0.455
1000 0.8 0.8 30 3 48 144 0.5 0.3 1 1.5275252 0.028 0.972 0.726
1000 0.8 0.8 30 3 48 144 0.5 0.25 1 1.7320508 0.027 1 0.937
1000 0.8 0.8 30 3 48 144 0.5 0.5 1 1 0.03 0.015 0.02
132
1000 0.25 0.25 100 3 50 150 0.5 0.7 1 0.6546537 0.029 0.977 0.757
1000 0.25 0.25 100 3 50 150 0.5 0.65 1 0.7337994 0.024 0.803 0.468
1000 0.25 0.25 100 3 50 150 0.5 0.6 1 0.8164966 0.025 0.4 0.205
1000 0.8 0.8 25 4 40 160 0.5 0.65 1 0.7337994 0.02 0.872 0.544
1000 0.8 0.8 25 4 40 160 0.5 0.6 1 0.8164966 0.023 0.482 0.245
1000 0.8 0.8 25 4 40 160 0.5 0.55 1 0.904534 0.022 0.136 0.081
1000 0.8 0.8 25 4 40 160 0.5 0.5 1 1 0.021 0.026 0.027
10000 0.8 0.8 25 4 40 160 0.5 0.65 1 0.7337994 0.0284 0.8561 0.5397
10000 0.8 0.8 25 4 40 160 0.5 0.6 1 0.8164966 0.0277 0.4744 0.2446
10000 0.8 0.8 25 4 40 160 0.5 0.55 1 0.904534 0.0283 0.1259 0.0738
10000 0.8 0.8 25 4 40 160 0.5 0.5 1 1 0.0279 0.0265 0.0249
1000 0.3 0.3 100 3 60 180 0.5 0.7 1 0.6546537 0.031 0.988 0.834
1000 0.3 0.3 100 3 60 180 0.5 0.65 1 0.7337994 0.033 0.831 0.526
1000 0.3 0.3 100 3 60 180 0.5 0.6 1 0.8164966 0.031 0.465 0.26
1000 0.8 0.8 40 3 64 192 0.75 0.75 0.5773503 0.5773503 1 1 0.013
1000 0.8 0.8 40 3 64 192 0.7 0.7 0.6546537 0.6546537 0.987 0.989 0.026
1000 0.8 0.8 40 3 64 192 0.65 0.65 0.7337994 0.7337994 0.851 0.839 0.023
1000 0.8 0.8 40 3 64 192 0.6 0.6 0.8164966 0.8164966 0.476 0.482 0.026
1000 0.8 0.8 40 3 64 192 0.55 0.55 0.904534 0.904534 0.109 0.111 0.025
1000 0.8 0.8 40 3 64 192 0.45 0.45 1.1055416 1.1055416 0.128 0.137 0.038
1000 0.8 0.8 40 3 64 192 0.4 0.4 1.2247449 1.2247449 0.477 0.48 0.024
1000 0.8 0.8 40 3 64 192 0.35 0.35 1.3627703 1.3627703 0.843 0.841 0.015
1000 0.8 0.8 40 3 64 192 0.3 0.3 1.5275252 1.5275252 0.988 0.986 0.024
1000 0.8 0.8 40 3 64 192 0.25 0.25 1.7320508 1.7320508 1 1 0.017
1000 0.8 0.8 40 3 64 192 0.5 0.75 1 0.5773503 0.024 1 0.966
1000 0.8 0.8 40 3 64 192 0.5 0.7 1 0.6546537 0.028 0.987 0.835
1000 0.8 0.8 40 3 64 192 0.5 0.65 1 0.7337994 0.023 0.858 0.533
1000 0.8 0.8 40 3 64 192 0.5 0.6 1 0.8164966 0.025 0.481 0.247
1000 0.8 0.8 40 3 64 192 0.5 0.55 1 0.904534 0.024 0.11 0.078
1000 0.8 0.8 40 3 64 192 0.5 0.45 1 1.1055416 0.025 0.134 0.079
1000 0.8 0.8 40 3 64 192 0.5 0.4 1 1.2247449 0.027 0.476 0.248
1000 0.8 0.8 40 3 64 192 0.5 0.35 1 1.3627703 0.023 0.853 0.52
133
1000 0.8 0.8 40 3 64 192 0.5 0.3 1 1.5275252 0.023 0.993 0.836
1000 0.8 0.8 40 3 64 192 0.5 0.25 1 1.7320508 0.024 1 0.976
1000 0.8 0.8 40 3 64 192 0.5 0.5 1 1 0.025 0.028 0.028
1000 0.8 0.8 25 5 40 200 0.5 0.65 1 0.7337994 0.023 0.923 0.677
1000 0.8 0.8 25 5 40 200 0.5 0.6 1 0.8164966 0.028 0.615 0.329
1000 0.8 0.8 25 5 40 200 0.5 0.55 1 0.904534 0.025 0.161 0.092
1000 0.8 0.8 25 5 40 200 0.5 0.5 1 1 0.024 0.034 0.029
10000 0.8 0.8 25 5 40 200 0.5 0.65 1 0.7337994 0.0278 0.9339 0.6696
10000 0.8 0.8 25 5 40 200 0.5 0.6 1 0.8164966 0.0282 0.595 0.3242
10000 0.8 0.8 25 5 40 200 0.5 0.55 1 0.904534 0.0285 0.1646 0.0882
10000 0.8 0.8 25 5 40 200 0.5 0.5 1 1 0.0285 0.0308 0.0308
1000 0.2 0.5 100 3 70 210 0.9 0.9 0.3333333 0.3333333 1 1 0.006
1000 0.5 0.2 100 3 70 210 0.9 0.9 0.3333333 0.3333333 1 1 0.004
1000 0.2 0.5 100 3 70 210 0.75 0.75 0.5773503 0.5773503 1 1 0.021
1000 0.5 0.2 100 3 70 210 0.75 0.75 0.5773503 0.5773503 1 1 0.017
1000 0.2 0.5 100 3 70 210 0.25 0.25 1.7320508 1.7320508 1 1 0.018
1000 0.5 0.2 100 3 70 210 0.25 0.25 1.7320508 1.7320508 0.999 1 0.022
1000 0.2 0.5 100 3 70 210 0.1 0.1 3 3 1 1 0.009
1000 0.5 0.2 100 3 70 210 0.1 0.1 3 3 1 1 0.011
1000 0.2 0.5 100 3 70 210 0.75 0.75 0.5773503 0.5773503 1 1 0.023
1000 0.5 0.2 100 3 70 210 0.75 0.75 0.5773503 0.5773503 1 1 0.02
1000 0.2 0.5 100 3 70 210 0.25 0.25 1.7320508 1.7320508 1 1 0.022
1000 0.5 0.2 100 3 70 210 0.25 0.25 1.7320508 1.7320508 0.999 1 0.022
1000 0.35 0.35 100 3 70 210 0.5 0.7 1 0.6546537 0.031 0.991 0.852
1000 0.35 0.35 100 3 70 210 0.5 0.65 1 0.7337994 0.035 0.888 0.574
1000 0.35 0.35 100 3 70 210 0.5 0.6 1 0.8164966 0.03 0.531 0.265
1000 0.2 0.5 100 3 70 210 0.5 0.9 1 0.3333333 0.033 1 1
1000 0.5 0.2 100 3 70 210 0.5 0.9 1 0.3333333 0.012 1 1
1000 0.2 0.5 100 3 70 210 0.5 0.75 1 0.5773503 0.04 1 0.985
1000 0.5 0.2 100 3 70 210 0.5 0.75 1 0.5773503 0.02 1 0.97
1000 0.2 0.5 100 3 70 210 0.5 0.25 1 1.7320508 0.039 1 0.971
1000 0.5 0.2 100 3 70 210 0.5 0.25 1 1.7320508 0.019 1 0.989
134
1000 0.2 0.5 100 3 70 210 0.5 0.1 1 3 0.03 1 1
1000 0.5 0.2 100 3 70 210 0.5 0.1 1 3 0.011 1 1
1000 0.2 0.5 100 3 70 210 0.5 0.75 1 0.5773503 0.04 1 0.984
1000 0.5 0.2 100 3 70 210 0.5 0.75 1 0.5773503 0.019 1 0.974
1000 0.2 0.5 100 3 70 210 0.5 0.25 1 1.7320508 0.036 1 0.97
1000 0.5 0.2 100 3 70 210 0.5 0.25 1 1.7320508 0.019 1 0.987
1000 0.2 0.5 100 3 70 210 0.5 0.5 1 1 0.039 0.025 0.032
1000 0.5 0.2 100 3 70 210 0.5 0.5 1 1 0.021 0.031 0.031
1000 0.8 0.8 50 3 80 240 0.75 0.75 0.5773503 0.5773503 1 1 0.019
1000 0.8 0.8 50 3 80 240 0.7 0.7 0.6546537 0.6546537 0.99 0.995 0.029
1000 0.8 0.8 50 3 80 240 0.65 0.65 0.7337994 0.7337994 0.904 0.901 0.017
1000 0.8 0.8 50 3 80 240 0.6 0.6 0.8164966 0.8164966 0.526 0.551 0.021
1000 0.8 0.8 50 3 80 240 0.55 0.55 0.904534 0.904534 0.154 0.13 0.027
1000 0.8 0.8 50 3 80 240 0.45 0.45 1.1055416 1.1055416 0.147 0.143 0.023
1000 0.8 0.8 50 3 80 240 0.4 0.4 1.2247449 1.2247449 0.504 0.555 0.02
1000 0.8 0.8 50 3 80 240 0.35 0.35 1.3627703 1.3627703 0.902 0.908 0.016
1000 0.8 0.8 50 3 80 240 0.3 0.3 1.5275252 1.5275252 0.991 0.989 0.029
1000 0.8 0.8 50 3 80 240 0.25 0.25 1.7320508 1.7320508 1 1 0.02
1000 0.8 0.8 50 3 80 240 0.5 0.65 1 0.7337994 0.028 0.897 0.597
1000 0.8 0.8 50 3 80 240 0.5 0.6 1 0.8164966 0.028 0.509 0.257
1000 0.8 0.8 50 3 80 240 0.5 0.55 1 0.904534 0.026 0.168 0.097
1000 0.8 0.8 50 3 80 240 0.5 0.75 1 0.5773503 0.021 1 0.98
1000 0.8 0.8 50 3 80 240 0.5 0.7 1 0.6546537 0.021 0.99 0.877
1000 0.8 0.8 50 3 80 240 0.5 0.65 1 0.7337994 0.021 0.9 0.611
1000 0.8 0.8 50 3 80 240 0.5 0.6 1 0.8164966 0.023 0.54 0.277
1000 0.8 0.8 50 3 80 240 0.5 0.55 1 0.904534 0.025 0.162 0.074
1000 0.8 0.8 50 3 80 240 0.5 0.45 1 1.1055416 0.022 0.138 0.082
1000 0.8 0.8 50 3 80 240 0.5 0.4 1 1.2247449 0.021 0.501 0.275
1000 0.8 0.8 50 3 80 240 0.5 0.35 1 1.3627703 0.022 0.908 0.615
1000 0.8 0.8 50 3 80 240 0.5 0.3 1 1.5275252 0.021 0.993 0.888
1000 0.8 0.8 50 3 80 240 0.5 0.25 1 1.7320508 0.021 1 0.984
1000 0.8 0.8 50 3 80 240 0.5 0.5 1 1 0.027 0.032 0.032
135
1000 0.8 0.8 50 3 80 240 0.5 0.5 1 1 0.023 0.02 0.027
10000 0.8 0.8 50 3 80 240 0.5 0.65 1 0.7337994 0.0286 0.9098 0.6119
10000 0.8 0.8 50 3 80 240 0.5 0.6 1 0.8164966 0.0284 0.5271 0.277
10000 0.8 0.8 50 3 80 240 0.5 0.65 1 0.7337994 0.0258 0.9027 0.6008
10000 0.8 0.8 50 3 80 240 0.5 0.6 1 0.8164966 0.0261 0.5297 0.2725
10000 0.8 0.8 50 3 80 240 0.5 0.5 1 1 0.0273 0.0263 0.0281
10000 0.8 0.8 50 3 80 240 0.5 0.5 1 1 0.0274 0.0272 0.0256
1000 0.4 0.4 100 3 80 240 0.5 0.7 1 0.6546537 0.049 0.995 0.886
1000 0.4 0.4 100 3 80 240 0.5 0.65 1 0.7337994 0.046 0.91 0.633
1000 0.4 0.4 100 3 80 240 0.5 0.6 1 0.8164966 0.049 0.552 0.322
10000 0.8 0.8 37.5 4 60 240 0.5 0.65 1 0.7337994 0.0293 0.9465 0.6885
10000 0.8 0.8 37.5 4 60 240 0.5 0.6 1 0.8164966 0.0288 0.6161 0.3279
10000 0.8 0.8 37.5 4 60 240 0.5 0.5 1 1 0.0297 0.0303 0.0305
1000 0.8 0.8 38 4 60 240 0.5 0.65 1 0.7337994 0.026 0.933 0.674
1000 0.8 0.8 38 4 60 240 0.5 0.6 1 0.8164966 0.028 0.629 0.334
1000 0.8 0.8 38 4 60 240 0.5 0.55 1 0.904534 0.029 0.16 0.109
1000 0.8 0.8 38 4 60 240 0.5 0.5 1 1 0.025 0.027 0.031
1000 0.8 0.8 30 5 48 240 0.5 0.65 1 0.7337994 0.03 0.972 0.75
1000 0.8 0.8 30 5 48 240 0.5 0.6 1 0.8164966 0.038 0.692 0.375
1000 0.8 0.8 30 5 48 240 0.5 0.55 1 0.904534 0.036 0.195 0.112
1000 0.8 0.8 30 5 48 240 0.5 0.5 1 1 0.035 0.03 0.028
10000 0.8 0.8 30 5 48 240 0.5 0.65 1 0.7337994 0.0319 0.96 0.7286
10000 0.8 0.8 30 5 48 240 0.5 0.5 1 1 0.0323 0.0345 0.031
1000 0.8 0.8 25 6 40 240 0.5 0.65 1 0.7337994 0.034 0.978 0.754
1000 0.8 0.8 25 6 40 240 0.5 0.6 1 0.8164966 0.037 0.721 0.403
1000 0.8 0.8 25 6 40 240 0.5 0.55 1 0.904534 0.038 0.205 0.104
1000 0.8 0.8 25 6 40 240 0.5 0.5 1 1 0.035 0.026 0.031
10000 0.8 0.8 25 6 40 240 0.5 0.65 1 0.7337994 0.0333 0.9691 0.763
10000 0.8 0.8 25 6 40 240 0.5 0.6 1 0.8164966 0.0326 0.6983 0.3931
10000 0.8 0.8 25 6 40 240 0.5 0.65 1 0.7337994 0.0326 0.971 0.763
10000 0.8 0.8 25 6 40 240 0.5 0.6 1 0.8164966 0.0334 0.7011 0.4051
10000 0.8 0.8 25 6 40 240 0.5 0.5 1 1 0.0323 0.0307 0.0358
136
10000 0.8 0.8 25 6 40 240 0.5 0.5 1 1 0.0343 0.0318 0.0342
10000 0.8 0.8 18.75 8 30 240 0.5 0.65 1 0.7337994 0.0346 0.9846 0.8091
10000 0.8 0.8 18.75 8 30 240 0.5 0.6 1 0.8164966 0.0354 0.7495 0.4415
10000 0.8 0.8 18.75 8 30 240 0.5 0.5 1 1 0.0358 0.0349 0.0321
1000 0.8 0.8 19 8 30 240 0.5 0.65 1 0.7337994 0.042 0.989 0.807
1000 0.8 0.8 19 8 30 240 0.5 0.6 1 0.8164966 0.041 0.714 0.419
1000 0.8 0.8 19 8 30 240 0.5 0.55 1 0.904534 0.042 0.25 0.124
1000 0.8 0.8 19 8 30 240 0.5 0.5 1 1 0.041 0.032 0.039
10000 0.8 0.8 12.5 12 20 240 0.5 0.65 1 0.7337994 0.0388 0.9879 0.8469
10000 0.8 0.8 12.5 12 20 240 0.5 0.6 1 0.8164966 0.0373 0.7861 0.4775
10000 0.8 0.8 12.5 12 20 240 0.5 0.5 1 1 0.0372 0.0433 0.0388
1000 0.8 0.8 13 12 20 240 0.5 0.65 1 0.7337994 0.034 0.989 0.858
1000 0.8 0.8 13 12 20 240 0.5 0.6 1 0.8164966 0.031 0.78 0.48
1000 0.8 0.8 13 12 20 240 0.5 0.55 1 0.904534 0.032 0.25 0.128
1000 0.8 0.8 13 12 20 240 0.5 0.5 1 1 0.031 0.039 0.047
1000 0.45 0.45 100 3 90 270 0.5 0.7 1 0.6546537 0.029 0.998 0.918
1000 0.45 0.45 100 3 90 270 0.5 0.65 1 0.7337994 0.034 0.935 0.69
1000 0.45 0.45 100 3 90 270 0.5 0.6 1 0.8164966 0.033 0.613 0.344
1000 0.8 0.8 60 3 96 288 0.75 0.75 0.5773503 0.5773503 1 1 0.019
1000 0.8 0.8 60 3 96 288 0.7 0.7 0.6546537 0.6546537 0.998 0.997 0.036
1000 0.8 0.8 60 3 96 288 0.65 0.65 0.7337994 0.7337994 0.927 0.921 0.018
1000 0.8 0.8 60 3 96 288 0.6 0.6 0.8164966 0.8164966 0.58 0.615 0.018
1000 0.8 0.8 60 3 96 288 0.55 0.55 0.904534 0.904534 0.155 0.158 0.028
1000 0.8 0.8 60 3 96 288 0.45 0.45 1.1055416 1.1055416 0.171 0.15 0.031
1000 0.8 0.8 60 3 96 288 0.4 0.4 1.2247449 1.2247449 0.547 0.6 0.024
1000 0.8 0.8 60 3 96 288 0.35 0.35 1.3627703 1.3627703 0.927 0.918 0.02
1000 0.8 0.8 60 3 96 288 0.3 0.3 1.5275252 1.5275252 0.997 0.996 0.022
1000 0.8 0.8 60 3 96 288 0.25 0.25 1.7320508 1.7320508 1 1 0.016
1000 0.8 0.8 60 3 96 288 0.5 0.75 1 0.5773503 0.024 1 0.993
1000 0.8 0.8 60 3 96 288 0.5 0.7 1 0.6546537 0.021 0.997 0.924
1000 0.8 0.8 60 3 96 288 0.5 0.65 1 0.7337994 0.027 0.93 0.662
1000 0.8 0.8 60 3 96 288 0.5 0.6 1 0.8164966 0.025 0.59 0.303
137
1000 0.8 0.8 60 3 96 288 0.5 0.55 1 0.904534 0.029 0.144 0.084
1000 0.8 0.8 60 3 96 288 0.5 0.45 1 1.1055416 0.028 0.171 0.113
1000 0.8 0.8 60 3 96 288 0.5 0.4 1 1.2247449 0.028 0.55 0.317
1000 0.8 0.8 60 3 96 288 0.5 0.35 1 1.3627703 0.028 0.936 0.664
1000 0.8 0.8 60 3 96 288 0.5 0.3 1 1.5275252 0.029 0.999 0.91
1000 0.8 0.8 60 3 96 288 0.5 0.25 1 1.7320508 0.024 1 0.988
1000 0.8 0.8 60 3 96 288 0.5 0.5 1 1 0.025 0.022 0.025
1000 0.2 0.8 100 3 100 300 0.9 0.9 0.3333333 0.3333333 1 1 0.014
1000 0.5 0.5 100 3 100 300 0.9 0.9 0.3333333 0.3333333 1 1 0.01
1000 0.8 0.2 100 3 100 300 0.9 0.9 0.3333333 0.3333333 1 1 0.007
1000 0.2 0.8 100 3 100 300 0.75 0.75 0.5773503 0.5773503 1 1 0.026
1000 0.5 0.5 100 3 100 300 0.75 0.75 0.5773503 0.5773503 1 1 0.025
1000 0.8 0.2 100 3 100 300 0.75 0.75 0.5773503 0.5773503 1 1 0.02
1000 0.2 0.8 100 3 100 300 0.25 0.25 1.7320508 1.7320508 1 1 0.028
1000 0.5 0.5 100 3 100 300 0.25 0.25 1.7320508 1.7320508 1 1 0.033
1000 0.8 0.2 100 3 100 300 0.25 0.25 1.7320508 1.7320508 1 1 0.03
1000 0.2 0.8 100 3 100 300 0.1 0.1 3 3 1 1 0.008
1000 0.5 0.5 100 3 100 300 0.1 0.1 3 3 1 1 0.007
1000 0.8 0.2 100 3 100 300 0.1 0.1 3 3 1 1 0.004
1000 0.2 0.8 100 3 100 300 0.75 0.75 0.5773503 0.5773503 1 1 0.026
1000 0.5 0.5 100 3 100 300 0.75 0.75 0.5773503 0.5773503 1 1 0.026
1000 0.8 0.2 100 3 100 300 0.75 0.75 0.5773503 0.5773503 1 1 0.017
1000 0.2 0.8 100 3 100 300 0.25 0.25 1.7320508 1.7320508 1 1 0.027
1000 0.5 0.5 100 3 100 300 0.25 0.25 1.7320508 1.7320508 1 1 0.031
1000 0.8 0.2 100 3 100 300 0.25 0.25 1.7320508 1.7320508 1 1 0.033
1000 0.5 0.5 100 3 100 300 0.5 0.7 1 0.6546537 0.03 0.997 0.928
1000 0.5 0.5 100 3 100 300 0.5 0.65 1 0.7337994 0.025 0.945 0.692
1000 0.5 0.5 100 3 100 300 0.5 0.6 1 0.8164966 0.022 0.603 0.323
1000 0.2 0.8 100 3 100 300 0.5 0.9 1 0.3333333 0.021 1 1
1000 0.5 0.5 100 3 100 300 0.5 0.9 1 0.3333333 0.019 1 1
1000 0.8 0.2 100 3 100 300 0.5 0.9 1 0.3333333 0.017 1 1
1000 0.2 0.8 100 3 100 300 0.5 0.75 1 0.5773503 0.027 1 0.997
138
1000 0.5 0.5 100 3 100 300 0.5 0.75 1 0.5773503 0.028 1 0.993
1000 0.8 0.2 100 3 100 300 0.5 0.75 1 0.5773503 0.026 1 0.993
1000 0.2 0.8 100 3 100 300 0.5 0.25 1 1.7320508 0.031 1 0.994
1000 0.5 0.5 100 3 100 300 0.5 0.25 1 1.7320508 0.031 1 0.995
1000 0.8 0.2 100 3 100 300 0.5 0.25 1 1.7320508 0.026 1 0.999
1000 0.2 0.8 100 3 100 300 0.5 0.1 1 3 0.021 1 1
1000 0.5 0.5 100 3 100 300 0.5 0.1 1 3 0.019 1 1
1000 0.8 0.2 100 3 100 300 0.5 0.1 1 3 0.023 1 1
1000 0.2 0.8 100 3 100 300 0.5 0.75 1 0.5773503 0.031 1 0.997
1000 0.5 0.5 100 3 100 300 0.5 0.75 1 0.5773503 0.027 1 0.994
1000 0.8 0.2 100 3 100 300 0.5 0.75 1 0.5773503 0.024 1 0.994
1000 0.2 0.8 100 3 100 300 0.5 0.25 1 1.7320508 0.029 1 0.994
1000 0.5 0.5 100 3 100 300 0.5 0.25 1 1.7320508 0.025 1 0.992
1000 0.8 0.2 100 3 100 300 0.5 0.25 1 1.7320508 0.025 1 0.999
1000 0.2 0.8 100 3 100 300 0.5 0.5 1 1 0.029 0.032 0.028
1000 0.5 0.5 100 3 100 300 0.5 0.5 1 1 0.027 0.041 0.03
1000 0.8 0.2 100 3 100 300 0.5 0.5 1 1 0.029 0.039 0.043
1000 0.8 0.8 50 4 80 320 0.5 0.65 1 0.7337994 0.032 0.964 0.754
1000 0.8 0.8 50 4 80 320 0.5 0.6 1 0.8164966 0.034 0.708 0.429
1000 0.8 0.8 50 4 80 320 0.5 0.55 1 0.904534 0.035 0.196 0.116
1000 0.8 0.8 50 4 80 320 0.5 0.5 1 1 0.037 0.022 0.037
10000 0.8 0.8 50 4 80 320 0.5 0.65 1 0.7337994 0.0308 0.9697 0.7688
10000 0.8 0.8 50 4 80 320 0.5 0.6 1 0.8164966 0.0312 0.708 0.3989
10000 0.8 0.8 50 4 80 320 0.5 0.55 1 0.904534 0.0313 0.2073 0.1115
10000 0.8 0.8 50 4 80 320 0.5 0.5 1 1 0.0319 0.0286 0.0312
1000 0.8 0.8 25 8 40 320 0.5 0.65 1 0.7337994 0.036 0.995 0.889
1000 0.8 0.8 25 8 40 320 0.5 0.6 1 0.8164966 0.037 0.845 0.516
1000 0.8 0.8 25 8 40 320 0.5 0.55 1 0.904534 0.037 0.293 0.166
1000 0.8 0.8 25 8 40 320 0.5 0.5 1 1 0.037 0.051 0.042
10000 0.8 0.8 25 8 40 320 0.5 0.65 1 0.7337994 0.0373 0.9946 0.8832
10000 0.8 0.8 25 8 40 320 0.5 0.6 1 0.8164966 0.0384 0.8326 0.5298
10000 0.8 0.8 25 8 40 320 0.5 0.55 1 0.904534 0.0377 0.2831 0.1581
139
10000 0.8 0.8 25 8 40 320 0.5 0.5 1 1 0.0395 0.039 0.0381
1000 0.55 0.55 100 3 110 330 0.5 0.7 1 0.6546537 0.039 0.998 0.936
1000 0.55 0.55 100 3 110 330 0.5 0.65 1 0.7337994 0.037 0.936 0.687
1000 0.55 0.55 100 3 110 330 0.5 0.6 1 0.8164966 0.037 0.626 0.351
1000 0.8 0.8 70 3 112 336 0.75 0.75 0.5773503 0.5773503 1 1 0.024
1000 0.8 0.8 70 3 112 336 0.7 0.7 0.6546537 0.6546537 0.998 0.998 0.023
1000 0.8 0.8 70 3 112 336 0.65 0.65 0.7337994 0.7337994 0.944 0.943 0.023
1000 0.8 0.8 70 3 112 336 0.6 0.6 0.8164966 0.8164966 0.624 0.634 0.033
1000 0.8 0.8 70 3 112 336 0.55 0.55 0.904534 0.904534 0.171 0.174 0.025
1000 0.8 0.8 70 3 112 336 0.45 0.45 1.1055416 1.1055416 0.203 0.164 0.026
1000 0.8 0.8 70 3 112 336 0.4 0.4 1.2247449 1.2247449 0.639 0.615 0.033
1000 0.8 0.8 70 3 112 336 0.35 0.35 1.3627703 1.3627703 0.943 0.944 0.04
1000 0.8 0.8 70 3 112 336 0.3 0.3 1.5275252 1.5275252 0.998 0.999 0.03
1000 0.8 0.8 70 3 112 336 0.25 0.25 1.7320508 1.7320508 1 1 0.023
1000 0.8 0.8 70 3 112 336 0.5 0.75 1 0.5773503 0.026 1 0.995
1000 0.8 0.8 70 3 112 336 0.5 0.7 1 0.6546537 0.024 0.998 0.918
1000 0.8 0.8 70 3 112 336 0.5 0.65 1 0.7337994 0.025 0.948 0.691
1000 0.8 0.8 70 3 112 336 0.5 0.6 1 0.8164966 0.025 0.633 0.332
1000 0.8 0.8 70 3 112 336 0.5 0.55 1 0.904534 0.028 0.177 0.088
1000 0.8 0.8 70 3 112 336 0.5 0.45 1 1.1055416 0.024 0.199 0.107
1000 0.8 0.8 70 3 112 336 0.5 0.4 1 1.2247449 0.023 0.638 0.358
1000 0.8 0.8 70 3 112 336 0.5 0.35 1 1.3627703 0.024 0.948 0.712
1000 0.8 0.8 70 3 112 336 0.5 0.3 1 1.5275252 0.026 0.999 0.936
1000 0.8 0.8 70 3 112 336 0.5 0.25 1 1.7320508 0.025 1 0.997
1000 0.8 0.8 70 3 112 336 0.5 0.5 1 1 0.026 0.021 0.029
1000 0.6 0.6 100 3 120 360 0.5 0.7 1 0.6546537 0.038 1 0.943
1000 0.6 0.6 100 3 120 360 0.5 0.65 1 0.7337994 0.036 0.965 0.725
1000 0.6 0.6 100 3 120 360 0.5 0.6 1 0.8164966 0.044 0.645 0.357
1000 0.8 0.8 80 3 128 384 0.75 0.75 0.5773503 0.5773503 1 1 0.02
1000 0.8 0.8 80 3 128 384 0.7 0.7 0.6546537 0.6546537 1 0.999 0.024
1000 0.8 0.8 80 3 128 384 0.65 0.65 0.7337994 0.7337994 0.959 0.958 0.025
1000 0.8 0.8 80 3 128 384 0.6 0.6 0.8164966 0.8164966 0.677 0.677 0.022
140
1000 0.8 0.8 80 3 128 384 0.55 0.55 0.904534 0.904534 0.192 0.207 0.028
1000 0.8 0.8 80 3 128 384 0.45 0.45 1.1055416 1.1055416 0.199 0.187 0.032
1000 0.8 0.8 80 3 128 384 0.4 0.4 1.2247449 1.2247449 0.665 0.645 0.026
1000 0.8 0.8 80 3 128 384 0.35 0.35 1.3627703 1.3627703 0.953 0.957 0.027
1000 0.8 0.8 80 3 128 384 0.3 0.3 1.5275252 1.5275252 1 1 0.017
1000 0.8 0.8 80 3 128 384 0.25 0.25 1.7320508 1.7320508 1 1 0.019
1000 0.8 0.8 80 3 128 384 0.5 0.75 1 0.5773503 0.026 1 0.998
1000 0.8 0.8 80 3 128 384 0.5 0.7 1 0.6546537 0.032 0.999 0.96
1000 0.8 0.8 80 3 128 384 0.5 0.65 1 0.7337994 0.029 0.959 0.724
1000 0.8 0.8 80 3 128 384 0.5 0.6 1 0.8164966 0.03 0.659 0.376
1000 0.8 0.8 80 3 128 384 0.5 0.55 1 0.904534 0.031 0.184 0.109
1000 0.8 0.8 80 3 128 384 0.5 0.45 1 1.1055416 0.032 0.202 0.098
1000 0.8 0.8 80 3 128 384 0.5 0.4 1 1.2247449 0.031 0.666 0.371
1000 0.8 0.8 80 3 128 384 0.5 0.35 1 1.3627703 0.03 0.954 0.719
1000 0.8 0.8 80 3 128 384 0.5 0.3 1 1.5275252 0.033 1 0.935
1000 0.8 0.8 80 3 128 384 0.5 0.25 1 1.7320508 0.024 1 0.999
1000 0.8 0.8 80 3 128 384 0.5 0.5 1 1 0.03 0.032 0.033
1000 0.5 0.8 100 3 130 390 0.9 0.9 0.3333333 0.3333333 1 1 0.019
1000 0.8 0.5 100 3 130 390 0.9 0.9 0.3333333 0.3333333 1 1 0.005
1000 0.5 0.8 100 3 130 390 0.75 0.75 0.5773503 0.5773503 1 1 0.019
1000 0.8 0.5 100 3 130 390 0.75 0.75 0.5773503 0.5773503 1 1 0.022
1000 0.5 0.8 100 3 130 390 0.25 0.25 1.7320508 1.7320508 1 1 0.023
1000 0.8 0.5 100 3 130 390 0.25 0.25 1.7320508 1.7320508 1 1 0.025
1000 0.5 0.8 100 3 130 390 0.1 0.1 3 3 1 1 0.017
1000 0.8 0.5 100 3 130 390 0.1 0.1 3 3 1 1 0.01
1000 0.5 0.8 100 3 130 390 0.75 0.75 0.5773503 0.5773503 1 1 0.021
1000 0.8 0.5 100 3 130 390 0.75 0.75 0.5773503 0.5773503 1 1 0.02
1000 0.5 0.8 100 3 130 390 0.25 0.25 1.7320508 1.7320508 1 1 0.023
1000 0.8 0.5 100 3 130 390 0.25 0.25 1.7320508 1.7320508 1 1 0.023
1000 0.65 0.65 100 3 130 390 0.5 0.7 1 0.6546537 0.028 1 0.951
1000 0.65 0.65 100 3 130 390 0.5 0.65 1 0.7337994 0.032 0.961 0.736
1000 0.65 0.65 100 3 130 390 0.5 0.6 1 0.8164966 0.033 0.657 0.369
141
1000 0.5 0.8 100 3 130 390 0.5 0.9 1 0.3333333 0.018 1 1
1000 0.8 0.5 100 3 130 390 0.5 0.9 1 0.3333333 0.029 1 1
1000 0.5 0.8 100 3 130 390 0.5 0.75 1 0.5773503 0.028 1 0.999
1000 0.8 0.5 100 3 130 390 0.5 0.75 1 0.5773503 0.034 1 0.997
1000 0.5 0.8 100 3 130 390 0.5 0.25 1 1.7320508 0.027 1 0.999
1000 0.8 0.5 100 3 130 390 0.5 0.25 1 1.7320508 0.034 1 1
1000 0.5 0.8 100 3 130 390 0.5 0.1 1 3 0.015 1 1
1000 0.8 0.5 100 3 130 390 0.5 0.1 1 3 0.024 1 1
1000 0.5 0.8 100 3 130 390 0.5 0.75 1 0.5773503 0.027 1 0.999
1000 0.8 0.5 100 3 130 390 0.5 0.75 1 0.5773503 0.035 1 0.996
1000 0.5 0.8 100 3 130 390 0.5 0.25 1 1.7320508 0.024 1 0.999
1000 0.8 0.5 100 3 130 390 0.5 0.25 1 1.7320508 0.036 1 1
1000 0.5 0.8 100 3 130 390 0.5 0.5 1 1 0.029 0.034 0.027
1000 0.8 0.5 100 3 130 390 0.5 0.5 1 1 0.037 0.037 0.029
1000 0.8 0.8 50 5 80 400 0.5 0.65 1 0.7337994 0.026 0.994 0.868
1000 0.8 0.8 50 5 80 400 0.5 0.6 1 0.8164966 0.03 0.808 0.502
1000 0.8 0.8 50 5 80 400 0.5 0.55 1 0.904534 0.031 0.249 0.131
1000 0.8 0.8 50 5 80 400 0.5 0.5 1 1 0.033 0.032 0.037
10000 0.8 0.8 50 5 80 400 0.5 0.65 1 0.7337994 0.0341 0.992 0.864
10000 0.8 0.8 50 5 80 400 0.5 0.6 1 0.8164966 0.0332 0.8156 0.4978
10000 0.8 0.8 50 5 80 400 0.5 0.55 1 0.904534 0.0347 0.269 0.1462
10000 0.8 0.8 50 5 80 400 0.5 0.5 1 1 0.0334 0.0347 0.0336
1000 0.7 0.7 100 3 140 420 0.5 0.7 1 0.6546537 0.028 0.999 0.954
1000 0.7 0.7 100 3 140 420 0.5 0.65 1 0.7337994 0.036 0.965 0.759
1000 0.7 0.7 100 3 140 420 0.5 0.6 1 0.8164966 0.037 0.715 0.386
1000 0.8 0.8 90 3 144 432 0.75 0.75 0.5773503 0.5773503 1 1 0.021
1000 0.8 0.8 90 3 144 432 0.7 0.7 0.6546537 0.6546537 1 1 0.023
1000 0.8 0.8 90 3 144 432 0.65 0.65 0.7337994 0.7337994 0.967 0.967 0.03
1000 0.8 0.8 90 3 144 432 0.6 0.6 0.8164966 0.8164966 0.676 0.689 0.028
1000 0.8 0.8 90 3 144 432 0.55 0.55 0.904534 0.904534 0.199 0.207 0.031
1000 0.8 0.8 90 3 144 432 0.45 0.45 1.1055416 1.1055416 0.241 0.209 0.026
1000 0.8 0.8 90 3 144 432 0.4 0.4 1.2247449 1.2247449 0.71 0.679 0.024
142
1000 0.8 0.8 90 3 144 432 0.35 0.35 1.3627703 1.3627703 0.964 0.968 0.026
1000 0.8 0.8 90 3 144 432 0.3 0.3 1.5275252 1.5275252 1 1 0.027
1000 0.8 0.8 90 3 144 432 0.25 0.25 1.7320508 1.7320508 1 1 0.027
1000 0.8 0.8 90 3 144 432 0.5 0.75 1 0.5773503 0.032 1 0.997
1000 0.8 0.8 90 3 144 432 0.5 0.7 1 0.6546537 0.034 1 0.957
1000 0.8 0.8 90 3 144 432 0.5 0.65 1 0.7337994 0.031 0.962 0.737
1000 0.8 0.8 90 3 144 432 0.5 0.6 1 0.8164966 0.032 0.686 0.378
1000 0.8 0.8 90 3 144 432 0.5 0.55 1 0.904534 0.033 0.2 0.12
1000 0.8 0.8 90 3 144 432 0.5 0.45 1 1.1055416 0.034 0.25 0.12
1000 0.8 0.8 90 3 144 432 0.5 0.4 1 1.2247449 0.031 0.718 0.416
1000 0.8 0.8 90 3 144 432 0.5 0.35 1 1.3627703 0.033 0.969 0.751
1000 0.8 0.8 90 3 144 432 0.5 0.3 1 1.5275252 0.028 1 0.956
1000 0.8 0.8 90 3 144 432 0.5 0.25 1 1.7320508 0.031 1 0.996
1000 0.8 0.8 90 3 144 432 0.5 0.5 1 1 0.033 0.037 0.03
1000 0.75 0.75 100 3 150 450 0.5 0.7 1 0.6546537 0.031 0.999 0.965
1000 0.75 0.75 100 3 150 450 0.5 0.65 1 0.7337994 0.031 0.974 0.752
1000 0.75 0.75 100 3 150 450 0.5 0.6 1 0.8164966 0.031 0.689 0.404
500 0.8 0.8 100 3 160 480 0.5 0.7 1 0.6546537 0.032 1 0.968
500 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.034 0.982 0.806
500 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.034 0.692 0.43
1000 0.8 0.8 100 3 160 480 0.9 0.9 0.3333333 0.3333333 1 1 0.011
1000 0.8 0.8 100 3 160 480 0.75 0.75 0.5773503 0.5773503 1 1 0.017
1000 0.8 0.8 100 3 160 480 0.25 0.25 1.7320508 1.7320508 1 1 0.029
1000 0.8 0.8 100 3 160 480 0.1 0.1 3 3 1 1 0.008
1000 0.8 0.8 100 3 160 480 0.7 0.7 0.6546537 0.6546537 0.999 1 0.024
1000 0.8 0.8 100 3 160 480 0.65 0.65 0.7337994 0.7337994 0.97 0.973 0.025
1000 0.8 0.8 100 3 160 480 0.6 0.6 0.8164966 0.8164966 0.707 0.681 0.038
1000 0.8 0.8 100 3 160 480 0.55 0.55 0.904534 0.904534 0.19 0.213 0.03
1000 0.8 0.8 100 3 160 480 0.45 0.45 1.1055416 1.1055416 0.202 0.19 0.019
1000 0.8 0.8 100 3 160 480 0.4 0.4 1.2247449 1.2247449 0.668 0.692 0.038
1000 0.8 0.8 100 3 160 480 0.35 0.35 1.3627703 1.3627703 0.971 0.976 0.033
1000 0.8 0.8 100 3 160 480 0.3 0.3 1.5275252 1.5275252 1 1 0.016
143
1000 0.8 0.8 100 3 160 480 0.75 0.75 0.5773503 0.5773503 1 1 0.015
1000 0.8 0.8 100 3 160 480 0.25 0.25 1.7320508 1.7320508 1 1 0.033
1000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.029 0.967 0.779
1000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.033 0.707 0.391
1000 0.8 0.8 100 3 160 480 0.5 0.55 1 0.904534 0.034 0.196 0.118
1000 0.8 0.8 100 3 160 480 0.5 0.7 1 0.6546537 0.029 1 0.973
1000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.023 0.972 0.758
1000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.028 0.68 0.379
1000 0.8 0.8 100 3 160 480 0.5 0.7 1 0.6546537 0.031 1 0.97
1000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.026 0.976 0.765
1000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.03 0.682 0.386
1000 0.8 0.8 100 3 160 480 0.5 0.9 1 0.3333333 0.025 1 1
1000 0.8 0.8 100 3 160 480 0.5 0.75 1 0.5773503 0.032 1 1
1000 0.8 0.8 100 3 160 480 0.5 0.25 1 1.7320508 0.032 1 0.998
1000 0.8 0.8 100 3 160 480 0.5 0.1 1 3 0.027 1 1
1000 0.8 0.8 100 3 160 480 0.5 0.75 1 0.5773503 0.033 1 1
1000 0.8 0.8 100 3 160 480 0.5 0.7 1 0.6546537 0.035 0.999 0.965
1000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.038 0.969 0.739
1000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.038 0.707 0.411
1000 0.8 0.8 100 3 160 480 0.5 0.55 1 0.904534 0.039 0.194 0.11
1000 0.8 0.8 100 3 160 480 0.5 0.45 1 1.1055416 0.04 0.202 0.12
1000 0.8 0.8 100 3 160 480 0.5 0.4 1 1.2247449 0.036 0.667 0.372
1000 0.8 0.8 100 3 160 480 0.5 0.35 1 1.3627703 0.04 0.975 0.792
1000 0.8 0.8 100 3 160 480 0.5 0.3 1 1.5275252 0.036 1 0.97
1000 0.8 0.8 100 3 160 480 0.5 0.25 1 1.7320508 0.032 1 0.998
1000 0.8 0.8 100 3 160 480 0.5 0.5 1 1 0.037 0.031 0.039
1000 0.8 0.8 100 3 160 480 0.5 0.5 1 1 0.035 0.033 0.023
2000 0.8 0.8 100 3 160 480 0.5 0.7 1 0.6546537 0.029 1 0.9625
2000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.033 0.966 0.767
2000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.0295 0.708 0.4
4000 0.8 0.8 100 3 160 480 0.5 0.7 1 0.6546537 0.034 1 0.966
4000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.0305 0.973 0.7635
144
4000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.03275 0.70175 0.39675
5000 0.8 0.8 100 3 160 480 0.5 0.7 1 0.6546537 0.0348 0.9996 0.964
5000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.034 0.9748 0.7796
5000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.0338 0.696 0.4018
8000 0.8 0.8 100 3 160 480 0.5 0.7 1 0.6546537 0.03275 0.999375 0.96425
8000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.033875 0.97525 0.77913
8000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.033625 0.6985 0.40125
10000 0.8 0.8 100 3 160 480 0.5 0.7 1 0.6546537 0.0298 0.9998 0.9638
10000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.0304 0.9729 0.773
10000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.0294 0.7095 0.4063
10000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.0277 0.9714 0.7718
10000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.0296 0.7092 0.4016
10000 0.8 0.8 100 3 160 480 0.5 0.55 1 0.904534 0.0305 0.2039 0.1115
10000 0.8 0.8 100 3 160 480 0.5 0.65 1 0.7337994 0.0288 0.9741 0.7704
10000 0.8 0.8 100 3 160 480 0.5 0.6 1 0.8164966 0.0309 0.7044 0.4005
10000 0.8 0.8 100 3 160 480 0.5 0.55 1 0.904534 0.0308 0.2147 0.1124
10000 0.8 0.8 100 3 160 480 0.5 0.5 1 1 0.0314 0.0311 0.0321
10000 0.8 0.8 100 3 160 480 0.5 0.5 1 1 0.0324 0.0325 0.0306
1000 0.8 0.8 75 4 120 480 0.5 0.65 1 0.7337994 0.042 0.99 0.87
1000 0.8 0.8 75 4 120 480 0.5 0.6 1 0.8164966 0.043 0.789 0.493
1000 0.8 0.8 75 4 120 480 0.5 0.55 1 0.904534 0.036 0.243 0.161
1000 0.8 0.8 75 4 120 480 0.5 0.5 1 1 0.038 0.038 0.036
10000 0.8 0.8 75 4 120 480 0.5 0.65 1 0.7337994 0.034 0.9919 0.855
10000 0.8 0.8 75 4 120 480 0.5 0.6 1 0.8164966 0.0341 0.7962 0.4893
10000 0.8 0.8 75 4 120 480 0.5 0.5 1 1 0.0346 0.0353 0.0356
1000 0.8 0.8 60 5 96 480 0.5 0.65 1 0.7337994 0.036 0.998 0.903
1000 0.8 0.8 60 5 96 480 0.5 0.6 1 0.8164966 0.03 0.859 0.563
1000 0.8 0.8 60 5 96 480 0.5 0.55 1 0.904534 0.033 0.319 0.195
1000 0.8 0.8 60 5 96 480 0.5 0.5 1 1 0.033 0.046 0.032
10000 0.8 0.8 60 5 96 480 0.5 0.65 1 0.7337994 0.0342 0.9962 0.9111
10000 0.8 0.8 60 5 96 480 0.5 0.6 1 0.8164966 0.0338 0.8534 0.5545
10000 0.8 0.8 60 5 96 480 0.5 0.5 1 1 0.0333 0.0378 0.0374
145
1000 0.8 0.8 50 6 80 480 0.5 0.65 1 0.7337994 0.034 0.998 0.939
1000 0.8 0.8 50 6 80 480 0.5 0.6 1 0.8164966 0.038 0.887 0.6
1000 0.8 0.8 50 6 80 480 0.5 0.55 1 0.904534 0.039 0.321 0.187
1000 0.8 0.8 50 6 80 480 0.5 0.5 1 1 0.035 0.04 0.044
10000 0.8 0.8 50 6 80 480 0.5 0.65 1 0.7337994 0.0428 0.9984 0.9313
10000 0.8 0.8 50 6 80 480 0.5 0.6 1 0.8164966 0.0447 0.8904 0.6029
10000 0.8 0.8 50 6 80 480 0.5 0.65 1 0.7337994 0.0414 0.9983 0.9307
10000 0.8 0.8 50 6 80 480 0.5 0.6 1 0.8164966 0.0423 0.8903 0.6133
10000 0.8 0.8 50 6 80 480 0.5 0.5 1 1 0.0423 0.0388 0.0403
10000 0.8 0.8 50 6 80 480 0.5 0.5 1 1 0.0431 0.0379 0.0376
10000 0.8 0.8 37.5 8 60 480 0.5 0.65 1 0.7337994 0.0411 0.9999 0.9578
10000 0.8 0.8 37.5 8 60 480 0.5 0.6 1 0.8164966 0.0419 0.9228 0.6625
10000 0.8 0.8 37.5 8 60 480 0.5 0.5 1 1 0.0404 0.0429 0.0403
1000 0.8 0.8 38 8 60 480 0.5 0.65 1 0.7337994 0.041 1 0.955
1000 0.8 0.8 38 8 60 480 0.5 0.6 1 0.8164966 0.047 0.93 0.673
1000 0.8 0.8 38 8 60 480 0.5 0.55 1 0.904534 0.04 0.382 0.196
1000 0.8 0.8 38 8 60 480 0.5 0.5 1 1 0.047 0.034 0.042
1000 0.8 0.8 25 12 40 480 0.5 0.65 1 0.7337994 0.038 1 0.978
1000 0.8 0.8 25 12 40 480 0.5 0.6 1 0.8164966 0.037 0.959 0.747
1000 0.8 0.8 25 12 40 480 0.5 0.55 1 0.904534 0.036 0.422 0.241
1000 0.8 0.8 25 12 40 480 0.5 0.5 1 1 0.036 0.046 0.045
10000 0.8 0.8 25 12 40 480 0.5 0.65 1 0.7337994 0.0451 0.9999 0.9748
10000 0.8 0.8 25 12 40 480 0.5 0.6 1 0.8164966 0.0462 0.9537 0.7257
10000 0.8 0.8 25 12 40 480 0.5 0.65 1 0.7337994 0.0457 0.9999 0.9784
10000 0.8 0.8 25 12 40 480 0.5 0.6 1 0.8164966 0.0439 0.9536 0.7289
10000 0.8 0.8 25 12 40 480 0.5 0.5 1 1 0.0454 0.0466 0.0458
10000 0.8 0.8 25 12 40 480 0.5 0.5 1 1 0.0449 0.0422 0.0423
1000 0.2 0.2 500 3 200 600 0.9 0.9 0.3333333 0.3333333 1 1 0.01
1000 0.2 0.2 500 3 200 600 0.75 0.75 0.5773503 0.5773503 1 1 0.032
1000 0.2 0.2 500 3 200 600 0.25 0.25 1.7320508 1.7320508 1 1 0.027
1000 0.2 0.2 500 3 200 600 0.1 0.1 3 3 1 1 0.02
1000 0.2 0.2 500 3 200 600 0.5 0.9 1 0.3333333 0.028 1 1
146
1000 0.2 0.2 500 3 200 600 0.5 0.75 1 0.5773503 0.029 1 0.999
1000 0.2 0.2 500 3 200 600 0.5 0.25 1 1.7320508 0.039 1 0.998
1000 0.2 0.2 500 3 200 600 0.5 0.1 1 3 0.025 1 1
1000 0.2 0.2 500 3 200 600 0.5 0.7 1 0.6546537 0.033 1 0.978
1000 0.2 0.2 500 3 200 600 0.5 0.65 1 0.7337994 0.032 0.985 0.819
1000 0.2 0.2 500 3 200 600 0.5 0.6 1 0.8164966 0.038 0.746 0.444
1000 0.2 0.2 500 3 200 600 0.5 0.55 1 0.904534 0.038 0.273 0.143
1000 0.2 0.2 500 3 200 600 0.5 0.5 1 1 0.036 0.036 0.041
1000 0.8 0.8 100 4 160 640 0.5 0.65 1 0.7337994 0.039 0.996 0.899
1000 0.8 0.8 100 4 160 640 0.5 0.6 1 0.8164966 0.043 0.827 0.537
1000 0.8 0.8 100 4 160 640 0.5 0.55 1 0.904534 0.044 0.274 0.16
1000 0.8 0.8 100 4 160 640 0.5 0.5 1 1 0.04 0.041 0.028
10000 0.8 0.8 100 4 160 640 0.5 0.65 1 0.7337994 0.0374 0.9965 0.8986
10000 0.8 0.8 100 4 160 640 0.5 0.6 1 0.8164966 0.0381 0.8465 0.547
10000 0.8 0.8 100 4 160 640 0.5 0.55 1 0.904534 0.0371 0.2961 0.1661
10000 0.8 0.8 100 4 160 640 0.5 0.5 1 1 0.0381 0.0364 0.0359
1000 0.8 0.8 50 8 80 640 0.5 0.65 1 0.7337994 0.057 1 0.984
1000 0.8 0.8 50 8 80 640 0.5 0.6 1 0.8164966 0.055 0.963 0.72
1000 0.8 0.8 50 8 80 640 0.5 0.55 1 0.904534 0.056 0.427 0.247
1000 0.8 0.8 50 8 80 640 0.5 0.5 1 1 0.056 0.058 0.054
10000 0.8 0.8 50 8 80 640 0.5 0.65 1 0.7337994 0.0406 0.9999 0.9807
10000 0.8 0.8 50 8 80 640 0.5 0.6 1 0.8164966 0.0421 0.9631 0.7434
10000 0.8 0.8 50 8 80 640 0.5 0.55 1 0.904534 0.0404 0.4467 0.2429
10000 0.8 0.8 50 8 80 640 0.5 0.5 1 1 0.0402 0.0417 0.0445
1000 0.25 0.25 500 3 250 750 0.5 0.7 1 0.6546537 0.037 1 0.981
1000 0.25 0.25 500 3 250 750 0.5 0.65 1 0.7337994 0.035 0.985 0.84
1000 0.25 0.25 500 3 250 750 0.5 0.6 1 0.8164966 0.039 0.781 0.512
1000 0.25 0.25 500 3 250 750 0.5 0.55 1 0.904534 0.039 0.254 0.152
1000 0.8 0.8 100 5 160 800 0.5 0.65 1 0.7337994 0.051 0.999 0.952
1000 0.8 0.8 100 5 160 800 0.5 0.6 1 0.8164966 0.046 0.938 0.667
1000 0.8 0.8 100 5 160 800 0.5 0.55 1 0.904534 0.048 0.381 0.211
1000 0.8 0.8 100 5 160 800 0.5 0.5 1 1 0.053 0.047 0.038
147
10000 0.8 0.8 100 5 160 800 0.5 0.65 1 0.7337994 0.0464 0.9994 0.9596
10000 0.8 0.8 100 5 160 800 0.5 0.6 1 0.8164966 0.0439 0.9255 0.6731
10000 0.8 0.8 100 5 160 800 0.5 0.55 1 0.904534 0.0433 0.384 0.2127
10000 0.8 0.8 100 5 160 800 0.5 0.5 1 1 0.0445 0.0425 0.0425
1000 0.3 0.3 500 3 300 900 0.5 0.7 1 0.6546537 0.036 1 0.99
1000 0.3 0.3 500 3 300 900 0.5 0.65 1 0.7337994 0.038 0.993 0.856
1000 0.3 0.3 500 3 300 900 0.5 0.6 1 0.8164966 0.038 0.804 0.486
1000 0.3 0.3 500 3 300 900 0.5 0.55 1 0.904534 0.037 0.263 0.138
1000 0.8 0.8 200 3 320 960 0.5 0.65 1 0.7337994 0.029 0.998 0.901
1000 0.8 0.8 200 3 320 960 0.5 0.6 1 0.8164966 0.035 0.831 0.498
1000 0.8 0.8 200 3 320 960 0.5 0.55 1 0.904534 0.032 0.256 0.137
1000 0.8 0.8 200 3 320 960 0.5 0.65 1 0.7337994 0.031 0.992 0.869
1000 0.8 0.8 200 3 320 960 0.5 0.6 1 0.8164966 0.032 0.804 0.493
1000 0.8 0.8 200 3 320 960 0.5 0.55 1 0.904534 0.03 0.269 0.147
1000 0.8 0.8 200 3 320 960 0.5 0.5 1 1 0.034 0.038 0.034
1000 0.8 0.8 200 3 320 960 0.5 0.5 1 1 0.035 0.03 0.031
10000 0.8 0.8 200 3 320 960 0.5 0.65 1 0.7337994 0.0393 0.9924 0.8582
10000 0.8 0.8 200 3 320 960 0.5 0.6 1 0.8164966 0.0395 0.8095 0.4956
10000 0.8 0.8 200 3 320 960 0.5 0.65 1 0.7337994 0.0339 0.993 0.8671
10000 0.8 0.8 200 3 320 960 0.5 0.6 1 0.8164966 0.0349 0.809 0.506
10000 0.8 0.8 200 3 320 960 0.5 0.5 1 1 0.0418 0.0368 0.0388
10000 0.8 0.8 200 3 320 960 0.5 0.5 1 1 0.0351 0.0414 0.0402
1000 0.8 0.8 150 4 240 960 0.5 0.65 1 0.7337994 0.041 0.999 0.931
1000 0.8 0.8 150 4 240 960 0.5 0.6 1 0.8164966 0.047 0.883 0.595
1000 0.8 0.8 150 4 240 960 0.5 0.55 1 0.904534 0.046 0.352 0.202
1000 0.8 0.8 150 4 240 960 0.5 0.5 1 1 0.042 0.05 0.04
10000 0.8 0.8 150 4 240 960 0.5 0.65 1 0.7337994 0.0449 0.9987 0.9322
10000 0.8 0.8 150 4 240 960 0.5 0.6 1 0.8164966 0.0442 0.9015 0.616
10000 0.8 0.8 150 4 240 960 0.5 0.5 1 1 0.0436 0.0398 0.0423
1000 0.8 0.8 120 5 192 960 0.5 0.65 1 0.7337994 0.038 1 0.971
1000 0.8 0.8 120 5 192 960 0.5 0.6 1 0.8164966 0.042 0.952 0.712
1000 0.8 0.8 120 5 192 960 0.5 0.55 1 0.904534 0.038 0.427 0.216
148
1000 0.8 0.8 120 5 192 960 0.5 0.5 1 1 0.037 0.037 0.043
10000 0.8 0.8 120 5 192 960 0.5 0.65 1 0.7337994 0.0421 0.9996 0.9676
10000 0.8 0.8 120 5 192 960 0.5 0.6 1 0.8164966 0.0415 0.9447 0.7078
10000 0.8 0.8 120 5 192 960 0.5 0.55 1 0.904534 0.0448 0.4113 0.232
10000 0.8 0.8 120 5 192 960 0.5 0.5 1 1 0.0428 0.0462 0.0438
1000 0.8 0.8 100 6 160 960 0.5 0.65 1 0.7337994 0.047 1 0.98
1000 0.8 0.8 100 6 160 960 0.5 0.6 1 0.8164966 0.05 0.958 0.721
1000 0.8 0.8 100 6 160 960 0.5 0.55 1 0.904534 0.045 0.458 0.243
1000 0.8 0.8 100 6 160 960 0.5 0.5 1 1 0.045 0.044 0.039
10000 0.8 0.8 100 6 160 960 0.5 0.65 1 0.7337994 0.041 1 0.9824
10000 0.8 0.8 100 6 160 960 0.5 0.6 1 0.8164966 0.0443 0.9652 0.7577
10000 0.8 0.8 100 6 160 960 0.5 0.55 1 0.904534 0.042 0.4612 0.254
10000 0.8 0.8 100 6 160 960 0.5 0.65 1 0.7337994 0.0463 0.9999 0.9815
10000 0.8 0.8 100 6 160 960 0.5 0.6 1 0.8164966 0.0457 0.9628 0.7486
10000 0.8 0.8 100 6 160 960 0.5 0.55 1 0.904534 0.0475 0.4579 0.2486
10000 0.8 0.8 100 6 160 960 0.5 0.5 1 1 0.0409 0.0465 0.0448
10000 0.8 0.8 100 6 160 960 0.5 0.5 1 1 0.0459 0.0445 0.0448
1000 0.8 0.8 75 8 120 960 0.5 0.65 1 0.7337994 0.043 1 0.996
1000 0.8 0.8 75 8 120 960 0.5 0.6 1 0.8164966 0.045 0.987 0.839
1000 0.8 0.8 75 8 120 960 0.5 0.55 1 0.904534 0.042 0.568 0.317
1000 0.8 0.8 75 8 120 960 0.5 0.5 1 1 0.045 0.046 0.046
10000 0.8 0.8 75 8 120 960 0.5 0.65 1 0.7337994 0.047 1 0.9937
10000 0.8 0.8 75 8 120 960 0.5 0.6 1 0.8164966 0.0481 0.9881 0.8323
10000 0.8 0.8 75 8 120 960 0.5 0.5 1 1 0.0486 0.0471 0.0469
1000 0.8 0.8 50 12 80 960 0.5 0.65 1 0.7337994 0.04 1 0.999
1000 0.8 0.8 50 12 80 960 0.5 0.6 1 0.8164966 0.039 0.998 0.915
1000 0.8 0.8 50 12 80 960 0.5 0.55 1 0.904534 0.038 0.63 0.363
1000 0.8 0.8 50 12 80 960 0.5 0.5 1 1 0.037 0.041 0.049
10000 0.8 0.8 50 12 80 960 0.5 0.65 1 0.7337994 0.0499 1 0.9989
10000 0.8 0.8 50 12 80 960 0.5 0.6 1 0.8164966 0.0499 0.9946 0.9032
10000 0.8 0.8 50 12 80 960 0.5 0.65 1 0.7337994 0.0468 1 0.9988
10000 0.8 0.8 50 12 80 960 0.5 0.6 1 0.8164966 0.0471 0.9966 0.9036
149
10000 0.8 0.8 50 12 80 960 0.5 0.5 1 1 0.0522 0.0492 0.0533
10000 0.8 0.8 50 12 80 960 0.5 0.5 1 1 0.0472 0.0507 0.0505
1000 0.35 0.35 500 3 350 1050 0.5 0.7 1 0.6546537 0.048 1 0.986
1000 0.35 0.35 500 3 350 1050 0.5 0.65 1 0.7337994 0.046 0.994 0.869
1000 0.35 0.35 500 3 350 1050 0.5 0.6 1 0.8164966 0.048 0.801 0.498
1000 0.35 0.35 500 3 350 1050 0.5 0.55 1 0.904534 0.044 0.289 0.167
1000 0.8 0.8 250 3 400 1200 0.5 0.55 1 0.904534 0.033 0.28 0.152
1000 0.8 0.8 250 3 400 1200 0.5 0.5 1 1 0.03 0.037 0.049
1000 0.4 0.4 500 3 400 1200 0.5 0.7 1 0.6546537 0.035 1 0.992
1000 0.4 0.4 500 3 400 1200 0.5 0.65 1 0.7337994 0.034 0.998 0.895
1000 0.4 0.4 500 3 400 1200 0.5 0.6 1 0.8164966 0.036 0.825 0.537
1000 0.4 0.4 500 3 400 1200 0.5 0.55 1 0.904534 0.033 0.263 0.142
1000 0.2 0.2 1000 3 400 1200 0.9 0.9 0.3333333 0.3333333 1 1 0.024
1000 0.2 0.2 1000 3 400 1200 0.75 0.75 0.5773503 0.5773503 1 1 0.038
1000 0.2 0.2 1000 3 400 1200 0.25 0.25 1.7320508 1.7320508 1 1 0.037
1000 0.2 0.2 1000 3 400 1200 0.1 0.1 3 3 1 1 0.012
1000 0.2 0.2 1000 3 400 1200 0.5 0.9 1 0.3333333 0.031 1 1
1000 0.2 0.2 1000 3 400 1200 0.5 0.75 1 0.5773503 0.038 1 1
1000 0.2 0.2 1000 3 400 1200 0.5 0.25 1 1.7320508 0.038 1 1
1000 0.2 0.2 1000 3 400 1200 0.5 0.1 1 3 0.027 1 1
1000 0.2 0.2 1000 3 400 1200 0.5 0.7 1 0.6546537 0.041 1 0.99
1000 0.2 0.2 1000 3 400 1200 0.5 0.65 1 0.7337994 0.04 0.997 0.897
1000 0.2 0.2 1000 3 400 1200 0.5 0.6 1 0.8164966 0.042 0.829 0.52
1000 0.2 0.2 1000 3 400 1200 0.5 0.5 1 1 0.04 0.037 0.045
1000 0.8 0.8 187.5 4 300 1200 0.5 0.55 1 0.904534 0.034 0.353 0.183
1000 0.8 0.8 187.5 4 300 1200 0.5 0.5 1 1 0.041 0.03 0.024
1000 0.8 0.8 150 5 240 1200 0.5 0.55 1 0.904534 0.044 0.455 0.233
1000 0.8 0.8 150 5 240 1200 0.5 0.5 1 1 0.049 0.04 0.034
1000 0.8 0.8 125 6 200 1200 0.5 0.55 1 0.904534 0.034 0.484 0.276
1000 0.8 0.8 125 6 200 1200 0.5 0.5 1 1 0.035 0.048 0.047
1000 0.8 0.8 93.75 8 150 1200 0.5 0.55 1 0.904534 0.049 0.561 0.333
1000 0.8 0.8 93.75 8 150 1200 0.5 0.5 1 1 0.053 0.042 0.048
150
1000 0.8 0.8 62.5 12 100 1200 0.5 0.55 1 0.904534 0.064 0.718 0.434
1000 0.8 0.8 62.5 12 100 1200 0.5 0.5 1 1 0.066 0.04 0.043
1000 0.8 0.8 200 4 320 1280 0.5 0.65 1 0.7337994 0.042 1 0.951
1000 0.8 0.8 200 4 320 1280 0.5 0.6 1 0.8164966 0.042 0.923 0.644
1000 0.8 0.8 200 4 320 1280 0.5 0.55 1 0.904534 0.038 0.358 0.189
1000 0.8 0.8 200 4 320 1280 0.5 0.5 1 1 0.044 0.047 0.05
10000 0.8 0.8 200 4 320 1280 0.5 0.65 1 0.7337994 0.0422 0.9994 0.9516
10000 0.8 0.8 200 4 320 1280 0.5 0.6 1 0.8164966 0.0425 0.9217 0.6618
10000 0.8 0.8 200 4 320 1280 0.5 0.55 1 0.904534 0.0424 0.3742 0.2034
10000 0.8 0.8 200 4 320 1280 0.5 0.5 1 1 0.0437 0.043 0.0463
1000 0.8 0.8 100 8 160 1280 0.5 0.65 1 0.7337994 0.047 1 0.997
1000 0.8 0.8 100 8 160 1280 0.5 0.6 1 0.8164966 0.055 0.996 0.877
1000 0.8 0.8 100 8 160 1280 0.5 0.55 1 0.904534 0.051 0.598 0.347
1000 0.8 0.8 100 8 160 1280 0.5 0.5 1 1 0.05 0.042 0.051
10000 0.8 0.8 100 8 160 1280 0.5 0.65 1 0.7337994 0.0531 1 0.9985
10000 0.8 0.8 100 8 160 1280 0.5 0.6 1 0.8164966 0.051 0.9928 0.8842
10000 0.8 0.8 100 8 160 1280 0.5 0.55 1 0.904534 0.0512 0.5945 0.3483
10000 0.8 0.8 100 8 160 1280 0.5 0.5 1 1 0.0519 0.0495 0.0501
1000 0.45 0.45 500 3 450 1350 0.5 0.7 1 0.6546537 0.042 1 0.989
1000 0.45 0.45 500 3 450 1350 0.5 0.65 1 0.7337994 0.047 0.993 0.891
1000 0.45 0.45 500 3 450 1350 0.5 0.6 1 0.8164966 0.046 0.84 0.517
1000 0.45 0.45 500 3 450 1350 0.5 0.55 1 0.904534 0.042 0.254 0.135
1000 0.5 0.5 500 3 500 1500 0.9 0.9 0.3333333 0.3333333 1 1 0.018
1000 0.5 0.5 500 3 500 1500 0.75 0.75 0.5773503 0.5773503 1 1 0.035
1000 0.5 0.5 500 3 500 1500 0.25 0.25 1.7320508 1.7320508 1 1 0.028
1000 0.5 0.5 500 3 500 1500 0.1 0.1 3 3 1 1 0.017
1000 0.5 0.5 500 3 500 1500 0.5 0.9 1 0.3333333 0.017 1 1
1000 0.5 0.5 500 3 500 1500 0.5 0.75 1 0.5773503 0.025 1 0.999
1000 0.5 0.5 500 3 500 1500 0.5 0.25 1 1.7320508 0.023 1 1
1000 0.5 0.5 500 3 500 1500 0.5 0.1 1 3 0.014 1 1
1000 0.5 0.5 500 3 500 1500 0.5 0.7 1 0.6546537 0.043 1 0.992
1000 0.5 0.5 500 3 500 1500 0.5 0.65 1 0.7337994 0.049 0.994 0.906
151
1000 0.5 0.5 500 3 500 1500 0.5 0.6 1 0.8164966 0.044 0.844 0.519
1000 0.5 0.5 500 3 500 1500 0.5 0.55 1 0.904534 0.039 0.306 0.168
1000 0.5 0.5 500 3 500 1500 0.5 0.5 1 1 0.023 0.043 0.04
1000 0.25 0.25 1000 3 500 1500 0.5 0.7 1 0.6546537 0.045 1 0.992
1000 0.25 0.25 1000 3 500 1500 0.5 0.65 1 0.7337994 0.041 0.995 0.883
1000 0.25 0.25 1000 3 500 1500 0.5 0.6 1 0.8164966 0.045 0.837 0.524
1000 0.8 0.8 333.3333333 3 533.33333 1600 0.5 0.55 1 0.904534 0.028 0.309 0.171
1000 0.8 0.8 333.3333333 3 533.33333 1600 0.5 0.5 1 1 0.035 0.043 0.044
1000 0.8 0.8 83.33333333 12 133.33333 1600 0.5 0.55 1 0.904534 0.046 0.776 0.471
1000 0.8 0.8 83.33333333 12 133.33333 1600 0.5 0.5 1 1 0.047 0.054 0.049
1000 0.8 0.8 250 4 400 1600 0.5 0.55 1 0.904534 0.049 0.374 0.192
1000 0.8 0.8 250 4 400 1600 0.5 0.5 1 1 0.046 0.037 0.037
1000 0.8 0.8 200 5 320 1600 0.5 0.55 1 0.904534 0.042 0.457 0.258
1000 0.8 0.8 200 5 320 1600 0.5 0.65 1 0.7337994 0.04 1 0.984
1000 0.8 0.8 200 5 320 1600 0.5 0.6 1 0.8164966 0.039 0.961 0.768
1000 0.8 0.8 200 5 320 1600 0.5 0.55 1 0.904534 0.04 0.448 0.27
1000 0.8 0.8 200 5 320 1600 0.5 0.5 1 1 0.043 0.042 0.042
1000 0.8 0.8 200 5 320 1600 0.5 0.5 1 1 0.037 0.042 0.05
10000 0.8 0.8 200 5 320 1600 0.5 0.65 1 0.7337994 0.0505 0.9999 0.9846
10000 0.8 0.8 200 5 320 1600 0.5 0.6 1 0.8164966 0.0517 0.9689 0.7629
10000 0.8 0.8 200 5 320 1600 0.5 0.55 1 0.904534 0.0513 0.4688 0.2661
10000 0.8 0.8 200 5 320 1600 0.5 0.5 1 1 0.0533 0.0452 0.0492
1000 0.8 0.8 125 8 200 1600 0.5 0.55 1 0.904534 0.056 0.63 0.369
1000 0.8 0.8 125 8 200 1600 0.5 0.5 1 1 0.058 0.043 0.049
1000 0.8 0.8 166.6666667 6 266.66667 1600 0.5 0.55 1 0.904534 0.057 0.526 0.311
1000 0.8 0.8 166.6666667 6 266.66667 1600 0.5 0.5 1 1 0.063 0.057 0.059
1000 0.55 0.55 500 3 550 1650 0.5 0.7 1 0.6546537 0.045 1 0.994
1000 0.55 0.55 500 3 550 1650 0.5 0.65 1 0.7337994 0.049 0.994 0.915
1000 0.55 0.55 500 3 550 1650 0.5 0.6 1 0.8164966 0.043 0.853 0.562
1000 0.55 0.55 500 3 550 1650 0.5 0.55 1 0.904534 0.039 0.316 0.177
1000 0.6 0.6 500 3 600 1800 0.5 0.7 1 0.6546537 0.041 1 0.996
1000 0.6 0.6 500 3 600 1800 0.5 0.65 1 0.7337994 0.045 0.996 0.913
152
1000 0.6 0.6 500 3 600 1800 0.5 0.6 1 0.8164966 0.045 0.871 0.574
1000 0.6 0.6 500 3 600 1800 0.5 0.55 1 0.904534 0.045 0.326 0.166
1000 0.3 0.3 1000 3 600 1800 0.5 0.7 1 0.6546537 0.025 1 0.994
1000 0.3 0.3 1000 3 600 1800 0.5 0.65 1 0.7337994 0.028 0.996 0.889
1000 0.3 0.3 1000 3 600 1800 0.5 0.6 1 0.8164966 0.032 0.848 0.541
1000 0.8 0.8 400 3 640 1920 0.5 0.55 1 0.904534 0.033 0.32 0.186
1000 0.8 0.8 400 3 640 1920 0.5 0.65 1 0.7337994 0.038 0.994 0.91
1000 0.8 0.8 400 3 640 1920 0.5 0.6 1 0.8164966 0.045 0.86 0.577
1000 0.8 0.8 400 3 640 1920 0.5 0.55 1 0.904534 0.045 0.32 0.182
1000 0.8 0.8 400 3 640 1920 0.5 0.5 1 1 0.041 0.032 0.042
1000 0.8 0.8 400 3 640 1920 0.5 0.5 1 1 0.032 0.046 0.043
10000 0.8 0.8 400 3 640 1920 0.5 0.5 1 1 0.0419 0.0364 0.0414
1000 0.8 0.8 300 4 480 1920 0.5 0.55 1 0.904534 0.042 0.418 0.222
1000 0.8 0.8 300 4 480 1920 0.5 0.5 1 1 0.048 0.045 0.042
10000 0.8 0.8 300 4 480 1920 0.5 0.5 1 1 0.0474 0.0439 0.0486
1000 0.8 0.8 240 5 384 1920 0.5 0.55 1 0.904534 0.044 0.484 0.287
1000 0.8 0.8 240 5 384 1920 0.5 0.5 1 1 0.052 0.05 0.051
10000 0.8 0.8 240 5 384 1920 0.5 0.5 1 1 0.0479 0.0473 0.0489
1000 0.8 0.8 200 6 320 1920 0.5 0.55 1 0.904534 0.054 0.59 0.356
1000 0.8 0.8 200 6 320 1920 0.5 0.5 1 1 0.046 0.051 0.051
10000 0.8 0.8 200 6 320 1920 0.5 0.65 1 0.7337994 0.0518 1 0.9951
10000 0.8 0.8 200 6 320 1920 0.5 0.6 1 0.8164966 0.0534 0.9887 0.8482
10000 0.8 0.8 200 6 320 1920 0.5 0.5 1 1 0.0529 0.0475 0.0535
10000 0.8 0.8 200 6 320 1920 0.5 0.5 1 1 0.0522 0.0499 0.0501
1000 0.8 0.8 150 8 240 1920 0.5 0.55 1 0.904534 0.05 0.659 0.4
1000 0.8 0.8 150 8 240 1920 0.5 0.5 1 1 0.053 0.065 0.06
10000 0.8 0.8 150 8 240 1920 0.5 0.5 1 1 0.0534 0.0534 0.0535
1000 0.8 0.8 100 12 160 1920 0.5 0.55 1 0.904534 0.056 0.778 0.491
1000 0.8 0.8 100 12 160 1920 0.5 0.65 1 0.7337994 0.059 1 1
1000 0.8 0.8 100 12 160 1920 0.5 0.6 1 0.8164966 0.057 1 0.968
1000 0.8 0.8 100 12 160 1920 0.5 0.5 1 1 0.058 0.052 0.055
10000 0.8 0.8 100 12 160 1920 0.5 0.55 1 0.904534 0.0547 0.7781 0.4988
153
10000 0.8 0.8 100 12 160 1920 0.5 0.55 1 0.904534 0.0535 0.7771 0.4915
10000 0.8 0.8 100 12 160 1920 0.5 0.65 1 0.7337994 0.0554 1 1
10000 0.8 0.8 100 12 160 1920 0.5 0.6 1 0.8164966 0.0543 0.9998 0.9713
10000 0.8 0.8 100 12 160 1920 0.5 0.5 1 1 0.0549 0.0542 0.0568
10000 0.8 0.8 100 12 160 1920 0.5 0.5 1 1 0.055 0.0569 0.0533
1000 0.65 0.65 500 3 650 1950 0.5 0.7 1 0.6546537 0.038 1 0.997
1000 0.65 0.65 500 3 650 1950 0.5 0.65 1 0.7337994 0.035 0.998 0.921
1000 0.65 0.65 500 3 650 1950 0.5 0.6 1 0.8164966 0.036 0.863 0.569
1000 0.65 0.65 500 3 650 1950 0.5 0.55 1 0.904534 0.032 0.3 0.161
1000 0.7 0.7 500 3 700 2100 0.5 0.7 1 0.6546537 0.04 1 0.998
1000 0.7 0.7 500 3 700 2100 0.5 0.65 1 0.7337994 0.042 0.996 0.924
1000 0.7 0.7 500 3 700 2100 0.5 0.6 1 0.8164966 0.04 0.861 0.581
1000 0.7 0.7 500 3 700 2100 0.5 0.55 1 0.904534 0.04 0.297 0.173
1000 0.35 0.35 1000 3 700 2100 0.5 0.7 1 0.6546537 0.042 1 0.995
1000 0.35 0.35 1000 3 700 2100 0.5 0.65 1 0.7337994 0.037 0.994 0.908
1000 0.35 0.35 1000 3 700 2100 0.5 0.6 1 0.8164966 0.041 0.875 0.578
1000 0.75 0.75 500 3 750 2250 0.5 0.7 1 0.6546537 0.033 1 0.995
1000 0.75 0.75 500 3 750 2250 0.5 0.65 1 0.7337994 0.029 0.997 0.899
1000 0.75 0.75 500 3 750 2250 0.5 0.6 1 0.8164966 0.034 0.864 0.573
1000 0.75 0.75 500 3 750 2250 0.5 0.55 1 0.904534 0.035 0.282 0.141
500 0.8 0.8 500 3 800 2400 0.5 0.75 1 0.5773503 0.03 1 1
500 0.8 0.8 500 3 800 2400 0.5 0.7 1 0.6546537 0.04 1 0.998
500 0.8 0.8 500 3 800 2400 0.5 0.65 1 0.7337994 0.048 0.998 0.918
500 0.8 0.8 500 3 800 2400 0.5 0.6 1 0.8164966 0.03 0.886 0.584
500 0.8 0.8 500 3 800 2400 0.5 0.55 1 0.904534 0.034 0.306 0.17
500 0.8 0.8 500 3 800 2400 0.5 0.45 1 1.1055416 0.038 0.322 0.164
500 0.8 0.8 500 3 800 2400 0.5 0.4 1 1.2247449 0.032 0.872 0.558
500 0.8 0.8 500 3 800 2400 0.5 0.35 1 1.3627703 0.034 0.996 0.91
500 0.8 0.8 500 3 800 2400 0.5 0.3 1 1.5275252 0.034 1 0.99
500 0.8 0.8 500 3 800 2400 0.5 0.25 1 1.7320508 0.034 1 1
500 0.8 0.8 500 3 800 2400 0.5 0.5 1 1 0.032 0.05 0.038
500 0.8 0.8 500 3 800 2400 0.55 0.55 0.904534 0.904534 0.3 0.312 0.044
154
500 0.8 0.8 500 3 800 2400 0.6 0.6 0.8164966 0.8164966 0.862 0.856 0.032
500 0.8 0.8 500 3 800 2400 0.65 0.65 0.7337994 0.7337994 0.996 0.99 0.042
1000 0.8 0.8 500 3 800 2400 0.9 0.9 0.3333333 0.3333333 1 1 0.016
1000 0.8 0.8 500 3 800 2400 0.75 0.75 0.5773503 0.5773503 1 1 0.029
1000 0.8 0.8 500 3 800 2400 0.25 0.25 1.7320508 1.7320508 1 1 0.034
1000 0.8 0.8 500 3 800 2400 0.1 0.1 3 3 1 1 0.018
1000 0.8 0.8 500 3 800 2400 0.75 0.75 0.5773503 0.5773503 1 1 0.035
1000 0.8 0.8 500 3 800 2400 0.7 0.7 0.6546537 0.6546537 1 1 0.045
1000 0.8 0.8 500 3 800 2400 0.65 0.65 0.7337994 0.7337994 0.992 0.995 0.036
1000 0.8 0.8 500 3 800 2400 0.6 0.6 0.8164966 0.8164966 0.884 0.884 0.032
1000 0.8 0.8 500 3 800 2400 0.55 0.55 0.904534 0.904534 0.341 0.313 0.038
1000 0.8 0.8 500 3 800 2400 0.45 0.45 1.1055416 1.1055416 0.327 0.336 0.044
1000 0.8 0.8 500 3 800 2400 0.4 0.4 1.2247449 1.2247449 0.854 0.866 0.051
1000 0.8 0.8 500 3 800 2400 0.35 0.35 1.3627703 1.3627703 0.996 0.996 0.035
1000 0.8 0.8 500 3 800 2400 0.3 0.3 1.5275252 1.5275252 1 1 0.044
1000 0.8 0.8 500 3 800 2400 0.25 0.25 1.7320508 1.7320508 1 1 0.037
1000 0.8 0.8 500 3 800 2400 0.5 0.9 1 0.3333333 0.027 1 1
1000 0.8 0.8 500 3 800 2400 0.5 0.75 1 0.5773503 0.039 1 1
1000 0.8 0.8 500 3 800 2400 0.5 0.25 1 1.7320508 0.044 1 1
1000 0.8 0.8 500 3 800 2400 0.5 0.1 1 3 0.029 1 1
1000 0.8 0.8 500 3 800 2400 0.5 0.7 1 0.6546537 0.043 1 0.996
1000 0.8 0.8 500 3 800 2400 0.5 0.65 1 0.7337994 0.049 0.993 0.915
1000 0.8 0.8 500 3 800 2400 0.5 0.6 1 0.8164966 0.044 0.891 0.578
1000 0.8 0.8 500 3 800 2400 0.5 0.55 1 0.904534 0.046 0.312 0.172
1000 0.8 0.8 500 3 800 2400 0.5 0.55 1 0.904534 0.04 0.309 0.179
1000 0.8 0.8 500 3 800 2400 0.5 0.75 1 0.5773503 0.035 1 1
1000 0.8 0.8 500 3 800 2400 0.5 0.7 1 0.6546537 0.038 1 0.992
1000 0.8 0.8 500 3 800 2400 0.5 0.65 1 0.7337994 0.044 0.998 0.908
1000 0.8 0.8 500 3 800 2400 0.5 0.6 1 0.8164966 0.037 0.896 0.593
1000 0.8 0.8 500 3 800 2400 0.5 0.55 1 0.904534 0.038 0.307 0.172
1000 0.8 0.8 500 3 800 2400 0.5 0.45 1 1.1055416 0.034 0.333 0.183
1000 0.8 0.8 500 3 800 2400 0.5 0.4 1 1.2247449 0.036 0.885 0.589
155
1000 0.8 0.8 500 3 800 2400 0.5 0.35 1 1.3627703 0.036 0.999 0.93
1000 0.8 0.8 500 3 800 2400 0.5 0.3 1 1.5275252 0.037 1 0.995
1000 0.8 0.8 500 3 800 2400 0.5 0.25 1 1.7320508 0.038 1 1
1000 0.8 0.8 500 3 800 2400 0.5 0.75 1 0.5773503 0.039 1 1
1000 0.8 0.8 500 3 800 2400 0.5 0.7 1 0.6546537 0.045 1 0.994
1000 0.8 0.8 500 3 800 2400 0.5 0.65 1 0.7337994 0.04 0.995 0.905
1000 0.8 0.8 500 3 800 2400 0.5 0.6 1 0.8164966 0.042 0.886 0.593
1000 0.8 0.8 500 3 800 2400 0.5 0.55 1 0.904534 0.04 0.332 0.183
1000 0.8 0.8 500 3 800 2400 0.5 0.45 1 1.1055416 0.041 0.322 0.179
1000 0.8 0.8 500 3 800 2400 0.5 0.4 1 1.2247449 0.042 0.848 0.585
1000 0.8 0.8 500 3 800 2400 0.5 0.35 1 1.3627703 0.046 0.998 0.912
1000 0.8 0.8 500 3 800 2400 0.5 0.3 1 1.5275252 0.034 1 0.995
1000 0.8 0.8 500 3 800 2400 0.5 0.25 1 1.7320508 0.042 1 1
1000 0.8 0.8 500 3 800 2400 0.5 0.5 1 1 0.049 0.044 0.028
1000 0.8 0.8 500 3 800 2400 0.5 0.5 1 1 0.038 0.03 0.025
1000 0.8 0.8 500 3 800 2400 0.5 0.5 1 1 0.041 0.048 0.042
2000 0.8 0.8 500 3 800 2400 0.5 0.75 1 0.5773503 0.0435 1 1
2000 0.8 0.8 500 3 800 2400 0.5 0.7 1 0.6546537 0.0445 1 0.9975
2000 0.8 0.8 500 3 800 2400 0.5 0.65 1 0.7337994 0.046 0.9955 0.9065
2000 0.8 0.8 500 3 800 2400 0.5 0.6 1 0.8164966 0.0415 0.851 0.567
2000 0.8 0.8 500 3 800 2400 0.5 0.55 1 0.904534 0.046 0.3275 0.1945
2000 0.8 0.8 500 3 800 2400 0.5 0.45 1 1.1055416 0.0445 0.3135 0.167
2000 0.8 0.8 500 3 800 2400 0.5 0.4 1 1.2247449 0.042 0.868 0.5735
2000 0.8 0.8 500 3 800 2400 0.5 0.35 1 1.3627703 0.0435 0.9965 0.9125
2000 0.8 0.8 500 3 800 2400 0.5 0.3 1 1.5275252 0.0425 1 0.995
2000 0.8 0.8 500 3 800 2400 0.5 0.25 1 1.7320508 0.0395 1 1
2000 0.8 0.8 500 3 800 2400 0.5 0.5 1 1 0.0435 0.0445 0.0385
2000 0.8 0.8 500 3 800 2400 0.55 0.55 0.904534 0.904534 0.326 0.318 0.0395
2000 0.8 0.8 500 3 800 2400 0.6 0.6 0.8164966 0.8164966 0.8705 0.868 0.038
2000 0.8 0.8 500 3 800 2400 0.65 0.65 0.7337994 0.7337994 0.9975 0.998 0.037
4000 0.8 0.8 500 3 800 2400 0.5 0.75 1 0.5773503 0.04075 1 1
4000 0.8 0.8 500 3 800 2400 0.5 0.7 1 0.6546537 0.039 1 0.99625
156
4000 0.8 0.8 500 3 800 2400 0.5 0.65 1 0.7337994 0.04175 0.9985 0.91
4000 0.8 0.8 500 3 800 2400 0.5 0.6 1 0.8164966 0.0425 0.86225 0.58225
4000 0.8 0.8 500 3 800 2400 0.5 0.55 1 0.904534 0.04475 0.31 0.16275
4000 0.8 0.8 500 3 800 2400 0.5 0.45 1 1.1055416 0.0435 0.327 0.182
4000 0.8 0.8 500 3 800 2400 0.5 0.4 1 1.2247449 0.04425 0.86325 0.57775
4000 0.8 0.8 500 3 800 2400 0.5 0.35 1 1.3627703 0.04275 0.9965 0.91225
4000 0.8 0.8 500 3 800 2400 0.5 0.3 1 1.5275252 0.0455 1 0.9955
4000 0.8 0.8 500 3 800 2400 0.5 0.25 1 1.7320508 0.041 1 1
4000 0.8 0.8 500 3 800 2400 0.5 0.5 1 1 0.04375 0.03775 0.0355
4000 0.8 0.8 500 3 800 2400 0.65 0.65 0.7337994 0.7337994 0.99675 0.99775 0.03725
4000 0.8 0.8 500 3 800 2400 0.55 0.55 0.904534 0.904534 0.31 0.3005 0.03575
4000 0.8 0.8 500 3 800 2400 0.6 0.6 0.8164966 0.8164966 0.86675 0.86725 0.0345
5000 0.8 0.8 500 3 800 2400 0.5 0.75 1 0.5773503 0.035 1 1
5000 0.8 0.8 500 3 800 2400 0.5 0.7 1 0.6546537 0.0368 1 0.997
5000 0.8 0.8 500 3 800 2400 0.5 0.65 1 0.7337994 0.0402 0.996 0.9136
5000 0.8 0.8 500 3 800 2400 0.5 0.6 1 0.8164966 0.0406 0.8768 0.5686
5000 0.8 0.8 500 3 800 2400 0.5 0.55 1 0.904534 0.042 0.311 0.17
5000 0.8 0.8 500 3 800 2400 0.5 0.45 1 1.1055416 0.039 0.3222 0.1784
5000 0.8 0.8 500 3 800 2400 0.5 0.4 1 1.2247449 0.0412 0.8702 0.58
5000 0.8 0.8 500 3 800 2400 0.5 0.35 1 1.3627703 0.0392 0.9972 0.9156
5000 0.8 0.8 500 3 800 2400 0.5 0.3 1 1.5275252 0.039 1 0.997
5000 0.8 0.8 500 3 800 2400 0.5 0.25 1 1.7320508 0.038 1 1
5000 0.8 0.8 500 3 800 2400 0.5 0.5 1 1 0.041 0.0428 0.0428
5000 0.8 0.8 500 3 800 2400 0.65 0.65 0.7337994 0.7337994 0.9972 0.9974 0.0358
5000 0.8 0.8 500 3 800 2400 0.55 0.55 0.904534 0.904534 0.3116 0.3198 0.0388
5000 0.8 0.8 500 3 800 2400 0.6 0.6 0.8164966 0.8164966 0.8736 0.8664 0.0364
8000 0.8 0.8 500 3 800 2400 0.5 0.75 1 0.5773503 0.034625 1 1
8000 0.8 0.8 500 3 800 2400 0.5 0.7 1 0.6546537 0.03925 1 0.99563
8000 0.8 0.8 500 3 800 2400 0.5 0.65 1 0.7337994 0.04225 0.996875 0.91613
8000 0.8 0.8 500 3 800 2400 0.5 0.6 1 0.8164966 0.040875 0.87275 0.58063
8000 0.8 0.8 500 3 800 2400 0.5 0.55 1 0.904534 0.040875 0.31825 0.17225
8000 0.8 0.8 500 3 800 2400 0.5 0.45 1 1.1055416 0.04125 0.318875 0.177
157
8000 0.8 0.8 500 3 800 2400 0.5 0.4 1 1.2247449 0.040125 0.871625 0.57863
8000 0.8 0.8 500 3 800 2400 0.5 0.35 1 1.3627703 0.0395 0.997625 0.91288
8000 0.8 0.8 500 3 800 2400 0.5 0.3 1 1.5275252 0.038375 1 0.99513
8000 0.8 0.8 500 3 800 2400 0.5 0.25 1 1.7320508 0.037 1 1
8000 0.8 0.8 500 3 800 2400 0.5 0.5 1 1 0.039 0.04225 0.04175
8000 0.8 0.8 500 3 800 2400 0.6 0.6 0.8164966 0.8164966 0.874125 0.866625 0.037
8000 0.8 0.8 500 3 800 2400 0.65 0.65 0.7337994 0.7337994 0.997 0.9965 0.0365
8000 0.8 0.8 500 3 800 2400 0.55 0.55 0.904534 0.904534 0.31375 0.318875 0.04013
10000 0.8 0.8 500 3 800 2400 0.5 0.75 1 0.5773503 0.0351 1 0.9999
10000 0.8 0.8 500 3 800 2400 0.5 0.7 1 0.6546537 0.0378 1 0.9954
10000 0.8 0.8 500 3 800 2400 0.5 0.65 1 0.7337994 0.0389 0.9957 0.9191
10000 0.8 0.8 500 3 800 2400 0.5 0.6 1 0.8164966 0.0378 0.8716 0.5806
10000 0.8 0.8 500 3 800 2400 0.5 0.55 1 0.904534 0.0383 0.3239 0.1774
10000 0.8 0.8 500 3 800 2400 0.5 0.45 1 1.1055416 0.0412 0.3097 0.1759
10000 0.8 0.8 500 3 800 2400 0.5 0.4 1 1.2247449 0.0389 0.8662 0.5758
10000 0.8 0.8 500 3 800 2400 0.5 0.35 1 1.3627703 0.0388 0.9967 0.9174
10000 0.8 0.8 500 3 800 2400 0.5 0.3 1 1.5275252 0.0381 1 0.9961
10000 0.8 0.8 500 3 800 2400 0.5 0.25 1 1.7320508 0.0347 1 0.9999
10000 0.8 0.8 500 3 800 2400 0.5 0.5 1 1 0.0399 0.0382 0.0404
10000 0.8 0.8 500 3 800 2400 0.6 0.6 0.8164966 0.8164966 0.8621 0.8655 0.0431
10000 0.8 0.8 500 3 800 2400 0.55 0.55 0.904534 0.904534 0.3203 0.318 0.0385
10000 0.8 0.8 500 3 800 2400 0.65 0.65 0.7337994 0.7337994 0.9967 0.9969 0.0404
1000 0.4 0.4 1000 3 800 2400 0.5 0.7 1 0.6546537 0.043 1 0.996
1000 0.4 0.4 1000 3 800 2400 0.5 0.65 1 0.7337994 0.035 0.999 0.924
1000 0.4 0.4 1000 3 800 2400 0.5 0.6 1 0.8164966 0.045 0.869 0.603
1000 0.8 0.8 375 4 600 2400 0.5 0.55 1 0.904534 0.04 0.414 0.226
1000 0.8 0.8 375 4 600 2400 0.5 0.5 1 1 0.038 0.023 0.03
1000 0.8 0.8 300 5 480 2400 0.5 0.55 1 0.904534 0.044 0.508 0.289
1000 0.8 0.8 300 5 480 2400 0.5 0.5 1 1 0.048 0.039 0.042
1000 0.8 0.8 250 6 400 2400 0.5 0.55 1 0.904534 0.061 0.557 0.354
1000 0.8 0.8 250 6 400 2400 0.5 0.5 1 1 0.057 0.057 0.054
1000 0.8 0.8 187.5 8 300 2400 0.5 0.55 1 0.904534 0.074 0.656 0.413
158
1000 0.8 0.8 187.5 8 300 2400 0.5 0.5 1 1 0.079 0.059 0.066
1000 0.8 0.8 125 12 200 2400 0.5 0.55 1 0.904534 0.068 0.835 0.533
1000 0.8 0.8 125 12 200 2400 0.5 0.5 1 1 0.075 0.046 0.063
1000 0.8 0.8 200 8 320 2560 0.5 0.65 1 0.7337994 0.049 1 1
1000 0.8 0.8 200 8 320 2560 0.5 0.6 1 0.8164966 0.049 1 0.952
1000 0.8 0.8 200 8 320 2560 0.5 0.55 1 0.904534 0.052 0.676 0.403
1000 0.8 0.8 200 8 320 2560 0.5 0.5 1 1 0.051 0.04 0.04
10000 0.8 0.8 200 8 320 2560 0.5 0.65 1 0.7337994 0.0503 1 0.9996
10000 0.8 0.8 200 8 320 2560 0.5 0.6 1 0.8164966 0.0488 0.9988 0.9383
10000 0.8 0.8 200 8 320 2560 0.5 0.55 1 0.904534 0.05 0.6935 0.4127
10000 0.8 0.8 200 8 320 2560 0.5 0.5 1 1 0.0512 0.0534 0.0515
1000 0.45 0.45 1000 3 900 2700 0.5 0.7 1 0.6546537 0.045 1 0.997
1000 0.45 0.45 1000 3 900 2700 0.5 0.65 1 0.7337994 0.043 0.999 0.923
1000 0.45 0.45 1000 3 900 2700 0.5 0.6 1 0.8164966 0.042 0.872 0.592
1000 0.5 0.5 1000 3 1000 3000 0.9 0.9 0.3333333 0.3333333 1 1 0.026
1000 0.5 0.5 1000 3 1000 3000 0.75 0.75 0.5773503 0.5773503 1 1 0.036
1000 0.5 0.5 1000 3 1000 3000 0.25 0.25 1.7320508 1.7320508 1 1 0.037
1000 0.5 0.5 1000 3 1000 3000 0.1 0.1 3 3 1 1 0.017
1000 0.5 0.5 1000 3 1000 3000 0.5 0.9 1 0.3333333 0.022 1 1
1000 0.5 0.5 1000 3 1000 3000 0.5 0.75 1 0.5773503 0.036 1 1
1000 0.5 0.5 1000 3 1000 3000 0.5 0.25 1 1.7320508 0.038 1 1
1000 0.5 0.5 1000 3 1000 3000 0.5 0.1 1 3 0.021 1 1
1000 0.5 0.5 1000 3 1000 3000 0.5 0.7 1 0.6546537 0.028 1 0.995
1000 0.5 0.5 1000 3 1000 3000 0.5 0.65 1 0.7337994 0.032 0.997 0.918
1000 0.5 0.5 1000 3 1000 3000 0.5 0.6 1 0.8164966 0.039 0.861 0.57
1000 0.5 0.5 1000 3 1000 3000 0.5 0.5 1 1 0.038 0.04 0.034
1000 0.8 0.8 333.3333333 6 533.33333 3200 0.5 0.55 1 0.904534 0.051 0.623 0.331
1000 0.8 0.8 333.3333333 6 533.33333 3200 0.5 0.5 1 1 0.052 0.053 0.052
1000 0.8 0.8 500 4 800 3200 0.5 0.55 1 0.904534 0.047 0.438 0.237
1000 0.8 0.8 500 4 800 3200 0.5 0.5 1 1 0.046 0.05 0.055
1000 0.8 0.8 400 5 640 3200 0.5 0.55 1 0.904534 0.053 0.498 0.263
1000 0.8 0.8 400 5 640 3200 0.5 0.5 1 1 0.054 0.046 0.058
159
1000 0.8 0.8 250 8 400 3200 0.5 0.55 1 0.904534 0.046 0.707 0.435
1000 0.8 0.8 250 8 400 3200 0.5 0.5 1 1 0.049 0.049 0.054
1000 0.8 0.8 666.6666667 3 1066.6667 3200 0.5 0.55 1 0.904534 0.031 0.3 0.182
1000 0.8 0.8 666.6666667 3 1066.6667 3200 0.5 0.5 1 1 0.034 0.037 0.03
1000 0.8 0.8 166.6666667 12 266.66667 3200 0.5 0.55 1 0.904534 0.069 0.835 0.55
1000 0.8 0.8 166.6666667 12 266.66667 3200 0.5 0.5 1 1 0.07 0.05 0.069
1000 0.55 0.55 1000 3 1100 3300 0.5 0.7 1 0.6546537 0.041 1 0.999
1000 0.55 0.55 1000 3 1100 3300 0.5 0.65 1 0.7337994 0.04 0.996 0.922
1000 0.55 0.55 1000 3 1100 3300 0.5 0.6 1 0.8164966 0.041 0.89 0.61
1000 0.6 0.6 1000 3 1200 3600 0.5 0.7 1 0.6546537 0.037 1 0.996
1000 0.6 0.6 1000 3 1200 3600 0.5 0.65 1 0.7337994 0.046 0.999 0.926
1000 0.6 0.6 1000 3 1200 3600 0.5 0.6 1 0.8164966 0.048 0.888 0.601
1000 0.8 0.8 200 12 320 3840 0.5 0.55 1 0.904534 0.064 0.859 0.604
1000 0.8 0.8 200 12 320 3840 0.5 0.65 1 0.7337994 0.064 1 1
1000 0.8 0.8 200 12 320 3840 0.5 0.6 1 0.8164966 0.069 1 0.986
1000 0.8 0.8 200 12 320 3840 0.5 0.5 1 1 0.058 0.067 0.066
10000 0.8 0.8 200 12 320 3840 0.5 0.55 1 0.904534 0.0585 0.8635 0.5762
10000 0.8 0.8 200 12 320 3840 0.5 0.65 1 0.7337994 0.0601 1 1
10000 0.8 0.8 200 12 320 3840 0.5 0.6 1 0.8164966 0.0583 1 0.992
10000 0.8 0.8 200 12 320 3840 0.5 0.5 1 1 0.06 0.0603 0.0557
1000 0.65 0.65 1000 3 1300 3900 0.5 0.7 1 0.6546537 0.037 1 0.997
1000 0.65 0.65 1000 3 1300 3900 0.5 0.65 1 0.7337994 0.03 0.996 0.92
1000 0.65 0.65 1000 3 1300 3900 0.5 0.6 1 0.8164966 0.037 0.863 0.584
1000 0.7 0.7 1000 3 1400 4200 0.5 0.7 1 0.6546537 0.03 1 0.993
1000 0.7 0.7 1000 3 1400 4200 0.5 0.65 1 0.7337994 0.036 0.998 0.92
1000 0.7 0.7 1000 3 1400 4200 0.5 0.6 1 0.8164966 0.038 0.883 0.601
1000 0.75 0.75 1000 3 1500 4500 0.5 0.7 1 0.6546537 0.035 1 0.996
1000 0.75 0.75 1000 3 1500 4500 0.5 0.65 1 0.7337994 0.035 0.998 0.917
1000 0.75 0.75 1000 3 1500 4500 0.5 0.6 1 0.8164966 0.042 0.874 0.59
500 0.8 0.8 1000 3 1600 4800 0.5 0.7 1 0.6546537 0.034 1 0.998
500 0.8 0.8 1000 3 1600 4800 0.5 0.65 1 0.7337994 0.032 0.998 0.92
500 0.8 0.8 1000 3 1600 4800 0.5 0.6 1 0.8164966 0.038 0.9 0.6
160
1000 0.8 0.8 1000 3 1600 4800 0.9 0.9 0.3333333 0.3333333 1 1 0.02
1000 0.8 0.8 1000 3 1600 4800 0.75 0.75 0.5773503 0.5773503 1 1 0.032
1000 0.8 0.8 1000 3 1600 4800 0.25 0.25 1.7320508 1.7320508 1 1 0.039
1000 0.8 0.8 1000 3 1600 4800 0.1 0.1 3 3 1 1 0.017
1000 0.8 0.8 1000 3 1600 4800 0.75 0.75 0.5773503 0.5773503 1 1 0.027
1000 0.8 0.8 1000 3 1600 4800 0.7 0.7 0.6546537 0.6546537 1 1 0.042
1000 0.8 0.8 1000 3 1600 4800 0.65 0.65 0.7337994 0.7337994 0.998 0.999 0.036
1000 0.8 0.8 1000 3 1600 4800 0.6 0.6 0.8164966 0.8164966 0.9 0.875 0.045
1000 0.8 0.8 1000 3 1600 4800 0.55 0.55 0.904534 0.904534 0.34 0.352 0.04
1000 0.8 0.8 1000 3 1600 4800 0.45 0.45 1.1055416 1.1055416 0.333 0.335 0.037
1000 0.8 0.8 1000 3 1600 4800 0.4 0.4 1.2247449 1.2247449 0.891 0.898 0.04
1000 0.8 0.8 1000 3 1600 4800 0.35 0.35 1.3627703 1.3627703 0.998 0.999 0.034
1000 0.8 0.8 1000 3 1600 4800 0.3 0.3 1.5275252 1.5275252 1 1 0.036
1000 0.8 0.8 1000 3 1600 4800 0.25 0.25 1.7320508 1.7320508 1 1 0.031
1000 0.8 0.8 1000 3 1600 4800 0.5 0.9 1 0.3333333 0.023 1 1
1000 0.8 0.8 1000 3 1600 4800 0.5 0.75 1 0.5773503 0.036 1 1
1000 0.8 0.8 1000 3 1600 4800 0.5 0.25 1 1.7320508 0.034 1 1
1000 0.8 0.8 1000 3 1600 4800 0.5 0.1 1 3 0.016 1 1
1000 0.8 0.8 1000 3 1600 4800 0.5 0.7 1 0.6546537 0.032 1 0.995
1000 0.8 0.8 1000 3 1600 4800 0.5 0.65 1 0.7337994 0.04 0.999 0.917
1000 0.8 0.8 1000 3 1600 4800 0.5 0.6 1 0.8164966 0.04 0.892 0.601
1000 0.8 0.8 1000 3 1600 4800 0.5 0.55 1 0.904534 0.039 0.324 0.184
1000 0.8 0.8 1000 3 1600 4800 0.5 0.7 1 0.6546537 0.03 1 0.995
1000 0.8 0.8 1000 3 1600 4800 0.5 0.65 1 0.7337994 0.04 0.999 0.916
1000 0.8 0.8 1000 3 1600 4800 0.5 0.6 1 0.8164966 0.04 0.895 0.612
1000 0.8 0.8 1000 3 1600 4800 0.5 0.75 1 0.5773503 0.03 1 1
1000 0.8 0.8 1000 3 1600 4800 0.5 0.7 1 0.6546537 0.031 1 0.995
1000 0.8 0.8 1000 3 1600 4800 0.5 0.65 1 0.7337994 0.036 0.999 0.924
1000 0.8 0.8 1000 3 1600 4800 0.5 0.6 1 0.8164966 0.031 0.899 0.6
1000 0.8 0.8 1000 3 1600 4800 0.5 0.55 1 0.904534 0.033 0.337 0.175
1000 0.8 0.8 1000 3 1600 4800 0.5 0.45 1 1.1055416 0.034 0.329 0.186
1000 0.8 0.8 1000 3 1600 4800 0.5 0.4 1 1.2247449 0.04 0.881 0.611
161
1000 0.8 0.8 1000 3 1600 4800 0.5 0.35 1 1.3627703 0.034 0.999 0.942
1000 0.8 0.8 1000 3 1600 4800 0.5 0.3 1 1.5275252 0.032 1 0.998
1000 0.8 0.8 1000 3 1600 4800 0.5 0.25 1 1.7320508 0.028 1 1
1000 0.8 0.8 1000 3 1600 4800 0.5 0.5 1 1 0.043 0.041 0.038
1000 0.8 0.8 1000 3 1600 4800 0.5 0.5 1 1 0.039 0.031 0.036
2000 0.8 0.8 1000 3 1600 4800 0.5 0.7 1 0.6546537 0.043 1 0.9965
2000 0.8 0.8 1000 3 1600 4800 0.5 0.65 1 0.7337994 0.0505 0.999 0.927
2000 0.8 0.8 1000 3 1600 4800 0.5 0.6 1 0.8164966 0.0445 0.8915 0.6105
4000 0.8 0.8 1000 3 1600 4800 0.5 0.7 1 0.6546537 0.036 1 0.99675
4000 0.8 0.8 1000 3 1600 4800 0.5 0.65 1 0.7337994 0.036 0.9995 0.93225
4000 0.8 0.8 1000 3 1600 4800 0.5 0.6 1 0.8164966 0.03875 0.883 0.599
5000 0.8 0.8 1000 3 1600 4800 0.5 0.7 1 0.6546537 0.0418 1 0.9974
5000 0.8 0.8 1000 3 1600 4800 0.5 0.65 1 0.7337994 0.0438 0.9984 0.9294
5000 0.8 0.8 1000 3 1600 4800 0.5 0.6 1 0.8164966 0.0412 0.8842 0.6078
8000 0.8 0.8 1000 3 1600 4800 0.5 0.7 1 0.6546537 0.03875 1 0.99713
8000 0.8 0.8 1000 3 1600 4800 0.5 0.65 1 0.7337994 0.038625 0.998375 0.92488
8000 0.8 0.8 1000 3 1600 4800 0.5 0.6 1 0.8164966 0.03825 0.88975 0.60725
10000 0.8 0.8 1000 3 1600 4800 0.5 0.7 1 0.6546537 0.0432 1 0.9965
10000 0.8 0.8 1000 3 1600 4800 0.5 0.65 1 0.7337994 0.0423 0.9974 0.929
10000 0.8 0.8 1000 3 1600 4800 0.5 0.6 1 0.8164966 0.0463 0.881 0.6017
10000 0.8 0.8 1000 3 1600 4800 0.5 0.55 1 0.904534 0.0409 0.3335 0.1826
10000 0.8 0.8 1000 3 1600 4800 0.5 0.5 1 1 0.0417 0.045 0.0433
1000 0.8 0.8 750 4 1200 4800 0.5 0.55 1 0.904534 0.039 0.478 0.261
1000 0.8 0.8 750 4 1200 4800 0.5 0.5 1 1 0.041 0.057 0.061
10000 0.8 0.8 750 4 1200 4800 0.5 0.5 1 1 0.0482 0.0487 0.0506
1000 0.8 0.8 600 5 960 4800 0.5 0.55 1 0.904534 0.048 0.576 0.338
1000 0.8 0.8 600 5 960 4800 0.5 0.5 1 1 0.048 0.063 0.052
10000 0.8 0.8 600 5 960 4800 0.5 0.5 1 1 0.0474 0.0494 0.0502
1000 0.8 0.8 500 6 800 4800 0.5 0.55 1 0.904534 0.054 0.631 0.385
1000 0.8 0.8 500 6 800 4800 0.5 0.5 1 1 0.059 0.05 0.054
10000 0.8 0.8 500 6 800 4800 0.5 0.5 1 1 0.0494 0.0558 0.0519
1000 0.8 0.8 375 8 600 4800 0.5 0.55 1 0.904534 0.057 0.765 0.494
162
1000 0.8 0.8 375 8 600 4800 0.5 0.5 1 1 0.061 0.035 0.043
10000 0.8 0.8 375 8 600 4800 0.5 0.5 1 1 0.0617 0.0536 0.0568
1000 0.8 0.8 250 12 400 4800 0.5 0.55 1 0.904534 0.067 0.891 0.614
1000 0.8 0.8 250 12 400 4800 0.5 0.5 1 1 0.067 0.064 0.056
10000 0.8 0.8 250 12 400 4800 0.5 0.5 1 1 0.0577 0.0561 0.0532
1000 0.2 0.2 5000 3 2000 6000 0.9 0.9 0.3333333 0.3333333 1 1 0.019
1000 0.2 0.2 5000 3 2000 6000 0.75 0.75 0.5773503 0.5773503 1 1 0.044
1000 0.2 0.2 5000 3 2000 6000 0.25 0.25 1.7320508 1.7320508 1 1 0.029
1000 0.2 0.2 5000 3 2000 6000 0.1 0.1 3 3 1 1 0.016
1000 0.2 0.2 5000 3 2000 6000 0.5 0.9 1 0.3333333 0.026 1 1
1000 0.2 0.2 5000 3 2000 6000 0.5 0.75 1 0.5773503 0.035 1 1
1000 0.2 0.2 5000 3 2000 6000 0.5 0.25 1 1.7320508 0.043 1 1
1000 0.2 0.2 5000 3 2000 6000 0.5 0.1 1 3 0.029 1 1
1000 0.2 0.2 5000 3 2000 6000 0.5 0.5 1 1 0.039 0.052 0.045
1000 0.8 0.8 1333.333333 3 2133.3333 6400 0.5 0.55 1 0.904534 0.051 0.327 0.19
1000 0.8 0.8 1333.333333 3 2133.3333 6400 0.5 0.5 1 1 0.045 0.039 0.054
1000 0.8 0.8 333.3333333 12 533.33333 6400 0.5 0.55 1 0.904534 0.054 0.89 0.616
1000 0.8 0.8 333.3333333 12 533.33333 6400 0.5 0.5 1 1 0.067 0.06 0.054
1000 0.8 0.8 1000 4 1600 6400 0.5 0.55 1 0.904534 0.046 0.441 0.24
1000 0.8 0.8 1000 4 1600 6400 0.5 0.5 1 1 0.043 0.055 0.049
1000 0.8 0.8 800 5 1280 6400 0.5 0.55 1 0.904534 0.056 0.548 0.303
1000 0.8 0.8 800 5 1280 6400 0.5 0.5 1 1 0.06 0.052 0.045
1000 0.8 0.8 500 8 800 6400 0.5 0.55 1 0.904534 0.048 0.763 0.464
1000 0.8 0.8 500 8 800 6400 0.5 0.5 1 1 0.044 0.069 0.057
1000 0.8 0.8 666.6666667 6 1066.6667 6400 0.5 0.55 1 0.904534 0.043 0.625 0.377
1000 0.8 0.8 666.6666667 6 1066.6667 6400 0.5 0.5 1 1 0.045 0.061 0.063
10000 0.8 0.8 833.3333333 6 1333.3333 8000 0.5 0.5 1 1 0.0522 0.0529 0.0523
10000 0.8 0.8 1250 4 2000 8000 0.5 0.5 1 1 0.0447 0.0482 0.0457
10000 0.8 0.8 1000 5 1600 8000 0.5 0.55 1 0.904534 0.0511 0.567 0.3295
10000 0.8 0.8 1000 5 1600 8000 0.5 0.5 1 1 0.0509 0.0508 0.0512
10000 0.8 0.8 625 8 1000 8000 0.5 0.5 1 1 0.0511 0.0561 0.0548
10000 0.8 0.8 416.6666667 12 666.66667 8000 0.5 0.5 1 1 0.0598 0.0603 0.0636
163
10000 0.8 0.8 1666.666667 3 2666.6667 8000 0.5 0.5 1 1 0.0435 0.0424 0.039
1000 0.2 0.2 10000 3 4000 12000 0.9 0.9 0.3333333 0.3333333 1 1 0.016
1000 0.2 0.2 10000 3 4000 12000 0.75 0.75 0.5773503 0.5773503 1 1 0.04
1000 0.2 0.2 10000 3 4000 12000 0.25 0.25 1.7320508 1.7320508 1 1 0.028
1000 0.2 0.2 10000 3 4000 12000 0.1 0.1 3 3 1 1 0.021
1000 0.2 0.2 10000 3 4000 12000 0.5 0.9 1 0.3333333 0.022 1 1
1000 0.2 0.2 10000 3 4000 12000 0.5 0.75 1 0.5773503 0.032 1 1
1000 0.2 0.2 10000 3 4000 12000 0.5 0.25 1 1.7320508 0.031 1 1
1000 0.2 0.2 10000 3 4000 12000 0.5 0.1 1 3 0.023 1 1
1000 0.2 0.2 10000 3 4000 12000 0.5 0.5 1 1 0.036 0.04 0.044
1000 0.5 0.5 5000 3 5000 15000 0.9 0.9 0.3333333 0.3333333 1 1 0.022
1000 0.5 0.5 5000 3 5000 15000 0.75 0.75 0.5773503 0.5773503 1 1 0.035
1000 0.5 0.5 5000 3 5000 15000 0.25 0.25 1.7320508 1.7320508 1 1 0.036
1000 0.5 0.5 5000 3 5000 15000 0.1 0.1 3 3 1 1 0.026
1000 0.5 0.5 5000 3 5000 15000 0.5 0.9 1 0.3333333 0.02 1 1
1000 0.5 0.5 5000 3 5000 15000 0.5 0.75 1 0.5773503 0.031 1 1
1000 0.5 0.5 5000 3 5000 15000 0.5 0.25 1 1.7320508 0.032 1 1
1000 0.5 0.5 5000 3 5000 15000 0.5 0.1 1 3 0.023 1 1
1000 0.5 0.5 5000 3 5000 15000 0.5 0.5 1 1 0.038 0.048 0.027
1000 0.8 0.8 5000 3 8000 24000 0.9 0.9 0.3333333 0.3333333 1 1 0.028
1000 0.8 0.8 5000 3 8000 24000 0.75 0.75 0.5773503 0.5773503 1 1 0.039
1000 0.8 0.8 5000 3 8000 24000 0.25 0.25 1.7320508 1.7320508 1 1 0.03
1000 0.8 0.8 5000 3 8000 24000 0.1 0.1 3 3 1 1 0.022
1000 0.8 0.8 5000 3 8000 24000 0.75 0.75 0.5773503 0.5773503 1 1 0.039
1000 0.8 0.8 5000 3 8000 24000 0.7 0.7 0.6546537 0.6546537 1 1 0.038
1000 0.8 0.8 5000 3 8000 24000 0.65 0.65 0.7337994 0.7337994 0.999 0.998 0.033
1000 0.8 0.8 5000 3 8000 24000 0.6 0.6 0.8164966 0.8164966 0.903 0.906 0.041
1000 0.8 0.8 5000 3 8000 24000 0.55 0.55 0.904534 0.904534 0.345 0.369 0.05
1000 0.8 0.8 5000 3 8000 24000 0.45 0.45 1.1055416 1.1055416 0.355 0.364 0.046
1000 0.8 0.8 5000 3 8000 24000 0.4 0.4 1.2247449 1.2247449 0.897 0.911 0.032
1000 0.8 0.8 5000 3 8000 24000 0.35 0.35 1.3627703 1.3627703 0.999 1 0.036
1000 0.8 0.8 5000 3 8000 24000 0.3 0.3 1.5275252 1.5275252 1 1 0.038
164
1000 0.8 0.8 5000 3 8000 24000 0.25 0.25 1.7320508 1.7320508 1 1 0.045
1000 0.8 0.8 5000 3 8000 24000 0.5 0.9 1 0.3333333 0.029 1 1
1000 0.8 0.8 5000 3 8000 24000 0.5 0.75 1 0.5773503 0.041 1 1
1000 0.8 0.8 5000 3 8000 24000 0.5 0.25 1 1.7320508 0.04 1 1
1000 0.8 0.8 5000 3 8000 24000 0.5 0.1 1 3 0.03 1 1
1000 0.8 0.8 5000 3 8000 24000 0.5 0.75 1 0.5773503 0.045 1 1
1000 0.8 0.8 5000 3 8000 24000 0.5 0.7 1 0.6546537 0.045 1 0.996
1000 0.8 0.8 5000 3 8000 24000 0.5 0.65 1 0.7337994 0.051 1 0.94
1000 0.8 0.8 5000 3 8000 24000 0.5 0.6 1 0.8164966 0.044 0.906 0.632
1000 0.8 0.8 5000 3 8000 24000 0.5 0.55 1 0.904534 0.04 0.348 0.201
1000 0.8 0.8 5000 3 8000 24000 0.5 0.45 1 1.1055416 0.04 0.359 0.193
1000 0.8 0.8 5000 3 8000 24000 0.5 0.4 1 1.2247449 0.045 0.894 0.622
1000 0.8 0.8 5000 3 8000 24000 0.5 0.35 1 1.3627703 0.046 1 0.942
1000 0.8 0.8 5000 3 8000 24000 0.5 0.3 1 1.5275252 0.041 1 0.999
1000 0.8 0.8 5000 3 8000 24000 0.5 0.25 1 1.7320508 0.038 1 1
1000 0.8 0.8 5000 3 8000 24000 0.5 0.5 1 1 0.043 0.052 0.041
1000 0.5 0.5 10000 3 10000 30000 0.9 0.9 0.3333333 0.3333333 1 1 0.031
1000 0.5 0.5 10000 3 10000 30000 0.75 0.75 0.5773503 0.5773503 1 1 0.034
1000 0.5 0.5 10000 3 10000 30000 0.25 0.25 1.7320508 1.7320508 1 1 0.035
1000 0.5 0.5 10000 3 10000 30000 0.1 0.1 3 3 1 1 0.026
1000 0.5 0.5 10000 3 10000 30000 0.5 0.9 1 0.3333333 0.029 1 1
1000 0.5 0.5 10000 3 10000 30000 0.5 0.75 1 0.5773503 0.038 1 1
1000 0.5 0.5 10000 3 10000 30000 0.5 0.25 1 1.7320508 0.037 1 1
1000 0.5 0.5 10000 3 10000 30000 0.5 0.1 1 3 0.031 1 1
1000 0.5 0.5 10000 3 10000 30000 0.5 0.5 1 1 0.038 0.037 0.04
1000 0.8 0.8 10000 3 16000 48000 0.9 0.9 0.3333333 0.3333333 1 1 0.025
1000 0.8 0.8 10000 3 16000 48000 0.75 0.75 0.5773503 0.5773503 1 1 0.033
1000 0.8 0.8 10000 3 16000 48000 0.25 0.25 1.7320508 1.7320508 1 1 0.036
1000 0.8 0.8 10000 3 16000 48000 0.1 0.1 3 3 1 1 0.023
1000 0.8 0.8 10000 3 16000 48000 0.75 0.75 0.5773503 0.5773503 1 1 0.035
1000 0.8 0.8 10000 3 16000 48000 0.7 0.7 0.6546537 0.6546537 1 1 0.042
1000 0.8 0.8 10000 3 16000 48000 0.65 0.65 0.7337994 0.7337994 1 0.998 0.044
165
1000 0.8 0.8 10000 3 16000 48000 0.6 0.6 0.8164966 0.8164966 0.897 0.912 0.047
1000 0.8 0.8 10000 3 16000 48000 0.55 0.55 0.904534 0.904534 0.356 0.356 0.048
1000 0.8 0.8 10000 3 16000 48000 0.45 0.45 1.1055416 1.1055416 0.358 0.358 0.039
1000 0.8 0.8 10000 3 16000 48000 0.4 0.4 1.2247449 1.2247449 0.9 0.895 0.044
1000 0.8 0.8 10000 3 16000 48000 0.35 0.35 1.3627703 1.3627703 0.998 1 0.04
1000 0.8 0.8 10000 3 16000 48000 0.3 0.3 1.5275252 1.5275252 1 1 0.039
1000 0.8 0.8 10000 3 16000 48000 0.25 0.25 1.7320508 1.7320508 1 1 0.033
1000 0.8 0.8 10000 3 16000 48000 0.5 0.9 1 0.3333333 0.034 1 1
1000 0.8 0.8 10000 3 16000 48000 0.5 0.75 1 0.5773503 0.041 1 1
1000 0.8 0.8 10000 3 16000 48000 0.5 0.25 1 1.7320508 0.048 1 1
1000 0.8 0.8 10000 3 16000 48000 0.5 0.1 1 3 0.031 1 1
1000 0.8 0.8 10000 3 16000 48000 0.5 0.75 1 0.5773503 0.045 1 1
1000 0.8 0.8 10000 3 16000 48000 0.5 0.7 1 0.6546537 0.044 1 0.999
1000 0.8 0.8 10000 3 16000 48000 0.5 0.65 1 0.7337994 0.047 0.998 0.93
1000 0.8 0.8 10000 3 16000 48000 0.5 0.6 1 0.8164966 0.048 0.896 0.628
1000 0.8 0.8 10000 3 16000 48000 0.5 0.55 1 0.904534 0.048 0.354 0.188
1000 0.8 0.8 10000 3 16000 48000 0.5 0.45 1 1.1055416 0.059 0.371 0.202
1000 0.8 0.8 10000 3 16000 48000 0.5 0.4 1 1.2247449 0.046 0.91 0.65
1000 0.8 0.8 10000 3 16000 48000 0.5 0.35 1 1.3627703 0.044 0.998 0.939
1000 0.8 0.8 10000 3 16000 48000 0.5 0.3 1 1.5275252 0.037 1 1
1000 0.8 0.8 10000 3 16000 48000 0.5 0.25 1 1.7320508 0.048 1 1
1000 0.8 0.8 10000 3 16000 48000 0.5 0.5 1 1 0.049 0.044 0.05
1000 0.2 0.2 50000 3 20000 60000 0.9 0.9 0.3333333 0.3333333 1 1 0.023
1000 0.2 0.2 50000 3 20000 60000 0.75 0.75 0.5773503 0.5773503 1 1 0.044
1000 0.2 0.2 50000 3 20000 60000 0.25 0.25 1.7320508 1.7320508 1 1 0.033
1000 0.2 0.2 50000 3 20000 60000 0.1 0.1 3 3 1 1 0.023
1000 0.2 0.2 50000 3 20000 60000 0.5 0.9 1 0.3333333 0.027 1 1
1000 0.2 0.2 50000 3 20000 60000 0.5 0.75 1 0.5773503 0.032 1 1
1000 0.2 0.2 50000 3 20000 60000 0.5 0.25 1 1.7320508 0.04 1 1
1000 0.2 0.2 50000 3 20000 60000 0.5 0.1 1 3 0.026 1 1
1000 0.2 0.2 50000 3 20000 60000 0.5 0.5 1 1 0.041 0.043 0.04
1000 0.2 0.2 100000 3 40000 120000 0.5 0.5 1 1 0.032 0.047 0.037
166
1000 0.5 0.5 50000 3 50000 150000 0.9 0.9 0.3333333 0.3333333 1 1 0.029
1000 0.5 0.5 50000 3 50000 150000 0.75 0.75 0.5773503 0.5773503 1 1 0.034
1000 0.5 0.5 50000 3 50000 150000 0.25 0.25 1.7320508 1.7320508 1 1 0.026
1000 0.5 0.5 50000 3 50000 150000 0.1 0.1 3 3 1 1 0.026
1000 0.5 0.5 50000 3 50000 150000 0.5 0.9 1 0.3333333 0.031 1 1
1000 0.5 0.5 50000 3 50000 150000 0.5 0.75 1 0.5773503 0.039 1 1
1000 0.5 0.5 50000 3 50000 150000 0.5 0.25 1 1.7320508 0.039 1 1
1000 0.5 0.5 50000 3 50000 150000 0.5 0.1 1 3 0.022 1 1
1000 0.5 0.5 50000 3 50000 150000 0.5 0.5 1 1 0.046 0.059 0.047
1000 0.8 0.8 50000 3 80000 240000 0.9 0.9 0.3333333 0.3333333 1 1 0.026
1000 0.8 0.8 50000 3 80000 240000 0.75 0.75 0.5773503 0.5773503 1 1 0.041
1000 0.8 0.8 50000 3 80000 240000 0.25 0.25 1.7320508 1.7320508 1 1 0.029
1000 0.8 0.8 50000 3 80000 240000 0.1 0.1 3 3 1 1 0.03
1000 0.8 0.8 50000 3 80000 240000 0.75 0.75 0.5773503 0.5773503 1 1 0.044
1000 0.8 0.8 50000 3 80000 240000 0.7 0.7 0.6546537 0.6546537 1 1 0.05
1000 0.8 0.8 50000 3 80000 240000 0.65 0.65 0.7337994 0.7337994 1 1 0.03
1000 0.8 0.8 50000 3 80000 240000 0.6 0.6 0.8164966 0.8164966 0.903 0.914 0.048
1000 0.8 0.8 50000 3 80000 240000 0.55 0.55 0.904534 0.904534 0.358 0.369 0.026
1000 0.8 0.8 50000 3 80000 240000 0.45 0.45 1.1055416 1.1055416 0.338 0.333 0.049
1000 0.8 0.8 50000 3 80000 240000 0.4 0.4 1.2247449 1.2247449 0.908 0.903 0.031
1000 0.8 0.8 50000 3 80000 240000 0.35 0.35 1.3627703 1.3627703 0.999 1 0.038
1000 0.8 0.8 50000 3 80000 240000 0.3 0.3 1.5275252 1.5275252 1 1 0.037
1000 0.8 0.8 50000 3 80000 240000 0.25 0.25 1.7320508 1.7320508 1 1 0.034
1000 0.8 0.8 50000 3 80000 240000 0.5 0.9 1 0.3333333 0.02 1 1
1000 0.8 0.8 50000 3 80000 240000 0.5 0.75 1 0.5773503 0.034 1 1
1000 0.8 0.8 50000 3 80000 240000 0.5 0.25 1 1.7320508 0.031 1 1
1000 0.8 0.8 50000 3 80000 240000 0.5 0.1 1 3 0.027 1 1
1000 0.8 0.8 50000 3 80000 240000 0.5 0.75 1 0.5773503 0.033 1 1
1000 0.8 0.8 50000 3 80000 240000 0.5 0.7 1 0.6546537 0.034 1 0.998
1000 0.8 0.8 50000 3 80000 240000 0.5 0.65 1 0.7337994 0.038 0.998 0.946
1000 0.8 0.8 50000 3 80000 240000 0.5 0.6 1 0.8164966 0.041 0.902 0.62
1000 0.8 0.8 50000 3 80000 240000 0.5 0.55 1 0.904534 0.034 0.353 0.206
167
1000 0.8 0.8 50000 3 80000 240000 0.5 0.45 1 1.1055416 0.036 0.339 0.194
1000 0.8 0.8 50000 3 80000 240000 0.5 0.4 1 1.2247449 0.036 0.914 0.651
1000 0.8 0.8 50000 3 80000 240000 0.5 0.35 1 1.3627703 0.035 1 0.935
1000 0.8 0.8 50000 3 80000 240000 0.5 0.3 1 1.5275252 0.035 1 1
1000 0.8 0.8 50000 3 80000 240000 0.5 0.25 1 1.7320508 0.035 1 1
1000 0.8 0.8 50000 3 80000 240000 0.5 0.5 1 1 0.038 0.047 0.05
1000 0.5 0.5 100000 3 100000 300000 0.5 0.5 1 1 0.044 0.057 0.046
1000 0.8 0.8 100000 3 160000 480000 0.75 0.75 0.5773503 0.5773503 1 1 0.032
1000 0.8 0.8 100000 3 160000 480000 0.7 0.7 0.6546537 0.6546537 1 1 0.036
1000 0.8 0.8 100000 3 160000 480000 0.65 0.65 0.7337994 0.7337994 0.999 1 0.034
1000 0.8 0.8 100000 3 160000 480000 0.6 0.6 0.8164966 0.8164966 0.902 0.891 0.045
1000 0.8 0.8 100000 3 160000 480000 0.55 0.55 0.904534 0.904534 0.376 0.356 0.04
1000 0.8 0.8 100000 3 160000 480000 0.45 0.45 1.1055416 1.1055416 0.356 0.334 0.036
1000 0.8 0.8 100000 3 160000 480000 0.4 0.4 1.2247449 1.2247449 0.902 0.909 0.036
1000 0.8 0.8 100000 3 160000 480000 0.35 0.35 1.3627703 1.3627703 1 0.999 0.042
1000 0.8 0.8 100000 3 160000 480000 0.3 0.3 1.5275252 1.5275252 1 1 0.038
1000 0.8 0.8 100000 3 160000 480000 0.25 0.25 1.7320508 1.7320508 1 1 0.033
1000 0.8 0.8 100000 3 160000 480000 0.5 0.75 1 0.5773503 0.041 1 1
1000 0.8 0.8 100000 3 160000 480000 0.5 0.7 1 0.6546537 0.049 1 1
1000 0.8 0.8 100000 3 160000 480000 0.5 0.65 1 0.7337994 0.044 0.998 0.943
1000 0.8 0.8 100000 3 160000 480000 0.5 0.6 1 0.8164966 0.041 0.907 0.655
1000 0.8 0.8 100000 3 160000 480000 0.5 0.55 1 0.904534 0.044 0.364 0.203
1000 0.8 0.8 100000 3 160000 480000 0.5 0.45 1 1.1055416 0.048 0.368 0.207
1000 0.8 0.8 100000 3 160000 480000 0.5 0.4 1 1.2247449 0.043 0.905 0.622
1000 0.8 0.8 100000 3 160000 480000 0.5 0.35 1 1.3627703 0.038 0.999 0.944
1000 0.8 0.8 100000 3 160000 480000 0.5 0.3 1 1.5275252 0.045 1 0.998
1000 0.8 0.8 100000 3 160000 480000 0.5 0.25 1 1.7320508 0.037 1 1
1000 0.8 0.8 100000 3 160000 480000 0.5 0.5 1 1 0.047 0.049 0.044
168
169

Supplementary Figure C.1. For each scenario simulated under H1 null, H2 null, H3 null, we counted the
proportion of simulations where the Bayesian evidence against allelic balance in condition 1 (H1) is less than 0.05
(A), against allelic balance in condition 2 (H1) is less than 0.05 (B), and against equal levels of AI (H3) is less than
0.05 (C). We generated a matrix of these proportions where each row (1000 of them) is a simulation and each
column is a scenario and created kernel density plots of the row averages of this matrix (x-axis).

A
B
C

Abstract (if available)

Abstract Studying transcriptional variation is important in establishing how genotypic variation influences variability in complex organismal phenotypes. Insights from such studies are vital to improving crop breeding and better understanding human health and disease. Here, we present two transcriptomic studies on a globally important oil crop, oil palm, and interspecific hybrids. Such studies have previously been limited to one oil palm species, Elaeis guineensis. In the first study, we validate candidate genes from prior QTL studies involved in the regulation of oil biosynthesis using RNA-seq data from two oil palm hybrid generations that have not previously been analyzed by this approach. We also find fatty acid and triacylglycerol synthesis genes differentially expressed between hybrid generations and up-regulated in later versus earlier stages of mesocarp development. In the second study, we used an independently generated backcross 1 population to look further into differences in expression between the hybrid and pure species parent due to how much genomic material the hybrid inherits from either parent. We find about 3700 genes expressed in at least one backcross 1 genotype but silent in both pure species parents that are enriched for several biological processes previously implicated in hybrid dysfunction or vigor. Focusing on five of these genes containing biallelic SNPs, we found three with increased in expression in samples heterozygous for that gene and, of these, two with this pattern specific to the later mesocarp developmental stage specific for two. While prior transcriptomic studies of regulatory incompatibilities find genes expressed in hybrids outside of their normal range of expression in parents, we find evidence for a novel type of incompatibility that leads to expression of genes in hybrids that are normally suppressed in parents. ❧ Measuring allele specific expression (ASE) allows us to identify specific genetic regulatory mechanisms that govern observed patterns of expression variation. Unequal expression of two alleles of a gene is referred to as allelic imbalance (AI). While there is extensive evidence on what factors inflate type I error in AI studies, the literature is lacking in what affects the power to not only detect AI in a condition (i.e. tissue, life stage, environment) but differences in AI between conditions. Are more reads or more biological replicates necessary to boost power to detect differences in AI? I develop software that allows users to simulate read count data with a previously published Bayesian model of AI with any number of replicates, reads, and AI and assess type I error and power. Using this software, I present the results of a simulation study that shows that increasing the number of biological replicates boosts power more so that increasing coverage without increasing type I error. I argue that these insights will inform the design of further RNA-seq experiments of oil palm interspecies hybrids balancing the need for more biological replicates with the challenges of breeding these crops with the goal of increasing power to study AI of potential candidate genes involved in hybrid incompatibilities and heterosis.

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Asset Metadata

Creator Sherbina, Katrina (author)

Core Title Probing the genetic basis of gene expression variation through Bayesian analysis of allelic imbalance and transcriptome studies of oil palm interspecies hybrids

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Computational Biology and Bioinformatics

Degree Conferral Date 2021-08

Publication Date 07/30/2021

Defense Date 06/08/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag allele specific expression,differential expression,hybrid dysfunction,hybrid vigor,misexpression,OAI-PMH Harvest,oil palm,RNA-seq,simulation

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nuzhdin, Sergey (committee chair), Chen, Liang (committee member), Thomas, Paul Denis (committee member)

Creator Email sherbina@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC15670114

Unique identifier UC15670114

Legacy Identifier etd-SherbinaKa-9950

Document Type Dissertation

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Rights Sherbina, Katrina

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

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