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An exploration of the spatiotemporal distribution of snow crab (Chionoecetes opilio) in the eastern Bering Sea: 1982 – 2018

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An exploration of the spatiotemporal distribution of snow crab (Chionoecetes opilio) in the eastern Bering Sea: 1982 – 2018

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An Exploration of the Spatiotemporal Distribution of Snow Crab (Chionoecetes opilio) in the
Eastern Bering Sea:

1982 – 2018

by

Bryna Michelle Mills

A Thesis Presented to the
FACULTY OF THE USC DORNSIFE COLLEGE OF LETTERS, ARTS AND SCIENCES
University of Southern California
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(GEOGRAPHIC INFORMATION SCIENCE AND TECHNOLOGY)

May 2021

Copyright © 2021 Bryna Michelle Mills

ii

To Grandpa Conroy

iii

Acknowledgements
Many thanks to my advisor, Dr. Bernstein, for guidance and support throughout the process of
creating this document and for the feedback from Drs. Loyola and Sedano, who helped make it
better. I am also grateful to all field biologists, survey technicians, and vessel crew who have
reliably collected data for the eastern Bering Sea bottom trawl survey and other fisheries
monitoring efforts in the region over decades, and the research councils and management
agencies like the National Marine Fisheries Service for continuing to conduct the surveys and
provide the data.

iv

Table of Contents
Dedication ....................................................................................................................................... ii
Acknowledgements ........................................................................................................................ iii
List of Tables ................................................................................................................................. vi
List of Figures ............................................................................................................................... vii
Abbreviations ................................................................................................................................. ix
Abstract .......................................................................................................................................... xi
Chapter 1 Introduction .................................................................................................................... 1
1.1. Study Area ..........................................................................................................................1
1.2. Snow Crab Spatial Biology .................................................................................................7
1.3. Fisheries Management ........................................................................................................8
1.4. Summary .............................................................................................................................9
Chapter 2 Related Work................................................................................................................ 11
2.1. Measuring Ecosystem Change in the Eastern Bering Sea ................................................11
2.1.1. Spatial Units .............................................................................................................12
2.1.2. Ecological Considerations .......................................................................................14
2.1.3. Space Time Exploration of Distribution ..................................................................16
2.2. GIS Modeling....................................................................................................................18
2.2.1. Spatiotemporal Analysis ..........................................................................................19
2.2.2. Predictive Modeling .................................................................................................23
2.2.3. Describing Relationships .........................................................................................24
2.3. Summary ...........................................................................................................................30
Chapter 3 Methods ........................................................................................................................ 32
3.1. Data Source: EBS Bottom Trawl Survey 1982-2018 .......................................................32
3.1.1. Data Distribution and Exploration ...........................................................................35

v

3.2. Space Time Cube Exploration of Distribution..................................................................36
3.2.1. Hot Spots ..................................................................................................................37
3.2.2. Local Clusters and Outliers ......................................................................................37
3.2.3. Time Series Clusters ................................................................................................38
3.3. Analysis of Relationships .................................................................................................38
3.3.1. Exploratory Regression ............................................................................................39
3.3.2. Global Regression ....................................................................................................40
3.3.3. Local Regression ......................................................................................................41
Chapter 4 Results .......................................................................................................................... 42
4.1. Space Time Cube and Snow Crab Distribution ................................................................42
4.1.1. Hot and Cold Spots ..................................................................................................54
4.1.2. Time Series Clusters ................................................................................................62
4.1.3. Local Clusters and Outliers ......................................................................................66
4.2. Lagged Relationships ........................................................................................................68
4.3. Global Relationship Trends ..............................................................................................72
4.4. Local Relationships ...........................................................................................................76
Chapter 5 Discussion .................................................................................................................... 82
5.1. Spatiotemporal Explorations .............................................................................................83
5.2. Regression Exploration .....................................................................................................84
5.3. Further Development ........................................................................................................87
5.4. Conclusion ........................................................................................................................90
References ..................................................................................................................................... 92
Appendix A EBS Bottom Temperatures, 2006 to 2018 ............................................................... 96
Appendix B GWR Local Variable Coefficients (including lag) ................................................... 99

vi

List of Tables
Table 1 EBS Spatiotemporal Data: 1982 – 2018 .......................................................................... 35
Table 2 Exploratory regression variables and lagged impact on 2018 snow crab CPUE............. 40
Table 3 Mann-Kendall data trends for CPUE, 1982 - 2018 ......................................................... 45
Table 4 Time series cluster trend statistics for snow crab CPUE temporal profile correlation .... 63
Table 5 Time series cluster trend statistics for Pacific cod CPUE temporal profile correlation .. 64
Table 6. Top three most significant lagged years (2006 and 2018) .............................................. 69
Table 7 Summary of OLS results model of 2018 snow crab CPUE, excluding lagged variables 72
Table 8 OLS model diagnostics for 2018 snow crab CPUE, with and without lagged variables 73
Table 9 Summary of OLS regression variable coefficients including top 3 lagged independent
variables from exploratory regression ................................................................................... 75
Table 10 GWR model performance and diagnostics .................................................................... 76
Table 11 GWR model performance and diagnostics including lag .............................................. 81

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List of Figures
Figure 1 Study area, the eastern Bering Sea and EBS shelf ........................................................... 3
Figure 2 EBS survey coverage area with cross-shelf domains (top) and northern, central,
and southern survey regions marked by canyons along the shelf edge (bottom) .................... 6
Figure 3 EBS average summer sea surface and bottom temperatures, 1982 – 2018 .................... 16
Figure 4 EBS annual total CPUE (number per nm square) for immature, mature female, and total
snow crab age classes, and Pacific cod, 1982 – 2018 ........................................................... 17
Figure 5 Space time cube views of snow crab CPUE due north (top) and south (bottom) .......... 43
Figure 6 Space time cube views of snow crab CPUE due east (top) and west (bottom) .............. 44
Figure 7 Stratified sample of survey station time cube stacks showing regional variation in snow
crab CPUE, 1982 – 2018 ....................................................................................................... 47
Figure 8 Individual time cube stacks from north to south and from outer to coastal domain
showing range of temporal profiles of snow crab CPUE, 1982 to 2018 ............................... 49
Figure 9 Space time cube views of immature snow crab (top) and mature female snow crab
(bottom) CPUE, 1982 to 2018 ............................................................................................... 51
Figure 10 Space time cube views of Pacific cod CPUE due north (top) and south (bottom) ....... 52
Figure 11 Stratified sample of survey station time cube stacks showing regional variation in
Pacific cod CPUE, 1982 – 2018 ............................................................................................ 53
Figure 12 Space time cube 1982 - 2018 snow crab CPUE hot spots (top), with emerging hot spot
trend summary (bottom) ........................................................................................................ 54
Figure 13 Snow crab CPUE hot spots for immature and mature female age classes, time cube
(top) and corresponding 2D emerging hot spots temporal summary (bottom) ..................... 55
Figure 14 Space time cube showing Pacific cod CPUE hot spots, 1982 to 2018 ......................... 57
Figure 15 Stratified sample of time cube stacks across the EBS shelf regions and domains
showing hot spots of snow crab CPUE, 1982 - 2018 ............................................................ 59
Figure 16 Stratified sample of time cube stacks across the EBS shelf regions and domains
showing hot spots of Pacific cod CPUE, 1982 - 2018 .......................................................... 60
Figure 17 Temporal trends in CPUE for total snow crab (top left), immature snow crab (top
right), mature female snow crab (bottom left), and Pacific cod (bottom right), 1982 to 2018
............................................................................................................................................... 61

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Figure 18 Time series clusters, four groups of survey stations with correlating temporal profiles
of snow crab CPUE, 1982 to 2018 ........................................................................................ 63
Figure 19 Average snow crab CPUE for each time series cluster group
* Indicates significant trend .......................................................................................................... 64
Figure 20 Time series correlation in temporal profile for Pacific cod CPUE, 1982 to 2018 ....... 65
Figure 21 Average Pacific cod CPUE for each time series cluster............................................... 65
Figure 22 Time cube views of CPUE clusters and outliers for snow crab (top left), immature
snow crab (top right), mature female snow crab (bottom left), and Pacific cod, 1982 to 2018
............................................................................................................................................... 66
Figure 23 Summary of CPUE clusters and outliers for snow crab (left) and Pacific cod (right),
1982 – 2018 ........................................................................................................................... 67
Figure 24 EBS bottom temperatures for the most significant lagged impact years for 2018 snow
crab CPUE since 2006, with 2018 bottom temperature as a reference (bottom) .................. 71
Figure 25 OLS standardized residuals for snow crab 2018 CPUE without (left) and with (right)
lagged independent variables since 2006 .............................................................................. 73
Figure 26 GWR model accuracy (local r
2
) ................................................................................... 77
Figure 27 GWR model residuals and standardized residuals showing spatial performance in
modeling 2018 snow crab CPUE .......................................................................................... 78
Figure 28 GWR local variable coefficients and scaled error for bottom temperature (top) and
surface temperature (bottom .................................................................................................. 79
Figure 29 GWR local variable coefficients and scaled error for depth (top) and Pacific cod CPUE
(bottom .................................................................................................................................. 80

ix

Abbreviations
ADFG Alaska Department of Fish and Game
AFSC Alaska Fisheries Science Center
BSFEP Bering Sea Fisheries Ecosystem Plan
CPUE Catch per unit effort
CV Coefficient of variation
EBM Ecosystem-based management
EBS Eastern Bering Sea
ERH Environmental ratchet hypothesis
GAM Generalized additive modeling
GIS Geographic information system
GISci Geographic information science
GLM Generalized linear modeling
GLR Generalized linear regression
GWR Geographically weighted regression
ML Machine learning
NMFS National Marine Fisheries Service
NOAA National Oceanic and Atmospheric Administration
NM Nautical mile
NPFMC North Pacific Fishery Management Council
OLS Ordinary least squares
RACE Resource Assessment and Conservation Engineering
RF Random forest

x

SSI Spatial Sciences Institute
TAC Total allowable catch
USC University of Southern California

xi

Abstract
Snow crab, Chionoecetes opilio, is the largest commercial crab fishery in Alaska. Populations in
the eastern Bering Sea have fluctuated over space and time, challenging statisticians attempting
to model their distribution and predict stock trends to support sustainable management decisions.
Climate change contributes to model uncertainty due to increased environmental variance and
subsequent shifts in species assemblages adapting to changing conditions in the region. This
research applied statistical toolkits and visualization techniques in GIS for spatiotemporal
analysis of snow crab distribution in the eastern Bering Sea over thirty-seven years (1982 –
2018). The National Marine Fisheries Service standardized bottom trawl survey provided a
robust dataset to statistically explore spatial and temporal patterns and relationships between
snow crab abundance in terms of catch per unit of effort to sea temperatures, depth, and Pacific
cod abundance. The temporal correlation in abundance patterns between snow crab year classes
or cohorts was tested using exploratory regression and geographically weighted regression was
used to visualize the nature and scale of relationships within the survey region. Overall spatial
patterns of snow crab distribution in the eastern Bering Sea reflected large scale warming trends
and contraction of the population to the north towards the Bering Strait. No significant
relationship was found between snow crab and Pacific cod distributions on a global scale but
there was evidence of a local scale inverse relationship in the southern survey region. In absence
of favorable bottom temperatures in 2018, snow crab distribution displayed a greater depth
dependence in the northernmost region. Temporal correlation was detected between age classes
of snow crab, suggesting connectivity between maternal cohorts and progeny. These results
identify local and global scale distribution trends which will support better predictive models for
fisheries.

1
Chapter 1 Introduction
Snow crab, Chionoecetes opilio (C. opilio), are widespread throughout the eastern Bering Sea
(EBS) and are harvested in the largest commercial crab fishery in Alaska. Managers monitor the
distribution and abundance of C. opilio and many other marine species of commercial and
ecological significance in the region to prevent overfishing and maintain sustainable populations.
Geographic Information Science (GIS) can be used to model these distributions spatially to
support traditional stock assessments.
Climate change in the Bering Sea region has been imposing pressure on species’
geographic ranges and the ecological structure of the EBS shelf habitat. Snow crab have
retreated to the north with sea temperature rise and reduced sea ice (Orensanz 2004) while
populations of groundfish species such as Pacific cod (Gadus macrocephalus) have increased
(Windle et al. 2012; Kotwicki and Lauth 2013). The influx of predatorial gadids like Pacific cod
further obfuscates the future of snow crab in the EBS with implications for both commercial
fisheries. The significance of the impact of these ecological relationships has been measured and
quantified in a variety of regression techniques with variable results to support predictive
modeling of fisheries stock distributions. The goal of this project is to describe the
spatiotemporal distribution of C. opilio distribution and abundance in relation to temperature,
depth, and Pacific cod abundance in the EBS through GIS and geostatistical analysis, and in
doing so, demonstrate how GIS can be applied towards marine ecology and fisheries science.
1.1. Study Area
The EBS shelf is a productive, sub-polar ecosystem supporting a diverse range of crab,
flatfish, and groundfish fisheries. This region extends approximately 270 nautical miles (nm)
seaward from the west coast of Alaska and breaks to the west near 200 m depth (Figure 1). The

2
main EBS shelf is relatively uniform in substrate and sea floor physiography, but rockier,
heterogenous habitat is found along the shelf edge where mature snow crab tend to cluster
(ADFG 2019). St. Lawrence Island (63°N 170°W) marks the northern entrance to the Bering
Strait which connects the Bering to the Chukchi Sea and Arctic Ocean beyond. South of St.
Lawrence is St. Matthew Island (60°N 172°W); continuing south the central region of the shelf
near 57°N is flagged by the Pribilof Islands to the west shelf edge and Nunivak Island to the east
nearer the coast. The Aleutian Islands form a southern border to the Bering Sea at about 54°N,
extending from the mainland Alaska Peninsula and Bristol Bay region towards Kamchatka
Peninsula and the east coast of Russia. St. Paul Island in the Pribilofs (57°N 170°W) is a main
port for commercial snow crab deliveries and serves as a geographic reference point throughout
this study.

3

Figure 1. Study area, the eastern Bering Sea and EBS shelf

4
The Alaska Coastal Current is diverted into the Bering Sea from the Gulf of Alaska and
Pacific Ocean. Much of the Coastal Current is directed through Unimak Pass, just west of the
Alaska Peninsula, where it becomes the Bering Slope current as it continues north along the
shelf’s edge. Nutrients carried up from the Aleutian Trench along the south side of the island
chain help to fuel a productive EBS ecosystem and form a productive front along the shelf edge
where adult snow crab aggregate. The Pribilof Islands and St. Matthew Island divert flow from
the Slope current. These island eddies provide a means of redistributing snow crab larvae and
nutrients across the shelf as the main Slope current pushes north (Orensanz 2004; Parada et al.
2010).
Sea ice forms in the Bering Sea during winter months as polar currents from the Chukchi
creep south over the shallow shelf region. Spring warming causes melt which sinks to the bottom
forming a pool of colder bottom temperatures, typically under 2℃ (NPFMC 2019). This cold
pool (Appendix A) and temperature gradient that forms on the EBS shelf defines the ecosystem
structure as it determines potential habitat for snow crab and other benthic marine species whose
physiological function is adapted to specific thermal range limits (Molinos et al. 2018).
Monitoring of temperature and climate tracking in the EBS is therefore vital to understanding
patterns of species distributions and to anticipate ecosystem change scenarios in the future.
Ice can extend as far south as Bristol Bay and the Pribilof Islands in cold years, but sea
ice formation and duration has decreased in recent years and the lowest recorded bottom
temperature in the summer of 2018 was 1.6℃ as reported by the National Marine Fisheries
Service (NMFS) (NPFMC 2019). Managers are concerned the warming trends could have a
detrimental impact on the snow crab fishery which may not be seen or detected for some years
while the effects are borne out through the population life cycle (ADFG 2019). The Bering Sea

5
Fishery Ecosystem Plan (BSFEP) was formalized by the North Pacific Fishery Management
Council (NPFMC) to begin development of ecosystem-based management (EBM) plans to
supplement traditional fisheries stock assessments through studies that incorporate important
variables like sea ice extent or sea temperatures along with spatially focused analyses of species
distribution and relationships (Foy and Armistead 2012; NPFMC 2019). GIS enables integration,
analysis, and visualization of spatiotemporal fisheries survey data and environmental variables of
interest to better understand the ecological processes driving species distributions towards EBM
goals.
Species abundance data gathered on standardized independent surveys designed by
statisticians provide the bulk of the data used to model stocks for commercial fisheries. Since the
1970s, NMFS has conducted an annual bottom trawl survey to provide the necessary data for
monitoring stocks and environmental conditions in the EBS. This trawl survey spans the shelf
region (about 216,000 nm
2
) from the Alaskan coast to the shelf edge as far west as 178°W and
from the Alaska Peninsula north beyond St. Matthew Island to 62°N. The 50 and 100 m depth
contours form the coastal, middle, and outer domains which describe the main geographic
regions across the shelf (see Figure 2). Nunivak Island and St. Paul Island mark the central
region of the shelf, defined by Zemchug Canyon to the north and Pribilof Canyon to the south.

6

Figure 2. EBS survey coverage area with cross-shelf domains (top) and northern, central, and
southern survey regions marked by canyons along the shelf edge (bottom)

7
1.2. Snow Crab Spatial Biology
Snow crab populations fluctuate in cyclical patterns where the frequency of pulse cycles
of abundance reflects connectivity between maternal year classes (cohorts) and progeny year
classes of immature snow crab (Ernst et al. 2005; Emond et al. 2015).
Different environmental conditions are preferred at each benthic life cycle stage of C.
opilio, so that the population becomes spatially stratified according to age/sex demographics
across the shelf. Snow crab begin their complex life cycle as larvae in the pelagic zone,
transported by currents and subjected to prevailing surface temperatures for 3 to 5 months before
settlement in the shallow and muddy coastal domain (Groβ et al. 2017). Immature snow crab
migrate towards the middle domain, normally the coldest region of the EBS. Mature crab
continue this migration towards the deeper outer domain and settle along the shelf edge in
mature stages where sea temperature is typically warmer and reproductive energetics are more
efficient (Orensanz et al. 2004).
Mature female age classes aggregate to the north of the main population and larger,
commercially targeted males form dense patches along the shelf edge (Orensanz et al. 2004;
Parada et al. 2010). Maternal cohorts release fertilized eggs in the outer domain near the edge;
currents then carry the eggs and resulting pelagic larvae towards the shallower coastal domain
where settlement occurs. Size and age frequency growth studies have shown that newly settled
crab, or instars, take approximately four to six years of growth to reach the immature age class
where it is large enough to be detected on survey, and reach maturity after another two to three
years of growth. As immature age classes make up the largest proportion of the total population,
this typically results in peaks in total abundance recurring every six to nine years. The contents
of Pacific cod stomachs collected from EBS survey samples have shown that small and immature

8
snow crab are preferred prey and make up a substantial proportion of Pacific cod diet (Orensanz
et al. 2004; Burgos et al. 2013; Groβ et al. 2017). This suggests that predation could be a major
source of juvenile mortality and express a lagged detrimental impact on snow crab abundance,
while the strength of maternal age classes would express a lagged positive correlation with future
snow crab abundance and pulse cycles.
Many factors impact growth and survival of snow crab as age classes move across the
shelf habitat in structured life history patterns, adapting to changing temperatures and species
interactions. Spatial and temporal variability make it difficult to describe trends in snow crab
abundance through global approaches to regression analysis alone (Ciannelli et al. 2008).
Exploration of the temporal correlation based on life history characteristics and investigation of
local scale relationships can help construct timelines of impact and describe regions where
relationships may vary from the overall trends.
1.3. Fisheries Management
An ecosystem regime shift occurred in the eastern Bering Sea according to survey data in
the late 1970s. Species assemblages and spatial distributions were shifting apparently in response
to warming surface and bottom temperatures and the related decline in sea ice extent and
duration. The temperature changes resulted in an influx of gadid fishes which began to tip the
ecological balance of biomass away from sub-polar benthic invertebrates in favor of temperate
groundfish species such as Pacific cod (Gadus macrocephalus) (Orensanz et al. 2004; Kotwicki
and Lauth 2013).
Commercial landings for the 2018 Bering Sea Aleutian Islands (BSAI) snow crab fishery
totaled 24,820,146 pounds at an ex-vessel price of $3.89 per pound and 130 million dollars for
the industry (ADFG 2020). The fishery has fluctuated in biomass and landings over decades,

9
with low periods in the mid-1980s and historical lows in the early 2000s. A changing climate and
shifting ecosystem contribute considerable uncertainty to stock assessment models which seek to
describe the population dynamics to make predictions for future scenarios in terms of fishery
productivity and sustainable fishing levels. Stock assessments are scrutinized by scientific review
boards, government agencies, fish processing and seafood industry associations, fishing
cooperatives, vessel owners, and permit holders prior to adoption of annual catch limits.
Historical spatial records captured by standardized surveys are particularly well suited for
analysis in GIS using statistical modeling developed for spatiotemporal datasets; and effective
spatial representation in map visuals can help communicate complex results and engage
stakeholders in the decision-making process for fishery management plans.
1.4. Summary
The overall goal of this study is to describe the spatiotemporal patterns of snow crab
distribution and abundance in relation to environmental conditions (surface temperature, bottom
temperature, depth) and predation (Pacific cod abundance). This study also seeks to demonstrate
how GIS can be applied in marine fisheries ecology towards exploring and modeling
relationships in space and time.
EBS bottom trawl survey data of snow crab distribution and abundance was gathered in
ArcGIS Pro 2.6.1. The Space time Pattern Mining Toolbox and Modeling Spatial Relationships
toolsets provided statistical modeling tools to analyze and visualize spatiotemporal trends across
the EBS from 1982 to 2018. Concurrent predator abundance and temperature data were included
for ecological context as two key explanatory variables impacting snow crab populations. Three-
dimensional (3D) rendering of the dataset provided context for regression analysis which

10
explored the scale and significance of the ecological relationships with snow crab distribution in
2018.
This thesis is presented in five chapters, beginning with this introduction to snow crab
spatial biology, significance of the fishery, and EBS ecosystem dynamics. Chapter 2 is a
collection of related work on the spatiotemporal analysis of species distribution and abundance
patterns in the EBS, including traditional regression techniques and more novel spatial
approaches. Each of these works served as a guide in development of the methods outlined in
Chapter 3, including dataset engineering, GIS integration, geostatistical tools, and analyses of
spatiotemporal patterns. Chapter 4 presents the results of the analysis and main findings, and
Chapter 5 expands on the results in a broader ecological context, discusses successes and
limitations of the chosen methodology and potential for further development. Chapter 5 also
presents the case for GIS as an effective analysis and visualization tool in marine fisheries
ecology.

11
Chapter 2 Related Work
This chapter outlines previous research related to species distribution and climate in the eastern
Bering Sea and provides examples of GIS as applied to spatiotemporal analysis and spatial
regression techniques in marine fisheries and ecology. Recent environmental and biological
trends are described for the EBS environment and C. opilio, and approaches to modeling
expansive spatiotemporal datasets that extend over a large and dynamic environment like the
EBS shelf are discussed. Examples from other regions and scientific domains which have
utilized GIS for statistical analysis are also provided to supplement the relatively few examples
of GIS and local regression analysis in marine fisheries studies.
Spatial non-stationarity is typical of species distributions in marine systems, but local
scale variation is often masked by global scale trends. A better understanding of local variation
can inform global regression model performance and development of hypotheses for the multi-
scalar processes underlying variation in snow crab distribution and abundance. This project
demonstrates the efficacy of GIS in performing exploratory spatiotemporal analysis and
regression modeling of large datasets through visualization and geostatistical analysis. Spatially
focused methods were structured to capture multi-scale patterns in snow crab distribution in the
EBS and to introduce alternative methods for exploring temporal correlation as well as
identifying local relationships in a large dataset.
2.1. Measuring Ecosystem Change in the Eastern Bering Sea
Temperature is a main determinate of marine species distribution and preferred habitat
range as it controls physiological function (metabolism, growth, reproductive rate) (Molinas et
al. 2018). Stevenson and Lauth (2018) have suggested that warming trends beginning in the
1970s coincide with a regime shift in which groundfish abundance began to increase and

12
overtake the ecosystem previously dominated by subpolar benthic invertebrates such as snow
crab. The shift occurred as subpolar species retreated to the north and colder temperatures
(Mueter and Litzow 2008; Stevenson and Lauth 2012; Kotwicki and Lauth 2013) but the
significance of the change and the magnitude varies amongst the research depending on
modeling approach and units of analysis. Though temperature has been identified as the most
significant environmental determinate of wide scale distribution patterns in snow crab and other
marine species, there is ongoing debate as to the significance of top-down predator-prey
relationships between invertebrates and groundfish as populations are shifting (Orensanz et al.
2004; Zheng and Kruse 2006; Parada et al. 2010; Windle et al. 2010; Windle et al. 2012; Murphy
2020).
2.1.1. Spatial Units
Fisheries and species distributions are often modeled through some form of global
regression analysis (Cianelli et. al 2008). For large study areas the region is usually divided into
smaller spatial units prior to analysis to improve model performance as a single equation is fit to
the spatial unit chosen. Some distribution and abundance studies divide the EBS according to
oceanographic patterns (Parada et al. 2010) or physical characteristics like depth (Ernst et al.
2005; Emond et al. 2015). Burgos et al. (2013) divided the EBS according to geographic domain
(coastal, middle, and outer as described in the introduction), a common reference system for the
region that was adopted for this study. Burgos et al. (2013) further divided the EBS into
transverse sections parallel with latitude, resulting in 13 spatial units in their analysis of snow
crab distribution. Global results for each unit were compared to describe pseudo-local variation
in distribution in relation to temperature and Pacific cod predation.

13
Snow crab distribution is often related to the extent of the cold pool, which can
alternately be defined by the 1° or 2℃ isotherms throughout literature. Kotwicki and Lauth
(2013) calculated the change in area over a 30-year time series of EBS survey data adhering to
the 1℃ definition of the cold pool. This change variable (∆) was an input parameter for a
generalized additive model (GAM) to determine the impact on snow crab distribution and is one
of the rare studies to report no significant relationship between temperature and species
distributions, as no significant trend was detected in the cold pool extent over the study period.
Trends in species distribution were attributed to temporal correlation, while environmental
variables were found to be less significant. Other studies have defined the cold pool by the 2℃
isotherm (Mueter and Litzow 2008; Marcello et al. 2012; Murphy 2020). Marcello et al. (2012)
applied a similar GAM technique to describe snow crab distribution data from surveys in the
northwest Atlantic and found significant correlation with lagged temperature variables.
The temporal units of analysis also vary from study to study. Year to year pairwise trends
have been used to model temporal correlation at single locations (Kotwicki and Lauth 2013).
Survey years have also been aggregated to investigate cumulative effects and large-scale
processes (Orensanz et al. 2004; Marcello et al. 2012). Temporal lag from environmental impacts
at various life history stages in the snow crab life cycle has been investigated to understand the
cyclical patterns of abundance or temporal correlation and connectivity between year classes of
snow crab (Ernst, Orensanz, and Armstrong, 2005; Marcello et al. 2012; Emond et al. 2015).
Spatiotemporal exploration and visualization of species distributions using a multiscale
approach in GIS can lead to better developed regression models and therefore better prediction of
species distributions and abundance. Geographically weighted regression (GWR) is used to
visualize how the strength and nature of relationships vary spatially by performing the regression

14
at each location in the study area, which can identify regions where relationships are consistent
and the dependent variable is predicted with higher accuracy – or regions where the model
performs poorly indicating a missing variable (bias) or non-linear relationship (Mitchell 2009).
In this way model results can help identify ecological regions and the conditions that shape
species distributions. Global and local regression techniques are discussed in section 2.2.3.
2.1.2. Ecological Considerations
As snow crab populations shift north, Parada et al. (2010) postulated that circulation
patterns in the EBS present a barrier to re-distribution into the southern EBS, even in years of
favorable conditions (<2°C). A previous study by Orensanz et al. (2004) had termed this
asymmetrical shift the ‘environmental ratchet hypothesis’ (ERH). In this case warming trends
initially provided a bottom-up control of crab recruitment and potential range of habitat, but EBS
currents, female migration patterns, and cod predation on juvenile crab prevented the southward
expansion during more favorable cold years. This has resulted in a realized niche or limited
extent of a species’ potential habitat.
Based on their study of female distribution and immature cohort classes, Burgos et al.
(2013) hypothesized that an extended cold period from 2006 to 2010 resulted in decreased
abundance of cod, and therefore predation, which allowed for the observed increase in
recruitment of immature crab to the middle domain in 2010. Pulses of high abundance have been
noted throughout the literature and are believed to correlate with the strength of female parent
cohorts, with some dampening effect of predation and the ERH proposed by Orensanz et al.
(2004).
Although temperature may be a main driver of species distributions and biogeography of
the EBS, multiple factors influence the survival and distribution of snow crab at different stages

15
in its life cycle. Sea surface temperature (SST) will impact the growth and survival of pelagic
larval stages, whose transport is controlled by surface currents in the EBS; bottom temperatures
then exert more influence in benthic distribution as immature crab preferentially settle in the
colder middle domain (Orensanz et al. 2004; Parada et al. 2010). Immature crab and small
females are preferential prey for Pacific cod, so predation pressure effects are also focused on
this segment of the population. Studies which break down the snow crab population into
population demographic groups or sex age classes have captured variable distribution and
abundance patterns that reflect sex and age class-specific preferences and ecological
relationships (Ernst, Orensanz, and Armstrong 2005; Ernst et al. 2012; Emond 2015; Murphy
2020). Variable life history stages and a fluctuating environment in terms of temperature and
predation suggests spatial non-stationarity, or locally variable relationships, that might contrast
with global trends in snow crab distribution and abundance.
Emond et al. (2015) and Boudreau, Anderson, and Worm (2011) also studied female
cohorts separately from the snow crab population total to describe temporal trends. They
observed, in many cases, a correlation between mature female abundance and a lagged
recruitment pulse approximately 4 years later as progeny presumably settled to the benthos.
Murphy (2020) tracked immature females, mature females, and mature males separately in an
analysis of snow crab and its cousin, tanner crab, in the EBS to flush out the relationships
between each demographic with temperature and depth.
Pacific cod stomach contents from the EBS survey have been analyzed in various studies
and indicate that snow crab is a main prey item (Lang et al. 2005; Boudreau, Anderson, and
Worm 2011; Burgos et al. 2013). Predation has also been postulated as a top-down control of
snow crab abundance, but global regression analyses have failed to capture any significant

16
relationship between predator species and snow crab. This may be due, in part, to significant
differences in spatial distribution and overlap on the EBS as well as in scales of abundance. This
scale factor and spatial variation between the two species drives much of the deviation in spatial
units of analysis seen in previous studies.
An exploration of the spatiotemporal distribution of snow crab sex-age classes and
historical environmental conditions can help visualize and define distribution patterns in space
and time that can inform progressive statistical analysis and support further hypothesis
development.
2.1.3. Space Time Exploration of Distribution
Bottom temperatures in the EBS have fluctuated between averages of .5 to 5℃ for the
shelf survey region since 1982. A recent warming trend began about 2011 and peaked in 2016;
after three years of no sea ice formation over the shelf average temperatures remain near peak
highs over 3℃ (ADFG 2019). Charts for average bottom and surface temperatures and CPUE
(number/ nm
2
) for total snow crab, immature snow crab, mature female snow crab, and Pacific
cod are shown in Figures 3 and 4.

Figure 3. EBS average summer sea surface and bottom temperatures, 1982 – 2018

17

Figure 4. EBS annual total CPUE (number per nm square) for immature, mature female, and
total snow crab age classes, and Pacific cod, 1982 – 2018

Snow crab abundance in the EBS over the time series was highest between 1986 and
1996. CPUE peaked at over 7 million in 1993, then dropped to under 500,000 by 1999. This was
the first time Pacific cod CPUE values overcame those of snow crab since 1985. Since the sharp
decline in 1998 and 1999 down to 500,000 CPUE, a small peak occurred in 2014 at just over
3,500,000 before CPUE again dropped to the historic low of 250,000 in 2016. Pacific cod
abundance fluctuated at a smaller scale than snow crab over the series and was relatively more
dispersed. Peak CPUE of Pacific cod on survey over the time series was just under 2,000,000 in
2014 and dropped to its lowest survey record in 2018 at 500,000 CPUE.
Prior to 1998 average bottom temperatures fluctuated between 2 and 3.5℃ (a 1.5℃
range) while post-1998 the average fluctuated between .5 and 5.5℃ (a 5℃ range). Average
bottom temperatures rose from 2℃ in 2006 to 4.5℃ in 2018. After a second year of no sea ice
formation over the EBS shelf, no cold pool formed in 2018. Only seven stations on the northeast
fringe of the survey area reached a summer low of 1.6℃ (bottom temperature maps for 2006 to
2018 are provided in Appendix A). In previous years when the cold pool formed it proliferated
south along the middle domain (50 – 100 m), and immature snow crab clustered here.

18
2.2. GIS Modeling
GIS is a technology increasingly used for integrating, analyzing, and visualizing
spatiotemporal data. Space time analysis and geostatistical methods have been used in various
domains to explore, quantify, and build on established theories, and the mapping of spatial
information and data visualization enhances communication. Visualizations can also promote
engagement in the fisheries management and decision-making process (Kemp and Meaden 2002;
Cianelli et al. 2008; Hardy et al. 2011).
Many of the previously mentioned studies apply basic GIS tools to interpolate data points
and derive surface maps of temperature and abundance patterns, or to plot time series of
population centers over time. These are simple yet effective methods of visualizing geographic
shifts in species ranges and ecological relationships. GIS also provides more sophisticated tools
for the analysis and visualization of spatiotemporal data, and cluster and outlier detection in
spatiotemporal correlation tests. The suite of regression tools available in ArcGIS Pro has been
expanded for global and local modeling techniques such as ordinary least squares (OLS) and
GWR.
Predictive modeling and machine learning (ML) is also being developed in GIS and may
provide fisheries managers with tools for making effective decisions for spatial quota allocations
(Cianelli et al. 2008; Hardy et al. 2011). Extensive, robust datasets and repetitive testing are
required to train models and accurately identify the scale of ecological processes in action, which
can change over time. GIS enables manipulation and interchange of variables and analysis units
(spatial or temporal) as input parameters in regression and ML algorithms towards better
predictive modeling.

19
2.2.1. Spatiotemporal Analysis
Standardized fisheries surveys are designed to collect repeated measurements at regular
frequency and locations to enable robust statistical analysis. This enables managers to measure
change and estimate its significance over time with some amount of probability or confidence
(Stamatopoulos 2002). Datasets with spatial locations and time stamps can be structured as a
space time cube with netcdf file formatting to enable spatiotemporal pattern mining and
statistical analysis in ArcGIS Pro. The cube structure enables visualization and analysis of
change over time at each location by assigning location IDs and time step interval designations
to each record. This makes space time cubes particularly well-suited for modeling ecological
systems and managing station data like the EBS bottom trawl survey.
Spatiotemporal analysis in GIS differs from traditional statistics which focus on the
attribute value in dataspace and assume independence between observations (Fotheringham
2002; Ciannelli et al. 2008). Spatial and temporal autocorrelation relate to Tobler’s first law of
geography in that nearby features are more similar than those located farther apart
(Fotheringham 2002). Spatiotemporal analysis accounts for the autocorrelation of attribute
values and accepts some degree of dependence between nearby observations by differentially
weighting features (in this case individual survey station records) according to the distance
between them (Mitchell 2009). For example, survey stations within a specified distance, or
spatial neighborhood, are more heavily weighted in spatiotemporal analyses than those outside
this distance since catch records of snow crab are likely comparable with catch records at nearby
survey stations. As distance between survey locations increases, the correlation in attribute
values is likely to decrease so the spatial neighborhood distance should represent the degree of
interaction or dependency between features.

20
Without any spatiotemporal autocorrelation the attribute values would appear randomly
distributed across the study area and over time (Mitchell 2009). GIS analyses quantify the level
of clustering (positive correlation) or dispersion (negative correlation) and incorporate this aspect
of the data in the calculation of statistics within the context of the spatial neighborhood to
determine how significantly the patterns diverge from a random distribution (see Mitchell 2009
for a detailed explanation of the mathematical formulas, or Fotheringham 2002 in the case of
GWR). A p-value is assigned in the statistical output to indicate whether the pattern is
significantly different than random, and a z-score with a negative or positive designation to
indicate if the trend is increasing or decreasing along a standard normal distribution curve (z-
score of zero would be equal to the mean).
The Mann-Kendall statistic is automatically applied at every defined location during
creation of a space time cube. This independent bin test summarizes the temporal trend in the
attribute over time at each station location by summing each bin as an increase (+1) or decrease
(-1), or tie (0) with the previous time step (Esri 2020). Time series cluster analysis in ArcGIS Pro
compares these temporal trends for the characteristic or attribute of interest, and groups stations
together based on correlation in the timing and proportional change in the value over time
(attribute profile correlation). Time series clusters represent areas of similar population growth
patterns which could be of interest to fisheries managers and ecologists.
Alternative spatiotemporal analyses are adapted from traditional methods to identify
clusters of similar values. Cluster locations provide context for regression modeling and
understanding relationships. The Anselin Local Moran’s I statistic (clusters and outliers analysis
in ArcGIS Pro) is calculated by comparing the target feature bin in the space time cube with
nearby (local) bins using the spatial neighborhood concept, then comparing the local mean

21
against the global mean of features to identify outliers and/or correlation in the characteristic of
interest (Esri 2020). Hot spot analysis calculates the Getis Ord Gi* statistic for each bin location
by comparing the target feature within the spatial neighborhood; hot spots are high value features
surrounded by other features with high values, and are considered statistically significant if
locally (in space and time) the sum characteristic of interest is greater in proportion than the
global sum. Hot and cold spots indicate areas of significant decline or growth in population.
Emerging hot spot analysis in ArcGIS Pro further describes the trend by classifying each station
location in the space time cube according to recent temporal patterns (for a full description of the
emerging hot spot classification scheme see Esri 2020).
Whereas the spatial component of a data point and visualization are typically secondary
to the quantitative results and the data attribute value, fisheries managers are increasingly calling
for spatially focused analyses (ADFG 2019; NPFMC 2019). Kemp and Meaden (2002)
developed a custom system to support decision making through spatiotemporal exploration,
visualization, and multivariate modeling via GIS. Their goal was to present users (managers)
with a tool for exploratory visualization through customized mining of spatiotemporal data. The
GIS application allowed users to specify input variables (species and/or sex age classes), analysis
units (spatiotemporal aggregation) and varied statistical tests. The development of customized
software is beyond the scope of this project, but the project goal demonstrates the value to
management of exploring spatiotemporal parameters to assess how choices in spatial
neighborhood and spatial units affect the results. GIS also offers the efficacy of having
immediate visual support of results.
There are few examples in related research which take advantage of the recently
developed space time pattern mining tools in ArcGIS. A Master’s thesis by C. Steves (2017)

22
demonstrated the efficacy of the space time cube in detecting change in the Alaska bottom trawl
fishery in terms of effort (number of trawl tows) and efficiency (weight per tow). Visualization
of change in these parameters relative to the location of marine protected areas (MPAs) and sea
ice extent in the EBS between 1993 and 2015 revealed clusters of increased (hot spots) or
decreased (cold spots) bottom impact and fishery productivity. These spatial and temporal trends
could help guide the decision-making process for identifying priority impact areas or low
productivity fisheries that could benefit from temporary or established conservation areas.
Epidemiology is another domain which has taken advantage of the space time capabilities
of ArcGIS software. Zulu, Kalipeni, and Johannes (2014) built a progressive, multi-scale
statistical analysis based on a 7-year time series of HIV infection in Malawi to better understand
spread of the disease. This case study applied spatiotemporal analysis and regression in GIS to
analyze HIV prevalence in Malawi over a seven-year time period. Anselin Local Moran’s I
statistic identified clusters of similar prevalence rates (high positive autocorrelation) and outliers
surrounded by much higher or lower prevalence rates (high negative autocorrelation). Clusters
indicated areas experiencing similar disease trajectories which provided context for the
regression analysis. OLS was used to measure drivers of infection such as population density and
distance to population centers. By applying the regression to national and local level district
administrative units, the results could provide a framework to implement intervention policy
plans at district and national levels to predict and mitigate the spread of disease.
The progressive statistical analysis using GIS and visualization techniques for the study
in Malawi serves as a model for this project’s methods structure. The EBS bottom trawl survey
provides a robust and extensive dataset to similarly explore space time trends and relationships
that could help understand how fisheries species distributions are changing in space and time in

23
order to more efficiently allocate quota spatially. As in the Zulu, Kalipeni, and Johannes example
(2014), preliminary space time explorations were used in this study to provide context to
regression modeling at multiple scales.
2.2.2. Predictive Modeling
A unique and creative application of ML and the space time cube was implemented by
Aydin and Butler (2019). In this case, random forest (RF) algorithms were used to determine the
ocean conditions impacting the health of seagrass habitat and predict the expansion or
degradation of these marine habitats globally. An effective map derived from this analysis
depicts the results of an emerging hot spot analysis, showing areas of increasing or decreasing
suitability for seagrass growth. A variation in the time cube 3D visualization structured rising
temperature along the z-axis rather than time; hot or cold spots were predicted for each location
depending on the magnitude of warming scenario as per degree of sea surface temperature
increase.
Considering the northward shift in species distributions and the limited spatial coverage
of the EBS survey, Hardy et al. (2011) developed a complex ensemble model for predicting the
distribution of snow crab in areas outside the range of the survey grid by integrating data from
the EBS with limited surveys conducted in the Chukchi and Beaufort Seas. Snow crab
abundance and biomass were overlaid with 20 layers of environmental predictor variables which
included typical ecological indicators such as sea surface temperature, nitrate concentration,
salinity, chlorophyll-a, total organic carbon, infaunal biomass (food source), dissolved oxygen,
and depth. The relative importance of each predictor was used to develop a quantitative model of
the ecological niche and generate a predictive surface of the entire region.

24
Prediction was not the goal of this project, but the ML examples provide insight that can
be incorporated in the current research to support choices of explanatory variables. The RF
model ranked 3 variations of surface temperature as the most important predictor of snow crab
distribution, supporting bottom temperature and SST as recorded at survey locations as
significant environmental indicators. While Hardy et al.’s (2011) results were relatively
successful in detecting the potential niche, the most successful algorithm still failed to accurately
predict presence or absence in multiple southern regions of the EBS. This supports further
investigation of factors other than temperature impacting snow crab distribution in the south
through techniques like GWR which capture this non-stationarity.
2.2.3. Describing Relationships
As demonstrated by the seagrass study and the ensemble model of snow crab distribution,
understanding ecological relationships is necessary to predict future scenarios for these vital
marine resources in the face of a changing climate. Modeling the distribution of mobile
organisms in a dynamic environment over time and deciphering the spatiotemporal correlations
of a multitude of biotic and abiotic interactions presents challenges. Spatiotemporal visual
exploration and analysis can be a strategic first step to identifying patterns and relationships to
support regression and eventually predictive modeling.
Regression techniques such as ordinary least squares (OLS) and GWR have recently been
developed for Esri’s ArcGIS platform and are included in the Modeling Spatial Relationships
toolset. Few examples exist in the literature for GWR as applied to fisheries, but the technique
shows promise as an exploratory tool and is well suited for GIS as each station location is
assessed individually, enabling visualizations of the results for each relationship in space.

25
2.2.3.1. Global regression
Many of the previously mentioned works apply global forms of regression such as GAM
and generalized linear models (GLM) in their approach to modeling distribution of snow crab in
relation to temperature, predation, and other variates. Global modeling results are highly
sensitive to the areal unit chosen as the analysis is based on the entire dataset as a single solution
is calculated for the intercept term, variable coefficients, and the model’s goodness of fit across
the study region.
Emond et al. (2015) investigated the cyclical fluctuation in the northwestern Atlantic
snow crab populations in relation to environmental drivers. By tracking groups of early benthic
instars over 23 years, this study was able to measure the strength of pseudocohorts (female year
classes) over time in relation to multiple variables using global regression and ordinary least
squares (OLS). Results suggested that intraspecies cannibalism and bottom water temperature
had the strongest influence on distribution and survival for early instars (three years old, newly
settled snow crab). This countered the hypothesis that historical predation or snow crab
abundance values were the more significant variables determining the fluctuations in total snow
crab abundance. Historical variables or lagged variables were incorporated as regression model
independent variables as representative of the temporal correlation between current snow crab
distribution patterns and past environmental conditions like sea temperatures, predator
abundance, and maternal age class abundance or larval production. The global OLS modeling
applied in this study may have been too large scale to capture local variation inherent in species
relationships, particularly predator-prey. North Atlantic cod and snow crab ranges only partially
overlap in this region so community scale relationships would have been dampened by OLS
which smooths the local variation in favor of the global average.

26
This study in the northwest Atlantic and the works mentioned in relation to spatial
analysis units highlight a limitation of global approaches to regression. An exploration of these
processes at multiple scales using GIS (global OLS and local GWR) captures global trends and
local variation, and spatiotemporal analysis provides context that may help with interpretation of
scale and autocorrelation.
2.2.3.2. Local regression
GWR is a local technique that can be applied in an exploratory way to support the fine-
tuning of global scale regression models (Fotheringham 2002; Foody 2004; Zhang and Shi 2004;
Bevan and Connolly 2009; Windle 2010). GWR has the advantage of visual exploratory power
through mapping of each independent variable’s coefficient, calculated at each location in the
study area. Clusters in residuals indicate collinearity or model misspecification and can therefore
help identify missing variables and appropriate scale or spatial units. Global and local scale
regression model diagnostics and the local variable coefficients in GWR can be compared to
visualize local variation in the strength of relationships as compared to the overall trends
described globally.
OLS model diagnostics include the Variance Inflation Factor (VIF), Joint F and Wald
statistics, the Koenker (BP) statistic, and Jarque-Bera statistic, each with associated probabilities
of significance. VIF scores greater than 7.5 indicate redundancy in the independent variables or
multicollinearity. The Koenker statistic determines the level of spatial and value consistency in
the relationship (nonstationarity). The null hypothesis for this test indicates a stationary process
in space and CPUE variation, while a significant Koenker (p-value < .05) indicates spatial non-
stationarity and further reasoning for GWR analysis. The Joint F statistic can be interpreted as a
measure of overall model significance if the Koenker test is not significant. If the null hypothesis

27
is rejected and nonstationarity results in a significant Koenker test statistic, the Wald statistic
should be used to determine model significance. A p-value < .05 for the Wald or F statistic
indicates a significant model. Lastly, the Jarque-Bera statistic test indicates a normal distribution
in the model residuals. If the Jarque-Bera test was statistically significant, this would indicate
that residuals were skewed and the model was biased towards over- or underestimating CPUE
values in certain regions on the map and/or in data space. Bias could be due to misspecification
(missing model variables), nonlinearity in the relationships, extreme outliers, or spatial
nonstationarity as indicated by the Koenker test.
Foody (2004) pioneered the application of GWR for ecological research on bird species
distributions in Europe and found that the relationship between bird species biodiversity,
temperature, precipitation, and NDVI varied spatially and at different scales in sub-Saharan
Africa. Similar determinations of spatial non-stationarity or inconsistent relationships across
space have been demonstrated in other domains in addition to ecology.
GWR outperformed global OLS models in Zhang and Shi’s (2004) forestry productivity
study that measured tree growth in relation to several local environmental parameters. In this
case, mapping of model coefficients provided visualizations of the nature of the relationship
between growth patterns, stand density, and timber yield for multiple tree species in New
Hampshire. Local coefficient mapping illustrated the spatial processes under study and supported
the development of established global models by identifying areas of poor model performance in
low r-squared (r
2
) values. GWR local r
2
values represent the proportion of variance in the
dependent variable accounted for by variance in the independent variables. A low amount of
variance explained indicated model misspecification or missing independent variables and
differences between tree species.

28
Bevan and Conolly (2014) also demonstrated the utility of GWR and mapping local
variable coefficients in the field of archaeology. Their investigation of pottery artifact density in
relation to slope, geology, and other environmental variables across a small island in Greece
enhanced the predictive ability in finding pottery deposits by identifying areas predicted to have
similar densities and could help focus sampling efforts to maximize discovery and collection of
artifacts and helped to focus sampling efforts in areas that transect sampling would have poorly
covered. Maps of regression model residuals showed a high degree of spatial correlation in the
pottery deposits and pockets of similar relationships, indicating what may be appropriate spatial
units of analysis for future studies. This work uncovered spatial structure in pottery deposits at
variable scales and enabled hypotheses of human settlement patterns and timelines, ultimately
supporting more accurate global spatial models of ancient civilizations and the geomorphological
processes which alter their archaeological record.
A single case of local modeling in fisheries was found in research which applied GWR.
Windle et al. (2010) compared the performance of global and local regression modeling
techniques to describe the spatial distribution of northern Atlantic cod off the coast of
Newfoundland and Labrador, Canada in relation to temperature, distance from shore, and
abundance of two key prey items (northern shrimp and snow crab). The predictive success (in
terms of model error or residuals) of a traditional global logistics and binomial GAM were each
compared to that of a logistic GWR. GWR outperformed the global GAM approach in terms of
error, and spatial variation in the strength and nature of relationships were visualized through
mapping of variable coefficients. Mapping of the GWR residuals in this northwestern Atlantic
example also facilitated the detection of areas where the model was less effective in explaining

29
the observed variance, which supported inference as to model mis-specification or multi-scalar
processes occurring in these areas.
In GWR and spatiotemporal analyses, the kernel bandwidth or spatial neighborhood
chosen for the analysis is critical as it represents the window surrounding the sample location
included in the local regression and spatially weighted statistical analysis. Windle et al. (2010)
and Bevan and Connolly (2009) each devised a measure of spatial non-stationarity by iterating
through increasing kernel bandwidths and comparing coefficient of variation (CV) scores to
determine the scale at which relationships became heterogenous. Other methods of determining
appropriate bandwidths include incremental adjustment of the distance until a minimum
Akaike’s Information Criterion (AIC) score is reached, indicating optimum model performance
(Fotheringham 2002; Windle et al. 2012).
The insight gained from Windle et al.’s (2010) initial exploration of
invertebrate/habitat/predator associations via GWR led to a second iteration in which snow crab
and shrimp were examined as dependent variables, rather than cod (Windle et al. 2012). This
study applied GWR to a 20-year time series but limited the spatial extent by first determining
core habitat ranges for shrimp and snow crab in the northwest Atlantic. Windle et al. (2012)
chose to highlight a warm (low abundance) and cold (high abundance) year from their time
series to compare the spatial variability of the GWR coefficients, which proved an effective
visualization technique. Model residuals were higher in shallower areas, indicating missing
variables and possible grounds for partitioning of the dataset.
As in the previous study, the relationships between crab and cod were relatively weak
and showed stronger dependence on depth and environmental factors. However, the species
assemblages in this region exhibit variable oceanographic patterns and ecosystem structures

30
compared to the EBS. In the northwestern Atlantic, warmer waters are found at shallower depths,
which is opposite that of the EBS. Species abundance for snow crab and cod are also much lower
in the Atlantic and diet studies show that shrimp are preferred over snow crab. For lack of
widespread presence Windle et al. (2012) restricted their study area to a ‘core habitat’ zone
where snow crab was more prevalent in survey samples. Snow crab and Pacific cod are both
widespread across the EBS and their ranges overlap to a greater extent than in the Atlantic. For
these differences, GWR may produce variable results in the EBS as a significant relationship
between shrimp and Atlantic cod was described in this study.
This second GWR study in the Atlantic also highlights an important point, or possible
pitfall, of regression modeling. Relationships must be linear for OLS and GWR modeling, and
scatterplots or histograms should be examined to determine if a data transformation is necessary.
Windle et al. (2012) tested univariate relationships to determine significance and nonlinearity,
then ran the regression with and without data transformations for the few variables that exhibited
nonlinear relationships. An interesting result was that there was no significant difference
between the analyses using transformed data. Methods were developed for this study with these
factors in mind, and extensive data exploration was performed to understand data distributions
and achieve a linear transformation. This process is discussed in the following chapters.
2.3. Summary
GIS enables integration, analysis, and visualization of complex, multivariate
relationships, and the detection of spatial and temporal correlation. While GIS tools do not
eliminate the pitfalls of the MAUP or scale when dealing with large datasets, exploration and
visualization can help to understand these data characteristics and lead to better informed
parameter choices.

31
This study seeks to build on these previous works of fisheries biologists and spatial
analysts to describe the spatiotemporal distribution and abundance patterns of C. opilio in the
EBS utilizing GIS visualization and statistical tools. Cues from other studies showing spatial
stratification of the population and temporal correlation in abundance support the breakdown of
the population into sex-age classes to investigate spatiotemporal patterns. The progressive
spatiotemporal and regression analysis performed by Zulu, Kalipeni, and Johannes (2014) served
as a basic methodology for space time and regression workflows while the approach of Windle et
al. (2010, 2012) in the application of GWR was adapted to the EBS survey dataset.

32
Chapter 3 Methods
GIS can provide a means of integrating and manipulating complex spatiotemporal datasets,
performing analysis, and visualizing results in three dimensions. The methods in this study were
implemented to demonstrate the capabilities and benefits of GIS for these purposes with a
specific application in fisheries surveys. Spatial and temporal explorations which describe where
and when change is occurring in these historical spatial datasets facilitate deeper investigations
into observed changes to understand the relationships and the mechanisms which shape species
distributions. The methods developed for this study were intended to demonstrate the utility of
GIS for spatiotemporal analysis and regression modeling, and the power of space time pattern
mining and GWR in supplementing more traditional methods of fisheries stock assessments and
statistical analyses.
3.1. Data Source: EBS Bottom Trawl Survey 1982-2018
A subset of the EBS bottom trawl survey conducted by National Oceanic and
Atmospheric Administration’s (NOAA) Alaska Fisheries Science Center (AFSC) and Resource
Assessment and Conservation Engineering (RACE) division was developed for spatiotemporal
analysis and regression modeling using ArcGIS Pro. A point feature class was created in ArcGIS
Pro from the geographic coordinates of each standard survey station (provided by NMFS in
decimal degrees) and projected to Alaska Albers Equal Area coordinate system. A space time
cube was created from this feature class for visual exploration and analysis of species
distributions and environmental conditions from 1982 - 2018.
This time series included 349 stations sampled annually from 1982 to 2018. EBS CPUE
survey data was downloaded from NOAA’s RACE division site (AFSC 2019). Catch per unit
effort (CPUE) was adopted as the species abundance variable in the analysis as it is a

33
standardized measure often applied in fisheries research and management as a relative index of
abundance (Orensanz et al. 2004; Parada et al. 2010; Zheng and Kruse 2006; ADFG 2019). The
dataset was organized so that each survey station annual record included the CPUE for (total)
snow crab, immature snow crab, mature female snow crab, and Pacific cod, as well as depth,
near bottom temperature and surface temperature.
In total the EBS bottom trawl survey samples nearly 216,000 nm
2
(400,000 km
2
) of the
shelf. Vessels typically tow for 30 minutes at a standard 3 knots (1.54 m/s), starting in the coastal
domain in late May/early June and ending in August or September with the outer domain
stations. The survey is designed so that established coordinate locations or stations are sampled
annually; 349 standard stations are stratified across the shelf in a 20 by 20 nm grid aligned with
latitude and longitude. Certain areas of high catch rates are fished in a denser grid by adding a
station at the corner of the 20 x 20 nm grid cell but these stations were excluded from the
analysis to maintain spatial and temporal consistency in the CPUE index. EBS survey data prior
to 1982 was excluded due to a change in trawl gear specifications, which likely impacted catch
efficacy. This resulted in over 12,913 data points over 37 years.
A bathymetric surface layer was interpolated from the depth of survey stations using the
geostatistical method kriging. Ordinary kriging defaults were accepted as the layer was for
visualization purposes only. The default cell size is 1/250
th
of the lesser extent, height or width,
in the output coordinate system linear reference – in this case Alaska Albers and meters. This
resulted in a raster of cell size 2 x 2 nm (3763 m), which was then clipped to the survey extent
within a 10 nm buffer. Depth contours at 50 and 100 m were derived from this raster layer as a
second visual aid to delineate the shelf domains (coastal, middle, outer). The cold pool expands
south from the Arctic along the wide and flat middle domain, between 50 and 100 m. Immature

34
snow crab are stenothermic and thrive within a narrow range of temperatures around 2℃ so the
cold pool extent is critical in shaping snow crab population spatial structure (Orensanz et al.
2004).
One limitation of the EBS survey design is that smaller and more fragile animals (early
settlement phase snow crab and youngest immature crab) can be missed in the larger net mesh or
destroyed in the trawling/sampling process. Some survey bias also likely results from timing.
The survey begins in May/June in the coastal domain and vessels fish towards the shelf edge and
deeper stations in the outer domain to finish in August/September every year. Climate change
may be affecting the timing of spring phytoplankton blooms which could affect the timing of
snow crab migration and reproductive cycles, and the sex-age class spatial structures observed
during summer months (Orensanz et al. 2004; Parada et al. 2010). Despite these timing and catch
efficiency biases, the length and consistency of the EBS bottom trawl survey provides a reliable
dataset that supports rigorous statistical analyses. A complete list of data variables and
definitions from the survey data used in this analysis is provided in Table 1.
Results of the spatiotemporal analyses and regression are highly dependent on the spatial
neighborhood distance or kernel bandwidth. A preliminary test of GWR was performed to
determine the optimal distance band that would minimize the AIC score. This was done to
synchronize the distance band with the spatial neighborhood distance applied in the
spatiotemporal analysis, to maintain scale for comparison. The Gaussian kernel bandwidth in the
GWR was first tested at 25 nm, or just over the distance between two survey stations. The
distance was incrementally increased by 20 nm to 45 and 65 nm (just over the distance between
three stations). The AIC scores dipped to a minimum at 45 nm before increasing again, so 45 nm
(85 km) was the adopted spatial neighborhood distance for the spatiotemporal analysis and

35
kernel bandwidth in the regression modeling. Snow crab CPUE in 2018 was elected as the
dependent variable for the regression analysis as this was the most current year available.

Table 1. EBS Spatiotemporal Data: 1982 – 2018

Attribute Definition Unit, resolution Data description
YEAR Year survey
conducted
Year, annual 1982 – 2018 surveys

STATION Survey station ID Nominal ID, unique 349 standard shelf stations
20 x 20 nm stratified grid

LATITUDE,
LONGITUDE
Station location decimal degrees, 1e
-05

°N, °W
Average geographic
coordinate location per
station (approximate centroid
of grid cell)
BOT_DEPTH Bottom depth

meters, .1 m Weighted average depth for
area swept
BOT_TEMP Near bottom
temperature
degrees Celsius, .1 ℃ Weighted average
temperature measured at
maximum depth of trawl
headrope

SURF_TEMP Surface
temperature

degrees Celsius, .1 ℃ Temperature measured at
surface
CPUE Catch number per
area swept
number/nm
2

Total Snow Crab
Immature Snow Crab
Mature Female Snow Crab
Pacific Cod

3.1.1. Data Distribution and Exploration
CPUE data distributions were explored, and a preliminary local regression test was
performed on snow crab CPUE to determine an appropriate spatial neighborhood or kernel
bandwidth for analysis. The presence of many records of zero CPUE interspersed throughout the
dataset by nature of the patchy distribution of snow crab resulted in a skewed data distribution.
To prevent the loss of any data and maintain a continuous model of distribution, a log (x +1)

36
transformation was applied to all CPUE values to normalize the data and enable regression
analysis. Twenty-nine stations were removed from the coastal domain which recorded zero
CPUE for snow crab the entire period (discussed further in the results for time series cluster
analysis).
Abundance data for snow crab remained slightly skewed following transformation
(Appendix A). Linear regression requires normally distributed data for optimal performance.
However, previous work of Windle et al. (2012) in their second GWR study showed that the
regression results did not significantly change by transforming the abundance data from a non-
normal distribution. Considering these results using similar survey data from the NW Atlantic,
the log (x +1) transformation sufficed for the exploratory intent of this study.
3.2. Space Time Cube Exploration of Distribution
A space time cube was created which organized the CPUE station data into bins for each
year and station location, and time represented in the vertical t dimension so that 37 bins stacked
represent a time series of CPUE at that location. The space time cube was input to Emerging Hot
Spots, Local Clusters and Outliers (Anselin Local Moran’s), and Time Series Clusters. Each
analysis is further explained below. The distance band discovered in the preliminary GWR
exploration was used to define the spatial neighborhood for these analyses. The results of each
analysis are written back to the space time cube .nc file in ArcGIS Pro. These spatiotemporal
trends were then visualized using the Space Time Cube Explorer extension.
The space time cube 3D visualization encompasses a large dataset of over 12,000 data
points. Many data classification methods are available in ArcGIS Pro for binning and visualizing
the range in CPUE values. Quantile classification is typically applied for linear datasets where
equal number of data values are assigned to each class; this can cause distortion between

37
adjacent classes when the data is not distributed normally. In this case many data values would
be spread into different classes although they were similar in value due to the skewed
distribution towards zero or low CPUE values. The geometric interval classification method was
chosen to accommodate the continuous but skewed CPUE data in this study. For a detailed
description of the mathematics involved with the class scheme see Esri’s online help (Esri 2020).
3.2.1. Hot Spots
The space time cube created from defined locations was input to emerging hot spot
analysis to identify hot and cold spots in snow crab CPUE for each age class (immature, mature
female, and total), and for Pacific cod. The time step interval or temporal neighborhood was left
as one year for this exploratory analysis, so that the temporal neighborhood consisted of three
years (one year before and one year after the year of the target feature). The spatial neighborhood
was set at 45 nm to coincide with the Gaussian kernel bandwidth used in the GWR analysis.
The emerging hot spots analysis categorizes bins as hot or cold then assesses each
location’s cumulative temporal series in a modified Mann Kendall test of snow crab and pacific
cod CPUE. The combination of temporal trend and hot spot classification was used to further
categorize each station location in the space time cube to form a 2D summary visualization of the
hot and cold spot results.
3.2.2. Local Clusters and Outliers
Clusters and outliers analysis identified significant spatiotemporal clustering of high or
low CPUE values and outliers of high CPUE stations surrounded by low CPUE stations or low
CPUE stations surrounded by high CPUE stations. This analysis was applied to each age class of
snow crab (immature, mature female, and total CPUE) and Pacific cod, using the same spatial
neighborhood distance as applied in the hot spot analysis and gaussian kernel bandwidth (45

38
nm). A local Moran’s I index value of correlation was calculated for each bin in the space time
cube and a cluster category was assigned if the pattern was statistically significant with at least
95% confidence (pseudo p-value < .05).
3.2.3. Time Series Clusters
Time series cluster analysis was applied to identify station locations with similar profiles
of CPUE for total snow crab and Pacific cod. Results from the default/initial pseudo-F
permutations analyzing snow crab CPUE time series were explored by specifying the number of
clusters to identify in the analysis, prior to running the test. Profile correlation in CPUE values
was selected to determine similarity between station locations.
3.3. Analysis of Relationships
Time cube visualization and spatiotemporal analysis of CPUE data helped describe the
distribution of snow crab and Pacific cod over the time series and provide context for regression
analysis. Exploratory regression was first used to identify significant temporal correlation with
historical conditions or abundance patterns. These lagged years of delayed impact on snow crab
distribution in 2018 were included in the next regression test to compare a global scale ordinary
least squares technique with and without lagged impact years included in the analysis as
independent variables. The survey period between 2006 and 2018 was selected to represent an
average snow crab life span which enabled the exploration of lagged temporal effects related to
life history stages and age classes, such as mature female snow crab abundance at time of likely
egg extrusion (maternal cohort connectivity), surface temperatures at time of pelagic larval phase
of development, and bottom temperatures or predation during settlement and early instar or
immature life history stages.

39
Model performance and accuracy was compared for GWR and OLS, interpreted through
Akaike’s Information Criterion (AICc) score and r
2
or explained variance. Model residuals were
mapped and compared for spatial autocorrelation which would indicate misspecification, bias,
and/or multicollinearity and lack of variation in model variables. For GWR, additional mapping
of model parameters for each explanatory variable enabled visualizations of the strength and
scale of relationships of snow crab abundance in space.
3.3.1. Exploratory Regression
The final twelve years of the time series were extracted for exploration of lagged impact.
Each survey station was represented by a single point feature with attribute fields pertaining to
annual CPUE records from 2006 to 2018. Exploratory regression was run individually for every
independent variable (bottom temperature, surface temperature, immature snow crab CPUE,
mature female snow crab CPUE, and Pacific cod CPUE) to determine which lagged years
correlated most significantly with snow crab distribution in 2018. A full description of the
variables and the lagged relationship with current snow crab distribution is provided in Table 2.

40
Table 2. Exploratory regression variables and lagged impact on 2018 snow crab CPUE

Independent Variables Lagged Impact on Distribution
Climate
Pressure

Surface Temperature Egg extrusion/hatching and pelagic larval
stages

Bottom Temperature Settlement phase to maturity

Environmental
Variable
Depth Immature to mature phase migration
(no temporal lag, does not vary in time)

Age Class
Connectivity
Mature female snow
crab CPUE
Abundance of maternal cohort year class is
reflected in progeny

Immature snow crab
CPUE
Immature snow crab represent the surviving
progeny of matrernal cohort

Predation
Pressure
Pacific cod CPUE Vulnerable immature age classes, small females

3.3.2. Global Regression
After testing each lagged variable, the top three most significant lagged years between
2006 and 2018 were selected as independent variables for the OLS regression using ArcGIS
Pro’s generalized linear regression (GLR, equivalent to OLS). This global regression approach
was also implemented using only 2018 variables (no lagged years as independent variables). The
strength and significance of the relationship with snow crab distribution per independent variable
was interpreted through the single, global variable coefficients. Model accuracy and performance
with and without lagged variables was compared through r
2
and AICc values. Spatial
autocorrelation in model residuals and the regression statistical diagnostics described in Chapter
2 were used to interpret results between global models, and between the global OLS and local
GWR models.

41
3.3.3. Local Regression
As in the OLS regression, 2018 snow crab CPUE was input as the dependent variable in
the GWR. Each station location was analyzed using a Gaussian (continuous) model type with a
distance band of 85 km or 45 nm (just over the distance of 2 survey grid cells, each 20 nm).
GWR local r
2
results and residuals were mapped to assess model performance spatially. Local
variable coefficients were mapped to visualize change across space in terms of relationship
strength and consistency. Local model coefficients were divided by the local standard error to
estimate a scaled magnitude of error, similar to a t-statistic (Esri 2020). The same regression
modeling diagnostics described in Chapter 2 and interpreted for global OLS tests were
interpreted for the results of the GWR.

42
Chapter 4 Results
This chapter outlines the patterns identified in the spatiotemporal analysis and statistical
diagnostics and of the regression analyses. Local GWR modeling more accurately modeled
snow crab distribution patterns observed in 2018 than the global OLS regression. Global
regression techniques were effective in detecting temporal correlation and lagged impact from
environmental variables but variance in the GWR local variable coefficients and spatiotemporal
patterns of snow crab CPUE suggest spatial non-stationarity and heteroskedasticity across the
EBS. Alternate linear transformations of the snow crab CPUE data should be explored to
minimize the effect of the skewed abundance patterns. Alternately, GWR derivative results
comparing local variable coefficients to local error identified transition zones in the relationships
which could be used to break the study area into smaller, ecologically defined units for further
spatiotemporal analysis and regression modeling.
4.1. Space Time Cube and Snow Crab Distribution
Raw CPUE data can be rendered in the space time cube to visualize overall distribution
patterns. After running each of the spatiotemporal analyses (hot spots, clusters and outliers) the
space time explorer can also render the cube according to the statistical results of each test.
ArcGIS Pro 3D scenes enable the user to explore the cube in any rendering scheme in 360° and
from adjustable heights and perspectives to view more detail. Snow crab CPUE in the EBS from
1982 to 2018 is shown in the space time cube from multiple angles in Figures 5 and 6.

43

Figure 5. Space time cube views of snow crab CPUE due north (top) and south (bottom)

44

Figure 6. Space time cube views of snow crab CPUE due east (top) and west (bottom)

45
The highest concentration of snow crab was located north of the Pribilof Islands along the
middle domain (50-100 m). Snow crab CPUE decreased from north to south along the middle
domain and was lowest along the coastal domain (<50 m) and Bristol Bay region in the
southeastern shelf (left foreground of bottom cube in Figure 6). The most recent survey showed
that snow crab CPUE has increased in the northeastern region and continues to increase in the
stations nearest the Bering Strait from west to east. These abundance gradients are inverse to
bottom temperature gradients in the EBS. As snow crab abundance has increased along the
northeastern front of the survey, the time cube view looking towards the east (top cube in Figure
6) shows a clearer view of CPUE trends decreasing over time along the outer domain and shelf
edge.
Despite these visible spatial trends, aspatial temporal analysis of snow crab CPUE
showed no significant global pattern of change in CPUE for any of the age class groups overall,
or in Pacific cod (see Table 3). The Mann-Kendall statistic did show that immature snow crab
numbers have increased slightly (1.2687 trend statistic) while the mature female age class has
declined (-.3270 trend statistic). The total population of snow crab has increased slightly (trend
statistic .5362), bolstered by the growth of the immature age class.

Table 3. Mann-Kendall data trends for CPUE, 1982 - 2018

CPUE Group Trend Direction Trend Statistic p-Value
Total Crab Not Significant 0.5362 .5918
Immature Crab Not Significant 1.2687 .2046
Mature Female Crab Not Significant -.3270 .7437
Pacific Cod Not Significant .1962 .8445

46
Since 1982 there has been a weakly positive trend in Pacific cod CPUE (.1962 trend
statistic) but the trend statistic for snow crab is stronger and also positive. Despite management
concerns of warming sea temperatures and the ecological implications of an influx of predatorial
Pacific cod populations in the EBS, the temporal trends in CPUE do not suggest a shift in
ecosystem structure between invertebrate and groundfish communities. Pacific cod and snow
crab do not show an inverse abundance relationship that might indicate top-down predation
control of the population at this scale of analysis.
Temporal patterns of CPUE vary spatially along two axes, from north to south and from
the coastal to outer domains. These gradients can be visualized through comparison of the
banding patterns amongst a stratified subsample of time cube stacks spanning the shelf
geographic regions (north, central, south) and domains (outer, middle, coastal). A group of stacks
spanning the shelf per each northern, central, and southern survey region are shown in Figure 7.
Each trio group includes one stack from the outer (>100 m), middle (50 to 100 m), and coastal
domain (<50 m).

47

Figure 7. Stratified sample of survey station time cube stacks showing regional variation in snow
crab CPUE, 1982 – 2018

48
The regional time cube stacks featured in Figure 7 are displayed individually and labeled
with station ID and survey year in Figure 8 to make further detailed temporal comparisons. In the
northern region, snow crab CPUE increased across-shelf from west to east, or from the outer to
middle domain. Abundance began increasing sequentially at these stations across the shelf
starting in the west or outer domain in 1985. The middle station in this northern region
subsample then began to increase in 1986, and the easternmost station lagged another year before
beginning to increase in 1987. This indicates a progression towards colder waters nearer the
Bering Strait and concentration of the population in the northern region of the survey.
Snow crab CPUE average over the time series increases from 488 in the south (station F-
07) to 80,542 in the north (station S-28), and 297,772 in the northeastern-most station closest the
Bering Strait (V-25). By contrast, the two coastal locations (<50 m) recorded an average CPUE
of 39 at the station closest Nunivak Island in the central region (N-01) and average CPUE of 5 in
the southernmost coastal station (I-10). Temporal profiles are revisited in the time series cluster
analysis results.
The peak and sustained high CPUE records of snow crab on survey from the mid-1980s
(bottom half of the stack) until the steep drop in 1998 (midway up the stacks) can be seen in the
banding patterns at each location. It is also of note from these individual stack visualizations that
the most variation in CPUE of snow crab occurs along the oceanographic fronts of the EBS: the
shelf edge along the outer domain where the slope current flows and the northeastern survey
region nearest the Bering Strait where Arctic currents approach from the north. Snow crab CPUE
in each of these areas fluctuate on an annual basis while the middle domain experiences more
gradual change in CPUE over time. This would seem another spatial indicator that bottom
temperatures maintain influence over snow crab distribution on the EBS.

49

Figure 8. Individual time cube stacks from north to south and from outer to coastal domain
showing range of temporal profiles of snow crab CPUE, 1982 to 2018

50
Space time cubes of immature and mature female snow crab distributions are shown in
Figure 9. The CPUE patterns for these age classes reflect the same north-to-south gradient
described in the general population but female snow crab are restricted to smaller clusters in the
north flanking either side of St. Matthew Island. The most recent bins along the northwestern
region of the survey in the outer domain have decreased in the latest time step in each age class.
Pacific cod do not follow the same environmental gradients observed in snow crab
distributions. Figure 10 shows the space time cube for Pacific cod CPUE. Stations with higher
CPUE (>7500) of Pacific cod are clustered along the coastal domain from Bristol Bay to
Nunivak Island, and additional clustering of high CPUE occurred around St. Matthew Island and
northeast of the Pribilof Islands.
Regional trends in CPUE of Pacific cod are shown in Figure 11 for the same subsample
of time cube stacks stratified across the survey region as described for snow crab CPUE. Pacific
cod abundance was historically low in the north and nearly absent in the northeast (station V-25)
but abundance has increased here recently in 2016 and 2018. Pacific cod abundance was highest
throughout the central survey region, but the southeast stack in Bristol Bay (station I-10)
recorded the highest average CPUE of Pacific cod over the study period (8863). Pacific cod
CPUE in the outer domain has decreased over the time series, similar to snow crab patterns
although this down trend was only visually apparent in the southern and northern survey region
time stacks in this example for Pacific cod.
This dataset and the time cubes encompass a large spatial and temporal range and the raw
CPUE values can be difficult to decipher. Spatiotemporal analysis of the magnitude scale of
change in hot spot Getis Ord Gi* and Anselin Local Moran’s I clusters and outliers tests can
better summarize this CPUE data.

51

Figure 9. Space time cube views of immature snow crab (top) and mature female snow crab
(bottom) CPUE, 1982 to 2018

52

Figure 10. Space time cube views of Pacific cod CPUE due north (top) and south (bottom)

53

Figure 11. Stratified sample of survey station time cube stacks showing regional variation in
Pacific cod CPUE, 1982 – 2018

54
4.1.1. Hot and Cold Spots
Survey stations in the northeastern region of the shelf showed significantly higher CPUE
values recently, as seen in the cluster of hot spots (red bins) in the time cube in Figure 12 (top).
Snow crab abundance at these 75 stations was significantly higher than the survey average, and
CPUE patterns were sporadic or intermittently high throughout the series. No cold spots were
detected at this scale of analysis applying a 45 nm spatial neighborhood.

Figure 12. Space time cube 1982 - 2018 snow crab CPUE hot spots (top), with emerging hot spot
trend summary (bottom)

55
Space time cubes showing CPUE hot spots for mature female and immature snow crab
age classes are shown alongside their corresponding 2D emerging hot spot summary in Figure
13. The immature age class results closely resemble the patterns described by the total
population, but the cluster is reduced to 64 stations. Two clusters of sporadic hot spots can be
seen in mature female snow crab CPUE that flank either side of St. Matthew, and new hot spots
have emerged only recently in this age class on the eastern flank of these hot spot clusters,
nearest the Bering Strait. These patterns reflect the spatial stratification described in previous
research that arises from settlement and migration patterns and movement from east to west so
that immature crab move to the colder domain and eventually migrate to the west.

Figure 13. Snow crab CPUE hot spots for immature and mature female age classes, time cube
(top) and corresponding 2D emerging hot spots temporal summary (bottom), 1982 – 2018

56
No cold spots were identified despite significant down-trends in CPUE captured by the
Mann-Kendall temporal trend test. Reasons are likely related to the heteroskedasticity in snow
crab abundance patterns, or the variation in CPUE variance between southern and northern
regions. Snow crab CPUE in the north could reach in the millions while in the south the range
was in the hundreds and thousands. So, despite significantly down-trending CPUE records in the
south, the intensity of this decrease was too weak to be detected as a cold spot due to extremely
high CPUE fluctuations in the northeastern hot spots. If exploring spatiotemporal patterns
further, the spatial neighborhood should be expanded to enable detection of more subtle variation
in the south. A second option would be to use the results of the GWR to explore spatial analysis
units so that the study area was broken up into ecological units that reflect the relationships
patterns described by local variable coefficients. These possibilities for further development are
revisited in the local clusters and outliers analysis and GWR results, and in the discussion.
Pacific cod CPUE hot spots were detected throughout the central region surrounding
Nunivak Island but were mostly restricted to a parallel band along the southern coastal domain
and Bristol Bay region in the southeast (see Figure 14). No significant temporal trends were
detected in the emerging hot spot analysis of Pacific cod CPUE and there were no hot spots in
the last time step (2018).

57

Figure 14. Space time cube showing Pacific cod CPUE hot spots, 1982 to 2018

As described previously in reference to the lack of cold spots detected in snow crab
CPUE over the time series, a lack of cold spots in Pacific cod CPUE may be accurate or the
analysis may have failed to identify relatively weak negative trends, or an inappropriate spatial
neighborhood may have been specified. The distance band (45 nm) in this study was developed
to optimize analysis of the total snow crab age class CPUE patterns and demonstrate the method
applied in GIS, but each group could be investigated independently to determine a more
appropriate spatial neighborhood for the species or age class of interest.
The spatial variation and timing of Pacific cod CPUE hot spots were visualized in the
regional subsample of survey stations (Figure 15). There were no hot spots for snow crab CPUE
in any of the southern region survey stations (C-04, F-07, I-10). One hot spot occurred near the
start of the series in 1983, in the central region stack nearest St. Paul in the outer domain (H-23).

58
Hot spots then appear in 1990 in the central-middle stack (K-20), closely followed by hot spots
in 1993 in the northern stations of the middle domain (S-28 and V-25) and the central-coastal
station nearest Nunivak (N-01). The central-middle stack was identified as a hot spot again in
2005, and hot spots occurred throughout the northern stacks about 2011. The two northeastern
stations of the middle domain (S-28 and V-25) have both been classified as snow crab CPUE hot
spots over the last few time steps (since 2016 and 2015). These trends are captured in the
sporadic hot spots in the northeast survey region and describe the northward shift and contraction
of the snow crab population towards colder temperatures.
Pacific cod CPUE hot spots are shown for the sample of survey stations in Figure 16.
There were no hot spots in any outer domain locations, or in the northern survey region. The first
hot spot occurred in the central-coastal domain (N-01) in 1982, followed by a short bloom over
two years from 1993 to 1994 in the southeastern Bristol Bay region (I-10) and central-middle
stack (K-20). The next hot spot of Pacific cod CPUE appeared in 2001 in the southeastern Bristol
Bay region again (I-10). A prolonged hot spot was identified between 2011 and 2016 spread
amongst the coastal domain stations (N-01 and I-10) and the central-middle stack to a lesser
extent (2014 to 2016).

59

Figure 15. Stratified sample of time cube stacks across the EBS shelf regions and domains
showing hot spots of snow crab CPUE, 1982 - 2018

60

Figure 16. Stratified sample of time cube stacks across the EBS shelf regions and domains
showing hot spots of Pacific cod CPUE, 1982 - 2018

61
The Mann-Kendall trend tests for each snow crab age class and Pacific cod CPUE over
the time series revealed regions of up- and down-trending abundance. Figure 17 shows the 2D
summary of temporal trends in the time cube at each station location for each age class of snow
crab and Pacific cod.

Figure 17. Temporal trends in CPUE for total snow crab (top left), immature snow crab (top
right), mature female snow crab (bottom left), and Pacific cod (bottom right), 1982 to 2018

Down trends were detected with 99% confidence in 150 of the 349 total survey stations
for immature crab CPUE and in 105 of 349 stations for the total population of snow crab, yet
overall, the global statistics reported previously in Table 3 were positive for both groups (.5362
and p=.5918 for total, 1.2687 and p=.2046 for immature class). This correlation test does not

62
reflect the magnitude of the trend, which was slight because CPUE of snow crab has been
historically and uniformly low in the southern region. The decreasing trend here was relatively
insignificant compared to the global dataset trends that are more heavily influenced by the hot
spots in the northeast. The down trends in snow crab CPUE in the south were too small in scale
to be identified in the hot spot analysis as significantly cold.
Pacific cod temporal trends were also spatially variable and disparate between the Mann-
Kendall trend test and hot spot analysis. The outer domain was classified entirely as down-
trending in Pacific cod CPUE despite a lack of cold spots and no significant global trend (trend
statistic for Pacific cod was slightly positive, .1962 with p=.8445). A group of four stations along
the northern fringe of the survey region was categorized as up-trending; these may represent the
most recent trends of increased CPUE of Pacific cod in the north that is not intense enough to be
identified as hot spots. Snow crab also showed up-trends in the north corresponding to hot spot
locations which further supports the ecological hypothesis of northward species shift.
4.1.2. Time Series Clusters
Time series correlation revealed four spatial clusters of survey stations with similar
temporal profiles of CPUE of snow crab in terms of the value and proportionate change over
time. Cluster trend statistics are provided in Table 4 with corresponding clusters mapped in
Figure 18. Cluster 4 showed a significant increase in snow crab CPUE over the time series
(1.6872, p=.0916) and was located in the northeast region of the survey where hot spots were
detected and the Mann-Kendall tests identified up-trends. This was the only significant trend
detected in any of the time series cluster groups (tested up to 7 clusters). Clusters 2 and 3 were
both decreasing but the trends were not significant. These stations were located to the east of
Cluster 4 along the outer domain and south across the southern shelf. Twenty-nine stations

63
identified as Cluster 1 in Figure 18 recorded zero CPUE of snow crab every year of the time
series. These stations along the easternmost coastal domain were removed from the dataset prior
to regression analysis as described in the Methods section. The issue of data transformation and
analysis units is revisited in the Discussion.

Table 4. Time series cluster trend statistics for snow crab CPUE temporal profile correlation
*Indicates statistically significant trend

Cluster ID Direction Statistic p-Value Locations
1
2
3
4
Not Significant
Not Significant
Not Significant
Increasing*
0.0000
-1.5302
-0.6932
1.6872
1.0000
0.1260
0.4882
0.0916
29
125
102
93

Figure 18. Time series clusters, four groups of survey stations with correlating temporal profiles
of snow crab CPUE, 1982 to 2018

64

Figure 19. Average snow crab CPUE for each time series cluster group
* Indicates significant trend

Time series cluster analysis identified two clusters of similar temporal profiles in Pacific
cod CPUE (see trend statistics in Table 5). The spatial clustering pattern reflects the trends seen
in the hot spot analysis and Mann-Kendall temporal trends, with decreasing CPUE along the
outer domain (Cluster 1 in Figure 18). Although Cluster 2 was increasing over the time period,
these stations were not identified as hot spots due to the recent decline in Pacific cod CPUE
which has brought the average for each cluster closer together nearest a historical low of 2,000
CPUE in 2018.

Table 5. Time series cluster trend statistics for Pacific cod CPUE temporal profile correlation
* Indicates statistically significant trend

Cluster ID Direction Statistic p-Value Locations
1 Decreasing* -2.8120 0.0049 210
2 Increasing* 2.5242 0.0116 139

65

Figure 20. Time series correlation in temporal profile for Pacific cod CPUE, 1982 to 2018

Figure 21. Average Pacific cod CPUE for each time series cluster (*indicates significant trend)

Pacific cod abundance peaked in Cluster 2 between 2012 and 2016, years identified in the
coastal domain as hot spots. These time series clusters describe spatial heteroskedasticity in the
data, or unequal change in the variables (CPUE) across space in both the snow crab and Pacific
cod CPUE data.

66
4.1.3. Local Clusters and Outliers
A large cluster of low CPUE of snow crab was identified by the Anselin local Moran’s I
statistic for nearly all survey stations located south of St. Paul and Nunivak. Time cube views for
all clusters and outliers results for age class of snow crab and Pacific cod are shown in Figure 22.

Figure 22. Time cube views of CPUE clusters and outliers for snow crab (top left), immature
snow crab (top right), mature female snow crab (bottom left), and Pacific cod, 1982 to 2018

Low-low clusters (low CPUE stations near other low CPUE stations) made up 49% of the
snow crab time cube bins overall (6,031 out of 12,913), and 50% of all survey station locations
(175 of 349). Snow crab CPUE within these clusters of stations decreased over the time series,

67
but this was an insignificant trend overall for the reasons related to scale and magnitude of
change as previously described in the hot spot and Mann-Kendall comparisons. The local
clusters and outliers analysis for snow crab and Pacific cod is summarized in 2D in Figure 23.
The southern trio of individual time cube stacks ranged from 0 to 18,817 CPUE. Variance in this
region ranged from 360 to 535,936 and increased by several orders of magnitude in the northern
region of the survey (up to 60,480,131,868 at station V-25) where CPUE fluctuated between
25,204 and 673,285. This heteroscedasticity has been visualized in the hot spot analysis regional
comparison in Figure 15 in which the timing, extent, and frequency of hot spots varies spatially
across the shelf domains and from north to south.

Figure 23. Summary of CPUE clusters and outliers for snow crab (left) and Pacific cod (right),
1982 – 2018

There were 175 survey stations in the southern region categorized as only low-low
clusters for snow crab CPUE, and 168 as multiple type where the correlation was weaker and
CPUE variance was higher. Correlation in CPUE of Pacific cod was highest along the outer
domain in 119 stations categorized as low-low clusters and 219 as multiple type clusters. Low-
low clusters formed a transverse corridor across the shelf of correlated CPUE in stations that

68
stretched from the south side of St. Matthew in the east to the southern flank of Zemchug
Canyon in the west. These low-low clusters divided the survey area into two clusters of multiple
type category that follow the cross-shelf depth gradient as opposed to north-south distribution
patterns seen in snow crab. These visual comparisons of CPUE trends and relationships are
explored quantitatively in the regression analysis.
4.2. Lagged Relationships
The top five variables from past years in terms of lagged correlation with 2018 CPUE of
snow crab since 2006 are listed in the vertical timeline in Table 6, based on the exploratory
regression (OLS) testing all independent variables separately. The top three most significant
years of impact per each independent variable (bottom and surface temperatures, immature and
mature female age classes CPUE, and Pacific cod CPUE) are outlined in Table 6 and were
included in the global OLS regression that follows. Positive correlation is presented to the right
of the timeline, and negative correlation to the left.
The highest significance in lagged mature female snow crab CPUE was identified for the
2006, 2008, and 2017 classes (100% associations). This suggests connectivity between maternal
age classes from 2006 to 2008 and progeny that have grown to and now constitute the total snow
crab population in 2018. The more recent correlation in 2017 is likely temporal correlation,
which was similarly identified in the immature age classes in 2017.

69
Table 6. Top three most significant lagged years (2006 and 2018)

Lagged Independent Variables
Snow Crab Population Group
(approximate life history stage)
2017 Mature Female Snow Crab CPUE Total Population
(mature reproductive stage)
2017 Immature Snow Crab CPUE
2016 Immature Snow Crab CPUE 2016
Surface Temperature
Immature Age Classes
(growth and development stage)
2015 Bottom Temperature
2014 Pacific Cod CPUE
2014 Bottom Temperature
2013 Bottom Temperature
2012 Pacific Cod CPUE
2011 Surface Temperature
2010 Surface Temperature
2008 Mature Female Snow Crab CPUE
Mature Female Age Classes
(egg extrusion stage)
2007 Immature Snow Crab CPUE
2006 Mature Female Snow Crab CPUE
2006 Pacific Cod CPUE
The years 2013 likely represent the transition period of growth from early benthic stages
to mature adults in 2018. Immature snow crab are highly stenothermic and typically aggregate in
the middle domain where there are colder temperatures (1℃). These were the most significant
impact years in the timeline for bottom temperature, further supporting evidence outlined in
previous research into the life history cycle and ecological niche differences between snow crab
age classes.
Lagged results for surface temperature showed positive and negative associations and are
more difficult to interpret but the significance of this variable is clustered between 2010 and
2016. These years correspond to the warming phase described in the time series charts of average
EBS sea temperatures at the beginning of this chapter. The exploratory regression also produced
mixed results for lagged impact of predation but the top three most significant years in the
timeline for the Pacific cod CPUE variable (2006, 2012 and 2014) expressed an inverse

70
correlation with snow crab CPUE. These years correspond to maternal age classes and the early
(more vulnerable) benthic stages of snow crab development.
Snow crab CPUE was most significantly correlated with bottom temperature in the
lagged years that would have coincided with immature life history stages (2013 – 2016) .
The shape of the cold pool (<2℃) in 2016 and 2017 reflects the spatial distribution of hot
spots observed in snow crab CPUE in Figure 11 and the similarity in these years likely
contributes to temporal correlation detected in immature and mature female age classes. There
was no cold pool formation in 2018. Only seven stations along the northeastern edge of the
survey reached a summer low of 1.6℃, which may impact the results of the regression analysis
if bottom temperatures drive snow crab distribution and the gradient has broken down. EBS
bottom temperatures were mapped for each year included in the lagged regression analysis, 2006
to 2018, and figures are provided in the Appendix.

71

Figure 24. EBS bottom temperatures for the most significant lagged impact years for 2018 snow
crab CPUE since 2006, with 2018 bottom temperature as a reference (bottom)

72
4.3. Global Relationship Trends
The global regression model was first tested without including lagged independent
variables identified in the exploratory regression. The OLS restricted to 2018 variables identified
depth, bottom temperature, and surface temperature as significantly related to snow crab CPUE.
The relationship with Pacific cod CPUE was positive and not significant, contrary to a presumed
negative impact. Summary results for each of the independent variables in the OLS (excluding
lag) are presented in Table 7 and show that bottom temperature has the strongest (negative)
relationship.

Table 7. Summary of OLS results model of 2018 snow crab CPUE, excluding lagged variables
* Indicates a statistically significant relationship

Variable Coefficient Std. Error t-Statistic p-Value VIF
Intercept 5.5649 3.0341 1.8341 0.0676 -
Depth -0.0658 0.0088 -7.4375 0.0000* 2.0837
Bottom Temperature -2.6118 0.2627 -9.9405 0.0000* 1.6161
Surface Temperature 1.8950 0.2685 7.0573 0.0000* 2.5039
Pacific Cod CPUE 0.2084 0.1998 1.0430 0.2978 1.2226

OLS model diagnostics in Table 8 include results of the global regression test with and
without including the lagged independent variables identified in the exploratory regression.
Interestingly, the Koenker (BP) statistic was not significant when lagged variables were
excluded, so the relationships between snow crab CPUE in 2018 and the independent variables
were determined to be spatially consistent. The BP test statistic was significant when lagged
independent variables were included, indicating inconsistent relationships. For this reason the
robust probability and Wald Statistic values were relied upon to determine coefficient
significance for the regression results including these lagged variables.

73
Table 8. OLS model diagnostics for 2018 snow crab CPUE, with and without lagged variables
* Indicates a statistically significant statistic

Statistic No Lag With Lag
Number of Observations 308 248
AICc 1654.8338 1108.1404
Multiple r
2
.4922 .7834
F/Wald 73.4247 (F)* 2056.1117 (Wald)*
Koenker (BP) 9.3174 39.4512*
Jarque-Bera 0.8949 5.3024

Jarque-Bera statistics were not significant in either regression (with or without lagged
variables). Therefore, the model residuals were normally distributed or not clustered or
significantly biased. Model residuals when excluding lagged variables were relatively small
(range of 19 from -6 to 13) with some underpredicting in the middle domain where snow crab
CPUE was higher. The range in residuals was further reduced including lagged variables (range
of 9, from -3 to 6). Standardized residuals for each of the OLS regression models are shown in
Figure 25.

Figure 25. OLS standardized residuals for snow crab 2018 CPUE without (left) and with (right)
lagged independent variables since 2006

74
As a measure of model performance including lag significantly reduced the AICc score
(from 1655 to 1108) and increased model accuracy and r
2
from .49 to .78 (% variance explained).
Due to missing surface and bottom temperature records in the dataset the predicted results when
including lagged variables were reduced to 248 survey stations; this has limited the efficacy of
including lagged variables in the regression despite the improved model accuracy and
performance despite the heavier dependency detected in temporal correlation with historical
CPUE. An alternate source of surface and/or bottom temperatures would improve the results of
the regression analysis. A summary of the OLS results including lagged year variables is
provided in Table 9.
Bottom temperature in 2018 was not significant according to OLS when including lagged
variables. Surface temperatures in 2011 and 2016 were the only significant temperature variables
identified. As previously stated, 2018 was an historically warm summer and no sea ice formed
the prior winter. Typical temperature associations are likely confounded by this change but the
lagged impact of the spatial and temporal correlation in previous years distributions of snow crab
populations supersedes the bottom temperature association when including lagged variables. One
other weakness in the model was a significant VIF for depth (> 7.5), indicating multicollinearity.
As there was very little variation in the high bottom temperatures observed in 2018, these two
variables likely expressed greater collinearity than average years.

Table 9. Summary of OLS regression variable coefficients including top 3 lagged independent
variables from exploratory regression
* Indicates a statistically significant relationship

75
** Indicates redundant variable

Variable Coefficient Robust SE Robust t Robust Pr VIF
Intercept -2.6273 3.1735 -0.8279 0.4086 --------
Depth -0.0236 0.0104 -2.2616 0.024653* 7.7238**
2018 Surface
Temperature
0.3714 0.1839 2.0198 0.044564* 3.5858
2018 Pacific Cod
CPUE
-0.1129 0.1558 -0.7245 0.4695 1.5141
2018 Bottom
Temperature
-0.0335 0.3167 -0.1058 0.9159 4.7847
2017 Mature Female
Snow Crab CPUE
0.2074 0.0632 3.2798 0.001213* 2.9622
2017 Immature Snow
Crab CPUE
0.2441 0.1025 2.3806 0.018094* 4.7612
2016 Surface
Temperature
0.3517 0.1392 2.5276 0.012153* 3.1770
2016 Immature Snow
Crab CPUE
0.1567 0.0688 2.2766 0.023725* 2.8841
2015 Bottom
Temperature
-0.2630 0.1771 -1.4853 0.1388 8.9154**
2014 Pacific Cod
CPUE
-0.0896 0.1460 -0.6133 0.5403 2.4020
2014 Bottom
Temperature
0.2759 0.2411 1.1445 0.2536 8.8868**
2013 Bottom
Temperature
-0.2672 0.1832 -1.4584 0.1461 4.1236
2012 Pacific Cod
CPUE
-0.1690 0.1335 -1.2658 0.2069 1.8920
2011 Surface
Temperature
0.3612 0.1967 1.8368 0.0675 6.2667
2010 Surface
Temperature
-0.2321 0.1132 -2.0501 0.041492* 3.9222
2008 Mature Female
Snow Crab CPUE
0.1157 0.0743 1.5568 0.1209 3.7557
2007 Immature Snow
Crab CPUE
0.1702 0.0694 2.4512 0.014980* 3.1556
2006 Pacific Cod
CPUE
0.3697 0.1385 2.6690 0.008150* 1.8548
2006 Mature Female
Snow Crab CPUE
0.0581 0.0542 1.0726 0.2846 2.2235

76
4.4. Local Relationships
The local form of regression in GWR including only 2018 variables (bottom and surface
temperatures, depth, Pacific cod CPUE) performed better than the global form and resulted in an
AICc score of 1410 compared to 1655 in the OLS (see Table 10). The amount of variance
explained also increased from 49% to 83%. These model results are comparable to the OLS
including lagged independent variables.

Table 10. GWR model performance and diagnostics

GWR Diagnostics
r
2
0.8328
Adjusted r
2
0.7913
AICc 1409.7732
Sigma-Squared 4.9775
Sigma-Squared MLE 3.9922
Effective Degrees of Freedom 247.0269

Local r
2
for the GWR is mapped in Figure 26. Model accuracy was poorest along the
southern edge of the survey along the Alaska Peninsula as well as the western edge along the
outer domain, south of Zemchug Canyon. GWR model accuracy was highest (local r
2
= .94) in
the central region and middle domain nearest Nunivak Island but averaged 78%, well above that
of the OLS (49%). This area coincides with higher snow crab CPUE and Pacific cod CPUE
values; locally weighted regression requires a certain amount of spatial variation in the
independent variables, which may explain the pattern of poor performance in other areas.

77

Figure 26. GWR model accuracy (local r
2
)

The poorest model performance was seen in Bristol Bay where snow crab CPUE was
consistently low without variance. Depth and temperature variables are spatially uniform across
the southeastern shelf region which may have contributed to the poor performance considering
multicollinearity or redundancy was detected in the OLS model when including lagged variables
(see Table 9, VIF>7.5 for depth and 2014, 2015 bottom temperatures).
Figure 26 shows that the western shelf edge was more difficult to model using GWR
compared to the middle domain and central region of the EBS, although the local r
2
along the
outer domain was still over 53%. Larger error residuals accompanied the locations with poorer
performance along the shelf edge (see Figure 27). There was no significant autocorrelation in the
model residuals but the map in Figure 27 (top) does show clustering in the Bristol Bay region.
Snow crab CPUE was perhaps too consistently low or depth and temperature variables lacked

78
enough variation for the regression to accurately model CPUE in the southeastern shelf at this
scale of analysis.

Figure 27. GWR model residuals and standardized residuals showing spatial performance in
modeling 2018 snow crab CPUE

79
The scaled magnitude of error, similar to a t-statistic, was calculated at each survey
station and the results are presented alongside the local variable coefficients in Figures 28 and
29. Areas of low coefficient to error ratios were identified as transition zones, where the variable
was not effectively modeled in the GWR (Esri 2020). These areas are symbolized as yellow
survey stations in Figures 28 and 29, and regions of higher coefficient to error ratios and
consistent strength in the coefficient are highlighted in red for each variable.

Figure 28. GWR local variable coefficients and scaled error for bottom temperature (top) and
surface temperature (bottom)

80

Figure 29. GWR local variable coefficients and scaled error for depth (top) and Pacific cod
CPUE (bottom)

Figure 28 shows the strongest local coefficient for the bottom temperature variable (-4.4)
occurred throughout the central region of the EBS, between Zemchug and Pribilof Canyons. The
scaled magnitude of error outside this region decreases, indicating a shift in the relationship
where other variables gain influence. Outside the central region, snow crab distribution
correlated (negatively) with depth to the north of Zemchug Canyon according to the highest
coefficient to error ratio. This matches the patterns identified in the time cube and spatiotemporal
analysis which showed a gradient of increasing CPUE of snow crab in this area moving from
west to east towards the Bering Strait and colder temperatures. By comparison snow crab CPUE

81
in the southern region of the EBS shelf appears to be dually influenced by a positive relationship
with surface temperature and a negative relationship with Pacific cod CPUE (Figure 29). The
transition zones delineated in the scaled magnitude of error maps represent possible boundaries
for spatial units of analysis, discussed further in the last chapter.
GWR was also applied to the same lagged independent variables tested in OLS
regression. The model diagnostics are listed in Table 11. Including lag decreased model
performance and AIC increased from 1108 to 1339. Local r
2
was high, 94%, or .84 adjusted for
the addition of extra explanatory variables (this increases the numerator for the GWR including
lag. The increased AIC score suggests that including lagged independent variables in a locally
weighted regression may be less appropriate than this approach using a global form of
regression. The local variable coefficient results are provided in Appendix B for the GWR with
lag included, but further research should be done prior to developing this model and is discussed
in the final chapter.

Table 11. GWR model performance and diagnostics including lag

GWR Diagnostics
r
2
0.9479
Adjusted r
2
0.8370
AICc: 1339.4155
Sigma-Squared: 3.1642
Sigma-Squared MLE: 1.0192
Effective Degrees of Freedom: 79.8827

82
Chapter 5 Discussion
Snow crab abundance patterns in terms of CPUE and ecological relationships in the EBS were
explored through spatiotemporal analyses and a multi-scale combination of global and local
regression techniques. The results confirmed basic findings of recent research using comparable
NMFS bottom trawl survey data and showed that snow crab were shifting north and east towards
the source of the cold pool and the Bering Strait. The varied methods and analyses applied here
demonstrated the versatility of GIS for performing biostatistical analysis and visualization of
species distributions from standardized fisheries surveys. Large and complex datasets like the
EBS trawl survey are easily and effectively modeled by the space time cube data structure.
GIS spatial analytics and visual explorations of snow crab distribution across space and
time in relation to key environmental variables like sea temperature and depth support
ecosystem-based fisheries management and ecological monitoring efforts. Global methods
indicated spatial autocorrelation or clustering of similar values. Quantifying local relationships
and visualizing how these variable coefficients varied in space helped to identify ecological
regions and transition zones that could be applied towards development of an improved global
regression model to support fisheries statistical analysis. This type of approach can supplement
traditional stock assessments that rely on purely statistical analyses which do not account for the
spatial and temporal correlation inherent in natural systems. As species distributions and by
extension fisheries in the EBS shift, managers can benefit from GIS and exploratory techniques
using the space time cube data structure and local regression analysis.
This chapter first summarizes the results, shortcomings, and solutions for improvement to
the spatiotemporal analysis section of the study. Regression results and suggestions are discussed

83
similarly, followed by a discussion of opportunities for further development or model
adaptations.
5.1. Spatiotemporal Explorations
The discrepancy in results observed between purely temporal (Mann-Kendall) and spatial
(Getis Ord Gi* or Anselin Moran’s I) statistics of snow crab abundance patterns highlights the
utility of performing this type of dual space time exploration to test each aspect of
autocorrelation in ecological and fisheries survey datasets. No significant global trends were
identified by the Mann Kendall temporal test but there was obvious regional spatial correlation in
snow crab CPUE trends. By incorporating spatial autocorrelation and neighborhood context, the
Getis Ord Gi* and Local (Anselin) Moran’s I tests were able to confirm significantly different
CPUE trends between northern and southern survey regions over the study period. The snow
crab population was shifting towards the Bering Strait according to hot spots in the northeast and
a slow but consistent decline in the south. The difference between observed snow crab CPUE
space time trends in northern and southern survey regions corroborated previous reports of a
northern shift in benthic species distributions, based on similar variations of the EBS survey data
(Orensanz et al. 2004; Parada et al. 2010; Stevenson and Lauth 2018).
Exploratory regression revealed temporal correlation in snow crab CPUE or age class
connectivity between the total snow crab population and maternal and immature age classes as
laid out by Ernst et al. (2012) and Emond et al. (2015). Snow crab CPUE exhibited a greater
dependency on historical abundance and the timing between life history cycles than to external
biological (Pacific cod) or environmental (bottom temperature) variables, historic or prevailing.
Age classes showed spatial stratification similarly described by Orensanz et al. (2004), evident in
the time cube visualizations of immature snow crab CPUE (clustered along the middle domain)

84
and mature female snow crab CPUE (aggregated to the north and west of the main
population/immature age classes).
The survey dataset was extensive and covered a wide spatial, temporal, and attribute
range. Its resulting space time cube contained 12,913 individual space time bins. A simpler view
of individual time cube stacks was more effective for regional comparisons of snow crab CPUE
(and Pacific cod CPUE). This stratified sampling approach to visualization also allowed space
for labeling with information such as survey year which helped to pinpoint the timing of hot spot
blooms and CPUE change. The spatial variation of temporal trends in snow crab CPUE was
effectively summarized in the time series profile correlation analysis and helped to visually
divide the survey region into zones exhibiting variable CPUE patterns, or spatial nonstationarity.
The arrangement and trend direction of each of the time series cluster zones showed that snow
crab CPUE varied differentially along each axis of the shelf: numbers decreased to the east and
west of the middle domain and even more drastically from north to south.
5.2. Regression Exploration
Following spatiotemporal analysis and visualization, progressive regression tests allowed
for the exploration of snow crab historical (lagged) and contemporary relationships with
ecological factors, just as Zulu et al. (2014) developed a spatiotemporal context throughout their
analysis of infection spread in Malawi. GWR performed better than the OLS according to AIC
and r
2
values, just as Windle et al. (2010) showed in their studies of snow crab in the north
Atlantic. The locally weighted regression became unstable when incorporating lagged
independent variables but the technique should be studied further in concert with OLS
development.

85
Extremely low, near-zero CPUE records occurred in Bristol Bay while near-millions
snow crab CPUE were recorded in the northeast survey region. These heteroskedastic abundance
patterns in the snow crab population highlight the limitation of relying solely on a global OLS
for regression modeling, which smoothed each of these trends to fit a single regression line; the
result might not reflect the northern or southern distribution trends accurately (Fotheringham
2002). Though the OLS model residuals were not clustered and there was no significant amount
of bias or model misspecification, the model diagnostics in the JB statistic identified significantly
inconsistent relationships, confirming the heteroskedastic attribute scale for snow crab CPUE.
GWR and an exploration of the local variation in snow crab relationships could then help to
pinpoint the independent variables which contribute more significantly to shaping the
distribution and ecologically consistent zones where relationships were stable according to the t-
statistic in the local variable coefficients.
The GWR local variable coefficient map of bottom temperature (excluding lag) showed a
large and consistent cluster of stations in the central survey region where the temperature
relationship was strongest and most stable. Other explanatory variables gained influence at either
end of the survey region: the snow crab CPUE relationship with depth was stronger and more
consistent in the north, while surface temperatures and Pacific cod CPUE were more influential
in the south. This stands to reason as Pacific cod CPUE increased in shallower areas near the
main islands in the EBS and the coastal domain, while in the coldest northern regions of the
survey range distribution varied more according to depth.
Results of the GWR and OLS comparison in this study are reflective of those discovered
by Windle et. al (2010) in the north Atlantic, in that environmental and biological relationships
varied locally, due to spatial dependence and spatial autocorrelation in the data. For these

86
ecological characteristics the locally weighted regression technique was better able to explain
local variation in snow crab CPUE and generate a better-fit model. Windle et al. (2010) have
taken the technique applied in this study one step further by applying a k-means cluster analysis
of local variable coefficient t-values (coefficient to error ratio) to spatially distinguish consistent
relationship zones. Multivariate clustering could be applied to the GWR local variable
coefficient/error in a similar approach to divide the study area into a pre-defined number of
clusters. Survey stations would be grouped according to likeness of CPUE values through an
unsupervised ML algorithm, so the attribute or analysis field is standardized to account for the
stronger influence of variables with large variances. To accomplish this standardization the
global mean of the attribute is subtracted from each attribute value, then divided by the standard
deviation for all values (Esri 2020). To investigate the north/south differential and where these
patterns in CPUE diverge, it may be appropriate to begin with the designation of two clusters in a
multivariate clustering analysis. GIS enables simple parameter adjustments so that additional
numbers of clusters could be easily explored. Significantly different clusters would identify areas
of significantly distribution patterns that would need to be managed according to separate
standards and/or regulations.
Though bottom and surface sea temperature were identified as significant independent
variable in the first OLS test, the OLS regression test when including lag showed that when
considering both temporal and spatial correlation throughout snow crab life history, bottom
temperature was not significant in any year. Temporal correlation and age class connectivity
were more significant at this scale of analysis, which again emphasizes how useful it can be to
explore both spatial and temporal autocorrelation, and to consider the dependent variable
variation at local and global scales to compare results and gain a better understanding of the scale

87
of the attribute as well as the spatial and temporal range. Applying the GWR to each year of
snow crab CPUE included in the exploratory regression similar to the work of Windle et al.
(2012) could also show how the ecological relationships have changed in space and/or strength
over time as climate conditions have shifted.
5.3. Further Development
The results of the spatiotemporal analysis showed that the snow crab population trends
were divergent at either end of the EBS survey range. The study area should be divided into
smaller spatial units of analysis that would more aptly represent this observed spatial structure in
the snow crab population. Previous research has parsed EBS survey data spatially in various
ways prior to analysis to achieve improved results of OLS and other global approaches to
regression (Ciannelli et al. 2008; Kotwicki and Lauth 2013). OLS regression showed that
temporal correlation and age class connectivity was the strongest determinant of snow crab
CPUE in 2018. Rather than use the results of spatiotemporal analyses it may prove more
representative to model the spatial analysis units after the spatial results of the temporal trend test
(Mann-Kendall); however, the location of the negative temporal trends in CPUE coincide with
the low-low CPUE cluster from the cluster and outlier analysis. This would divide the study area
between northern and southern analysis units and likely increase the accuracy of the OLS model.
Dividing the shelf between north and south according to where the statistically significant
downward trends in snow crab CPUE or the low-low cluster of survey stations were identified
would divide the shelf into northern and southern spatial analysis units at 167°W longitude (just
west of Nunivak).
Snow crab CPUE data remains skewed and requires a more effective linear
transformation. The log (x + 1) transformation improved but did not fully normalize the data.

88
Other work applying GWR alongside a global scale regression by Windle et al. (2012) showed
the significance of the relationships in their results did not vary whether using transformed or
raw data for shrimp, snow crab and Pacific cod abundance variables. For this study the log (x +
1) transformation was accepted with the acknowledgement that the significance of the results
should be interpreted carefully and only in an exploratory nature. An alternative transformation
such as box cox should be developed to increase the reliability of the global or local regression
modeling results.
One crucial statistical parameter used in this study that deserves further exploration was
the spatial neighborhood definition in the spatiotemporal analysis. The EBS survey dataset for
the standardized 20x20nm stations was left intact and treated as a single spatial unit, and the
neighborhood distance band remained fixed at 45 nm throughout the spatiotemporal analysis to
match the gaussian kernel bandwidth applied in the GWR regression. However, the fixed
neighborhood distance (45 nm) was optimized for the GWR, not necessarily the time cube. This
parameter should be further tested towards representing the spatial and temporal autocorrelation
inherent in the entire dataset or space time cube frame. The most common method using ArcGIS
statistical analysis to determine an appropriate spatial neighborhood distance involves measuring
the level of spatial autocorrelation at increasing distance band intervals using the Global Moran’s
I statistic and selecting the distance at which spatial autocorrelation or the I-statistic peaks
(Mitchell 2009; Steves 2017; Esri 2020). Preliminary exploration following the conclusion of
these results indicated that peak z-scores in spatial autocorrelation (clustering) occurred at a
greater neighborhood distance than found for the optimal Gaussian kernel (45 nm). The spatial
neighborhood applied in the spatiotemporal analysis and the spatial bandwidth of the kernel
applied in the GWR should each now be fine-tuned according to optimized AIC scores in the

89
case of GWR, and optimal autocorrelation in the case of spatiotemporal analysis. This will likely
result in varied results for the hot spot analysis, which failed to identify any cold spots in the
entire series using the 45 nm bandwidth for neighborhood context despite wide-ranging
downward temporal trends in snow crab CPUE in the southern survey region.
Other adjustments to the spatiotemporal parameters should be tested, including the
temporal neighborhood. A single year/annual time step was selected for this preliminary
exploration of the space time cube and the EBS survey data. Expanding the temporal
neighborhood by two or three survey years or aggregating the data into multi-year bins should be
explored in tandem with adjustments to the spatial neighborhood and spatial analysis units.
As in previous studies (Orensanz et al. 2004; Windle et al. 2009), regression results
(excluding lagged independent variables) suggested that snow crab distribution was more
dependent on bottom-up environmental pressures and climate-scale processes rather than top-
down predation by cod. However, climate change and ecological shifts could result in shifts in
diet. Including CPUE catch records of other predatory fish such as yellowfin sole or Pacific
halibut in the predation pressure index by aggregating these attributes into a single predation
index might provide a better representation of this type of impact on snow crab.
There are many biological and environmental variables that could be further explored
using these methods. One key factor which could significantly impact all benthic species in the
EBS is commercial bottom trawling. C. Steves (2015) showed that gear impact was increasing in
certain areas on the shelf through a spatiotemporal analysis of trawl fishing effort in Alaska. This
trend is likely to continue as groundfish and other trawled species increase in the EBS as a result
of the rising temperatures. In addition to habitat damage, trawling can quickly deplete
populations of non-target species. Vessels are required carry observers to measure and report

90
commercial bycatch of snow crab and other prohibited or managed quota species to state or
federal regulatory agencies. Annual bycatch estimates could shed light on a missing model
parameter.
Oceanographic data to supplement or replace the bottom and surface temperature data
from the EBS bottom trawl survey may improve regression model performance, particularly
when including lag as many survey station bins were missing values at some point in the time
series, and these locations could not be included in the results. Satellite and remote sensing
datasets could provide a means of supplementing surface temperature data, which was significant
in the relationship with snow crab distribution in the OLS with and without lag variables. Ocean
color satellite imagery can also be analyzed to measure primary production as an independent
variable (Brody, Lozier, and Dunne 2013). Care should be taken to assess the resolution, range,
and overall quality or reliability of any data external to the fishery standardized survey.
5.4. Conclusion
The goal of this project was to explore the spatiotemporal distribution of snow crab in the
EBS using GIS to support marine fisheries and ecosystem-based management decisions. Spatial
analytics incorporate autocorrelation and, in some cases, reveal trends masked by traditional
statistical testing or global regression modeling. Spatiotemporal analysis also provides context to
regression modeling to better understand the strength and significance of key ecological
relationships. The space time cube was an effective data structure for modeling standardized
surveys and enabled pattern mining and regression analyses supportive of traditional regression
modeling and statistical assessments. Spatiotemporal analysis and regression modeling in GIS
were effective and complimentary approaches to fisheries monitoring and ecosystem-based
spatial management based on this study. The exploratory regression of lagged environmental

91
variables shows that temporal correlation of snow crab abundance can reveal age-class
connections between maternal parent classes, immature classes, and total population in a
timeline. Exploratory temporal correlation can also identify significant past events in the life
history of snow crab such as climate pressure from sea temperature warming or predation from
Pacific cod.
GIS is a versatile platform that can manage large and complex datasets typical of
standardized biological surveys and should be explored further to support traditional single
species stock assessments. With further development these techniques could be developed in an
ecosystem-based approach towards fisheries management. Spatiotemporal autocorrelation can
identify homogenous areas of the attribute of interest, and zones of consistent ecological
relationships that could be applied towards determining or allocating quota.

92
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Appendix A EBS Bottom Temperatures, 2006 to 2018

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Appendix B GWR Local Variable Coefficients (including lag)

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Abstract (if available)

Abstract Snow crab, Chionoecetes opilio, is the largest commercial crab fishery in Alaska. Populations in the eastern Bering Sea have fluctuated over space and time, challenging statisticians attempting to model their distribution and predict stock trends to support sustainable management decisions. Climate change contributes to model uncertainty due to increased environmental variance and subsequent shifts in species assemblages adapting to changing conditions in the region. This research applied statistical toolkits and visualization techniques in GIS for spatiotemporal analysis of snow crab distribution in the eastern Bering Sea over thirty-seven years (1982 – 2018). The National Marine Fisheries Service standardized bottom trawl survey provided a robust dataset to statistically explore spatial and temporal patterns and relationships between snow crab abundance in terms of catch per unit of effort to sea temperatures, depth, and Pacific cod abundance. The temporal correlation in abundance patterns between snow crab year classes or cohorts was tested using exploratory regression and geographically weighted regression was used to visualize the nature and scale of relationships within the survey region. Overall spatial patterns of snow crab distribution in the eastern Bering Sea reflected large scale warming trends and contraction of the population to the north towards the Bering Strait. No significant relationship was found between snow crab and Pacific cod distributions on a global scale but there was evidence of a local scale inverse relationship in the southern survey region. In absence of favorable bottom temperatures in 2018, snow crab distribution displayed a greater depth dependence in the northernmost region. Temporal correlation was detected between age classes of snow crab, suggesting connectivity between maternal cohorts and progeny. These results identify local and global scale distribution trends which will support better predictive models for fisheries.

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Asset Metadata

Creator Mills, Bryna Michelle (author)

Core Title An exploration of the spatiotemporal distribution of snow crab (Chionoecetes opilio) in the eastern Bering Sea: 1982 – 2018

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 02/17/2021

Defense Date 12/11/2020

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

Tag fishery survey,geostatistics,GIS,marine ecology,OAI-PMH Harvest,regression modeling,snow crab,space-time modeling,spatial analysis

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Bernstein, Jennifer (committee chair), Loyola, Laura (committee member), Sedano, Elisabeth (committee member)

Creator Email brynamichelle@gmail.com,brynamil@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-421464

Unique identifier UC11667851

Identifier etd-MillsBryna-9271.pdf (filename),usctheses-c89-421464 (legacy record id)

Legacy Identifier etd-MillsBryna-9271.pdf

Dmrecord 421464

Document Type Thesis

Rights Mills, Bryna Michelle

Type texts

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

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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