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Using pattern oriented modeling to design and validate spatial models: a case study in agent-based modeling

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Using pattern oriented modeling to design and validate spatial models: a case study in agent-based modeling

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Content USING PATTERN ORIENTED MODELING TO DESIGN AND VALIDATE SPATIAL
MODELS: A CASE STUDY IN AGENT-BASED MODELING

by

Jerry Patrick Corum

A Thesis Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(GEOGRAPHIC INFORMATION SCIENCE AND TECHNOLOGY)

December 2014

Copyright 2014 Jerry Patrick Corum

ii
DEDICATION
I dedicate this document to my parents and siblings for their constant support, and to my
grandmother, without whom I would not have received a college education.

iii
ACKNOWLEDGMENTS
I will be forever grateful to my mentor, Professor Kemp and the professors who introduced me to
agent-based modeling as an undergrad, Drs. Marco Janssen and Amber Wutich. Thank you also
to my family and friends, without whom I could not have made it this far.

iv
TABLE OF CONTENTS
DEDICATION II
ACKNOWLEDGMENTS III
LIST OF TABLES VII
LIST OF FIGURES VIII
ABSTRACT X
CHAPTER ONE: INTRODUCTION 11
1.1 Understanding moving-object behavior 12
1.2 Overview of the study 13
1.3 Research Objective and Process 16
CHAPTER TWO: THEORETICAL FRAMEWORK 17
2.1 Ecological Analysis and Moving-object Data 18
2.2 Agent-based modeling 18
2.2.1 Modeling languages for ABM 19
2.2.2 ABM building blocks 20
2.2.3 Validation of ABM Results 21
2.2.4 Pattern Oriented Modeling 22
2.3 The R Project and Ecological analysis 23
2.3.1 R functions and Packages used in this study 24
CHAPTER 3: METHODS 27
3.1 Investigating moving-object data, the Galapagos Swallow-tailed Gull 28
3.1.1 Seabird track shape and activity 28
3.1.2 Seabird relocation independence 33

v
3.1.3 Seabird home range analysis 34
3.2 Development of study models through POM 35
3.2.1 Building the basic structure of the models 36
CHAPTER 4: ITERATIVE MODEL DEVELOPEMNT AND ANALYSIS 38
4.1 A Starting Point; the Simple Random Walk as a process for bird movement 38
4.1.1 Shape and the use of space by agents with SRW movement programming 39
4.1.2 SRW relocation independence, pattern in random values 43
4.1.3 The use of space: home range 44
4.2 Incorporating a correlated random walk to modify spatial behavior 45
4.2.1 Shape and the use of space by agents with CRW movement programming 46
4.2.2 CRW relocation independence, pattern in random values 49
4.2.3 CRW home range analysis 50
4.3 Incorporating speed variation into the correlated random walk 51
4.3.1 Shape and the use of space by agents with CRWS movement programming 52
4.3.2 CRWS relocation independence, pattern in less random values 55
4.3.3 CRWS home range analysis 56
CHAPTER 5: DISCUSSION 58
5.1 Spatial elements 58
5.2 Conclusions 60
5.3 Lessons learned 61
5.4 Questions for the future 61
REFERENCES 63
APPENDICES 65

vi
APPENDIX 1: TRAJECTORIES 65
APPENDIX 2: REDISCRETIZED TRAJECTORIES 67
APPENDIX 3 SMOOTHED COSINE VALUES 70
APPENDIX 4: ACF VALUES FOR INDIVUDAL BIRD AND NETLOGO TURTLE
RELATIVE ANGLE CHANGES 72
APPENDIX 5: NEAREST-NEIGHBOR CLUSTERING ANALYSIS OF HOME
RANGE ESTIMATES 74
APPENDIX 6: SPEED, FROM RANDOM TO NORMAL 77

vii
LIST OF TABLES
Table 1 Summary of R functions used to investigate ABM 26
Table 2 Galapagos Swallow-tailed Gull 'ltraj' characteristics 29
Table 3 Individual seabird P-values from the Wald-Wolfowitz test of randomness 34
Table 4 SRW, CRW and CRWS ‘lraj’ characteristics Error! Bookmark not defined.
Table 5 WaWo test results for SRW Model Output 44
Table 6 WaWo test results for CRW Model Output 50
Table 7 WaWo test results for CRWS model output 56

viii
LIST OF FIGURES
Figure 1 Galapagos Swallow-tailed Gull relocation flight paths constructed from tracking data 13
Figure 2 Seabird discrete movement paths sampled at 5-minute intervals 28
Figure 3 100m Rediscretized movement paths of Galapagos Swallow-tailed Gulls 30
Figure 4 Galapagos Swallow-tailed Gull smoothed cosine values of the relative angles 31
Figure 5 ACF values of seabird relative angles 33
Figure 6 Home range analysis of seabird data using 'clusthr' 34
Figure 7 Netlogo modeling environment with vector graphic of Santa Cruz Island 37
Figure 8 Seabird (left) and SRW Model movement tracks 39
Figure 9 Rediscretized seabird (left) and SRW movement paths 40
Figure 10 Seabird (left) and SRW smoothed relative angle changes over time 41
Figure 11 ACF of relative angle changes in seabird (top) 42
Figure 12 Seabird (left) and SRW home range size from ‘clusthr’ 45
Figure 13 Seabird (left) and CRW movement tracks 47
Figure 14 Rediscretized seabird (left) and CRW movement paths 47
Figure 15 Seabird (left) and CRW smoothed relative angle changes over time 48
Figure 16 ACF results of relative angle changes in seabird (top) 49
Figure 17 Seabird (left) and CRW home range size from ‘clusthr’ 50
Figure 18 Seabird (left) and CRWS movement tracks 52
Figure 19 Rediscretized seabird (left) and CRWS movement paths 53
Figure 20 Seabird (left) and CRWS smoothed relative angle changes over time 54
Figure 21 ACF results of relative angle changes in seabirds (top) and CRWS agents 55
Figure 22 Seabird (left) and CRWS home range size from ‘clusthr’ 56

ix
Figure 23 CRWS agents speed distributions Error! Bookmark not defined.
Figure 24 Galapagos Swallow-tailed Gull speed distributions Error! Bookmark not defined.
Figure 27 Movement of Netlogo gulls with a simple random walk 65
Figure 28 Movement of Netlogo gulls with a correlated random walk 65
Figure 29 Movement of Netlgo gulls with a correlated random walk and variable speed 66
Figure 30 Movebank.org Gull relocations 67
Figure 31 Correlated random walk with variable speed 67
Figure 32 Simple Random Walk 68
Figure 33 Correlated Random Walk 69
Figure 34 Correlated random walk with variable speed 70
Figure 35 Simple random walk 71
Figure 40 Seabird relative angle ACF 72
Figure 41 SRW relative angle ACF, clockwise from upper left, bird 0-3 73
Figure 42 CRW relative angle ACF, clockwise from upper left, bird 0-3 73
Figure 43 CRWS relative angle ACF, clockwise from upper left, bird 0-3 73
Figure 44 Simple Random Walk ‘clusthr’ home range results. 74
Figure 45 ‘Clustr’ home range results from the Correlated Random Walk with Variable Speed 75
Figure 46 ‘Clustr’ home range results from the Correlated Random Walk 75
Figure 47 ‘Clustr’ home range results from Moving-Object Bird data set 76

x
ABSTRACT
Complexity in spatial simulation models developed without an iterative development
process can lead to models that produce inaccurate or nearly random results. This case study
examines how real world moving-object data can be used to inform the model development
process. Moving-object analysis provides a template for understanding movement behaviors
evident in both empirical data and model output. Moving object data generally consists of the
GPS points from tracked animals, and is usually acquired as a comma separated values file.
Agent-based simulation model development in this case study is informed by pattern oriented
modeling, an iterative process used to control a model’s complex variables while gradually
improving model design. Three simple agent-based models were constructed and a best fit
model whose output most closely matches the spatial characteristics of the Galapagos Swallow-
tailed Gull moving object data was identified.
.

11
CHAPTER ONE: INTRODUCTION
This study demonstrates how ecological analysis of moving-object data can be used to
empirically validate agent-based models (ABMs) and presents a combination of methods that can
be used to analyze moving-object data to inform model development. Integrating ecological
analysis in the modeling process proves effective at providing a framework for model
development and validation.
Spatial modeling in scientific terms is both a simplified way of representing a spatial
system that is being studied and a tool for understanding and predicting processes and behavior
(O'Sullivan and Perry 2013). Models are useful to explore changes in the real world as well as
help us understand the processes that generate the patterns we observe in the system.
Models are often used for prediction and to assist in data collection, but can also be used
as a tool to enable critical thinking about the real world. Examples of this may include
predicting weather, identifying critical habitat areas to investigate with sampling techniques, or
providing a framework to explore environmental factors and their effect on an ecological system.
In this case study I will use a simulation model to explore the process of movement through
space and time in an effort to understand and reproduce seabird movement activities.
Spatial modeling comes with a few challenges, especially that of identifying when too
much complexity is present for the model to be useful. It is also necessary to decompose the
real-world into component parts that are modeled and decide which factors are more likely to
affect the system in a meaningful way. In some cases, a lesson learned early on in exploring
agent-based models for this study, too much complexity can slow a model down and also
produce unpredictable and unreliable results.

12
This study demonstrates an iterative process for validating a random walk model, a
fundamental building block model of agent-based modeling, designed to simulate bird flight
tracks. The objective is to integrate Geographic Information Science (GIScience) methodologies
with computer science and ecological epistemologies to inform model development through a
gradual process beginning with simple movement. The methodology builds on work in agent-
based model validation and ecological analysis to provide a multidisciplinary tool for examining
agent-based models during the development process using moving-object data.
1.1 Understanding moving-object behavior
Home range estimation, tortuosity or searching intensity, and linear or sequential spatial
autocorrelation are tests of range, behavior and independence in movement patterns and provide
important insight into the structure of moving-object data. Ecological studies using records of
movement tracks of insects, birds and marine and terrestrial mammals commonly include many
such tests of the track trajectories to assist in developing an understanding of the moving-object’s
behavior (Bence 1995; Benhamou 2004; Brillinger et al 2002; Colomb et al 2012; Fauchald and
Tveraa 2003; Kareiva and Shigesada 1983; Lichstein et al 2002; Root and Kareiva 1984). As
illustrated in this study, modeling is an effective tool for understanding the structure of a moving
object’s motive force and assists in the exploration of the real-world data.
Knowledge of movement patterns in animal behavior is imperative for understanding the
results of simulated behavior in ABMs. Through the use of analysis techniques developed in
ecological studies of animal behavior, it is possible to look at the overall shape of the animal’s
track without regard to its feeding or nesting behavior, making it a suitable approach for
analyzing movement patterns simulated by agent-based models. In Figure 1, the paths of four

13
Galapagos Swallow-tailed Gulls are displayed. These four birds were tracked using GPS collars
and are the moving-object data for this study.

Figure 1 Galapagos Swallow-tailed Gull relocation flight paths constructed from tracking
data
It is the goal of this study to decompose the moving-object data’s spatial elements to their
component parts and use those parts to act as a filter for the agent-based modeling movement
processes.
1.2 Overview of the study
The study began with the review of a set of analytical tools in ecological analysis that
include statistics for the shape of the movement track, the independence of the movements and
the home range area. These were evaluated to design a framework for the analysis of patterns in
empirical data available from Movebank.org, a repository of tracking data collected and shared
with an open source license. Using these analysis tools, a moving-objects dataset which records

14
the flight paths of Galapagos Swallow-tailed Gulls off the coast of Santa Cruz, Ecuador was
analyzed to evaluate movement metrics that describe the patterns observed in a form that is
transferrable to ABM. Then, three agent-based models were developed to simulate the birds’
movement using increasingly complex forms of a random walk model with identical analytic
techniques applied to filter out results that are inconsistent with real world behaviors.
The agent-based models were programmed to simulate three different mathematically
modeled movement patterns: a simple random walk, a correlated random walk and a correlated
random walk with variations in speed that match the mean and standard deviation of a normally
distributed curve modeled from the empirical data. Each model revision was intended to add
structure to the simulated movement patterns that better replicated the actual movement tracks.
Importantly, the models are not designed to predict the movement patterns evident in the seabird
dataset, rather they seek to reproduce similar overall movement patterns, and thus provide insight
into mechanisms behind the observed patterns. This means it is possible to model reactions to
environmental change or habitat incursion without actually changing the real-world environment.
The data from Movebank.org acted as a means to assess for and filter out poor program design
decisions, eliminating choices that were unable to produce similar trajectories and movement
structures.
Agent-based modeling is a bottom up approach to modeling that looks for pattern from
process (O'Sullivan and Perry 2013). These models simulate the decisions of multiple
individuals simultaneously and allow patterns to emerge from this complexity. One classic
example of agent-based modeling is a predator-prey model, which tracks each individual
predator and prey’s actions and bases the decisions they make on environmental and neighboring
attributes. While a predator-prey model is relatively simple, often these models can be

15
incredibly complex. In these cases standards for the ABM empirical validation process are
called for but are often ignored (Janssen and Ostrom 2006).
Through agent-based modeling it is possible to examine the processes that create
movement patterns in moving-object data. It is possible to use an ABM to explore the effects of
habitat extent and resource availability on movement and resource exploitation. The exploration
of these effects requires validated simulation output to be meaningful.
The method of empirical validation is specific to each model and the processes and
patterns that are modeled. In the analysis of moving-object data in ecology, trajectory and home
range analysis can help validate the simulated movements. The ecological techniques may, for
example, decompose the animals’ track into relative angle changes between each track segment
or a habitat area into a cluster of core movements. The ‘clusthr’ tool identifies three locations
with a minimum mean nearest-neighbor joining distance (NNJD), which forms the first cluster.
Then, in set steps the search expands and locations (which in this case are relocations, or the
sequential locations observed in the dataset) are added based on the next set of NNJD clusters
with the minimum mean distance to the first, until 100% of the locations are incorporated. Such
decomposed behavior can be simulated with an agent-based model and exported for analysis and
validation against real-world data.
Using the seabird data as a case study, the use of empirical data to evaluate the success of
interactively developed agent-based models was demonstrated. Applying the same tools and
metrics used to evaluate the movement patterns evident in the Movebank.org data to the
simulated data resulting from the agent-based models indicates that it is possible to assess
whether an agent-based model can accurately reproduce the structural components of moving-
object data.

16
1.3 Research Objective and Process
The objective of this research was to examine the practical aspects of using an analysis of
moving-object data to validate an agent-based model during the iterative model development
process. The model generates moving-object data for analysis in a geographic information
system using the ecological analysis tools in the R-project for statistical computing, including
sequential autocorrelation, habitat estimation, and trajectory analysis. Model development began
by modeling very basic random walks, incorporating more complex random walk models as
analysis progressed. Based on ecological analysis carried out during modeling, it was concluded
that correlated random walks and correlated random walks with varying speed produce results
that most closely match real-world observations. Further development involving modifications
based on animal behavior will be necessary to replicate the empirical data.
The remainder of this document describes the study in detail. Chapter 2 provides the
multidisciplinary framework used in this study and establishes the link between agent-based
modeling and ecological analysis. Chapter 3 provides detailed methods and results. Chapter 4
discusses the results and Chapter 5 sums up the study, provides conclusions from the results and
raises questions for future research.

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CHAPTER TWO: THEORETICAL FRAMEWORK
Two scientific fields provide the theory and methods used in this research, agent-based
modeling and ecological analysis. Agent-based modeling provides a tool to investigate processes
that underlay complex patterns in social science, biology, and other disciplines. The tools of
ecological analysis decompose complex patterns and provide quantifiable observations of real-
world processes. Ecological analysis laboratory studies of bugs in a maze (Colomb et al. 2012)
and tracked animal data (Brillinger et al. 2002) provide a framework for decomposing moving-
object data. The building blocks of agent-based modeling (see O’Sullivan and Perry 2013)
provide the basis for using decomposed moving-object data as a means of structuring an agent-
based model to simulate movement behaviors accurately using an iterative model development
process.
Several approaches are used in each discipline, however there are unifying elements such
as the assumptions made regarding animal movement, which make this study possible. Simple
and correlated random walks are the subject of much discourse in both agent-based modeling and
ecological studies (Kareiva and Shigesada 1983, Grimm et al 2005, Haefner 2005).
Fundamentally both walking styles form the basis of modeling animal foraging behavior in both
agent-based modeling and ecological analysis and even have many applications in economics,
psychology, physics, chemistry and biology (Van Kampen 1992, Goel and Richter-Dyn 1974, De
Gennes 1979, Weiss 1994).
Several software applications and statistical techniques were used in this study to create
the models and analyze the output. Agent-based models were created in the Netlogo modeling
environment using the language of the same name. The ecological analysis was done in R using

18
several packages that are tailored to ecological movement analysis, the main package being
‘adehabitatlt’ and its dependencies, ‘sp’, ‘CircStats’ and others installed automatically.
2.1 Ecological Analysis and Moving-object Data
Tracked animal behaviors in ecological analysis form an important part of this study.
Ecology is the scientific study of interactions between and among organisms, thus movement
takes an important role in an ecological analysis. Moving-object data consists of a set of
relocations, either from GPS tracking or sighting and observations. These can be part of an
ecological study, lab study, or any set of data with tracked movement. Encoding and storing
moving-object data in a useful way is critical not only for analysis but for meaningful sharing of
data. Data without a standard, especially without metadata, can be difficult to decipher and use
even for the original collector if enough time passes. Storing and using moving-object data is the
focus of several associations including the Open Geospatial Consortium, who develop standards
for open spatial data storage to extend usability.
2.2 Agent-based modeling
Agent-based (sometimes called individual-based) models (ABM) are composed of
collections of individual objects that are unique and autonomous, interacting with each other and
their immediate spatial environment (Railsback and Grimm, 2012). While generally based on
cellular automata models developed in the 1940’s by John Von Neumann, it was the Game of
Life by John Conway that spurred the development of methods of modeling of simple rules to
investigate complex patterns (Neumann and Burks 1966; Gardner 1970, 120-123). In many
cases agent-based modeling is considered modeling from the bottom up (i.e. from the individual
actions that combine into the big picture).

19
In agent-based modeling an agent is the individual agent that makes decisions based on
the patches around it. The Netlogo patches are a raster surface. The patches can be both agents
and dynamic variables (resource quantities, environmental conditions, weather, etc.) that change,
assess and react during each tick, or time-step, along with agents, also called turtles, which move
across the surface. Each agent assesses the world around it during a tick, makes the decisions
based on how it is programmed and organizes or prepares any variables it needs for the next tick.
2.2.1 Modeling languages for ABM
Many software platforms have been created for agent-based modeling. Repast, Swarm,
Netlogo, and the Multi-Agent Simulator Of Neighborhoods (MASON) are just a few. These
languages may have been developed for specific purposes, such as modeling social complexity,
as in the case of MASON, or they can be general purpose like Repast and Netlogo. Netlogo was
selected for this study because of its supportive community of users, relatively easy learning
curve and access to high quality tutorials and textbooks. Netlogo was developed by Uri
Wilensky in 1999 at Northwestern University and is derived from the educational programming
language Logo, known for Turtle, a robot whose movements across the floor could be easily
programmed by school children. Netlogo is likewise an easy to learn programming language
that is well documented and supported by a community of active developers including students,
professors and professional consultants (www.ccl.northwestern.edu/netlogo). There is a wide
variety of open simulations to play with and learn from, and many instructional books. The
output is spatial in nature, with x and y coordinates marking location in the Netlogo world,
making it intuitive to use the tools of a GIS to analyze the results.

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2.2.2 ABM building blocks
While developing and understanding complex, agent-based models about the real-world
is usually very difficult, O’Sullivan and Perry (2013) suggest that there are three fundamental
building blocks that make up a complete agent-based model’s basic structure. These building
blocks, grouping, mobility and spread, are discussed below.
Grouping is comprised of segregation and aggregation processes that produce
heterogeneity in the landscape. These processes are used as a part of models that explore
neighborhood segregation or the evolution of patchy landscapes in ecological studies. Most
often these processes use operations like local averaging, in which each tick provides a chance
for an agent to move closer to other agents with similar attributes. This behavior is directly
observable in the real-world; examples include gentrification and ecosystems models showing
clear patches of homogeneity in a landscape.
Mobility is embodied in random walk models. These involve the movement decisions
that cause an agent to act on, and react to, the environment around it. Simple random walks
involve picking a random direction on a grid and moving one step, then repeating the process.
Since there are 360 possible directions to move in the study models, over time the agent is not
likely going to be far from its point of origin (O'Sullivan and Perry 2013; Šalamon 2011;
Railsback and Grimm 2011). A more complex version of the random walk, called a correlated
random walk, provides a more realistic process for movement. In a correlated random walk, the
decision on which direction to move is related to the direction previously traveled, meaning if the
agent moved east in the previous tick, the agent will have higher odds of choosing a direction
that is similar. Restricting an agent’s change in direction by limiting the relative angle of
movement on subsequent ticks is one way of programming a correlated random walk.

21
The use of random walks for modeling real-word behavior is supported by biological and
ecological studies (Kareiva and Shigesada 1983, 234-238; Benhamou 2004, 209-220). The
random walk is considered a stochastic model, but it does not focus on the end product – the
combined movements of the animals -- rather it models how each individual contributes to the
overall movement of the population (O'Sullivan and Perry 2013). While often used in physics
(Berg 1993; Rudnick and Gaspari 2004), pure random walks may seem unrealistic for ecological
analysis, since it is likely that almost no living animals move in this way. Nevertheless,
variations on random walks are the focus of this particular study, as random walks form a
foundation for understanding movement without directly modeling observed movement itself.
Spread, or growth and reproduction form the final building block. This deals with how
agents procreate and spread their influence across a landscape. This is different from simply
moving through an area as in the random walk because the agent becomes a part of the landscape,
acting on it and changing it. It incorporates that landscape into its area of influence, or home
range.
2.2.3 Validation of ABM Results
Validation of agent-based models can be a long process and can be very difficult. The
entire system must be checked against all the possible variations present in the programs
structure. In the simple models in this study, only a few variables exist, such as allowed relative
angle changes and speed, however in models that incorporate foraging behaviors, exploration,
memory, and links between agents (growth and reproduction) the number of variables that must
be tested can be intimidating.
Sensitivity analysis alone represents a significant investment in time (Janssen and
Ostrom 2006, 37; Grimm et al. 2006, 115-126; Macal and North 2007, 95-106; Parker and

22
Meretsky 2004, 233-250; Topping, Høye, and Olesen 2010, 245-255; Valbuena et al. 2010, 185-
199). Sensitivity and Uncertainty analysis require repeated model runs with small variations in
parameters. Sensitivity analysis often allows a model builder to filter out obviously incorrect
model behavior by observing which variables have the most effect on the outcome. Using tools
such as Netlogo’s BehaviorSpace it is possible to automate the runs and set ranges for variables
to vary. This produces a great deal of output, both tabular and spatial that needs stored and
analyzed. Both running the model and the analysis can be extremely time consuming. In early
models runs using Scott Hekbert’s 2013 model, MayaSim, one hundred runs produced over 30
gigabytes of data and took between 24-36 hours to complete on a personal computer.
2.2.4 Pattern Oriented Modeling
Evaluating uncertainty on each building block in the iterative development process will
not produce results worth the significant investment of time needed to run the model enough
times to perform the analysis. Pattern Oriented Modeling (POM) helps minimize these analysis
steps by identifying relevant patterns in a real system that are relevant to the questions being
asked, preventing a model from becoming over-parameterized (Grimm and Railsbeck, 2012).
Since the model building step begins with identifying patterns, or behaviors that fall beyond
random variation that are then reproduced indirectly but purposefully in the model, the analysis
step will begin with a series of controlled experiments on the model itself (Grimm and Railsbeck,
2012, Salamon 2011).
POM begins with patterns found in real-world systems and develops a hypothesis to
explain the pattern. Predictions based on that pattern are then tested and the model is adjusted
accordingly and the process begins again. POM is used to assist in the development of an ABM.
This allows model parameters that are not adequately explaining the observed real world patterns

23
to be filtered out. It is an iterative and incremental method to tweak the model and balance the
model’s complexity with that relevance of what can be learned from it (Railsback and Grimm
2011; Šalamon 2011; O'Sullivan and Perry 2013).
Pattern oriented modeling can be used in any agent-based modeling programming
language or environment. The approach presented here should be a part of the iterative model
development process (see Salamon 2011; Grimm and Railsback, 2012;), preceding and
supporting the sensitivity analysis.
2.3 The R Project and Ecological analysis
The R Project for Statistical Computing is an open source statistical programming
language and software environment used for statistical computing and graphics (www.r-
project.org). The core functionality of the environment was originally developed at the
University of Auckland in New Zealand. R is available for a variety of operating systems. It is
community supported, with many online forums for questions and a robust set of tutorials and
publications providing tutorials and support. In R, custom sets of tools called packages make
research using discipline-specific analytical techniques more accessible to non-specialists. There
are many packages available through the Comprehensive R Archive Network (CRAN). To make
it easy to find packages for specific purposes, CRAN offers several task views that organize
packages into thematic subsets such as Environmetrics, Spatial or SpatioTemporal groups.
Packages are open source and made available in CRAN with a reference manual and optional
vignette document with a walkthrough and illustration of the package functions.

24
2.3.1 R functions and Packages used in this study
ACF and PACF take a time series of recorded values as input with missing values
removed. These functions provide a tool for looking at periodicity in the datasets by
investigating repeating patterns in the dataset and are also used to investigate sampling error
(Venables and Ripley 2002). Used in this study on the changing relative angles of each
relocation, both ACF and PACF look for patterns that can show searching behavior of real world
tracked seabirds, a movement which may be difficult to reproduce in an agent-based model
(Bence 1995, 628-639; Lichstein et al. 2002, 445-463). PACF is primarily used to fit an
Autoregressive Integrated Moving Average (ARIMA) model, which does not fall within the
scope of this study and is not used. ACF may be used to test sampling error in both the real
world dataset and the simulated one (which represents a simulated sample).
R’s ‘adehabitatLT’ package was chosen for this study because of its flexible nature and
ability to convert a wide variety of data formats to its ‘ltraj’ object class, as well as providing
compatibility with other packages tailored to ecological analysis and the study of moving-objects.
Adehabitat is a collection of tools for analyzing habitat selection by animals and includes tools
for modeling error and uncertainty as well as understanding how animal tracks influence habitat
range.
A relocation in the ‘adehabitatLT’ package is considered a sequential or timed
observation of an animal’s location in space. This data must contain coordinates and a sequence
identifier, or time and often includes information related to the observation such as weather,
wind speed and direction, elevation, and other miscellaneous data. This data is imported into the
‘ltraj’ object class in order to begin the analysis. The ‘ltraj’ object calculates additional measures
when the data is converted that enable more advance analysis by the package. Critical to this

25
study is the calculation of relative angle changes, referred to in ‘adehabitatLT’ literature as the
shape of an animal’s movement. The ‘ltraj’ object calculates the following measures:
1. Change in x-coordinate (dx)
2. Change in y-coordinate (dy)
3. Distance to previous relocation
4. Absolute angle change
5. Relative angle change
Because the ‘ltraj’ object contains calculated values for the relative angle changes
between each relocation, it is possible to begin investigating the overall shape of movement
through space and time. Extracting the relative angle changes makes it possible to use time series
analysis to investigate periodicity and the overall shape of the relocations. The relative angle
values of sequential relocations can then be converted to smoothed cosine values for analysis in
the time series. The ‘sliwinltr’ transformation in the ‘adehabitatLT’ package creates a sliding
window chart of smoothed cosine values, which is used to investigate tortuosity, or searching
behaviors (Benhamou 2004, 209-220). Benhamou states that cosine values near 0.5 are
considered tortuous searching behaviors, possibly when the bird is circling an area looking for
prey, while values close to 1 or 0 are more linear behaviors, possibly indicating navigating to a
location from memory or fleeing a predator.
This study uses several functions found within the core R package as well as the
‘adehabitatLT’ and ‘tseries’ packages. Each of the functions used in this study is summarized in
Table 1.

26
Table 1 Summary of R functions used to investigate ABM
Function Name Found in package Brief Description Example Use
acf Core R Autocorrelation
function
Examine linear
autocorrelation of
relative angle
changes
wawotest adehabitatLT Wald-Wolfowitz
test of
independence
Finds data in a
sequence that
doesn’t belong.
clusthr adehabitatHR Estimates home
range by single-
linkage cluster
analysis and
produces a
Multiple Convex
Hull object to
store the data
Identify home
range extent from
tracked animals
relocation data
MCHu2hrsize adehabitatHR Calculates home
range size from
Multiple Convex
Hull object with
specified
percentage levels
for the home
range
Examines the rate
of home range
increase – can
identify
exploration and
foraging behaviors
sliwinltr adehabitatLT Applies any
function to an
‘ltraj’ object using
a sliding window
Used to
investigate
relative angle
changes
ts.plot stats (core R) Plots a time series Used to plot the
relative angle
changes through
time
testang.ltraj adehabitatLT Independence test
for successive
angles (relative or
absolute)
Tests for abnormal
patterns or
periodicity that
can result from
sampling error

27
CHAPTER 3: METHODS
In this chapter the basic methods of agent-based modeling and ecological analysis will be
reviewed. I have chosen to place the analysis and results of the seabird data in this chapter in
order to provide a context for understanding the ecological metrics that are used. Additionally,
since the analysis of this real-world data was necessary prior to beginning the model
development process, this step is part of the methods.
The statistical software available through the R-Project for Statistical Computing, and
several associated packages tailored to GIS and ecological habitat modeling were used to assess
the moving-object data. The primary packages used are adehabitatLT and adehabitatHR
(Calenge, C., 2006). Using Movebank.org, tracked locations of Galapagos Swallow-tailed Gulls,
collected by Martin Wikelski from 2008 to 2010 were downloaded to provide real world,
moving-object data to act as a filter for building the agent-based model. These paths are
displayed in Figure 2. This data was assessed prior to creating the model to provide statistical
measures to be used as a filter for validating the output of the agent-based model (ABM). Both
the general method and results are presented below.
Data was imported into R from a comma-separated values (CSV) file downloaded from
Movebank or generated by the ABM. Movebank is an online database of animal tracking data
stored at the Max Planck Institute for Ornithology. Scientists are free to put their data on the site,
sharing it with others, while still enabling them manage the data closely. It contains several
datasets of tracked animals, including tortoise, whales and seabirds. The Galapagos Swallow-
tailed Gull dataset (Movebank ID 5503590) provided breeding and non-breeding period data for
this study. The XY coordinates, time/sequence and a unique identifier for each tracked location
are used. In this case the objects are imported as an ‘ltraj’ object of class II, meaning that the

28
exact time of the observations is ignored in favor of placing the relocations in the correct
sequence. The use of the class II ‘ltraj’ object enables comparison between the Netlogo model
output and the real-world bird tracking data.
3.1 Investigating moving-object data, the Galapagos Swallow-tailed Gull
In this study, the simulated data captured from the agent-based model contains four
columns; x and y coordinates, the unique agent identifier, and the Netlogo tick number. The
Galapagos moving-object data contains latitude, longitude, a time stamp, temperature readings,
speed, heading, height (above sea level) and the unique identifier.
3.1.1 Seabird track shape and activity

Figure 2 Seabird discrete movement paths sampled at 5-minute intervals
Figure 2 displays the discrete movements of the real-world gulls, sampled every 5
minutes over a time period ranging from approximately 3-8 hours. The starting point is identical
for each seabird, right off the coast of the island. Several incidents, including battery

29
consumption and tag damage, can cause the end point. The seabird data imported into the ‘ltraj’
class includes a unique ID for each bird, the number of relocations, or observations taken by the
GPS tag, and the number of missing relocations (NA values), or relocations that do not occur
every 5 minutes. These numbers are given in Table 2 however in this dataset there are no NA
values.
Table 2 Galapagos Swallow-tailed Gull 'ltraj' characteristics
ID Number of Relocations
PLS-13 99
PLS-2 134
PLS-4 143
PLS-8 22

In order to analyze the overall shape of the seabird relocations, a rediscretizing step is
taken, adding or removing point locations to create relocations at regular intervals in space,
rather than in time. In mathematics, the process of taking continuous data and breaking it up is
called discretizing. Since this has already been done in the seabird data, i.e. the continuous flight
path of the gulls is discretized by the GPS sampling their position, the rediscretizing step models
a best fit continuous path and discretizes it at the spatial or time intervals chosen for the study.
This means that instead of a sequence of relocations 50, 90, 20 and 11 meters distance, all the
distances are computed and relocations added or removed to enforce a particular distance as the
standard. This effectively fills in the blanks of the relocation data and allows several R tools to
assess the changes in relative and absolute angle between each successive relocation (Calenge
2011, Turchin 1998, Benhamou, 2004). The rediscretized movement paths for Galapagos
Swallow-tailed Gull observations is given in Figure 3.

30

Figure 3 100m Rediscretized movement paths of Galapagos Swallow-tailed Gull
observations
Smoothed cosine values of these rediscretized trajectories’ relative angles, i.e. the angle
changes between each successive movement, provide information on the tortuosity, or intensity
of searching behavior in the tracked animal (Benhamou 2004, Colomb 2012). Tortuosity refers
to the sharper turn angles of an animal searching for food or a safe location to nest/rest. The use
of ‘sliwinltr’ provides the visual display of these relative angle cosine values in Figure 4. Cosine
values near 1 indicate a relatively straight trajectory, while values that approach 0.5 indicate a
sharp turn and are commonly considered food or resource searching behaviors (Benhamou, 2004,
Calenge, 2011). The seabird data in Figure 4 demonstrates these varied behaviors, linked by
Benhamour (2004) to searching behaviors.

31

Figure 4 Galapagos Swallow-tailed Gull smoothed cosine values of the relative angles
demonstrating searching behaviors
The cosine values of the relative angles in Figure 4 do not show periodic patterns but do
demonstrate the same intermittent searching behaviors, with values near 1 and values in the mid-
range at times demonstrating tortuous angles, or searching behaviors. Simulating searching
behaviors themselves will require a modification of the entire model to include foraging and
energetics concepts, additionally predicting the foraging areas will require a model more
complex than time will allow for this exploratory study. Thus, foraging locations and behavior
are not simulated with these study models. We can test that the underlying movement processes
of the foraging behavior are present, specifically that these values vary without any periodic
components and that straight line travel and tortuous trajectories are present. The relative cosign
values are important for understanding the overall shape of an animal’s trajectory. If model
development continues beyond the scope of this paper, later iteration of this ABM will
necessarily revisit this test as a means of validating foraging behaviors.

32
Since moving-object data is spatially linear and sequential, the standard tools for
investigating error and independence (autocorrelation) in space will not provide useful
information. The spatial location of the animal is correlated to its last location because it came
from that location; a different approach is needed. Instead, using R and the adehabitatLT
package ‘ltraj’ object, it is possible to extract the sequential changes in relative angles to
investigate searching behavior. After extracting the data, R’s standard autocorrelation ACF
function can be used.
The data from the ‘ltraj’ object is exported to an R dataframe, which is similar to a
Microsoft Excel spreadsheet with column names and provides access to the ‘ltraj’ object’s
calculated values for the relative angles in each burst, which is the set of relocations for one
animal. It is necessary to omit any NA values from the data in order for the ACF function to run,
though in this case the real-world seabird data has no NA values.
Figure 5 provides the ACF for individual seabirds in the dataset. Both in the bird dataset
and the Netlogo model simulation output, autocorrelation at time equals zero is near 1. The
initial angle change has no reference to compare it to, i.e., there is no prior angle for the value to
be compared against, causing an edge effect. The ACF values indicate the similarity of
observations and identify when abnormal observations occur, whether these are the events of a
bird recovering from capture or sampling error from the GPS tracking tags.

33

Figure 5 ACF values of seabird relative angles
3.1.2 Seabird relocation independence
Building on the examination of each relocation as a statistically independent event, an
overall test of randomness known as the Wald and Wolfowitz Test of Independence (WaWo) is
included with the ‘adehabitatLT ’ package. In the seabird data the p-values are very small for
each of the four birds tracked. These values are presented in Table 3. Each is low enough to be
considered zero for delta x (dx), delta y (dy), and distance. The WaWo test is a tool for detecting
randomness in a sequence of sample values. If the p-values are high, it suggests that there are
values present that do not fit in the sequence, i.e. values that are unlikely to occur in a normal
distribution.

34
Table 3 Individual seabird P-values from the Wald-Wolfowitz test of randomness

3.1.3 Seabird home range analysis
Home range estimation can be done with several different tools in R and ArcGIS. A
simple plot of the birds movement tracks is provided in Figure 2. In this case, the ‘ltraj’ object is
not needed and a staple of R’s spatial analysis packages, ‘sp’, is used instead called a Spatial
Points Data Frame. This is basically an Excel sheet but the coordinate values are hidden and
accessed through a variety of special calls in the ‘sp’ package. The ‘clusthr’ tool provides an
intuitive graph of home range size over home-range level, where level is the percentage of points
included to calculate the home range (Figure 6).

Figure 6 Home range analysis of seabird data using 'clusthr'

35
It is apparent from these charts that with around 75-80% of points included, the home
range begins to increase at an increasing rate. This suggests that a good estimate for the home
range will occur with around 75-80% of the points around the first set of clusters identified by
the tool. This is important when considering a model of seabird behaviors and suggests that
exploration activities may make up around 30% of the relocations for each seabird, though it is
possible they are attempting to seek out their home range area after being captured, tagged and
released.
3.2 Development of study models through POM
When the real-world data is analyzed, it becomes possible to begin thinking about the
creation of the models and how to use the real-world data as a filter on the model output. When
comparing a simple random walk model to the moving-object data, there is a large difference in
nearly every metric. A truly random walk forms a cluster around the origin point with the
probability of movement away from the origin decreasing with distance (O'Sullivan and Perry
2013). The initial form of random walk used in this study is slightly modified to restrict
simulated seabird movement over land. After each tick, or time step, the code checks if the
seabird is headed toward land or is over land and adjusts the heading out to sea if the movement
will take it more than a few hundred meters inland. This location check was developed after
examining the tracking data, which revealed rare flights over or near land, and provides a spatial
restriction for all three models.
The three simulations model seabird movement off Santa Cruz Island in the Galapagos
Islands. The simulation area is modeled to scale after the real-world environment where the
tracked data is located. The geography is loaded into the Netlogo environment using Netlogo’s

36
GIS extension. The simulation time is one 8-hour tracking period with observations every 5
minutes to match the 5 minute intervals of the GPS tracking data.
The movement speed for the models is based off the analysis of the seabird data. Each
movement in the simple random walk and correlated random walk models is 16 patches per tick.
This was calculated based of the average speed of the seabirds, 1217.6 meters per 5 minutes,
which when transformed to a Netlogo speed is 16 patches per tick. This is based off the original
size of the model area, 53,244.5 m
2
, determined using ArcGIS and creating a polygon to cover
the extent of the study area, which is used to bound the Netlogo environment. Given that there
are two square grids, one 54,244.5 meters in length and the other 701 patches in length, then, the
real-world length of one patch in the Netlogo grid is the real world distance divided by the
number of patches on one side. This is a ratio based method of transformation and results in
approximately 76 meters per Netlogo patch.
These models were constructed specifically for this study, and are very similar. The
random walk building block is modified sequentially after investigating the patterns in relation to
the real-world data. Code from demonstration models in the Netlogo Modeling Commons,
which is included with a Netlogo install, as well as example models from O’Sullivan and Perry
(2013) were used to construct each model, with some customization for the environmental
restrictions.
3.2.1 Building the basic structure of the models
Three agent-based models were constructed iteratively to investigate the trajectory,
movement and home range behaviors of simulated bird movements. I have termed these models
the simple random walk (SRW), correlated random walk (CRW), and correlated random walk
with variable speed (CRWS) after the elements that were adjusted to get closer to the real-world

37
data patterns. The basic structure of each model is the same. A vector outline of Santa Cruz
Island in the Galapagos Islands is used to match the location of the seabird data and can be seen
in Figure 7 with airplanes representing the seabird agents in mid-simulation. In this case the
black area is the ocean and the brown is the island of Santa Cruz, Ecuador.

Figure 7 Netlogo modeling environment with vector graphic of Santa Cruz Island
Seabirds return to land only to nest or shelter and spend most of their lives out at sea, thus
the agent-based model restricts their movements over land by choosing a random angle that is
directed seaward if they end up over the landmass. This behavior is coded into all three models
very simply, if the turtle will be over land in one tick, it is directed to pick an angle 180 degrees
opposite its current direction, then randomly vary it 90 degrees left or right, enabling the turtle to
travel parallel to the coast or go farther out to sea. While this does not prevent a bird from
ending up overland entirely, it does allow for some variation in movement when near the coast to
approximate seabird behaviors.

38
CHAPTER 4: ITERATIVE MODEL DEVELOPEMNT AND ANALYSIS
The following sections demonstrate the iterative model development process informed by
ecological analysis techniques and presents the results. The simple random walk (SRW) model
is the starting point, with the hypothesis that the birds simply have to move through space
somehow, ideally in the least complex way possible, avoiding land. The SRW model does not
meet the expectations setup by the real-world data and the next step in the iterative process, the
correlated random walk (CRW) model is implemented. The final model, the correlated random
walk with variable speed (CRWS) model provides the best fit without incorporating behavioral
parameters.
4.1 A Starting Point; the Simple Random Walk as a process for bird movement
The simple random walk model is presented as a starting point. This is the simplest way
of creating agent movement in Netlogo. Since we need agents to move across the landscape,
using the most basic method possible, it was expected the analysis would result in some
similarities with the real-world data. Using the SRW, the agent engages these steps:
1. Pick a direction randomly from 360 degrees
2. Check if that will intersect land
a. If yes, pick a direction 90 degrees plus or minus the angle that is 180
degrees opposite the original direction
3. Move 16 patches in that direction
4. Start over at Step 1
The model will persist with these actions until 96 ticks have been completed, simulating
an 8-hour time period of tracking. Other than movement over land, there are no additional
restrictions. Model runs where birds reached the edge of the map extent were discarded as this

39
causes an edge effect that is unsuitable for analysis, however if future models need to extend
farther from the island, the programming will not need adjustment. The data is exported into a
CSV file and the analysis in R can begin.
4.1.1 Shape and the use of space by agents with SRW movement programming
When comparing the SRW output to the seabird data (Figure 8) it is clear through visual
inspection that this is not the correct model for movement programming. The simulated agents
are tightly clustered and do not exhibit the range or deliberateness found in any of the seabird
tracks.

Figure 8 Seabird (left) and SRW Model movement tracks
The movement tracks can be decomposed further by analyzing the spatial components
that make up their movement. The ‘ltraj’ object is used to examine the shape of movements in
space and the object itself contains basic characteristics displayed when the object is created
which are identical for each model with 96 relocations and 4 simulated birds, referred to as
agents. Without device or battery failure there are no missing observations, and the tracks
contain the same number of relocations.

40
Following the steps used for analyzing the seabird data, the SRW data is rediscretized,
producing even more tightly clustered areas. In Figure 9, the rediscretization of the SRW paths
provides a more continuous path, but the tight clustering and lack of real-world behaviors is
apparent.

Figure 9 Rediscretized seabird (left) and SRW movement paths
To further decompose the shape of movements into spatial components that can be
compared without regard to seabird origin or spatial extent, the cosine values of relative angles
changes are used. This method of inspecting the cosine values of relative angle changes also
provides an insight into the differences between the seabird data and the simulated movements.
To understand these charts it is necessary to know that cosine values near 1 and zero indicate
near straight line travel, while values closer to 0.5 indicate what is called a tortuous trajectory,
think flying in circles looking for something or a jet fighter pilot avoiding incoming fire. In the
SRW output, there is almost no indication of straight line behavior, (Figure 10) instead the
cosine values appear to vary widely at every tick indicating movements in completely random

41
directions with no pattern. This implies that the agents are not moving relative to their previous
heading, but instead careening around as though in a pinball machine.

Figure 10 Seabird (left) and SRW smoothed relative angle changes over time
These same relative angle values can be analyzed using R functions that are able to look
for patterns in the sequential values. The ACF function tests if the model is selecting truly

42
random numbers or if an underlying pattern is working on the selection of angles. The presence
of autocorrelation in these data suggests there is an error in the model and that it is not a random
walk. This is true, since we have restricted the agent’s movement over land, which forces the
system to use a different set of rules and select an angle value from a different distribution. The
values above and below the blue lines in Figure 11 indicate autocorrelation that is statistically
significant, and that our movement programming needed adjusted for the next iteration of model
development.

Figure 11 ACF of relative angle changes in seabird (top)
and SRW simulation movements
While it would be possible to begin the new iteration here a few remaining tests exists
that can help explore and understand the data generated by the ABM and shed light into why a

43
simple random walk is not suitable for modeling moving-object data in the context of animal
tracking. The tests above look at the overall shape of the travel paths and begin investigating the
underlying values that compose the overall shape. These tests are used to determine the
geometric processes acting on the movements, identify searching behaviors and begin testing for
independence and sampling error. The tests below will further investigate independence and
begin to incorporate the use of space, or home range, into the analysis.
4.1.2 SRW relocation independence, pattern in random values
The WaWo test continues the investigation into the process of movements by examining
the distribution of changes in the xy coordinates and distance traveled. WaWo tests examine the
sequence of values by looking for values that do not belong and are from a different distribution.
Recall that the seabird P-values for dx, dy and dist are very low, meaning that the null hypothesis
of the WaWo test holds true, the values are consistent with no unexpected values in the sequence.
This test suggests that the movement process of the seabirds has a normal distribution and that
they are not moving randomly, but moving with a purpose. While this seems like common sense,
obviously birds do not randomly careen about like drunkards, having a mathematical test validate
this is useful when examining the simulation data since it allows for the quantitative comparison
of the model values with the real-world data and checks the randomness of the movement
process in Netlogo.
For the SRW model, the WaWo test results are presented in Table 4. The dx and dy p-
values are consistently low enough that the test is confident they are independently drawn from
the same distribution. Error here would indicate flaws in the tracking data itself, a bad location
fix, or a value in sequence from a different datum. In the simulation, these values are near zero
because Netlogo is controlling the coordinate system for all the values. The dist values however

44
are completely different. These values are much higher and the WaWo test indicates that they
are not independently drawn from the same distribution. This is true, since the distance traveled
is related to the speed of the agent, which we have set to a constant 16 patches per tick.
Table 4 WaWo test results for SRW Model Output
Agent ID dx dy dist
1 1.13E-10 1.84E-10 0.6036293
2 1.43E-09 2.12E-08 0.6631326
3 6.19E-08 2.34E-08 0.45736442
4 5.38E-07 1.53E-07 0.1883668

4.1.3 The use of space: home range
The minimum convex polygon (MCP) that contains 90-95% of all relocations in a set of
tracks is a common measure of home range (Kenward, et al 2001, Calenge 2011). The results of
the density and linkage estimator ‘clusthr’ are presented in Figure 12. This test identifies a core
group of clusters and begins incorporating other clusters into the group until 100% of the
relocation points are included. It is often used prior to creating an MCP to identify the
percentage of points to include that excludes exploration behaviors. In the seabird data from
around 50-75% there is very steady increase in home range area as the percentage of points
included increases and demonstrates an exponential increase in area. The simulation results are
more parabolic, with increases beginning at or around 50-60% of the home-range level and
increasing quickly. This suggests that the SRW model is not utilizing the space in the same way
as the seabirds, which is supported by the analysis of shape and space above.

45

Figure 12 Seabird (left) and SRW home range size from ‘clusthr’
In summary, the SRW produces agent movement paths that are tightly clustered, tortuous,
and autocorrelated due to programming restrictions. These evidently do not utilize space in the
same way as the seabirds. Overall the SRW model clearly does not produce movements accurate
enough to model seabird behaviors.
The next stage in the model development was to test a correlated random walk. The
correlated random walk is more complex since it changes the process by which the agents pick a
direction to move in, making it less random and more directional, it was hypothesized that it
would prevent the tightly clustered movement paths and change the overall use of space by the
simulation.
4.2 Incorporating a correlated random walk to modify spatial behavior
Adding the correlated random walk changes the behavior of agents at each tick. In this
model the agents are still looking out for the landmass, and avoiding it, but the angle changes
they are allowed make are restricted. The decision was made to allow the agents to pick a
direction that is no more than 45 degrees off their previous heading. This means the agent will

46
not be able to move back toward its origin point without making a more sweeping turn to do so
and was expected to bring the model output closer to that of the seabirds since it is unlikely they
are making 180 degree turns often.
The correlated random walk model is presented as the second iteration in the basic
movement model. When this model is initialized, the agents are given a random heading chosen
from the full 360 degrees available for them to move in. After initializing the model, the agents
in the correlated random walk model follow these steps:
1. Pick a direction plus or minus 45 degrees off your current heading
2. Check if that will intersect land
a. If yes, pick a direction 90 degrees plus or minus the angle that is 180
degrees opposite the original direction
b. If no, continue
3. Move 16 patches in that direction
4. Start over at Step 1
4.2.1 Shape and the use of space by agents with CRW movement programming
In Figure 13 it is apparent that the correlated random walk does bring us closer to the
movement model of the seabirds. The agent paths have become much less clustered and tortuous
in comparison to the SRW model output. Rediscretizing the movement steps, shown in Figure
14, prior to decomposing the spatial components of the movement tracks, reveals that there are
still more clusters in the CRW tracks than are present in the seabird tracks.

47

Figure 13 Seabird (left) and CRW movement tracks

Figure 14 Rediscretized seabird (left) and CRW movement paths
The cosine values are less torturous than the SRW model produces, with some of the wild
oscillations seen in the previous model reduced somewhat. While these values still vary a great
deal compared to the seabird data, they are showing a reduction in tortuous behaviors overall,

48
with cosine values mostly in the 0.8-0.95 range, indicating relatively straight flight paths with
occasionally sharp heading changes.

Figure 15 Seabird (left) and CRW smoothed relative angle changes over time

The ACF function for the CRW in Figure 16 reveal autocorrelation very similar to that of
the SRW model, with regular spikes of statistically significant autocorrelation. The spikes are

49
nearly identical to that of the SRW. Solla et al (1999) suggest that ecological relationships are
often related to the spatial environment and it is common to observe autocorrelation in real-world
data, however it is unlikely that it occurs with the regularity observed in the SRW and CRW
models.

Figure 16 ACF results of relative angle changes in seabird (top)
and CRW simulation movements
4.2.2 CRW relocation independence, pattern in random values
The results of the WaWo test on the CRW output are in Table 5. Similar to the SRW the
dx and dy p-values remain at zero, but the dist p-value is more interesting. One of the agents

50
achieved a value near zero, however the remaining agents all fail the test of independence. This
is interesting because the speed is still set to a constant 16 patches per tick.
Table 5 WaWo test results for CRW Model Output
Agent ID dx dy dist
1 1.82E-14 3.34E-12 2.44E-15
2 1.36E-12 1.16E-13 0.6945514
3 3.53E-09 1.37E-14 0.9069382
4 1.94E-14 8.71E-13 0.9889598

4.2.3 CRW home range analysis
The results of the density and linkage estimator on CRW results are presented in Figure
17. The simulation results are almost linear, with increases beginning at or around 50-60% of
the home-range level and increasing at nearly the same rate. This suggests that the CRW model
is still not using space in the same manner as the seabirds.

Figure 17 Seabird (left) and CRW home range size from ‘clusthr’

51
To summarize, the movement tracks themselves are closer to that of the seabird data than
the SRW model results. There is less clustering, though some still exists in random places. The
smoothed relative angle changes are beginning to show less wild oscillations, however
something is still causing the WaWo test to indicate that the changes in distance between each
relocation are not pulled from the same distribution. Home range levels increase linearly and
still do not match the expected gradual increase to 75-80% found in the real world data.
4.3 Incorporating speed variation into the correlated random walk
When looking at the original map of relocations in Figure 8and Figure 13 the ABM
output consistently delivered points at regular intervals in both space and time. The seabird data
would have many points separated by larger distances and small clusters of points close together;
indicating that speed played an important role in the overall shape of the seabird movements
when decomposed. Adding the variable speed to the correlated random walk again changes the
behavior of agents at each tick. In this model the agents are still looking out for the landmass,
and avoiding it, the angle changes they are allowed make are restricted and now their speed will
vary with the same mean and standard deviation observed in the aggregated seabird data set.
The CRWS model is presented as the third iteration in the basic movement model. When
this model is initialized, the agents are given a random heading chosen from the full 360 degrees
available for them to move in. After initializing the model, the agents in the correlated random
walk model follow these steps:
1. Pick a direction plus or minus 45 degrees off your current heading
2. Generate a random speed from a normal distribution centered around the mean of
16, with a standard deviation of 16.1, discarding negative values
3. Check if that speed will cause the agent to intersect land

52
a. If yes, pick a direction 90 degrees plus or minus the angle that is 180 degrees
opposite the original direction
b. If no, continue
4. Move at the random speed in that direction
5. Start over at Step 1
4.3.1 Shape and the use of space by agents with CRWS movement programming
In Figure 18 it is apparent that the CRWS model brings us even closer to the movement
model of the seabirds. The agent paths have become much less clustered and tortuous in
comparison to the SRW model output and the varied speed as made clusters of relocations
matching that of the seabirds that should be reflected in the investigations below. Rediscretizing
the movement steps, shown in Figure 19, prior to decomposing the spatial components of the
movement tracks reveals that there are significantly less clusters than the SRW model and it was
expected that the results would match the seabird data more closely.

Figure 18 Seabird (left) and CRWS movement tracks

53

Figure 19 Rediscretized seabird (left) and CRWS movement paths
The cosine values are significantly less torturous than those of the SRW and CRW
models, with oscillations that more closely resemble that of the seabird data. Also of note is a
more similar range of values to the seabird data. There are still some discrepancies and the
values still appear to be influenced by the random number generator control the angle changes.
It is possible that GPS accuracy issues may play a role in cloaking the more wild variations
observed in the CRWS movements. If the seabird is tightly circling in an area less than 30m,
searching for food, the GPS error may not capture these tortuous angle changes. At this point, I
am confident that this test is better applied at a point in the iterative process where foraging
behaviors can be integrated.

54

Figure 20 Seabird (left) and CRWS smoothed relative angle changes over time
The ACF function for the CRWS agents in Figure 21 reveal autocorrelation very similar
to that of the seabirds, without the regular spikes of autocorrelation found in the CRW and SRW
agent paths. Since the only change in the model was varied speed this suggests that speed plays
a significant role in the autocorrelation of relative angle changes.

55

Figure 21 ACF results of relative angle changes in seabirds (top) and CRWS agents
4.3.2 CRWS relocation independence, pattern in less random values
The results of the WaWo test run on the CRWS output are in Table 6. Even with the
third model iteration using CRWS agents, the paths are still not a statistical match to the real-
world data. Similar to the SRW and CRW agent paths, the dx and dy p-values remain near zero.
In this case the dist values become an important indicator. These values are consistently lower
than those of the previous models, closer to the seabird values, which suggests that adding a
behavioral element to the model, varied speed, made a bigger difference than changing the
geometric processes that govern movement. Nevertheless, the CRWS agents are still rejecting
WaWo’s null hypothesis. This is interesting because the speed value is programmed to come
from the same distribution.

56
Table 6 WaWo test results for CRWS model output
Agent ID dx dy dist
1 0.000476589 0.000592477 0.4073415
2 0.000231885 0.000320847 0.47143726
3 8.91121E-05 0.01447694 0.7902441
4 0.006280511 0.02280497 0.580764

4.3.3 CRWS home range analysis
The results of the density and linkage estimator on CRWS results are presented in Figure
22. The simulation results are very similar to that of the seabird data, with increases beginning at
or around 75-80% of the home-range level and increasing rapidly after. This suggests that the
CRWS model agents are forming a similar core of movements that the density and linkage
estimators are identifying as similar to the seabird movements.

Figure 22 Seabird (left) and CRWS home range size from ‘clusthr’
In summary, the movement tracks themselves are closer to that of the seabird data than
the any of the previous model agents. There is significantly less clustering in the overall
movements and the smoothed relative angle changes show far less wild oscillations. However,
something is still causing the WaWo test to indicate that the changes in distance between each

57
relocation are not pulled from the same distribution. Calenge (2011) and the CRWS results
suggest that speed is a very significant factor. Home range levels increase linearly and still do
not match the expected gradual increase to 75-80% found in the real world data.
Additional testing was done to investigate the programmatic errors that may arise from
Netlogo itself. An example of testing the random number generator can be found in Appendix 7.
This appendix shows how the speed distribution of the simulated data differs from that of the
real-world data.

58
CHAPTER 5: DISCUSSION
Shape of the sequential relocations in space, independence, and home range are all
considered as model outcome key performance indicators. The indicators provide a common
language for comparing ecological data with agent-based modeling output. In general,
simulations are simplified versions of the real world, implying that some variation between
observations and simulations is expected. The problem then becomes selecting a best-fit
simulation model that emulates a selection of processes found to be critical in real world data.
5.1 Spatial elements
The overall shape of real-world animal’s movement trajectory is likely impossible to
predict since an animal’s movement track will be unique in an ever changing environment.
Variables such as weather and food availability vary a great deal and prevent specific predictions
of movement. The mechanisms behind movement can be identified and programmed to produce
similar overall behaviors to the real world data, with some caveats. The CRWS model produced
results, shown by both the trajectory analysis and home range clustering (Kareive and Shigesada
1983) that mimic the same characteristics as the seabird data. The overall changes in relative
angle and percent home range estimates most closely match the output of the CRWS Netlogo
model. Other models fail at producing acceptable results on all counts, either displaying no
patterns matching the real-world data, as in the case of the simple random walk data or by
revealing a completely new pattern. One step in the analysis, that of deconstructing the cosine
values of the relative angles and performing a time series analysis is likely better suited at a later
point in the iterative development of the model.
The cosine values of relative angles in the real world data reveal signs of tortuous
trajectories or searching behaviors (Benhamou 2004). This implies that in order for the agent-

59
based model to accurately mimic the processes that create such trajectories, a great deal of time
must be spent informing the model about bird predatory habits and behaviors, as well as
incorporating memory and inter-agent communication. Restricting the turn angle to a range
around the current direction the simulated agent is facing provides movement paths that more
closely mimic that of the real world relocation patterns, which becomes quickly evident when
compared, even with modifications to the models to avert seabird movement over land. The
smoothed cosine values then inform an iterative step in the model development relating to
resource harvesting behavior rather than agent movement. This enables the structure of an ABM
to more closely match the processes that develop aggregate behaviors in the real world.
Agent movement, largely controlled by very simple programming, is put to the test using
a sequential analysis test that looks for values that are unexpected. Wald and Wolfowitz test of
independence (WaWo) results for dx and dy are consistent with the seabird data. The distance
variable however seems very dependent on speed, as the results of the CRWS model indicate
WaWo test p-values in dx and dy remain consistently low enough to accept the null
hypothesis that the values are independent and normal, dist values however, are not independent
with p-values as high as 0.98 in the SRW model. Looking at the structure of the model itself,
this is related to the speed value chosen during the analysis steps on the original real-world
moving-object data. The gull data was used to find the mean movement speed of the Galapagos
Swallow Tail Gull during the model movement, as well as the standard deviation of that speed.
In the simple random walk and correlated random walk models the speed was set to that average,
while for the correlated walk with variable speed the model was instructed to choose a speed at
random during each step from a normal distribution created with the mean and average of the

60
real-world data. The values for the CRWS model are the closest to the real-world data,
indicating that variable speed is an important element.
5.2 Conclusions
Several tests with quantifiable or visual comparisons enable a model builder to assess the
movement component of an agent-based model. Nearly any model in which independent agents
move and have expected behaviors in the real world such as movement restrictions (the birds in
the model presented here rarely fly over land), would benefit from quantitative analysis to ensure
the model behavior is consistent with real world observations, the goal of Pattern Oriented
Modeling.
As demonstrated here, each small step in the iterative model building approach, referred
to by Railsbeck and Grimm (2012) as Pattern Oriented Modeling, can take time and careful
research. If patterns are identified in the target structure, i.e., the real-world moving-object data,
they should be used as filters for the model not only at the end of the programming and
development process, but during and before. This is especially so if moving-object data is
available for comparison.
Continuing this iterative process through to the development of a complete
comprehensive model of the bird behavior would take a considerable amount of time.
Incorporating feeding and reproductive behaviors could take up to a year to complete if an
appropriate multidisciplinary team could be polled for parameter data. Parameters such as
energy consumption, fatigue and resource degradation could be tested in the complete model.
Nevertheless, such a complete model would be useful for many reasons. In a real-world system,
collapsing a component of the ecosystem, such as a fishery, to see how an animal responds
would be impossible to justify. With an ABM, it is possible to simulate the collapse of a

61
resource, or any change in the environment, and observe the patterned outcome. This would
allow the ABM to become a valuable tool for policy makers which could be used to inform their
decisions on environmental management and business policies as well as to help direct
conservation efforts.
5.3 Lessons learned
This study demonstrates the need for iterative model development and testing throughout
the programming phase. If movement rules had been chosen that are not a best fit for the real-
world object modeling it may not appear until sensitivity analysis is performed several steps
further into the model building effort, meaning a return to the foundational programming of a
model. It suggests that model complexity must be carefully balanced against the needs of the
researcher. Complex models that are not validated may provide data that is unusable, something
that can only be discovered after hours of investigation.
5.4 Questions for the future
As more complex agent-based models emerge from the iterative process it becomes
necessary to investigate them thoroughly. Initial study designs incorporated models whose
complexity was not easily understood and could not produce consistent results. Further research
is needed into identifying when a model’s complexity reaches a point where it no longer is able
to provide useful information and speak meaningfully about the system it is modeling.
Additionally, other methods could be incorporated into the iterative validation process
that is specific to a scientific discipline interested in agent-based modeling. It may also be
possible to use sets of data that do not include tracked moving-objects but rather single-event
observations, such as marine mammal or seabird observations from on board a survey ship. The

62
use of such data would restrict the tools available within the ecological framework but may still
provide important insights into the results of an agent-based model.

63
REFERENCES
Bence, J. 1995. Analysis of short time series: Correcting for autocorrelation. Ecology: 628-39.
Benhamou, S. 2004. How to reliably estimate the tortuosity of an animal's path:: Straightness,
sinuosity, or fractal dimension? Journal of Theoretical Biology 229 (2): 209-20.
Gardner, M. 1970. Mathematical games: The fantastic combinations of John Conway’s new
solitaire game “life”. Scientific American 223 (4): 120-3.
Grimm, V, U. Berger, F. Bastiansen, S. Eliassen, V. Ginot, J. Giske, J. Goss-Custard, T. Grand,
S. Heinz, and G. Huse. 2006. A standard protocol for describing individual-based and agent-
based models. Ecological Modelling 198 (1): 115-26.
Janssen, M. and E. Ostrom. 2006. Empirically based, agent-based models. Ecology and Society
11 (2): 37.
Lichstein, J., T. Simons, S. Shriner, and K. Franzreb. 2002. Spatial autocorrelation and
autoregressive models in ecology. Ecological Monographs 72 (3): 445-63.
Macal, C., and M. North. 2007. Agent-based modeling and simulation: Desktop ABMS. Paper
presented at Proceedings of the 39th conference on Winter simulation: 40 years! The best is
yet to come, .
Neumann, J. and A. Burks. 1966. Theory of self-reproducing automata.
O'Sullivan, D, and G. Perry. 2013. Spatial simulation: Exploring pattern and processJohn Wiley
& Sons.
Parker, D., and V. Meretsky. 2004. Measuring pattern outcomes in an agent-based model of
edge-effect externalities using spatial metrics. Agriculture, Ecosystems & Environment 101
(2): 233-50.

64
Railsback, S., and V. Grimm. 2011. Agent-based and individual-based modeling: A practical
introduction Princeton University Press.
R Core Team (2014). R: A language and environment for statistical computing. R Foundation for
Statistical Computing, Vienna, Austria. http://www.R-project.org/.
Šalamon, T. 2011. Design of agent-based models: Developing computer simulations for a better
understanding of social processesTomáš Bruckner.
Solla, D., R. Shane, R. Bonduriansky, and R. Brooks. 1999. Eliminating autocorrelation reduces
biological relevance of home range estimates. Journal of Animal Ecology 68 (2): 221-34.
Topping, C., T. Høye, and C. Olesen. 2010. Opening the black box—Development, testing and
documentation of a mechanistically rich agent-based model. Ecological Modelling 221 (2):
245-55.
Valbuena, D., P. Verburg, A. Bregt, and A. Ligtenberg. 2010. An agent-based approach to model
land-use change at a regional scale. Landscape Ecology 25 (2): 185-99.
Venables, W., and B. Ripley. 2002. Modern applied statistics with SSpringer.
Wikelski, M., and Kays, R. 2014. Movebank: archive, analysis and sharing of animal movement
data. World Wide Web electronic publication. http://www.movebank.org
(last accessed on 5/13/2014).

65
APPENDICES
APPENDIX 1: TRAJECTORIES

Figure 23 Movement of Netlogo gulls with a simple random walk

Figure 24 Movement of Netlogo gulls with a correlated random walk

66

Figure 25 Movement of Netlgo gulls with a correlated random walk and variable speed

67
APPENDIX 2: REDISCRETIZED TRAJECTORIES

Figure 26 Movebank.org Gull relocations

Figure 27 Correlated random walk with variable speed

68

Figure 28 Simple Random Walk

69

Figure 29 Correlated Random Walk

70
APPENDIX 3 SMOOTHED COSINE VALUES

Figure 30 Correlated random walk with variable speed

71

Figure 31 Simple random walk

72
APPENDIX 4: ACF VALUES FOR INDIVUDAL BIRD AND NETLOGO TURTLE
RELATIVE ANGLE CHANGES

Figure 32 Seabird relative angle ACF, clockwise from upper left, PLS-13, PLS-2, PLS-4,
PLS-8

73
Figure 33 SRW relative angle ACF, clockwise from upper left, bird 0-3

Figure 34 CRW relative angle ACF, clockwise from upper left, bird 0-3

Figure 35 CRWS relative angle ACF, clockwise from upper left, bird 0-3

74
APPENDIX 5: NEAREST-NEIGHBOR CLUSTERING ANALYSIS OF HOME RANGE
ESTIMATES

Figure 36 Simple Random Walk ‘clusthr’ home range results.

75

Figure 37 ‘Clustr’ home range results from the Correlated Random Walk with Variable
Speed

Figure 38 ‘Clustr’ home range results from the Correlated Random Walk

76

Figure 39 ‘Clustr’ home range results from Moving-Object Bird data set

77
APPENDIX 6: SPEED, FROM RANDOM TO NORMAL
Speed obviously played a more significant role in two of the tests than I had anticipated
when investing ecological analysis methods. After the third and final model iteration, digging
deeper into the variation between seabird speed distributions and CRWS speed distributions
seemed relevant. The CRWS agents speed distribution, in Error! Reference source not found.
approximates the distributions in the seabird data in Error! Reference source not found..
Small variation is present in the probability distribution of the correlated random walk with
variable speed model. It does however follow a very similar pattern to the real world data. The
seabird data has several characteristically different curves, however the overall shape of the
distribution is identical to the model values.

Figure 40 CRWS agents speed distributions

78

Figure 41 Galapagos Swallow-tailed Gull speed distributions
:

Abstract (if available)

Abstract Complexity in spatial simulation models developed without an iterative development process can lead to models that produce inaccurate or nearly random results. This case study examines how real world moving-object data can be used to inform the model development process. Moving-object analysis provides a template for understanding movement behaviors evident in both empirical data and model output. Moving object data generally consists of the GPS points from tracked animals, and is usually acquired as a comma separated values file. Agent-based simulation model development in this case study is informed by pattern oriented modeling, an iterative process used to control a model’s complex variables while gradually improving model design. Three simple agent-based models were constructed and a best fit model whose output most closely matches the spatial characteristics of the Galapagos Swallow-tailed Gull moving object data was identified.

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Core Title Using pattern oriented modeling to design and validate spatial models: a case study in agent-based modeling

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Publication Date 09/10/2014

Defense Date 08/13/2014

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