NEW MODELS OF ANIMAL MOVEMENT By ANDREW M. HEIN A DISSERTATION PRESENTED ...

112 Pages·2002·2.25 MB·English

NEW MODELS OF ANIMAL MOVEMENT
By
ANDREW M. HEIN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2013
⃝c 2013 Andrew M. Hein
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To my parents, brothers, and sister
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ACKNOWLEDGMENTS
I want to begin by thanking my committee chair, Jamie Gillooly, for his guidance,
encouragement, and his infectious enthusiasm for ideas. I will continue to strive to
emulate his willingness to consider any scientific question without being intimidated
by paradigm. I also want to thank my committee co-chair, Scott McKinley, for his
constant willingness to collaborate and for his commitment to rigorous logic in science.
The afternoons spent at his chalk board have been among my most educational and
enjoyable experiences as a graduate student.
The work presented in this dissertation benefitted greatly from discussions with
my committee members Doug Levey, Bob Holt, and Jose Principe, and also with Mary
Christman and Ben Bolker. Individual chapters were greatly improved by comments
from S. P. Vogel, T. Bohrmann, A. P. Allen, and J. H. Brown, J. Casas, M. Vergassola,
I. Couzin, A. Brockmeier, E. Kriminger, and many others. I am very grateful for funding
from a University of Florida Alumni Fellowship, a National Science Foundation Graduate
Research Fellowship under Grant No. DGE-0802270, and the National Science
Foundation under Grant 0801544 in the Quantitative Spatial Ecology, Evolution and
Environment Program at the University of Florida.
I could not have completed this work without the encouragement and support of
my family and friends. I especially want to thank my brother, Luke. I also owe special
thanks to Gabriela Blohm, who spent many long hours discussing ideas with me and
exhibited a saintly patience when I had a new idea or discovery that I could not help but
share with someone. Finally, I want to thank my parents: my father, for encouraging my
philosophical tendencies, and my mother for always reminding me of the right to pursue
my curiosity.
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TABLE OF CONTENTS
page
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
CHAPTER
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.1 New Models of Animal Movement: Constraints of Physics, Constraints
of Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2 Biomechanics, Energetics, and Animal Migration . . . . . . . . . . . . . . 14
1.3 Sensory Information and Models of Animal Movement . . . . . . . . . . . 15
1.4 Linking Movement Behavior and Encounter Rates of Interacting Species . 16
2 ENERGETIC AND BIOMECHANICAL CONSTRAINTS ON ANIMAL MIGRATION
DISTANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.1 Parameterizing Model for Walking, Swimming, and Flying Migrants 19
2.1.2 Model Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 SENSING AND DECISION-MAKING IN RANDOM SEARCH . . . . . . . . . . 33
3.1 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.1 Searching Without Olfactory Data . . . . . . . . . . . . . . . . . . . 36
3.1.2 Incorporating Olfactory Data to Make Search Decisions . . . . . . 37
3.1.3 Interpreting Scent Signals . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.1 Scent Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.2 Simulation Details . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.1 Visual-Olfactory Predators Find Targets Faster and More Reliably
Than Visual Predators . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.2 Visual-Olfactory Predators Learn From No-Signal Events . . . . . . 42
3.3.3 Visual-Olfactory Predators Concentrate Search Effort Near Targets 43
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
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4 SENSORY INFORMATION AND ENCOUNTER RATES OF INTERACTING
SPECIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.1 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1.1 Encounter Rate and Search Behavior: Some Definitions . . . . . . 51
4.1.2 Framework for Modeling Movement Decisions . . . . . . . . . . . . 52
4.1.2.1 Sensory signals and search behavior . . . . . . . . . . . 52
4.1.2.2 Perfect sensing and response . . . . . . . . . . . . . . . 53
4.1.2.3 Purely random search . . . . . . . . . . . . . . . . . . . . 54
4.1.2.4 Imperfect sensing and response . . . . . . . . . . . . . . 55
4.1.3 Encounter Rate Simulations . . . . . . . . . . . . . . . . . . . . . . 56
4.1.4 Estimation of Scaling Regimes and Exponents . . . . . . . . . . . 57
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.1 Encounter Rates of Purely Random Predators are Near-linear in
Prey Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.2 Encounter Rates of Signal-modulated Predators Change Nonlinearly
with Prey Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.3 Sensory Response Allows Predators to Encounter Nearby Targets
more Frequently . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
APPENDIX
A MIGRATION MODEL DERIVATION, SENSITIVITY, AND STATISTICAL
ANALYSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
A.1 General distance equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
A.1.1 Walking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
A.1.2 Swimming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
A.1.3 Flying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
A.2 Parameter estimation and model sensitivity . . . . . . . . . . . . . . . . . 74
A.2.1 Estimation of p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
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A.2.2 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
B DERIVATION OF DISTRIBUTIONS, A NOTE ON THE USE OF BAYES’ RULE,
AND SUPPLEMENTARY SIMULATION RESULTS . . . . . . . . . . . . . . . . 83
B.1 True Distance Distribution (TDD) and a Comment on the Use of Bayes’
Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
B.2 Robustness of Results to Search Conditions . . . . . . . . . . . . . . . . 84
B.2.1 Target Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
B.2.2 Signal Emission Rate . . . . . . . . . . . . . . . . . . . . . . . . . . 84
B.2.3 Variation in Predator Scanning Times . . . . . . . . . . . . . . . . . 85
B.3 The Role of No-signal Events . . . . . . . . . . . . . . . . . . . . . . . . . 85
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C MODEL OF SCENT PROPAGATION AND DEPENDENCE OF REGIME
TRANSITIONS ON SIGNAL PROPAGATION LENGTH . . . . . . . . . . . . . . 90
C.1 Scent Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
C.2 Dependence of Regime Break on Signal Propagation Length . . . . . . . 91
C.3 Encounter Rate of a Predator with Perfect Sensing and Response, and
Non-Zero Encounter Radius . . . . . . . . . . . . . . . . . . . . . . . . . . 91
C.4 Encounter Probabilities in the Sparse Regime . . . . . . . . . . . . . . . . 92
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
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LIST OF TABLES
Table page
A-1 Empirical values of the normalization constant . . . . . . . . . . . . . . . . . . 75
A-2 Sensitivity of distance equations to variation in input parameters. . . . . . . . . 76
A-3 Body mass and migration distance data . . . . . . . . . . . . . . . . . . . . . . 76
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LIST OF FIGURES
Figure page
2-1 Schematic of migration process . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2-2 Migration distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2-3 Number of body lengths traveled . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2-4 Observed and predicted migration distances . . . . . . . . . . . . . . . . . . . 32
3-1 Schematic of predator search behavior . . . . . . . . . . . . . . . . . . . . . . 46
3-2 Mean predator search times and variability about mean search time . . . . . . 47
3-3 Typical search paths of simulated predators . . . . . . . . . . . . . . . . . . . . 48
3-4 Information gain as a function of the ratio of visual to olfactory radius . . . . . . 49
3-5 Area-restricted-search behavior of visual and visual-olfactory predators . . . . 49
4-1 Perfect sensing and response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4-2 Scan points during search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4-3 Encounter rates of purely random and signal-modulated predators . . . . . . . 64
4-4 Encounters rate of signal-modulated predators . . . . . . . . . . . . . . . . . . 65
4-5 Empirical encounter probability as a function of target density . . . . . . . . . . 66
B-1 Searchs time at low density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
B-2 Search times with reduced emission rate . . . . . . . . . . . . . . . . . . . . . 87
B-3 Search times and scanning phase length . . . . . . . . . . . . . . . . . . . . . 88
B-4 Likelihood funcions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
B-5 Search time with conditional response to olfactory signals . . . . . . . . . . . . 89
C-1 Breakpoint between linear and sublinear regime . . . . . . . . . . . . . . . . . 94
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Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
NEW MODELS OF ANIMAL MOVEMENT
By
Andrew M. Hein
August 2013
Chair: James F. Gillooly
Cochair: Scott A. McKinley
Major: Zoology
Movement is an iconic feature of life; microorganisms swim up chemical gradients,
motile predators search their environments for prey, and migratory animals make
journeys that can take them across the planet. Advances in biomechanics and sensory
biology have created opportunities to develop new mathematical models of animal
movement that incorporate organismal biomechanics and sensory physiology. Such
models are useful for understanding the ecological and evolutionary drivers of animal
movement behavior, and also for predicting basic ecological rates and scales–for
example, the rate of interactions among moving predators and their prey, or the spatial
scale of movements made by seasonal migrants. This Dissertation is an attempt to
develop such general models, and to use them to learn about both the origins and the
implications of animal movement behavior. In Chapter 2, I began by investigating the
physical constraints related to one of the most well studied movements that animals
make: migration. I used a mathematical model to show how body mass influences the
maximum distances that migrants travel through its effect on locomotion. I confirmed
model predictions using a new global-scale dataset of animal migration distances.
In Chapter 3, I sought to better understand how to model animal search behavior in
the presence of noisy sensory signals, and how sensory information might affect the
movement behavior of a searching animal. I developed a new mathematical framework
for modeling the use of sensory data in movement decision-making. Results showed
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