Modeling Motives for Movement: Theory for Why Animals Migrate

Modeling Motives for Movement: Theory
for Why Animals Migrate
Allison K. Shaw
A Dissertation
Presented to the Faculty
of Princeton University
in Candidacy for the Degree
of Doctor of Philosophy
Recommended for Acceptance
by the Department of
Ecology and Evolutionary Biology
Advisers: Iain D. Couzin and Simon A. Levin
September 2012

c○ Copyright by Allison K. Shaw, 2012.
All Rights Reserved

Abstract
Migration, the seasonal movement of organisms among different locations, is a ubiquitous
phenomenon in the animal kingdom: there are migratory species found in all major verte-
brate groups (birds, fish, mammals, reptiles, amphibians), as well as in many invertebrate
groups (insects, crustaceans). Despite this, most discussion of migration tends to be taxo-
nomically restricted, and little work has been done to draw comparisons across taxonomic
groups. Furthermore, although scientists have long been fascinated by migratory species, we
still have little understanding of why migration is such a common strategy and what specific
ecological factors have favored its evolution and maintenance. At a basic level, organisms
migrate because they benefit through growth, survival, and/or reproduction, and though
it has long been suggested that organisms can migrate for different reasons, the distinct
motivations for migration have generally received little attention.
In this dissertation, I examine migration as an adaptive response to variable ecologi-
cal conditions, and use the motivations that drive migration to gain an understanding of
the conditions favoring migration, spanning taxonomic boundaries. To achieve this, I use
a variety of approaches: meta-analyses of the migration literature to determine the types
of motivation that drive migration and how these combine into different round-trip pat-
terns (Chapter 2), individual-based simulations to determine what types of spatiotemporal
resource distributions select for migration (Chapter 3), analytic models based on these mo-
tivations for migration (Chapter 4-5), and fieldwork to study a migratory terrestrial crab
species in more detail (Chapter 6-7). The main conclusions of this dissertation research are
that animal migration is driven by a few distinct reasons, and that these motivations span
taxonomic boundaries, shape both the ecological conditions selecting for migration as well
as the tradeoffs organisms face when making the decision to migrate, and influence what
impact a changing environment will have on both the migratory behavior and survival of a
species.
iii

Acknowledgements
Primary thanks goes to my advisors, Simon Levin and Iain Couzin, for their support, and
to the other members of my committee, Dan Rubenstein and Andy Dobson for much-
appreciated feedback. Thanks are also due to other members of the faculty – especially
to Henry Horn for insightful discussions and valuable feedback at possibly every talk I gave
while at Princeton, and to both Martin Wikelski and Jeanne Altmann for their encourage-
ment early on.
Much of this research was inspired by conversations about migration with a variety of
people over the years and across the globe. Thanks go to
• Max Orchard, Eddly, Azmi bin Yon, Meryl Jenkins, Kent, Chris Boland, Kathie Kelly,
Mike Misso, Linda Cash, Marjorie Gant and others on Christmas Island, Australia for
early discussions on crab migration and assistance with fieldwork in 2008.
• Silke Bauer, John McNamara, and others for organizing the 2009 “Animal Migration -
linking models and data” Workshop at the Lorentz Center (Leiden, Netherlands) and
providing financial support for me to attend, as well as to the Evolution of Migration
discussion group (Christian Jørgensen, Julian Metcalfe, Jason Chapman, Graeme Hays,
Theunis Piersma, and Eileen Rees).
• The Santa Fe Institute’s 2009 Complex Systems Summer School (Santa Fe, NM), and
especially to Liliana Salvador, Andrew Berdahl, Steven Lade, and Kate Behrman.
• Ben Chapman and others for organizing the 2011 Symposium on The Ecology and
Evolution of Partial Migration at the Centre for Animal Movement Research (Lund,
Sweden) and providing financial support for me to attend. Also to Per Lundberg and
Hanna Kokko for discussions on partial migration.
• Gita Gnanadesikan, James Watson, Guy Ziv, and Charles Yakulic for many enjoyable
conversations about mammal, fish, and tortoise migration, in Princeton NJ.
iv

Special thanks go to Daniel Stanton and my family, for keeping me grounded the past
several years, to Anna Berman for reminding me there is life outside the EEB department,
and to Shoshi Lavinghouse for reminding me there is life outside graduate school. Invaluable
support and advice was provided by Jenny Ouyang, Carla Staver, Liliana Salvador, Car-
oline Farrior, Maya Echeverry, (despite their travel schedules I could usually find at least
one in town). Thanks to my cohort, the EEB graduate students both past and present,
both the Levin and Couzin labs, and the EEB department for providing such a stimulating
environment to be a graduate student.
My ability to conduct this research was much improved by continuous logistical support.
Thanks to Colin Torney for extensive help setting up and running simulations using CUDA.
Thanks to the IT Team (Jesse Saunders, Axel Haenssen, Raj Chokshi) for always ensuring
computers were running, and thanks to Sandi Milburn, Lolly O’Brien, Terry Guthrie, Amy
Bordvik, Bernadette Penick, Diane Carlino, Richard Smith, Mary Guimond, and Pia Ellen
for help coordinating meetings, schedules, paperwork, and other logistical details.
This material is based upon work supported by the National Science Foundation Grad-
uate Research Fellowship under Grant No. DGE-0646086 to AKS (2009-2012). Additional
funding was provided by a Princeton University First Year Fellowship in Science and Engi-
neering, Princeton University (2007-2008), a National Geographic / Waitt Institute for Dis-
covery grant (2008-2009), the Max Planck Institute for Ornithology (2008-2009), the APGA
Dean’s Fund for Scholarly Travel (2011), and funding through the PEI/Grand Challenges
Summer Internship Program (2011).
v

Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
1 Introduction 1
2 Motives for round-trip migrations, with a focus on mammals 6
2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Motivations for Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Migration Patterns Across Taxa . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5.1 Invertebrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5.2 Amphibians and Reptiles . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.3 Fish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.4 Birds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Migration in Mammals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3 Migration or residency? The evolution of movement behavior and infor-
mation usage in seasonal environments 21
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
vi

3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3.1 Ecological conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.2 Individual behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.3 Fitness functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.4 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4.1 Residency or migratory behavior . . . . . . . . . . . . . . . . . . . . 32
3.4.2 Information availability . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.1 Conditions favoring migration . . . . . . . . . . . . . . . . . . . . . . 36
3.5.2 Caveats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.3 Information availability . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 To breed or not to breed: a model of partial migration 41
4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Low-Frequency Breeding Migrations . . . . . . . . . . . . . . . . . . . . . . . 44
4.4 To Skip or Not? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.5 Stochasticity & Bet-Hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5 Partial migration and the evolution of intermittent breeding 59
5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 Intermittent breeding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4 Model Equilibria and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.5 Evolutionarily Stable Strategies . . . . . . . . . . . . . . . . . . . . . . . . . 66
vii

5.5.1 Scenario 1: Reproduction has time cost . . . . . . . . . . . . . . . . . 69
5.5.2 Scenario 2: Reproduction has energy cost . . . . . . . . . . . . . . . . 70
5.5.3 Scenario 3: Reproduction has survival cost . . . . . . . . . . . . . . . 70
5.6 Empirical Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.7 Fluctuating Population Size . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.8 Stochastic Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.8.1 Mixed strategies in response to mixed conditions . . . . . . . . . . . . 75
5.8.2 Mixed strategies to spread the risk . . . . . . . . . . . . . . . . . . . 77
5.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6 Rainfall-driven migration timing in the Christmas Island red crab (Gecar-
coidea natalis) 81
6.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.3.1 Study System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.3.2 Climate Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.3.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.4.1 ENSO and Rainfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.4.2 Rainfall and Migration . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.4.3 ENSO and Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7 Variation in Christmas Island red crab (Gecarcoidea natalis) migratory
direction 96
7.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
viii

7.3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
A Motives for migration: Mammal migration data 104
B Migration or residency: Extra figures & details 130
B.1 Appendix: Analytic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
B.1.1 Conditions favoring migration . . . . . . . . . . . . . . . . . . . . . . 136
B.1.2 Transition between residency and migration . . . . . . . . . . . . . . 139
C Partial migration: ESS calculation details 142
D Intermittent breeding: Stability analysis 146
ix

Chapter 1
Introduction
Migration, the seasonal movement of animals among different locations, has fascinated peo-
ple for centuries – from herds of wildebeest in Africa, to swarms of locusts, to songbirds
disappearing every fall and returning in the spring. Migration is a ubiquitous phenomenon
in the animal kingdom; there are migratory species found in all major vertebrate groups
(birds, fish, mammals, reptiles, amphibians), as well as in many invertebrate groups (insects,
crustaceans). Despite this, most discussion of migration tends to fall along taxonomic lines,
partly due to the fact that migratory movement can look very different when performed by
different species. However, the lack of integration, understanding and cross-communication
of migration studies across taxonomic groups is still seen as one of the factors hampering
research progress in the field (Bauer et al., 2009).
The earliest studies of migratory organisms date to at least a century ago (Phillips, 7
May 2009). Initially it was believed that migration served as a ‘safety valve’ to remove
excess individuals from the population (Southwood, 1962). Only in the past half century
has migration been viewed, as David Lack put it, as “a product of natural selection,” which
should be expected to occur when the benefits outweigh the costs (Lack, 1954). It was
around this time as well that MacArthur (1959) produced one of the first studies to examine
the relationship between migratory behavior and habitat. However, despite these ideas being
1

set forth decades ago, we still lack a synthesis of what specific types of ecological conditions
select for migration.
At a basic level, organisms migrate because they benefit through growth, survival and/or
reproduction, and in a round-trip migration, the movement in each direction must be ben-
eficial. While it has long been suggested that organisms can migrate for different reasons
(Heape, 1931), the distinct motivations for migration have generally received little attention.
Part of the reason for this is that the early migration literature was dominated by work on
birds, mostly European passerines, where individuals migrate for similar reasons – to avoid
harsh high-latitude winters. The handful of models that have been constructed to under-
stand the conditions favoring migration have mostly been framed within this avian system
(but see Alexander 1998; Wiener and Tuljapurkar 1994; Holt and Fryxell 2011) and focus
on the scenario of partial migration where migratory and non-migratory individuals coexist
within a single population (e.g. Cohen, 1967; Lundberg, 1987; Kaitala et al., 1993; Taylor
and Norris, 2007; Griswold et al., 2010).
The aim of this dissertation is to examine migration as an adaptive response to variable
ecological conditions, and to use the motivations for migration to gain an understanding of
the conditions favoring migration that spans taxonomic boundaries. To achieve this, I use a
variety of approaches: individual-based simulations (Chapter 3), meta-analyses of migration
literature (Chapter 2, 4), analytic models (Chapter 4, 5), and fieldwork (Chapter 6, 7). The
key findings are that animal migration is driven by a few distinct motivations, which span
taxonomic boundaries, shape both the ecological conditions selecting for migration and the
tradeoffs organisms face when making the decision to migrate, and influence what impact a
changing environment will have on both the migratory behavior and survival of a species.
2

Section 1: Motivations for migration
In the first section (Chapter 2), I survey the motivations for migration across different
migratory species and propose that there are three main forms of round-trip migration:
refuge (movement away from breeding areas to avoid seasonally harsh conditions), breeding
(movement between a feeding and a breeding ground), and tracking (continuous movement
following predictable changes in food distributions). I describe the distribution of these
types across all taxonomic groups (based on taxon-specific migration reviews) and across all
mammals (based on primary literature describing migration in individual species).
Section 2: Conditions favoring migration
At a fundamental level, migration should only be expected to occur when there is both
spatial and temporal variation in the resources that an organism needs to survive, grow,
and reproduce successfully. In the second section of my dissertation (Chapter 3) I determine
what types of spatiotemporal resource distributions favor the use of a migratory strategy
instead of a non-migratory one. I find that different types of migration evolve depending on
the ecological conditions and availability of information, and that the conditions selecting
for migration depend on what motivation (food, climate, or breeding) drives migration. I
also present empirical support for my results, drawn from migration patterns exhibited by a
variety of taxonomic groups.
Section 3: Modeling breeding migrations
Of the three types of migration determined in Section 1, only one (refuge migration) has
received any theoretical consideration. In the third section of my dissertation (Chapters
4-5), I present models for one of the other types: breeding migrations, where adults feed in
one area and migrate to breed in second location. In many species with breeding migrations,
3

only a fraction of adults will migrate in a given season, while the rest skip migration and
forgo reproduction for that season. Although this is an example of partial migration, it does
not fit into the framework for existing models of partial migration which assume a refuge
migration scenario where the decision to migrate is based on a tradeoff between survival and
competition. Instead, for breeding migrations, the decision to migrate is based on a tradeoff
between current and future reproduction, and requires a different model formulation.
In Chapter 4, I develop such a model where individuals can either migrate and reproduce
annually or skip migration in a single year before migrating and reproducing the following
year. I determine the conditions favoring partial migration (skipped breeding) in both de-
terministic and stochastic environments. This model is broad enough to be applied to any
of the crustacean, fish, amphibian, mammal or reptile species with breeding migrations, and
the model predictions compare well to documented migratory patterns. Furthermore, as
this is the first model to consider partial migration in the breeding migration context, this
work was highlighted in the special Partial Migration edition of Oikos in which the paper
appeared (Chapman et al., 2011).
In Chapter 5, I expand this model to allow individuals to skip multiple years between
breeding attempts a biologically trivial extension, but mathematically more challenging.
I also broaden the biological context to consider the phenomenon of intermittent breed-
ing (where sexually mature adults will skip breeding opportunities in between reproduction
events) more generally, not just in the context of migration. In both models, I find that
individuals should skip breeding attempts when the benefits of skipping are high (increased
fecundity in future breeding attempts), and when the accessory costs associated with repro-
duction are high (e.g. high mortality during migration).
4

Section 4: Case study of a breeding migration
The fourth and final section of my dissertation (Chapter 6-7) examines an example of a
species with breeding migration in more detail: the Christmas Island red crab (Gecarcoidea
natalis), In Chapter 6, I show that the timing of the annual crab breeding migration is
closely related to the amount of rainfall during a ‘migration window’ period, which is in
turn correlated with SOI, an ENSO index. Examining the relationship between migration
and climate is a step towards being able to predict how migration may be affected by future
climate change. Past studies have looked at migration timing with respect to temperature
in temperate species, but this is one of the first studies on migration timing to either look
at precipitation or consider a tropical migratory species.
In Chapter 7, I document individual variation in migratory direction, and the onset of
migratory behavior in G. natalis, using GPS/accelerometer tags. The GPS data indicate
that individual red crabs from the same location migrate in completely different directions,
a finding in complete contrast to a previous study on the same species. The accelerometer
data indicate that individual crabs change their behavioural patterns drastically with the
onset of the wet season, a finding that complements previous observations on annual crab
activity levels.
All Chapters (except for 2, which is still ongoing with Gitanjali Gnanadesikan) are in
manuscript form. Chapter 3, coauthored with Iain Couzin, is currently in review for the
American Naturalist, Chapter 4 was published last year in Oikos (Shaw and Levin, 2011),
Chapter 5, coauthored with Simon Levin, is drafted for submission (potentially to the Ameri-
can Naturalist) Chapter 6, coauthored with Kathryn Kelly, is drafted for submission to Global
Change Biology, and Chapter 7 is in revision for the Australian Journal of Zoology (a Short
Communication).
5

Chapter 2
Motives for round-trip migrations,
with a focus on mammals 1
2.1 Abstract
Migration is a strategy, found throughout the animal kingdom, which is used for dealing
with a variable environment. Although it has long been recognized that migratory behav-
ior should be favored when the costs outweigh the benefits (and that these depend on an
organism’s ecological conditions) we still lack a clear picture of what specific motivations
drive animal migration and how these vary across species. Here we examine patterns of
round-trip migration in terms of the motivation for migration in each direction, and propose
that most can be classified into three broad types: refuge, breeding, and tracking. We show
that these types are common at a number of taxonomic levels: across vertebrate classes,
across orders within mammals, and across species within mammalian orders. Understanding
these ultimate factors that drive animal migration is a first step in being able to predict how
migratory species might adapt to changing environmental conditions in the future.
1 Authors: Allison K. Shaw and Gitanjali Gnanadesikan; Status: Manuscript in preparation for sub-
mission.
6

2.2 Introduction
Migration, the predictable seasonal movement of animals between multiple locations on a
regular basis, is a common strategy for dealing with a spatially and temporally variable
environment. While it has long been accepted that migratory behavior can be acted on
by natural selection (Lack, 1954), and that the costs and benefits of migrating depend
on ecological conditions (MacArthur, 1959), we still do not have a clear picture of what
motivations drive migration, and how these vary across species.
Although migration is a widespread phenomenon, found in all major vertebrate groups
(birds, fish, mammals, reptiles, amphibians) as well as in many invertebrates (insects, crus-
taceans), most discussion of migration tends to fall along taxonomic lines. Early discussions
of migration tended to exclude mammal and invertebrate species (Dingle, 1980). Although
more recent treatments of migration span all taxonomic groups (e.g. Dingle, 1996), there
is still a lack of integration, understanding and cross-communication of migration research
across taxonomic groups, which is seen as one of the factors currently hampering research
progress in the field (Bauer et al., 2009).
Part of the reason for this lack of integration is that migratory movement comes in a vari-
ety of forms and this variation is often used to classify migration by, for example, taxonomic
group (bird, fish), distance (short, long), timing (seasonal, irruptive), composition (partial,
differential, facultative, obligate) and location (altitudinal, longitudinal, latitudinal) (Dingle
and Drake, 2007). Although migration can be driven by a variety of different motivations, a
fact that has been noted since at least the early 1900s (Heape, 1931), there has been little
effort to use these motivation as a way of gaining insight into migration patterns spanning
taxonomic groups.
Here we examine patterns of round-trip migration across all taxonomic groups in terms of
the motivation for movement in each direction, and propose that migration patterns can be
classified into three broad types. While we recognize that this is just one more way to par-
tition migration we argue that this classification, which transcends taxonomic boundaries,
7

allows us to better understand why species migrate, and predict how shifting ecological con-
ditions (due to e.g. climate change, habitat fragmentation) will affect migratory behavior.
After outlining these migration types, we describe the distribution of each type across all tax-
onomic groups for which migration has been well summarized. However, since we recognize
that even summaries of migration in taxonomic groups can be inherently biased, we picked
one group (mammals) in which to examine migration patterns in every species for which
data are currently available. While mammals represent only a fraction of all animals and are
generally over-studied with respect to other characteristics, their migration patterns are less
well studied than those of birds or fish, and there is generally more information available on
their movement patterns than reptiles, amphibians or most invertebrates, making them an
ideal group to consider in detail.
2.3 Methods
To determine what motivations drive movement in each direction, and how these combine
into round-trip migration patterns, we surveyed a combination of primary and secondary
literature. We read through general reviews of migration across all taxonomic groups (e.g.
Dingle, 1980, 1996; Hack and Rubenstein, 2001), as well as surveys by taxonomic group for
crustaceans (Wolcott and Wolcott, 1985; George, 2005), amphibians (Russell et al., 2005),
reptiles (Russell et al., 2005; Southwood and Avens, 2010), fish (Northcote, 1978; Lucas and
Baras, 2001), birds (Bildstein, 2006; Newton, 2008), and mammals (Lockyer and Brown,
1981; Harris et al., 2009).
Since reviews inherently gloss over details, we also surveyed primary literature of all
known migratory mammals, searching for papers that described the migration patterns and
motivations for individual species. To start, we compiled a list of all migratory mammals
drawing on entries from three different databases: all mammals listed in Appendices I and II
of the Convention on Migratory Species (www.cms.int/pdf/en/CMS Species 6lng.pdf, Febru-
8

ary 2012), all mammals in the YouTHERIA database (http://www.utheria.org/; Jones et al.
2009) that included information on migration, and all mammals in the Animal Diversity Web
database (http://animaldiversity.ummz.umich.edu/site/index.html) that were listed as mi-
gratory. In the process of looking up these species, we came across many other mammalian
species that are clearly migratory, but were not included in any of the three databases. We
are currently surveying all mammals (approximately 5,400 species) to determine which are
migratory (ongoing work with G. Gnanadesikan).
For each species, we searched for any papers that described the migratory behavior, in-
cluding motivations for migration, and classified the species into one of four categories: 1)
migratory (there was evidence of regular seasonal movement), 2) non-migratory (no evidence
of seasonal movement, individuals of the species observed in the same location year-round),
3) unclear (some evidence of seasonal movement or seasonal change in population size, but
unclear if migratory) and 4) unknown (no clear documentation of either migratory or seden-
tary behavior). If there was documentation of both migratory and non-migratory behavior
for a species, we classified it as migratory. For those species that were classified as migratory,
we recorded what resource or motivation drives individuals in each leg of the migration.
2.4 Motivations for Migration
Migratory movements in a single direction can be driven by a variety of different motiva-
tions. Heape (1931) first described three main types: “alimental movement” (to increase
access to food or water), “climatic movement” (to avoid unfavorable climate conditions),
and “gametic movement” (to reproduce). Within the fish migration literature these have
also been referred to as “feeding”, “wintering” and “spawning” movements, respectively
(Northcote, 1978; Lucas and Baras, 2001). (Note that these authors actually referred to
these one-way movements as “migrations” but we have changed the wording to “movement”
and use “migration” only to refer to round-trip movement, to avoid confusion below.)
9

Figure 2.1: Schematic depicting the three types of migration: refuge, breeding, and tracking,
and the timing of energy intake and reproduction over an annual cycle.
While round-trip migrations could potentially be driven by any combination of these three
factors, in reality most migrations fall into one of three categories which we term “refuge”,
“breeding”, and “tracking” migrations (Figure 2.1). Refuge migrations are those where
individuals breed in the same place they primarily forage, but leave the area seasonally and
seek refuge to avoid temporarily unfavorable conditions (e.g. too cold, too dry, too flooded).
Breeding migrations are those where individuals breed in a different location than where they
primarily forage, and undergo migrations each time they reproduce. Tracking migrations are
those where individuals continuously move, tracking changing resource distributions.
The fundamental distinction among these types can be thought of in terms of the timing
of energy intake with respect to reproduction over the course of a year (Figure 2.1). In
refuge migrations individuals tend to breed at the same time they have a peak in energy
intake, whereas in breeding migrations individuals acquire energy at one location and store it
before reproducing elsewhere a distinction similar to the one between ‘income’ and ‘capital’
breeding, where individuals fund their reproduction either with energy as they acquire it
10

or from energy stored ahead of time (Jonsson, 1997). In tracking migrations, individuals
are constantly acquiring energy over the course of a year, although often these species still
display seasonal reproduction. A number of species with tracking migrations follow prey
species that are themselves migratory.
2.5 Migration Patterns Across Taxa
The majority of taxonomic groups include species whose migratory patterns fit each of these
three general patterns, although the relative frequency of each type varies. Examples of each
of the three migration types from each taxonomic group are shown in Table 2.1.
2.5.1 Invertebrates
Both true land crabs (family Gecarcinidae) and land-dwelling hermit crabs (Coenobitidae)
have breeding migrations. Adults migrate seaward to reproduce seasonally (since larvae
require high-salinity water to develop) and return inland for the rest of the year to decrease
aggressive interactions (competition, cannibalism) and increase access to food (Wolcott and
Wolcott, 1985). In some species mating occurs prior to migration and only females migrate
to the shore (e.g. Gecarcoidea lalandii and Epigrapsus notatus; Liu and Jeng 2005, 2007),
while in others both females and males migrate, and then mate at the shore (e.g. Gecarcoidea
natalis and Johngarthia lagostoma; Hicks 1985; Hartnoll et al. 2006).
Spiny lobsters display several forms of migratory behavior (George, 2005). In some
species adults have breeding migrations and move from their main grounds to breeding sites,
located either in shallow habitat (e.g. Palinurus delagoae) or in areas where the current will
carry larvae to juvenile grounds (e.g. Sagmariasus verreauxi). Other species have refuge
migrations where adults migrate seasonally to avoid winter storms (e.g. Panulirus argus
argus) or to avoid oxygen depletion (e.g. Jasus lalandii).
No insect has what would be considered a round-trip migration by vertebrate standards,
11

Table 2.1: Examples of each round-trip migration pattern (refuge, breeding, tracking) from
different taxonomic groups.
Group Refuge Breeding Tracking
Invertebrates
Spiny lobster (Panulirus
argus): migrates
from shallow
water to deep, to
avoid seasonal storms
(Kanciruk and Her-
rnkind, 1978)
Amphibia Green frog (Rana
clamitans): migrates
from summer areas
to streams, which
do not freeze during
winter (Lamoureux
and Madison, 1999)
Reptilia Garter snake
(Thamnophis sirtalis):
migrates
between hibernation
dens in winter and
marshes in summer
(Larsen, 1987)
Fish Common roach (Rutilus
rutilus): spends
summers in lakes,
moves to streams
in winter to avoid
predation (Jepsen and
Berg, 2002)
Aves White-ruffed Manakin
(Corapipo altera):
breeds in mountains,
migrates to low elevations
to avoid seasonal
storms (Boyle et al.,
2010)
Christmas Island Red
Crabs (Gecarcoidea
natalis): terrestrial
adults migrate to drop
their eggs in the ocean
so they can develop
(Gibson-Hill, 1947)
Spotted salamander
(Ambystoma maculatum)
migrates to
ponds in spring to
breed (Husting, 1965)
Estuarine crocodile
(Crocodylus porosus):
occupies small home
range during dry
season, migrates to
nesting habitat in wet
season (Kay, 2004)
Pacific salmon (Oncorhynchus
spp.):
juveniles born in
freshwater, migrate to
ocean for adult life,
return to breed in
streams (Quinn and
Dittman, 1990)
Emperor penguin
(Aptenodytes forsteri):
feeds in the ocean, migrates
to rookeries to
mate and breed during
the winter (Pinshow
et al., 1976)
12
Desert locust
(Schistocerca gregaria):
follows
the rains, tracking
green vegetation
(Cheke and
Tratalos, 2007)
None known.
Water python
(Liasis fuscus):
migrates following
dusky rat prey
(Madsen and
Shine, 1996)
Basking sharks
(Cetorhinus maximus):
migrates
along the coastal
shelf tracking productivity
hotspots
(Sims, 2008)
Red-billed quelea
(Quelea quelea):
feeds on grass
seeds and follows
rain belt
movement across
tropical Africa
(Jones, 1989)

Table 2.1 (cont’d).
Group Refuge Breeding Tracking
Mammalia
Dusky rat (Rattus colletti):
migrate from
backswamp to woodland
to avoid flooding
during the wet season
(Madsen and Shine,
1996)
Humpback whale
(Megaptera novaeangliae):
migrate seasonally
between
high latitude feeding
grounds and low latitude
breeding grounds
(Craig and Herman,
1997)
Common Wildebeest(Connochaetestaurinus):
circular
migration, following
changing
vegetation (Boone
et al., 2006)
where a single individual makes the entire migration journey (Holland et al., 2006), although
many species display seasonal movement patterns that span several generations. For exam-
ple, monarch butterflies (Danaus plexippus) in North America migrate south and overwinter
in Mexico then migrate slowly northward in the spring, tracking the availability of milkweed
(Dingle, 1996), a process that takes four generations and is somewhat of a cross between
a refuge and a tracking migration. The milkweed bug (Asclepias spp.) has a similar mi-
gration pattern. Other species have refuge migration to avoid hot dry conditions – bogong
moths (Agrotis infusa) in Australia and ladybird beetles (Hippodamia convergens) in North
America both migrate to high elevation to spend summer estivating in caves (Dingle, 1996).
A number of locust species have tracking migrations in response to rainfall and changes in
vegetation availability (Dingle, 1996).
2.5.2 Amphibians and Reptiles
Many amphibians have an aquatic larval stage and terrestrial adult stage, so the majority
of migratory amphibians undergo breeding migrations as adults to aquatic breeding grounds
(Russell et al., 2005). Some species have refuge migrations between summer feeding and
breeding areas and overwintering sites (e.g. Rana clamitans, R. sylvatica, Scaphiopus hol-
brookii, Bufo hemiophrys; Russell et al. 2005).
13

The majority of reptiles are non-migratory but those that do migrate do so for a variety
of reasons – aquatic species often undertake breeding migration to find suitable terrestrial
nesting sites, while terrestrial species can display refuge or tracking migrations. Species in
three of the four orders that make up reptiles have been observed to migrate (Testudines,
Crocodilia, and Squamata), while movement patterns of tuataras (order Rhynchocephalia)
are not well characterized (Southwood and Avens, 2010). Within Testudines (turtles) the
most notable migrations are those of all seven sea turtle species, where adults move be-
tween foraging areas and breeding grounds (Luschi et al., 2003). A number of terrestrial
(e.g. Geochelone spp), freshwater (e.g. Chelydra serpintina, Apalone spinifera, Podocnemis
sextuberculata) and estuarine (e.g. Malaclemys terrapin) turtle species also have breeding
migrations (Southwood and Avens, 2010). Other turtle species have refuge migration to over-
wintering sites (e.g. Chelydra serpentina) or tracking migrations following seasonal shifts in
food (e.g. Geochelone gigantea) (Russell et al., 2005). Most crocodilians nest within their
home range but a few (e.g. Crocodylus niloticus) migrate to suitable nesting sites (Russell
et al., 2005). Other species (e.g. Caiman crocodilus) have refuge migrations from swamps
to permanent bodies of water in the dry season (Russell et al., 2005).
Most squamates (lizards and snakes) are non-migratory. However, many temperate
snake species have refuge migrations between summer areas and winter hibernacula (e.g.
Thamnophis sirtalis, Crotalus atrox) to avoid cold winter temperatures (Russell et al., 2005;
Southwood and Avens, 2010). The migrations of tropical snakes are driven not by tempera-
ture but by food and water availability (Southwood and Avens, 2010); water pythons (Liasus
fuscus) have tracking migrations, following their prey, the dusky rat (Southwood and Avens,
2010) and Arafura filesnakes (Acrochordus arafurae) display refuge migrations, moving from
flooded grasslands to permanent ponds during the dry season (Russell et al., 2005). Lizards
are generally non-migratory, although a number of iguanas (Iguana iguana, Cyclura spp.,
Conolophus subcristatus) display breeding migrations (Russell et al., 2005).
14

2.5.3 Fish
In general, fish migrations fall into three broad categories: diadromous migrations between
fresh and salt water, potomadromous migrations within freshwater, and oceanodromous
migrations within the ocean (Dingle, 1980).
Diadromous migrations can be further split into three types: where adults live and forage
in salt water but migrate to spawn in freshwater (anadromy), where adults live and forage
in fresh water and migrate to spawn in salt water (catadromy), or where movement be-
tween fresh and salt water is not linked to breeding (amphidromy) (McDowall, 1987). Both
anadromous and catadromous migrations are by definition breeding migrations, although
anadromy (87 species, including lampreys, sturgeons, salmonids, osmerids, salangids, and
shads) is more common in temperate regions while catadromy (41 species, including eels and
mullets) is more common in the tropics (McDowall, 1987). This is thought to be due to the
fact that in the tropics, freshwater productivity is higher (and so fish born in saltwater can
increase their growth rate by migrating to feed in freshwater), and in the temperate zone,
saltwater productivity is higher and anadromy is favored (Gross et al., 1988).
A number of potomadromous species have refuge migrations – in the tropics, some species
(e.g. Sarotherodon mossambicus) spend the wet season in marshes and floodplains and
migrate into permanent bodies of water during the dry season (Northcote, 1978). Some
temperate species like the common roach (Rutilus rutilus) spend the summer in lakes and
move to streams in winter to avoid predation (Jepsen and Berg, 2002). Some arctic fish are
through to undergo spawning migrations entirely within streams (Northcote, 1978).
Oceandromous migrations are less well studied, due to the difficulty of tracking individ-
uals. At least a number of species (herring, cod, plaice) are known to have breeding mi-
grations within the ocean (Dingle, 1996). Most migratory sharks are oceandromous (Field
et al., 2009), some of which seem to have tracking migrations, moving seasonally to location
of high prey abundance (basking sharks, possibly whale sharks; Wilson et al. 2006; Sims
2008).
15

2.5.4 Birds
Approximately 4,000 of the 10,000 species of birds are migratory (Bildstein, 2006), the
majority of which seem to have refuge migrations, although the details vary across species.
By far most migratory birds breed in high-latitude high-productivity breeding sites in the
summer and migrate to lower latitudes for the winter – a pattern typically studied in Northern
Hemisphere species, but which also holds for Southern Hemisphere ones (Jahn et al., 2004).
Many tropical species migrate altitudinally, breeding at high elevation and move to lowlands,
e.g. to avoid seasonal storms (Boyle et al., 2010), a form of refuge migration. A number
of waterfowl species have moult (refuge) migrations where individuals migrate from their
nesting sites to a protected area to shed and regrow their feathers (Newton, 2008).
Within raptors, most migratory species have north-south refuge migrations, but a number
of species (e.g. osprey) have tracking migrations, following their prey as they move (Bildstein,
2006) in what is sometimes called a ‘fly-and-forage’ strategy (Strandberg and Alerstam,
2007). Red-billed queleas (Quelea quelea) also have a form of tracking migration (referred
to as ‘itinerant breeding’; Newton 2008) where individuals forage on grass seeds and follow
the rain belt as it moves across tropical Africa.
Many oceanic birds spend most of their time tracking oceanic upwellings and return to
restricted breeding sites on coastlines or islands to reproduce (Dingle, 1996; Newton, 2008).
This appears to be a breeding migration, since individuals that skip breeding do not migrate
to the breeding sites, indicating that forage better in non-breeding areas (as in the case of the
Wandering Albatross, Diomedia exulans; Newton 2008). Some penguins have a similar form
of breeding migration where adults migrate to rookeries to breed and then make extensive
trips back to ocean to forage (e.g. Emperor penguins, Aptenodytes forsteri Pinshow et al.,
1976).
16

2.6 Migration in Mammals
Across all three databases searched, we found a total of 221 mammal species listed as mi-
gratory. For 105 of these, we were able to find clear descriptions in the literature of their
migration patterns and motivations for migrating. Of the rest, 32 species had clear descrip-
tions of migration but we could not find details of the motivations for migrating, 22 had
unclear movement (some seasonal change but not clear if migratory), 21 were found to be
non-migratory (and presumably listed as migratory in the initial databases due to either no-
madic or dispersal behavior), and for the remaining 41 we could not find enough information
to determine movement patterns.
For the migratory species where there was sufficient information, we were able to classify
all 105 into one of the three migration types described above: refuge, breeding, and tracking
(Table A.1). In some cases we were only able to narrow down the migration type to one of
two patterns. For example, we could not determine if Narwhals (Monodon monoceros) have
refuge or breeding migrations: adults leave their summer feeding grounds in the winter, but
it is unclear if they feed during this time and whether the movement is to increase their
own survival or that of their calf’s. Snow leopards (Panthera uncia) migrate altitudinally,
but it is unclear whether their movements are to avoid harsh weather (refuge), to track prey
(tracking), or both. For the purpose of the analyses below, cases where we could not decide
between two migration patterns were counted as half of each.
Overall, about 50% of all migratory mammals showed refuge migrations, 20% breeding
migrations and 30% tracking migrations. All three patterns were represented in each mam-
malian order that contained a number of migratory species, although their frequencies varied
considerably (Figure 2.2). The majority of migratory dugongs and manatees (Sirenia) and
bats (Chiroptera) had refuge migrations. In both cetaceans and carnivores, breeding and
tracking migrations were equally common, while in ungulates (Artiodactyla and Perisso-
dactyla) tracking migrations were the most common. Ungulates with tracking migrations
usually moved to follow changes in vegetation, whereas carnivores with tracking migrations
17

Figure 2.2: The fraction of migratory species in each mammalian order that were found
to have refuge (black), breeding (grey), and tracking (white) migrations. The numbers
in parentheses indicate the number of species that could be classified in terms of their
motivation, out of the total number listed as migratory for that group.
moved to follow prey species that were often migratory themselves.
Mammals are essentially the only taxonomic group where migrants can travel by walking,
swimming, or flying (Dingle, 1980), allowing us to examine variation in migration patterns
by locomotion type: walking, swimming, flying. Most flying migrants had refuge migrations,
most swimming migrants had breeding migrations, and most walking migrants had tracking
migrations (Figure 2.3).
2.7 Discussion
Here we have presented a framework for classifying round-trip migration into three main
types based on the motivations for movement in each direction. We have demonstrated that
these three types are sufficient to characterize the migration patterns generally seen across
18

Figure 2.3: The fraction of migratory mammals by each form of locomotion that were found
to have refuge (black), breeding (grey), and tracking (white) migrations. The numbers
in parentheses indicate the number of species that could be classified in terms of their
motivation, out of the total number listed as migratory for that group.
all taxonomic groups, as well as across all individual mammal species where migration has
been well characterized.
Although migration is extensively studied and has long been considered an adaptive
response to ecological conditions, little work has been done to understand exactly what mo-
tivations drive migration, which we do here. The fundamental importance of this perspective
is that it gives us insights into how different environmental changes may affect the motiva-
tions for migration, altering the selective pressure on migratory behavior. These changes
will potentially have drastically different consequences for both the migratory behavior and
for a species generally, depending on the motivation driving migration.
For example, a species with a refuge migration driven by avoidance of cold tempera-
tures or deep snow is likely to response to warmer winter conditions by ceasing to migrate
away from the breeding grounds. This is likely to have dire consequences for the survival of
19

this species and in fact already seems to be happening in some European birds (Pulido and
Berthold, 2010). In contrast, species with breeding migrations may have a more difficult time
adapting to change since they move between an area suitable for adults and one suitable for
juveniles. Many of these species have physiological adaptations associated with this transi-
tion that are likely difficult to reverse (e.g. land crabs, amphibians, sea turtles, diadromous
fish). In these cases if migration cannot occur, it would likely mean the extinction of the
species.
Species with tracking migrations may be particularly sensitive to habitat fragmentation
that disrupts migratory routes. In ungulates with tracking migrations, movement also allows
escape from predation and maintenance of a larger population size (Fryxell et al., 1988). So
while the disruption of tracking migrations may not drive species extinct, it could lead to a
sharp deecline in population size (Harris et al., 2009), which could have dire consequences for
the ecosystem (Dobson et al., 2010). In these cases, it is worth considering the importance
of conserving migration in and of itself as a phenomenon and ecosystem service (Wilcove
and Wikelski, 2008).
20

Chapter 3
Migration or residency? The
evolution of movement behavior and
information usage in seasonal
environments 2
3.1 Abstract
Migration is a widely used strategy for dealing with seasonally variable environments. How-
ever, most discussion of migration occurs at the species level and relatively little work has
been done to understand migration as a general phenomenon. This narrow scope fails to ad-
dress underlying cross-taxa commonalities, such as determining what ultimate factors drive
migration. We have developed a spatially explicit, individual-based model in which we can
evolve behavior rules via simulations under a wide range of ecological conditions to answer
two questions. First, under what types of ecological conditions can an individual maximize
its fitness by migrating (versus being a resident)? Second, what types of information do indi-
2 Authors: Allison K. Shaw and Iain D. Couzin; Status: Manuscript in review for the American Naturalist;
Also presented at the Ecological Society of America meeting (Austin, TX, 2011).
21

viduals use to guide their movement? We show that migration is selected for when resource
seasonality is high compared to local patchiness, and residency (non-migratory behavior) is
selected for when patchiness is high compared to seasonality. When selected for, migration
evolves as both a movement behavior and an information-usage strategy. We also find that
different types of migration can evolve, depending on the ecological conditions and availabil-
ity of information. Finally, we present empirical support for our main results, drawn from
migration patterns exhibited by a variety of taxonomic groups.
3.2 Introduction
Migration is a widely used strategy for dealing with seasonally variable environments. It has
long been accepted that organisms should exhibit this strategy only when it is advantageous
(Lack, 1954), and that the costs and benefits of migrating depend on ecological conditions
(MacArthur, 1959). Furthermore, at least within birds, it’s believed that the machinery for
migration evolved in an early ancestor and is now present across all lineages (Berthold, 1999),
such that populations currently evolve to be migrants or residents mainly as a function of
their present ecological conditions (Alerstam et al., 2003; Salewski and Bruderer, 2007). (In
this manuscript, we use the term ‘evolution’ in the sense of the maintenance and modification
of a trait, not its first appearance; Zink 2002). However, we still lack a synthesis of what
specific types of ecological conditions select for migration. This is due primarily to a lack of
work on the ultimate factors driving animal migration (Bauer et al., 2009), studies of which
are understandably rare due to their difficulty. A handful of empirical studies have used
careful manipulations (e.g. Olsson et al., 2006; Brodersen et al., 2008; Grayson and Wilbur,
2009) or extensive cross-species comparisons (e.g. Levey and Stiles, 1992; Chesser and Levey,
1998; Boyle and Conway, 2007) to tease apart the factors that drive migration in a species
or a small taxonomic group. Our aim is to gain an understanding of the ecological drivers
more broadly. To do so, we take a theoretical approach. Surprisingly, especially given the
22

large amount of work done on migration, there are very few simple models in the literature
aimed at understanding the factors that drive the evolution of animal migration (Fryxell
et al., 2011, but see Guttal and Couzin 2010; Torney et al. 2010; Holt and Fryxell 2011).
Existing general models of why animals migrate have focused primarily on how migratory
and non-migratory individuals can coexist within a single partially migratory population (e.g.
Cohen 1967; Lundberg 1987; Kaitala et al. 1993; Taylor and Norris 2007; Griswold et al.
2010; Shaw and Levin 2011/Chapter 4), rather than determining the ecological conditions
favoring migration in the first place. Alexander (1998) estimated the costs and benefits of
migration in terms of survival and growth rate for species that swim, walk or fly to move.
A more recent model (Holt and Fryxell, 2011) determined the conditions favoring residency
or migration, assuming no cost to migration and a model by Wiener and Tuljapurkar (1994)
showed that negative correlation between two patches selects for movement between them.
However each of these models only considers space implicitly and assumes migrants move
between two discrete locations. Since migration is an adaptive response to resources that
are heterogeneously distributed in space and time (Cresswell et al., 2011), spatially explicit
models may provide insight that spatially implicit ones cannot. A number of spatially explicit
models have been developed, most of which are designed to understand migration patterns
in a particular population of a given species (e.g. Hubbard et al., 2004; Barbaro et al., 2009;
Carr et al., 2005; Holdo et al., 2009, but see Guttal and Couzin 2010, 2011).
To our knowledge, no simulation model has tried to map out which resource distributions
select for migration. This is probably due, at least in part, to the difficulty of defining
migration in terms of a behavioral parameter that can be evolved across a simulation. While
no single definition of migration is agreed upon, most definitions of the term refer to both a
physical movement as well as a behavioral pattern of information usage (Dingle and Drake,
2007). For example, the definition used by Kennedy (1985) describes migration as “persistent
and straightened out movement effected by the animal’s own locomotory exertions or by its
active embarkation upon a vehicle. It depends on some temporary inhibition of station
23

keeping responses but promotes their eventual disinhibition and recurrence.”
Here, we develop an individual-based model to determine what ecological conditions
favor migration over residency. In the ‘Methods’ section, we describe our model, which
consists of a resource distribution (‘Ecological conditions’ section) and individuals whose
movement is guided by different sources of information (‘Individual behavior’). We quantify
an individual’s fitness in several ways (‘Fitness functions’) and use a genetic algorithm to
evolve individual behavior over the course of a simulation (‘Selection’). We use our model
to answer two questions, as described in ‘Results’. First, what types of ecological conditions
select for migratory behavior versus resident behavior (‘Residency or migratory behavior’)?
Second, what types of information (resource, historical, or social) do individuals use to guide
their movement and what happens if not all sources of information are available (‘Information
availability’)? Finally we discuss empirical support for, and implications of, our findings with
respect to both the ‘Conditions favoring migration’ and the ‘Information availability’.
3.3 Methods
Our model consists of a spatially explicit patchy resource distribution and individuals with
movement rules (Figure 3.1), each described in more detail below. Migration is a round-
trip movement usually between two locations (although it can take several generations to
complete, as in insects). Often migration in each direction is driven primarily by a different
ecological condition (see ‘Ecological conditions’ below), each of which would be represented
by a different fitness function (see ‘Fitness functions’ below). Instead of simulating all
possible pair-wise combinations of factors driving round-trip migration, we only simulate
movement in a single direction. In order for migration between multiple locations (e.g.
location A and location B) to be favored, it must be beneficial for the organism to move
along each leg of the migration (e.g. both from A to B and from B to A). Note that the phrase
“evolution of migration” is used to refer to two distinct aspects: the first-ever appearance
24

Figure 3.1: Schematic of the model components, including a heterogeneously distributed
resource (a-c, f) and moving individuals (d-e). The resource (a) is the sum of a linear trend
in resources of slope ψ (b) plus a patchy resource distribution of quality pq and average
width pw (c, f), where darker indicates higher resource quality. Individuals move across the
resource distribution (d), driven in part by the position and velocity of other individuals
within a small repulsion radius rR and attraction radius rA (e). Note that this schematic
is for illustrative purposes and not to scale. See ‘ecological conditions’ section of text for
details.
of migration in a lineage, and the current-day maintenance of migration (Zink, 2002). In
the first case, the question is how did a non-migratory species evolve the complex suite of
machinery required for migration (e.g. navigation, energy stores)? In the second case, which
is the one we consider, the question is given that a lineage has evolved the machinery it
needs to migrate, under what ecological conditions is migration favored?
3.3.1 Ecological conditions
Animal migration can be driven by food and water availability; survival from climatic con-
ditions, predators, parasites, and disease; and factors related to reproduction such as mate
availability, nesting sites, and juvenile survival (Heape, 1931; Dingle, 1996). Many of these
factors come into play at some point during migration, although movement in each direction
25

is often driven by a single factor. For example, many migratory birds (in both hemispheres)
move between high latitude breeding grounds and low latitude wintering grounds (Jahn
et al., 2004), such that pole-ward movement is driven by both food and reproduction, and
equator-ward movement is driven by increased winter survival. Most baleen whales also feed
at high latitudes, but migrate to low latitudes to reproduce (Lockyer and Brown, 1981).
Here, pole-ward movement is driven by food and equator-ward movement by reproduction
and survival while calving (Corkeron and Connor, 1999). Migratory ungulates (e.g. wilde-
beest) are driven by continuously changing food resources and, as a result, move in a circuit
following the changing food gradient (Table 2 in Harris et al., 2009; Holdo et al., 2009).
Our simulated resource distribution represents any ecological factor that could potentially
drive migration (e.g. distribution of food, temperature, or nesting sites). The total resource
distribution (Figure 3.1a) consists of a linear trend in resource availability (Figure 3.1b)
plus a superimposed patchy resource distribution (Figure 3.1c). This is meant to represent
any sort of resource gradient that individuals might migrate along including latitudinal (e.g.
some birds and butterflies), altitudinal (e.g. some mammals and birds), or salinity (e.g. some
fish and crustaceans) gradients. The resource is defined by three parameters: the slope of the
linear trend (ψ), and the quality (pq) and average width (pw) of the patch distribution. In a
seasonal environment the direction of the trend would reverse over the course of a year, and
so ψ can be considered a measure of the degree of seasonality in the resource (the difference
in average resource abundance in a single area between the high-abundance season and the
low-abundance season). The patch quality pq and patch width pw are measures of how patchy
the resource is. A high value of pq corresponds to a resource that has high quality patches
present year-round regardless of season, and so pq is a measure of how buffered the resource
is against seasonality. Finally, the patch width pw is a measure of average habitat patch
size. We varied each of these three parameters to generate a range of different ecological
conditions (see zoomed-in snapshots of the resource shown in Figure 3.2a, B.3a, B.4a).
We generated the resource patch distribution using an algorithm for the creation of
26

colored (correlated in space and time) noise (García–Ojalvo et al., 1992). Due to the com-
putational constraints of simulating such a large field, we simulated a 256x256 pixel square
(where 1 pixel = 0.78 body length, BL) shown in Figure 3.1f and tiled it to get the overall
field (1024x1024) shown in Figure 3.1c (the patch distribution has periodic boundaries such
that tiling does not introduce discontinuities). This tiling should not affect the overall results
since individual step size is small compared to the tile size. Since local resource patches are
not static and likely to shift over a season, we changed the patch distribution by a slight
amount (correlated in time) every 100 steps.
3.3.2 Individual behavior
‘Migration’ is usually defined at the individual level in terms of both a movement pattern
(“persistent and straightened out movement”; Kennedy 1985) and an information usage
strategy (“temporary inhibition of station keeping responses”; Kennedy 1985). We chose
to encode individual behavior in terms of information usage (instead of movement pattern)
– in our simulations individuals were able to use three types of information to direct their
movements: resource, historical and social, given by vectors R, H, and S, respectively. The
resource vector R, calculated analytically (García–Ojalvo et al., 1992; Torney et al., 2011),
gave the direction of highest local resource increase from the perspective of an individual’s
specific location, representing the direction towards the highest quality local resource patch.
The historical vector H represents pre-existing historical information and can be interpreted
as being either genetically inherited or acquired by that individual during a previous mi-
gration (see also Mueller and Fagan, 2008). For most of our simulations, we assume that
individuals have perfect knowledge of H, which in turn is a reliable source of information to
locate the best resources. This was encoded by setting H to be the vector [0 1] (the direction
of increasing ψ) for all individuals and all generations. (Note that when we ran simulations
where individuals had to evolve the direction of H de novo, they were easily able to do so;
Figure B.1.) We also considered what happens if H is either imperfectly remembered or
27

is an unreliable source of information. This was encoded by setting it to be a vector that
was rotated from [0 1] by a small angle θ (chosen from a Gaussian distribution with mean
0 and standard deviation σ). We ran simulations under various values of σ. Finally, the
social vector S was given by a zonal model of social interactions (e.g. Reynolds, 1987; Couzin
et al., 2005) where individuals moved away from neighbors within a repulsion radius (rR,
set to be 1 BL), moved towards and align with neighbors within an attraction radius (rA,
set to be 6 BL), and did not interact with neighbors outside of rA (Figure 3.1e). These
radius values were chosen based on two recent empirical studies that estimated radius values
from groups of surf scoters (Melanitta perspicillata; Lukeman et al., 2010) and golden shiners
(Notemigonus crysoleucas; Katz et al., 2011). Each individual moved based on a combina-
tion of these three directions, as determined by the value of its parameters ωH, ωS and ωR
such that at each step, its preferred direction was H with probability ωH, S with probability
ωS, and R with probability ωR. Individuals were only allowed to turn towards their preferred
direction by at most θmax per step. (See Appendix Table B.1 for all parameters and values.)
Simulated individuals move in two-dimensional space with constant speed. Each indi-
vidual is characterized by a position, a velocity vector, and a set of information preference
weights (ωH, ωS and ωR), which direct their movement over the course of the simulation
(Figure 3.1d). Each individual begins with a random x-coordinate in [0, 1] and y-coordinate
in y0 ± N/(2ρ), where N is the number of individuals and ρ is the initial density. Individuals
move by amount ∆y each step (set to be 0.1 BL), in the direction given by their velocity
vector, for a total of T steps per generation. The value of T was chosen so that individuals
cannot cross the entire space during the course of one generation. In Kennedy’s 1985 defi-
nition, migration is inherently a temporary behavior held for one time period and followed
by a second non-migratory period. However, since residents are essentially non-migratory
for both time periods, the difference between residents and migrants occurs during the first
time period. To simplify things, in our model we only simulate the first period, instead of
trying to simulate two periods with a switch point in between them, which would double the
28

number of evolving parameters.
3.3.3 Fitness functions
The costs and benefits of migration can manifest themselves in a number of ways. For some
species, the benefit of migration comes from the resources accumulated along the way. For
example, ungulates that feed as they migrate (e.g. wildebeest, Connochaetes taurinus) derive
benefit from the accumulation of resources as they move, often foraging so much that they
significantly deplete the local plant biomass as they move through an area (McNaughton,
1976). In other species, the benefit of migration comes in the final location. For example,
Norwegian spring-spawning herring (Clupea harengu) adults migrate as far south as possible
before spawning, since temperature is the main factor determining larval survival (Slotte
and Fiksen, 2000). Finally, for other species the cost of migration is the risk of mortality
during the journey. For example, in many migratory songbirds (e.g. Catharus thrushes),
the cost of migration is due to coping with cold temperatures along the migratory journey,
a cost that can be higher than the extra energy expenditure from sustained flight (Wikelski
et al., 2003).
To account for this variety of costs and benefits, we ran simulations with three types of
fitness functions: cumulative, end-point, and minimum. For the cumulative fitness function,
an individual’s fitness was calculated as the sum of the values of resource it passed through at
every time step over the course of a generation (to mimic the ungulate continuously foraging
scenario). For the end-point fitness function, an individual’s fitness was calculated as the
value of the resource at its final position at the end of a generation (to mimic a fish migrating
to spawn scenario). For the minimum fitness function, an individual’s fitness was calculated
as the lowest resource value it passed through within a generation (for example, to mimic a
song bird surviving through harsh conditions).
29

3.3.4 Selection
We evolved the ω-values of individuals across many generations within an evolutionary sim-
ulation. At the start of a simulation, each of N individuals was assigned a random value for
ωH, ωS and ωR between 0 and 1 (probabilities were then evenly normalized to sum to 1).
At the end of each generation, individuals were selected to pass their ‘strategy’ (ωH, ωS and
ωR values), with some small mutation rate (a Gaussian random number with mean 0 and
standard deviation µ), to individuals in the next generation. Individuals were selected with
replacement (a single individual could be selected more than once) where the probability of
an individual being selected was proportional to its fitness. Each simulation was run for G
generations, where each generation was run for C copies of T steps each. (See Appendix
Table B.1 for all parameters and values.) For each copy of a generation, the resource dis-
tribution was regenerated (with the same parameter values) and individuals were assigned
new random starting positions (described above). This was done to ensure that differences
in fitness between individuals were due primarily to differences in their parameter values
rather than due to differences in their random starting positions.
3.4 Results
For each set of ecological parameter values (seasonality, patch quality, and patch width),
we quantified the behavior that evolved after many generations in two ways: in terms of
the information usage strategy (ω-values), and in terms of the movement behavior (total
distance traveled along the y-axis, the direction of increasing ψ). Overall, two distinct types
of behavior emerged. In the first case, individuals evolved to move almost entirely based on
resource information (ωR ≈ 1), and to ignore historical and social information (Figures 3.2b
and B.2-B.4). These individuals essentially did not move along the y-axis (Figures 3.2c and
B.2-B.4), and so we refer to these as “residents”. In the second case, all individuals within a
population evolved to rely to some extent on historical information (ωH > 0; Figures 3.2d and
30

Figure 3.2: The information usage strategies (b & d) and movement behavior (c) that
evolves in environments (a) with different values of ψ and constant values of pq (10) and
pw (8 BL), indicate that low seasonality selects for residency and high seasonality selects
for migration. The frequency distribution (darker indicates more individuals) of normalized
migratory distance traveled by individuals within a population is shown in (c), where each
vertical slice shows the results for a different simulation. Ternary plots are shown in (b) and
(d) where each dot shows the three evolved ω-values of a single individual in the population,
and corners correspond to behavior dominated by the indicated ω parameter (see Figure
B.2b for alternative labeling). Results from a simulation where individuals evolved to be
residents are shown in (b) and for a simulation where individuals evolved to be migrants is
shown in (d). Each simulation was run using the cumulative fitness function (see ‘fitness
functions’ section of text for details).
B.2-B.4), where the specific value of ωH depended on the ecological conditions and the fitness
function used (see below). These individuals traveled very far along the y-axis (Figures 3.2c
and B.2-B.4), and so we refer to these as “migrants”. Distances shown are normalized such
that the maximum distance an individual could travel during the simulation is set to be 1.
31

3.4.1 Residency or migratory behavior
Whether simulated individuals evolved to be residents or migrants depended on the values
of ecological parameters ψ (seasonality), pq (local patch quality), pw (local patch width) and
also on the fitness metric used (cumulative, end-point, or minimum). When patchiness (pq
and pw) is high compared to seasonality (ψ), individuals evolve to be residents, whereas
when pq and pw are low compared to ψ, individuals evolve to be migrants (Figures 3.2c
and B.2-B.4). This is true for all three fitness functions, although the parameter values at
which the shift from resident to migratory behavior occurs differs. The one exception is that
under the end-point fitness function, high levels of pw do not select for residency (Figure
B.4c). Also for simulations with the minimum fitness function, migration only occurs when
patchiness is essentially nonexistent and the resource increases approximately monotonically
up the y-axis (Figure B.3d).
The range of ecological conditions under which migration was favored depended in large
part on the main factor driving migration (the fitness function used). Migration occurred
under the broadest conditions for end-point fitness (e.g. migration to a breeding site),
followed by cumulative fitness (e.g. foraging migratory ungulate), then minimum fitness
(e.g. song bird surviving through harsh conditions). We confirmed these results by deriving
the conditions under which migration should be favored over residency in a simple analytic
model (see Appendix B: Analytic model). We find that migration should be favored under
an end-point fitness if
ψ ∆y T > δres , (3.1)
which is true under a broader range of conditions (values of ψ and δres) than the conditions
favoring migration under a cumulative fitness
ψ ∆y
(T + 1)
2
32
> δres
(3.2)

where ψ, ∆y and T have the same meaning as in our simulation model, and δres is the
average patch quality that a resident encounters, assuming it can seek out good patches.
This makes intuitive sense – in our, admittedly extreme, end-point fitness scenario, migrants
are not affected at all by conditions along their journey, and are therefore not disrupted by
patchiness as easily. This is most clearly demonstrated by the fact that high values of pw
did not select for residency in simulations with the end-point fitness (Figure B.4c).
3.4.2 Information availability
In our simulations, the consistent distinction between migrants and residents is the use of
historical information, which represents either memory or inherited information. That mi-
gration has evolved independently across many taxa, and that transition between migratory
and residential behaviors occurs without large phylogenetic constraints (Alerstam et al.,
2003) suggest that migration is a behavior that is relatively easily picked up and dropped
in response to changing environmental conditions. Arguably organisms that had never mi-
grated before would not have access to this form of information, and even ones that had
migrated previously may not be able to perfectly remember the migratory direction.
To determine what would happen if historical information was unavailable, we ran simu-
lations where individuals were only able to use social and resource information. We find that
for low ψ, individuals do not migrate and for high ψ individuals migrate far, as before (Figure
3.3, solid line). However, migrating individuals were not able to travel as far as during mi-
grations where they could use historical information (Figure 3.2c versus Figure 3.3), and the
information usage pattern differed slightly. For low ψ (Figure 3.3, region I) all individuals
within a population evolve to have ωR ≈ 1 and ωS ≈ 0, indicating a high reliance on resource
information, and almost no reliance on social information. For intermediate ψ (Figure 3.3,
region II) all individuals evolve to have fairly high ωS values, indicating a higher reliance on
social information when migrating. For high ψ (Figure 3.3, region III), individuals evolve to
have ωR ≈ 1 and ωS ≈ 0, but were still traveling far in the y-direction. Taken together, these
33

Figure 3.3: For intermediate seasonality, social individuals can travel farther than asocial
ones, when neither type has access to historical information. Shown is the movement behavior
(distance traveled) that evolved in environments with different values of ψ and constant
values of pq (10) and pw (8 BL), where no historical information was available and individuals
could use either both social and resource information (solid line) or just resource information
(dashed line). For low ψ (region I), individuals evolved to have ωS ≈ 0, for intermediate
ψ (region II), individuals evolved to have high ωS, and for high ψ (region III), individuals
evolved to have ωS ≈ 0.
results suggest that without access to historical information, migratory individuals will rely
on social information only when it allows them to travel further than they could based on
local resource information alone (Figure 3.3, dashed line).
To determine what would happen if historical information was available but unreliable,
we ran simulations where the vector H varied in reliability (Figure 3.4a). This represents
a situation where historical information is either remembered imperfectly (e.g. individuals
are constrained in their memory abilities) or where information is not a good indicator of
resource distributions (e.g. if the best resource location is not consistent from one year to the
next). We find that when H was very reliable (low σ), individuals relied on H to direct their
migrations (ωH ≈ 1, ωS ≈ 0 and ωR ≈ 0) and when H was not reliable (high σ), individuals
relied more on S to migrate (Figure 3.4b). This suggests that as the quality of historical
information deteriorates, migratory individuals would be expected to rely more heavily on
social information instead.
34

Figure 3.4: Individuals shift to rely more on social information during migration as historical
information becomes more inaccurate. Information usage (b) that evolved in environments
with constant values of ψ (0.2), pq (10) and pw (8 BL), but with different accuracy levels
of historical information, H as shown in (a). Ternary plots are shown in (b) where each
dot shows the three evolved ω-values of a single individual in the population, and corners
correspond to behavior dominated by the indicated ω parameter, and each panel shows the
result of a simulation with a different value of σ.
3.5 Discussion
Although migration is a well-studied phenomenon, surprisingly there are relatively few mod-
els that seek to explain the ecological conditions under which migration should be favored.
Here we present such a model, in the form of an individual-based simulation where indi-
viduals move across a spatially explicit patchy resource distribution, guided by a number of
different information sources. We evolve each individual’s strategy, defined by the relative
weight values (ωH, ωS and ωR) that it gives to each source of information (historical, so-
cial, and resource), under a variety of ecological conditions and fitness functions in order to
determine what conditions select for migratory behavior, and what information individuals
use to guide their movement.
We quantified our results in terms of both the values of evolved parameters, and the
movement behavior of individuals with those parameter values. Two distinct behavior types
emerged in the simulations. “Residents” predominantly use resource information to direct
35

their movement and, as a result, tend not to travel far in the y-direction. “Migrants”
primarily use non-resource (historical or social) information, and as a result traveled far
in the y-direction. This result confirms the concept that migration corresponds to both a
change in information usage behavior (temporarily ignoring local resources) and also physical
movement (traveling relatively long distances).
3.5.1 Conditions favoring migration
The type of behavior (resident or migrant) that simulated individuals evolved depended on
the spatial distribution of resources – some resource distributions selected for residency be-
havior and others selected for migratory behavior. In our model, the benefit of migration
comes from an increase in average local resources (determined by ψ), and the cost of mi-
gration comes from the locally poor resource patches (determined by pq and pw) that the
individual passes through during the migration. Migration only occurred in a seasonal envi-
ronment (ψ > 0), and within seasonal environments, migration evolved if pq and pw were low
compared to ψ and the benefits of migrating outweighed the costs, and residency evolved
if the reverse was true – a straightforward result that can be confirmed analytically (see
Appendix B: Analytic model). The conditions for residency are similar to the concept of a
low signal-to-noise ratio, with the difference that in our model its not that individuals are
unable to follow the ‘signal’ but that it does not pay (in terms of fitness) for them to do so.
As is the case with all models, some results are quite general while others are model-specific.
In our model, we found a sharp transition between those ecological conditions that select for
migration and those that select for residency, although this result seems to be model-specific
(see Appendix B: Analytic model).
In our model we do not simulate a round-trip migration, but rather we simulate the
migratory movement of one leg of a migration (since movement in the reverse direction is
conceptually the same). For the second, return, leg of migration to occur the conditions
must be reversed, such that the location with lower quality resources in one season becomes
36

the location with higher quality resources the next season and vice versa.
For species where migration is driven by the same resource in each direction (e.g. food)
or where migration is driven by different but correlated factors in each direction (e.g. food
and temperature), our results predict that highly seasonal environments should select for
migration. This result is supported by comparative studies across species in European birds
(Herrera, 1978), North American birds (Newton and Dale, 1996), raptors (Kerlinger, 1989),
and bats (Fleming and Eby, 2003), and across populations within a species in striped bass,
Morone saxatilis (Coutant, 1985). Our results also predict that seasonal non-buffered re-
sources should select for migration, while seasonal buffered resources should select for res-
idency. Which particular resource this refers to (food, temperature, breeding sites, etc.)
depends on the species. Extensive comparative studies on neotropical birds match our pre-
dictions – species living in unbuffered open habitats and feeding on fruit tend to migrate,
while those in more buffered habitats (forest interior; feeding on insects) tend to be residents
(Levey and Stiles, 1992; Chesser and Levey, 1998; Boyle and Conway, 2007). Bell (2011)
also found that while migration frequency in North American passerines generally increases
with latitude (increased resource seasonality), the variance in this trend can be explained
by residency being more common in species that rely on buffered resources. Similarly, tem-
perate bat species that roost in open trees are more likely to migrate than cave-roosting
bats, since caves offer a more buffered (constant temperature) environment during harsh
winters (Popa-Lisseanu and Voigt, 2009). Finally, our results predict that migration should
be more common in seasonal environments with smaller habitat patches – a prediction that
has been supported in white-tailed deer (Odocoileus virginianus), where individuals in areas
with large average forest patch size were less likely to migrate (Grovenburg et al., 2011).
For some species, migration is driven by different factors in each direction, the most com-
mon example being species that migrate between feeding site and spawning sites (e.g. Shaw
and Levin 2011/Chapter 4). In this case ψ is no longer a measure of seasonality but rather
a measure of how much better it is, on average, to breed at site A than at B and to feed at
37

site B than at A. Here, migration is expected to occur in species where the best reproduction
and feeding habitats are in different locations. This prediction matches migration patterns
in a number of species, including baleen whales, which migrate between high-latitude feeding
grounds and low-latitude breeding grounds (Corkeron and Connor, 1999); land crabs, which
migrate from terrestrial feeding areas to aquatic breeding areas (Wolcott and Wolcott, 1985);
and diadromous fish, which move between freshwater and saltwater, based on which area
has higher productivity (catadromy in the tropics and anadromy in temperate regions; Gross
et al., 1988).
While we have so far only discussed migration as a seasonal (annual) event, the results
of our model could be applied to organismal movement across a broader range of tempo-
ral scales. For example, if ψ is interpreted as resource fluctuations on a daily time scale,
our model matches the observation that daily fluctuations in light levels are necessary for
zooplankton daily vertical migration to occur (Dodson, 1990). On the other end of the
time spectrum, if ψ is interpreted on the order of thousands of years, our model matches
the observation that glacial-interglacial periods seem to force patterns of forest migration
(McGlone, 1996).
3.5.2 Caveats
In our model, we focus on the conditions that select for migration to be maintained in a
population (assuming individuals have the necessary migratory machinery) and not on the
conditions that first selected for this machinery. This separation of timescales is a reasonable
assumption for birds (Berthold, 1999; Alerstam et al., 2003; Salewski and Bruderer, 2007),
but at this time it is unknown to what extent it holds in other taxonomic groups. Addition-
ally, migration is thought to interact with a number of other life-history factors such as body
size (Roff, 1988) and mating systems (García–Peña et al., 2009), which we do not explicitly
consider in our model.
38

3.5.3 Information availability
When all three sources of information (historical, social, resource) were available to individ-
uals, migrants relied primarily on historical information. If historical information was either
unavailable or inaccurate, migrants relied on social and resource information – essentially
pooling their knowledge of local resource conditions via social interactions in order to mi-
grate (the ‘many wrongs principle’; Simons, 2004). This suggests that a population with
no previous history of migration could establish migratory behavior through extended social
behavior. However, once the migratory route is learned (if possible), individuals should rely
on this new historical information rather than social interactions, since in our simulations
migrants that relied on historical information traveled longer distances, and had higher fit-
ness than migrants relying on only social information (Figure 3.2c versus Figure 3.3). Within
migratory populations where the direction of highest resource changes frequently or is un-
reliable, we expect that individuals would rely more heavily on social rather than historical
information. Unfortunately this is currently difficult to test since little is known about the
relative importance of historical, environmental and social cues in migratory species (No-
ordwijk et al., 2006; Brown and Laland, 2003). Since our main interest was determining
what behavior evolved given certain constraints on information availability, we did not allow
the historical vector (H) to evolve during our simulations. Recent work suggests that if the
accuracy of H can be improved at a cost (relative to obtaining social information), there is
a strong information-based frequency dependence, where some individuals evolve to invest
in highly accurate H and are then exploited by other individuals in the population (Guttal
and Couzin, 2010; Torney et al., 2010).
3.6 Conclusions
Here we have presented an individual-based simulation model designed to determine what
types of ecological conditions select for migration. We derive a number of predictions, which
39

are all supported by examples from a number of different taxonomic groups. The creation
of such a general model has two main benefits. First, it allows us to conduct essentially
an extended thought experiment and test ideas that would be difficult to test empirically.
Second, by keeping the model generic and generating predictions that can be tested in a
number of species, we can draw parallels across a variety of taxonomic groups, which we
hope will inspire further cross-taxonomic comparisons of migratory patterns.
40

Chapter 4
To breed or not to breed: a model of
partial migration 3
4.1 Abstract
Migration is used by a number of species as a strategy for dealing with a seasonally variable
environment. In many migratory species, only some individuals migrate within a given
season (migrants) while the rest remain in the same location (residents), a phenomenon called
“partial migration”. Most examples of partial migration considered in the literature (both
empirically and theoretically) fall into one of two categories: either species where residents
and migrants share a breeding ground and winter apart, or species where residents and
migrants share an overwintering ground and breed apart. However, a third form of partial
migration can occur when non-migrating individuals actually forgo reproduction, essentially
a special form of low-frequency reproduction. While this type of partial migration is well
documented in many taxa, it is not often included in the partial migration literature, and has
not been considered theoretically to date. In this paper we present a model for this partial
migration scenario and determine under what conditions an individual should skip a breeding
3 Authors: Allison K. Shaw and Simon A. Levin; Status: Published in Oikos (2011) 120: 1871–1879;
Also presented at the Symposium on the Ecology and Evolution of Partial Migration (Lund, Sweden, 2012).
41

opportunity (resulting in partial migration), and under what conditions individuals should
breed every chance they get (resulting in complete migration). In a constant environment,
we find that partial migration is expected to occur when the mortality cost of migration is
high, and when individuals can greatly increase their fecundity by skipping a year before
breeding. In a stochastic environment, we find that an individual should skip migration more
frequently with increased risk of a bad year (higher probability and severity), with higher
mortality cost of migration, and with lower mortality cost of skipping. We discuss these
results in the context of empirical data and existing life history theory.
4.2 Introduction
Migration is used by a number of species, including birds, fish, invertebrates, and mammals,
as one strategy for dealing with a seasonally variable environment. In many cases, migra-
tion is obligate, but in some species, within a migratory population only some individuals
migrate in a given season (migrants), while the rest remain in the same location (residents),
a phenomenon called“partial migration” (Dingle, 1996; Chapman et al., 2011).
Partial migration was first described in avian species in which residents and migrants
share a breeding ground but overwinter apart (e.g. Lack, 1943, 1944). In more recent years,
it has been recognized that partial migration can also occur when residents and migrants
share a wintering ground but breed in separate locations (e.g. American Dippers; Morrissey
et al., 2004). A third form of partial migration occurs when non-migrating individuals
actually forgo reproduction – this is essentially a special form of low-frequency reproduction.
Figure 4.1 illustrates these three types of partial migration. Although this third type of
partial migration is well documented in salamanders, newts, sea turtles, and many species
of fish (see Bull and Shine, 1979; Rideout et al., 2005, for reviews), it is not often included
in the partial migration literature.
The development of partial migration theory has closely shadowed the empirical studies:
42

Figure 4.1: Schematic of three different types of partial migration: a) residents and migrants
share a breeding habitat but spend the non-breeding season apart, b) residents and migrants
share a non-breeding habitat and breed apart, and c) resident and migrants are apart during
the breeding season, but since migration is required for reproduction only migrant individuals
reproduce. Each panel shows the fraction of the population in each of the two habitats (A and
B) during each of two seasons (non-breeding and breeding). Shaded bars indicate individuals
that are reproducing.
43

the first models of partial migration only considered the case of a shared breeding ground and
found that the extent of partial migration should depend on the strength of both density-
dependence and environmental stochasticity (Cohen, 1967; Lundberg, 1987; Kaitala et al.,
1993; Taylor and Norris, 2007). A more recent theoretical paper found that that the sce-
narios of shared-breeding and shared-wintering migration are not equivalent and can lead
to different amounts of partial migration (Griswold et al., 2010). However, no models have
yet considered the third type of partial migration, where individuals that do not migrate
skip reproduction altogether. Unlike the first two types of partial migration, which involve
mainly tradeoffs in space (e.g. between one location with low survival and another with
high competition), the third type involves a tradeoff in time (between current and future
reproduction). As such, it seems likely that current theory would not apply to this type.
Our goal is to understand what conditions lead to partial migration in this third scenario.
In this paper we present a model of the evolution of partial migration in species where, in
a given season, individuals either migrate and reproduce, or skip migration and forgo repro-
duction. We determine under what conditions individuals should breed at every opportunity,
and under what conditions they should skip some breeding opportunities. We also examine
the effect of environmental stochasticity on optimal migratory behavior.
4.3 Low-Frequency Breeding Migrations
In this paper we consider partial migration in species with low-frequency breeding migrations.
For example, most baleen whales feed at high latitudes, and migrate to low latitude breeding
grounds to reproduce (Corkeron and Connor, 1999). Adult land crabs are terrestrial but their
eggs must develop in seawater and so adult females migrate to the coast to release their eggs
in the sea (Wolcott, 1988). Similarly, many adult amphibians that live terrestrially need
to migrate back to ephemeral ponds to reproduce (Russell et al., 2005). Adult sea turtles
spend most of their lives foraging at sea but migrate back to specific beaches in the tropics
44

to nest (Musick and Limpus, 1997). In each of these cases, an individual spends the majority
of its life in one habitat, but must make a costly migration to another location in order to
reproduce. In most years, a fraction of the population will actually skip migration and forgo
reproduction (Table 4.1).
Breeding migrations often have a high mortality cost, such that the annual survival of
an individual that chooses to migrate and reproduce (σr) is often much lower than that of
an individual that chooses to skip migration and reproduction (σs). For our purposes, we
assume that σr = (1 − m)σs where m is a measure of the relative mortality cost of migration
(0 ≤ m ≤ 1).
While migrating individuals have a lower survival, they gain the benefit of immediate
reproduction (with fecundity φ), whereas individuals that skip migration must wait until
a future opportunity to reproduce. In many species with breeding migration (such as sea
turtles, salmon and land crabs), individuals store energy across seasons and only migrate
when they reach a certain threshold (Thorpe, 1994; Hays, 2000; Solow et al., 2002; Caut
et al., 2008, Hartnoll pers. comm.). Therefore it seems reasonable to assume that fecundity
is higher for a reproducing individual that skipped the breeding opportunity the previous
year (φ2), than for a reproducing individual that did not skip reproduction the previous year
(φ1).
The question is, given these tradeoffs, under what conditions does it pay for an individual
to skip a breeding opportunity? Suppose an individual reproduces in a given year, after
having reproduced the previous year, with probability θ. Alternatively, it skips a breeding
opportunity with probability 1−θ. The best strategy, if it exists, is the Evolutionarily Stable
Strategy (ESS), which we denote θ ∗ – the value of θ that, when adopted by a population of
individuals, cannot be invaded by a mutant with any other value of θ (Maynard Smith and
Price, 1973). A value of θ ∗ less than one indicates that the best individual strategy is to skip
some breeding opportunities, which results in a partially migratory species. Alternatively
if θ ∗ is one, this indicates that the best strategy for an individual is to reproduce annually,
45

Table 4.1: Known examples of species with breeding migrations where at least some individuals
skip migration each year. Species names (latin and common), the frequency of breeding
when known, and the reference for each is given.
Species Freq. Reference
Crustaceans
Callinectes sapidus (blue crab) some skip Aguilar et al.
2005
Gecarcinus ruricola (black land crab) some skip Hartnoll et al.
2007
Gecarcoidea natalis (Christmas Island red crab) some skip Green 1997
Fish
Galeorhinus australis (Australian school shark) 2 yrs Olsen 1954
Acipenser fulvescens (Lake sturgeon) 4-6 yrs Scott and Crossmann
1973
Acipenser transmontanus (White sturgeon) 4-11 yrs Scott and Crossmann
1973
Clupea harengus (Atlantic herring) 1-2 yrs Engelhard and
Heino 2005
Catostomus commersonii (White sucker) some skip Quinn and Ross
1985
Salmo salar (Atlantic salmon) 1-2 yrs Jonsson et al.
1991
Salvelinus malma (Dolly varden) 1-2+ yrs Scott and Crossmann
1973
Hoplostethus atlanticus (Orange roughy) some skip Bell et al. 1992
Lates calcarifer (Barramundi) some skip Moore and
Reynolds 1982
Acanthopagrus australis (Surf bream) some skip Pollock 1984
Amphibians
Ambystoma maculatum (spotted salamander) 1-4 yrs Husting 1965
Taricha granulosa (rough-skinned newt) 1-2 yrs Pimentel 1990
Taricha rivularis (red-bellied newt) 2-3 yrs Twitty et al.
1964
Taricha torosa (California newt) 2 yrs Bull and Shine
1979
Triturus alpestris (Alpine newt) 1-2 yrs Bull and Shine
1979
Mammals
Megaptera novaeangliae (humpback whale) some skip Craig and Herman
1997
Physeter macrocephalus (sperm whale) some skip Mellinger et al.
2004
46

Table 4.1 (cont’d).
Species Freq. Reference
Reptiles
Iguana iguana (green iguana) 1-2 yrs Bock et al. 1985
Caretta caretta (loggerhead sea turtle) 1-6 yrs Hatase et al.
2004
Chelonia mydas (green sea turtle) 2-4 yrs Mortimer and
Carr 1987
Dermochelys coriacea (leatherback sea turtle) 2-7 yrs Saba et al. 2007
Eretmochelys imbricata (hawksbill sea turtle) 3-6 yrs Carr and Stancyk
1975
Lepidochelys kempii (Kemp’s ridley sea turtle) 1-4 yrs Pritchard and
Márquez 1973
Lepidochelys olivacea (olive ridley sea turtle) 1-4 yrs Schulz 1975
Natator depressus (flatback sea turtle) 2-4 yrs Hughes 1995
which results in a completely migratory species.
The simplest model is where an individual either reproduces annually or skips exactly
one year before reproducing (see Chapter 5 for a model allowing individuals to skip more
than one year). Based on the above assumptions, our model is given by
N(t + 1) =
⎡
⎢
⎣ θσr + θφ1DD σr + φ2DD
(1 − θ)σs 0
⎤
⎥
⎦ N(t) (4.1)
where N(t) = [N1(t), N2(t)], N1 are individuals that reproduced during the previous sea-
son and N2 are individuals that skipped reproduction during the previous season. This is
a discrete-time matrix population model, where time (t) corresponds to sequential poten-
tial breeding opportunities (e.g. years) and each class (Ni) corresponds to an individual’s
‘condition’, the number of seasons since it last reproduced. The fecundity of an individual
in each of these two classes is given by φ1 and φ2 respectively, where φ1 ≤ φ2, and these
values include density-independent mortality. The density-dependence (DD) is assumed to
47

Figure 4.2: Life cycle graph of our two-stage matrix model (4.1) where Ni is the number of
individuals who have gone i years since last reproducing, φi is their corresponding fecundity,
σr and σs are the annual survival rates of individuals that reproduce and skip reproduction
respectively, θ is the probability than an individual reproduces annually, and DD is the
density-dependence term (4.2).
be continuously differentiable, and otherwise can be of any form as long as
and
DD(N1 = 0, N2 = 0) = 1 , (4.2a)
∂DD
< 0 ,
∂N1
(4.2b)
∂DD
< 0 .
∂N2
(4.2c)
This can be viewed as representing either competition among adults (adults compete for
a limited number of breeding sites and only those that are successful can reproduce) or
as competition among eggs (all reproducing adults produce eggs, only a fraction of which
survive).
Individuals that skip a breeding opportunity move up a condition class. All individuals
that have reproduced move back into the N1 class, having exhausted their energy stores,
and all new individuals start in this class (see Figure 4.2). For species with a juvenile phase,
where individuals go through one or more seasons before they become sexually mature, the
juvenile survival rate is also included in the φiDD term.
48

Under our model, a population is only viable (does not decay to zero) if the condition
1 − [θσr + (1 − θ)σsσr] < θφ1 + (1 − θ)σsφ2
is met. If (4.3) holds, then the stable equilibrium is given by
DD = 1 − θσr − (1 − θ)σrσs
θφ1 + (1 − θ)σsφ2
(4.3)
. (4.4)
If the fecundity rates φ1 and φ2 are too high, this fixed-point equilibrium will become unstable
and the system goes through a series of bifurcations leading to stable periodic, quasi-periodic,
and chaotic attractors, in turn. Since most biological systems have relatively low fecundity
rates (see Fig. 2 in Hassell et al., 1976), for the purpose of this paper we only consider
the region of parameter space with a stable fixed-point equilibrium, and leave the rest of
parameter space for discussion in a future paper (see Chapter 5).
4.4 To Skip or Not?
To determine under what conditions an individual should skip a breeding opportunity, we
calculate θ ∗ (the ESS value of θ) analytically (Appendix C) as
θ ∗ = 1 if
and θ ∗ = 0 if
φ1
1 − σr
φ1
1 − σr
> σsφ2
1 − σsσr
< σsφ2
1 − σsσr
(4.5a)
. (4.5b)
This is to say that θ ∗ = 1 (all adults reproduce every season; complete migration) if the
ratio of growth to death rate for individuals reproducing immediately exceeds the same ratio
for individuals skipping one year and then reproducing, and that θ ∗ = 0 (adults skip every
other breeding season; partial migration) if the reverse is true. Note that the value of θ ∗
49

is never intermediate between zero and one, which is quite unusual for a model containing
density-dependence.
From these results we expect that partial migration should occur in cases where the
mortality cost of migration is high (σr

adults are fully terrestrial but their eggs must develop in sea water. This leads to mass
migrations by adults to breed and spawn their eggs into the ocean each year. Juvenile
crabs spend a few weeks in the ocean before returning to land, but there is high variation
in inter-annual juvenile survival; in some years juveniles cover the beaches as they return
from the sea and in other years there are so few that they escape detection (Gibson-Hill,
1947). Similarly, sea turtles face inter-annual variation in sea surface temperature, which
affects upwelling of nutrient-rich water, and in turn likely leads to inter-annual variation in
fecundity (Solow et al., 2002; Saba et al., 2007).
We included environmental stochasticity in our model to determine how it would affect
optimal migratory behavior. We implemented stochasticity by allowing fecundity to vary
randomly across years. We assumed that at each time t the environment was randomly in one
of two possible states, A and B, with probability p and 1 − p respectively. State A represents
a ‘bad’ year where φ1 = φ1lo and φ2 = φ2lo (with φ1lo ≤ φ2lo), and state B represents a ‘good’
year where φ1 = φ1hi and φ2 = φ2hi (with φ1hi ≤ φ2hi), with the assumption that all classes
have equal or higher fecundity in good years than bad (φ1lo ≤ φ1hi and φ2lo ≤ φ2hi). With
stochastic fluctuations, the population size is no longer constant and the value of θ ∗ must
be calculated in terms of the average growth rate, where the average is taken across all the
population sizes that the system visits (Appendix C). Since the distribution of population
sizes cannot be expressed analytically, it must be simulated. For simulations we used Ricker-
type density-dependence of the form
DD = e −β[θφ1N1(t)+φ2N2(t)]
(4.6)
where β is a constant (Ricker, 1975). Using a different form of density-dependence did not
qualitatively change our results.
As in the deterministic model, the value of θ ∗ was often zero or one. However there were
cases where an intermediate value of θ ∗ evolved, suggesting an additional mechanism that
51

can select for postponing reproduction and partial migration. An intermediate value of θ ∗
means that there is a mixture of strategies within the population, with some individuals
reproducing annually and some biennially (or, equivalently, individuals changing between
annual and biennial strategies within their lifetime). Intermediate values of θ ∗ evolved under
environmental conditions where some years favored θ = 0 strategies and some years favored
θ = 1 strategies. This only occurred in regions of parameter space that are close to the
boundary defined by condition (4.5). For example, consider a scenario where good years
favor reproducing annually and bad years favor skipping reproduction. The higher the risk
of a bad year (higher probability of a bad year, lower fecundity in a bad year), the lower
the value of θ ∗ (Figure 4.3). Additionally, the lower the cost to postponing reproduction
(smaller difference between the fitness of θ = 0 and θ = 1 strategies), the higher the level of
bet-hedging selected for (Figure 4.4a). Finally, the more costly migration is (higher m), the
more often individuals will skip reproduction (Figure 4.3b).
From these results we expect that intermediate values of θ ∗ should occur in popula-
tions where environmental variation results in conditions that fluctuate between favoring
annual reproduction and postponing reproduction. Testing this in biological systems re-
quires long-term monitoring of individuals within multiple populations, and being able to
quantify environmental variability in each population. Not surprisingly, such studies are
rare. However, there is evidence from sea turtles suggesting that variation in remigration
intervals of both green (Chelonia mydas) and leatherback sea turtles is related to temporal
variation in sea surface temperature (Solow et al., 2002; Saba et al., 2007). Additionally, a
recent study compared life-history strategies of two populations of Black-browed albatross
(Thalassarche melanophrys), one breeding at South Georgia in the Atlantic Ocean and the
other breed at Kerguelen in the Indian Ocean. The authors found that albatrosses in the
first, more variable population, skipped breeding more often than individuals in the second
population (Nevoux et al., 2010). Albatrosses that skip breeding do not actually skip mi-
gration, so this example does not quite fit the scenario for our model. However, this is one
52

Figure 4.3: The ESS value of θ (θ ∗ ) as a function of (a) p, the probability of a bad year
occurring, and (b) φlo, the fecundity of both classes in a bad year (the severity of a bad year).
Dotted lines show values of θ ∗ in simulations with no stochasticity, and dashed and solid
lines show values of θ ∗ in simulations with different amounts of stochasticity. For parameter
combinations where the population was not viable, the ESS could not be calculated and
therefore was not plotted. All simulations were run with φ1hi = φ2hi = 3, σs = 0.9 and
m = 0.9.
53

Figure 4.4: The ESS value of θ (θ ∗ ) as a function of (a) σs, the annual survival probability of
an individual postponing reproduction; and (b) m, the relative mortality cost of reproducing.
Dotted lines show values of θ ∗ in simulations with no stochasticity, and dashed and solid
lines show values of θ ∗ in simulations with different amounts of stochasticity. For parameter
combinations where the population was not viable, the ESS could not be calculated and
therefore was not plotted. All simulations were run with φ1hi = φ2hi = 3, σs = 0.9 and
m = 0.9 unless otherwise indicated.
54

of the only examples with sufficient data that details how organisms adjust their breeding
behavior in response to environmental stochasticity.
4.6 Discussion
Partial migration, in which only some individuals in a population migrate while the rest do
not, is common across a variety of taxa (e.g. mammals: Hebblewhite and Merrill 2011; birds:
Nilsson et al. 2011; fish: Brodersen et al. 2011). The majority of partial migration studies,
both empirical and theoretical, focus on species where both migrants and non-migrants
reproduce annually and either share breeding or share wintering grounds. However, in a
subset of species with partial migration only the migrants reproduce, and non-migrants
by skipping migration forgo reproduction. Existing partial migration models, which focus
on tradeoffs between survival and competition, cannot be applied to these species where
behavior is driven instead by a tradeoff between current and future reproduction.
In this paper we present a model for this partial migration scenario and determine under
what conditions an individual should skip a breeding opportunity, and under what conditions
individuals should breed every chance they get. Our model is simplistic in that it only allows
the possibility of skipping a single year, not two or more (which many species are known
to do). The main goal of our model was to understand general trends in skipped breeding
migrations. Extending the model to allow for extensive skipping would be analytically much
more difficult and would, we believe, still produce generally similar trends (see Chapter 5).
We looked at the extent of partial migration in both constant and stochastic environ-
ments. In a constant environment, we find that partial migration is expected to occur when
the mortality cost of migration is high, and when individuals can greatly increase their
fecundity by skipping a year before breeding. Both of these predictions are supported in
the empirical literature (in leatherback and loggerhead sea turtles, and Atlantic salmon,
discussed above). In a stochastic environment, we find that an individual should skip mi-
55

gration more frequently with increased risk of a bad year (higher probability and severity).
We also find that individuals should be more likely to skip migration when the mortality
cost of migration is high, and when the mortality cost of skipping is low. While our specific
results are not directly comparable to those of models of the other two types of partial mi-
gration (where both residents and migrants reproduce annually and share either a wintering
or breeding ground), our results with respect to environmental stochasticity are generally
similar: we find that it is possible to explain partial migration without invoking environ-
mental stochasticity (as in Kaitala et al., 1993), but that environmental stochasticity, when
included, influences the degree of partial migration (as in Cohen, 1967).
Our model could potentially be used to understand the evolution of skipped breeding
(also termed “intermittent breeding”) in general. Skipped breeding has been observed in a
number of species that have a high ‘accessory’ cost associated with reproduction, of which
migration is just one example (Bull and Shine, 1979). In these cases, it is thought that
adults tradeoff current reproductive success in favor of future reproduction (the prudent
parent hypothesis; Le Bohec et al., 2007), as in the case of our model. Skipped reproduction
is also observed in species with annual breeding opportunities where the total reproductive
cycle is longer than 12 months (e.g. blue king crabs; Jensen and Armstrong, 1989), which can
be trivially accounted for in our model by setting φ1 to zero (individuals that try to reproduce
again mid-cycle produce no offspring). A third reason some species skip breeding is when
breeding must be alternated with another, usually maintenance, activity where both cannot
be completed within 12 months, such as moult in birds (Langston and Rohwer, 1996). This
scenario is not as easily accounted for by our model, but it has been found in state-dependent
life history models (e.g. Barta et al., 2006).
Our results, while novel in the field of animal migration are similar to existing results
in other areas of life-history theory. For example, in a model of age at first reproduction,
G˚ardmark et al. (2003) found that organisms should first reproduce as two-year-olds instead
56

of three-year-olds when
f2 > cf3s2
1 − s3
(4.7)
where fi is the fecundity at age i, si is the survival probability at age i, and c is the added
cost of early reproduction, or in other words, when the fecundity of two-year-olds, discounted
by the cost of early reproduction and probability of surviving as a two-year-old, is greater
than the fecundity of three-year-olds, discounted by the probability of dying between two
and three years of age. This finding, which is quite similar to our condition (4.5), suggests
that similar pressures determine age at first reproduction and breeding frequency.
There are also parallels from past theoretical studies on dormancy. Cohen (1966, 1968)
developed a density-independent model of optimal reproduction in an annual plant to de-
termine what fraction of seeds should germinate immediately, and what fraction should go
dormant before germinating at a later date, given some environmental uncertainty. These
models predict that the fraction of seeds germinating should decrease with both increased
probability of a bad year and with increased viability of dormant seeds. These results, which
closely parallel our own Figures 4.3a and 4.4a, suggest that skipping breeding is essentially a
form of reproductive dormancy. Ellner (1985a,b) showed that adding density-dependence to
the Cohen model reversed some results: germination can increase with increased probability
of a bad year (if the probability is between 0.5 and 1). We did not find evidence in support
of this, although for our simulations the population was never viable at such high probabil-
ities of a bad year (Figure 4.3a). Roerdink (1988) and Tuljapurkar and Istock (1993) each
present stage-structured version of the Cohen model (with equal fecundity in all classes) and
found that, with environmental stochasticity, the best strategy is to have an intermediate
fraction of seeds diapausing (better than none or all). This does not match our finding that
there are cases under which the best strategy is to have no individuals skipping migration
(equivalent to no diapause). Menu et al. (2000) present a stochastic simulation model for
57

extended diapause in chestnut weevil larvae, where a fraction of individuals have one year
of diapause and the rest have two years of diapause. They find that when survival during
the extra diapause year is low, the optimal strategy is only to diapause for a single year.
On the other hand, when survival during diapause is high, the optimal strategy is to have
some larvae diapause one year and some two years. Survival during diapause in this case
is analogous to survival when skipping reproduction in our model, and these results match
ours (Figure 4.4b).
In the non-stochastic version of our model, very large values of φ1 and φ2 lead to equi-
librium population sizes that are periodic or chaotic, not a fixed point. Although we leave
extensive exploration of this behavior for a future paper, we found that fluctuations in pop-
ulation size acted like environmental stochasticity in that they selected for ESS values of
θ intermediate between 0 and 1. It has previously been demonstrated that fluctuations in
population size alone are enough to select for dormancy behavior (Ellner, 1987; Lalonde and
Roitberg, 2006).
Our model provides the first theoretical framework for partial migration in species where
individuals that do not migrate actually forgo reproduction. We predict conditions under
which partial migration should occur, in both constant and stochastic environments. Our
model is useful for understanding the general conditions affecting the degree of partial mi-
gration in a species. It could be further tested by comparing data on the actual fraction of
a population that skips migration with estimates generated by the model. However to do
so would require parameterizing the model with biological data that is not easy to obtain:
annual survival of both migrating and non-migrating individuals, and estimates of average
fecundity as a function of the years since an individual last reproduced.
58

Chapter 5
Partial migration and the evolution of
intermittent breeding 4
5.1 Abstract
A central issue in life history theory is how organisms trade-off current and future reproduc-
tion. A variety of organisms exhibit intermittent breeding, meaning sexually mature adults
will skip breeding opportunities between reproduction attempts. It’s thought that intermit-
tent breeding occurs when reproduction incurs an extra cost in terms of survival, energy, or
recovery time. We have developed a matrix population model for intermittent breeding, and
use adaptive dynamics to determine under what conditions individuals should breed at every
opportunity, and under what conditions they should skip some breeding opportunities (and
if so, how many). We also examine the effect of environmental stochasticity on breeding
behavior. We find that the evolutionarily stable strategy (ESS) for breeding behavior de-
pends on an individuals expected growth and mortality, and that the conditions for skipped
breeding depend on the type of reproductive cost incurred (survival, energy, recovery time).
In constant environments there is always a pure ESS, however environmental stochasticity
4 Authors: Allison K. Shaw and Simon A. Levin; Status: Manuscript in preparation for submission.
59

can select for a mixed ESS. Finally, we compare our model results to patterns of intermittent
breeding in species from a range of taxonomic groups.
5.2 Introduction
One of the central issues of life history theory concerns the timing of reproduction. Past
theoretical work has addressed the problem of whether to reproduce once or multiple times
(Charnov and Schaffer, 1973) as well as at what age to start reproducing (Wittenberger,
1979; G˚ardmark et al., 2003). However in many iteroparous species, sexually mature adults
will skip breeding opportunities in between reproduction events, a behavior known as ‘in-
termittent breeding’ (e.g. Calladine and Harris, 1997) or ‘low-frequency reproduction’ (e.g.
Bull and Shine, 1979).
This is thought to occur for two main reasons – either due to a constraint or due to
an adaptive response to a life-history tradeoff. Individuals can be constrained either by a
reproductive cycle that last for more than 12 months (e.g. blue king crabs – Jensen and
Armstrong 1989; king penguins – Le Bohec et al. 2007; blacktip sharks – Castro 1996; snow
skinks – Olsson and Shine 1999) or constrained by limited access to breeding sites due to
environmental conditions (e.g. inclement weather in snow petrels – Chastel et al. 1993) or
social factors (e.g. competition in Eurasian oystercatcher – Bruinzeel 2007). Tradeoffs can
be among a number of factors, but all relate to the general tradeoff between current re-
productive success and future potential reproduction (the prudent parent hypothesis; Drent
and Daan 1980). In some species (e.g. those with breeding migrations; Shaw and Levin
2011/Chapter 4), reproduction incurs an extra mortality cost, forcing individuals to trade
off adult survival with current reproduction. In other species, seasonally limited access to
resources leads to individuals requiring a year or more after reproducing to recover their
body condition or to complete a maintenance activity (e.g. birds have to balance time spend
on reproduction and moult; Barta et al. 2006). Finally, species with indeterminate growth
60

or ‘capital’ breeding (e.g. most ectotherms; Bonnet et al. 1998) often have a fecundity ben-
efit associated with skipping reproduction, either through growing to a larger body size or
storing more resources. Within the bird literature the individual heterogeneity in quality hy-
pothesis is often invoked to explain the coexistence of breeding and non-breeding individuals
within a single population where non-breeding individuals are often of ‘poorer quality’ (e.g.
Bradley et al., 2000; Cam and Monnat, 2000). However this hypothesis addresses the exis-
tence of variance in strategies across a population, and not the motivation for non-breeding
individuals to skip reproduction.
In this paper, we present a model for the evolution of intermittent breeding. We deter-
mine under what conditions individuals should breed at every opportunity, and under what
conditions they should skip some breeding opportunities (and if so, how many). We also
examine the effect of environmental stochasticity on breeding behavior. In a previous paper,
we studied intermittent breeding in the context of breeding migrations and limited our anal-
ysis to the situation where individuals could either reproduce annually or skip at most one
year before reproducing (Shaw and Levin 2011/Chapter 4). Here we extend this analysis to
model the scenario where individuals can skip any number of years between reproduction
attempts.
5.3 Intermittent breeding
Intermittent breeding is most commonly exhibited by long-lived species that have a costly
‘accessory’ activity associated with reproduction (e.g. breeding migration, live bearing, egg
brooding – Bull and Shine 1979). The accessory cost can be in terms of survival (e.g. higher
mortality during reproduction), time (e.g. recovery period post-breeding), or energy (e.g.
incubating eggs). We allow for these different types of costs in our model and discuss our
results in terms of each cost type below. To account for the case where reproduction incurs
a survival cost, we assume that the annual survival, σr, of an individual that chooses to
61

eproduce is less than or equal to that of an individual that chooses to skip reproduction,
σs (σr ≤ σs). Although reproducing individuals may have a lower survival, they gain the
benefit of immediate reproduction (with fecundity φ), whereas individuals that skip must
wait until a future opportunity to reproduce. In ‘capital breeding’ species, individuals can
store energy across seasons (Bonnet et al., 1998; Stephens et al., 2009). Here we assume
that the fecundity of an individual that skips an extra year is potentially higher than if it
had reproduced the previous year (φi ≤ φi+1, where φi is the fecundity of an individual that
has gone i years since last reproducing). We explore several variants of the exact fecundity
function Φ (the vector of φi), but generally assume that it is monotonically increasing. The
question we seek to answer is, given these tradeoffs, how many breeding opportunities should
an individual skip between reproduction attempts?
For an individual that has currently waited i years since it last reproduced, we denote the
probability that it will now reproduce as θi. Alternatively it skips this breeding opportunity
with probability 1−θi. The strategy of an individual is then defined by its vector of θi values
(i = 1, 2, 3, . . .), which we denote Θ. The best strategy, if it exists, is the Evolutionarily Stable
Strategy (ESS), which we denote Θ ∗ – the vector Θ that, when adopted by a population of
individuals, cannot be invaded by a mutant with any other Θ (Maynard Smith and Price,
1973).
We considered a simpler version of this model, where an individual either reproduces
annually or skips exactly one year before reproducing, in a previous paper (Shaw and Levin
2011/Chapter 4). Here we extend this work to consider a model where individuals can skip
any number of years (up to n) before reproducing (Figure 5.1), which is given by
N(t + 1) = AN(t) (5.1a)
62

Figure 5.1: Life cycle graph of our n-stage matrix model (equation 5.1) where Ni is the
number of individuals who have gone i years since last reproducing, ui is the probabilities
that an individual in class i chooses to skip an additional year before reproducing and
survives, vi is the probability that an individual in class i chooses to reproduce and survives,
and fi is number of juveniles born to a reproducing individual in class i.
where
⎡
v1 + f1
⎢ u1 ⎢
A = ⎢ 0
⎢ .
⎣
v2 + f2
0
u2
.
v3 + f3
0
0
.
. . .
. . .
. . .
. ..
vn + fn
⎥
0 ⎥
0 ⎥
. ⎥
⎦
0 0 . . . un−1 0
⎤
(5.1b)
and N = [N1, N2, . . . , Nn] is a vector of the number of individuals that have gone i years since
reproducing. This is a discrete-time matrix population model, where time (t) corresponds to
sequential potential breeding opportunities (e.g. years) and each class (Ni) corresponds to
an individual’s ‘condition,’ the number of years since it last reproduced. Here, ui = (1−θi)σs
is the probability an individual moves up a class (skips reproduction and survives), vi = θi σr
is the probability an individual reproduces and survives, and fi = θi φi DD is the fecundity
of a reproducing individual. We assume that the density-dependence (DD) is continuously
63

differentiable, and otherwise it can be of any form as long as
DD(N1 = 0, N2 = 0, ..., Nn = 0) = 1 , (5.2a)
and
∂DD
∂Ni
< 0 ∀ Ni . (5.2b)
This form of density-dependence can be viewed as representing either competition among
adults (adults compete for a limited number of breeding sites and only those that are suc-
cessful can reproduce) or as competition among eggs (all reproducing adults produce eggs,
only a fraction of which survive).
Individuals that skip a breeding opportunity move up a condition class. All individuals
that have reproduced move back into the N1 class, having exhausted their energy stores, and
all newborn individuals start in this class (see Figure 5.1). For species with a juvenile phase
where individuals go through one or more seasons before they become sexually mature, the
juvenile survival rate is included in the fi term. For now, we assume that annual survival
when skipping a breeding opportunity (σs) is the same, no matter how many breeding oppor-
tunities have been skipped previously, and similarly that annual survival when reproducing
(σr) is the same, no matter how many breeding opportunities have been skipped.
5.4 Model Equilibria and Stability
Before we can determine the best breeding behavior strategy (the Evolutionarily Stable
Strategy vector Θ ∗ ), we first need to find the equilibria of the model (5.1) and their stability.
In addition to the trivial equilibrium, there is a single non-trivial equilibrium, which is given
64

y
DD = L
K
(5.3a)
n
where K = θiφili , (5.3b)
i=1
L = 1 −
n
i=1
livi
(5.3c)
and li = i−1
j=1 uj is the probability that an individual skips breeding and survives to class i
(l1 = 1). We can determine under what conditions this equilibrium is stable, by considering
the Jacobian,
where
⎡
H1
⎢ u1 ⎢
J = ⎢ 0
⎢ .
⎣
H2
0
u2
.
H3
0
0
.
. . .
. . .
. . .
. ..
Hn
⎥
0 ⎥
0 ⎥
. ⎥
⎦
0 0 . . . un−1 0
n
∂DD
Hi = vi + θiφiDD + θjφjN j
∂Ni
At equilibrium N i = liN 1, which allows us to rewrite this as
j=1
Hi = vi + θiφiDD + KN 1
∂DD
∂Ni
eq
⎤
eq
(5.4a)
. (5.4b)
. (5.4c)
We can show, using logic similar to that in Levin and Goodyear (1980), that this equilibrium
exists biologically (equilibrium population size is non-negative) as long as
L < K (5.5)
65

(see Appendix D for details). For the analysis that follows, we assume this non-trivial equi-
librium is stable, however if the fecundity rates φi are too high, this fixed-point equilibrium
will become unstable and the system goes through a series of bifurcations leading to stable
periodic, quasi-periodic, and chaotic attractors, in turn.
5.5 Evolutionarily Stable Strategies
To determine the number of opportunities an individual should skip between reproduction
attempts, we calculate Θ ∗ (the vector of ESS values of θi). As long as the population size is
constant, we can calculate Θ ∗ analytically as follows (Metz et al., 1992; Ferriere and Gatto,
1995; Caswell, 2001; McGill and Brown, 2007). The growth rate of a mutant type (with
Θ = ΘM) in a resident population (with Θ = ΘR) is governed by the matrix, J, given by
where
⎡
⎢
J = ⎢
⎣
v1 + f 1 v2 + f 2 v3 + f 3 . . . vn + f n
u1 0 0 . . . 0
0 u2 0 . . . 0
. . .
. .. .
0 0 . . . un−1 0
ui = (1 − θi,M)σs
vi = θi,M σr
⎤
⎥
⎦
(5.6a)
(5.6b)
(5.6c)
f i = θi,M φi DD(ΘR) (5.6d)
and the density-dependence is a function of the resident equilibrium population size (N i,R)
given by equation (5.3). Since this is a non-negative irreducible matrix, by the Perron-
Frobenius theorem we know that it has a positive real dominant eigenvalue, which is the
66

growth rate G(ΘM, ΘR). The ESS is the vector Θ ∗ such that
G(Θ ∗ , Θ ∗ ) > G(ΘM, Θ ∗ )
or
G(Θ ∗ , Θ ∗ ) = G(ΘM, Θ ∗ ) and G(Θ ∗ , ΘM) > G(ΘM, ΘM) (5.7)
for all values of ΘM. To find this, we consider the characteristic equation of the Jacobian,
which is given by
λ n
1 −
n
λ −i
(vi + f i)li = 0 .
i=1
When λ = 1, the term in square brackets becomes
ρ(ΘM, ΘR) = 1 − L(ΘM) + K(ΘM)DD(ΘR) .
For Θ ∗ to be an ESS, we must have ρ(Θ ∗ , Θ ∗ ) = 1, and ρ(ΘM, Θ ∗ ) < 1 for all ΘM, or
alternatively stated,
K(Θ ∗ )
L(Θ ∗ )
> K(ΘM)
L(ΘM)
. (5.8)
Considering the value of each θi one at a time, L and K can be rewritten, separating out
the components that depend on θ1 from the rest, as
L = 1 −
n
i=1
θi σr(i) σ i−1
s
i−1
(1 − θj)
j=1
= 1 − θ1 σr(1) − (1 − θ1) α1(Θ)
67

and
K =
n
i=1
θi φi σ i−1
s
i−1
(1 − θj)
j=1
= θ1 φ1 + (1 − θ1) γ1(Θ)
where α1(Θ) and γ1(Θ) include all the terms that depend on θ2, θ3, . . . , θn. Plugging these
values into inequality (5.8), we find that the ESS value of θ1 is
θ ∗ 1 =
⎧
⎪⎨
⎪⎩
1 if φ1 1 − α1(Θ)
0 otherwise .
> γ1(Θ) 1 − σr(1)
(5.9)
If θ ∗ 1 = 1, the value of θ2 is irrelevant. However, if θ ∗ 1 = 0, then we can calculate θ ∗ 2 as above.
Generally, if θ ∗ a = 0 for all a < b, then θ ∗ b
out the components that depend on θb, as
L = 1 − θb σr(b) σ b−1
s
and K = θb φb σ b−1
s
can be calculated by rewriting L and K, separating
− (1 − θb) αb(Θ)
+ (1 − θb) γb(Θ)
where αb(Θ) and γb(Θ) include all the terms that depend on θb+1, . . . , θn. Then θ ∗ b
by
θ ∗ b =
⎧
⎪⎨
⎪⎩
1 if φb σb−1
s 1 − αb(Θ) > γb(Θ)
0 otherwise .
1 − σr(b) σ b−1
s
is given
(5.10)
By induction we can see that all θ ∗ i values will be equal to either 0 or 1 and we are only
concerned with the value of a θ ∗ j if θ ∗ j−1 = 0 (since otherwise if θ ∗ j−1 = 1, the value of θ ∗ j is
irrelevant). Therefore the ESS strategy is θ ∗ i = 0 for all i except i = j where j is the first
68

value where
σj−1 s φj
1 − σrσ j−1
s
> σj s φj+1
1 − σrσ j s
. (5.11)
The left hand side of the inequality (5.11) is ratio of the growth rate to mortality rate
of an individual that reproduces every j years and the right hand side is the same ratio for
an individual that reproduces every j + 1 years, so the ESS is essentially the strategy that
maximizes the ratio between growth and mortality. For a given set of model parameters,
there is always one best behavior – individuals should always reproduce after j years, no
more no less, meaning the ESS is always a pure strategy (each θ ∗ i is equal to 0 or 1). This
ESS condition can be interpreted in further detail by considering the three types of cost to
migration mentioned above: time, energy, and survival.
5.5.1 Scenario 1: Reproduction has time cost
If there is no fecundity benefit to postponing reproduction (i.e. φi = φi+1) then intermittent
breeding will never be favored, even if there is a survival cost to reproduction (σr < σs).
However, if we let survival during reproduction (σr) be a function of the number of years
skipped, i.e. σr = σr(i), then intermittent breeding will be favored in the absence of a
fecundity benefit as long as
σr(j + 1) − σr(j) >
1 − σs
σ j s
. (5.12)
Note that intermittent breeding will only be favored here if annual survival is sufficiently
high (σs > 0.5). This scenario is likely to be true for species that require a lengthy recov-
ery period following reproduction, where individuals would potentially have lower survival
if they tried to reproduce in two sequential years, than if they skipped a year between re-
production attempts. This scenario also applies to species where individuals must complete
a time-consuming maintenance activity, like moult in birds. Birds moult in order to replace
69

deteriorating feathers, which impact flight ability, and consequently the enegetic costs of
flight as well as the ability to escape predators (Barta et al., 2006). This time tradeoff leads
to some annual breeding species where individuals occasionally forgo breeding in a give year
in order to moult (Langston and Rohwer, 1996).
5.5.2 Scenario 2: Reproduction has energy cost
If there is no survival cost to reproduction and no post-reproduction recovery time needed
(σs = σr) then intermittent breeding is only favored when the fecundity benefit to skipping
is quite high, i.e.
φi+1
φi
> 1 − σi+1
σ(1 − σ i )
. (5.13)
In order to skip even one year, the fecundity (φ2) must be more than double the individual’s
fecundity if it were to breed annually (φ1). This could occur if, for example as described
in Bull and Shine (1979), an individual can accumulate enough energy to produce 20 eggs
each year but must pay an energetic cost equivalent to 10 eggs per reproduction event. An
individual reproducing annually will be able to produce 10 each year, but an individual
reproducing biennially will be able to produce 30 eggs every other year (assuming it has the
capacity to store the extra energy).
5.5.3 Scenario 3: Reproduction has survival cost
Finally, if no recovery time is needed, σr(i) = σr(i + 1), but there is a survival cost to
reproduction (in terms of increased mortality m), such that σr = (1−m)σs, where 0 ≤ m ≤ 1,
then only a slight fecundity benefit is required to select for intermittent breeding. This is the
scenario we will consider for the remainder of the paper. In this case, the ESS behavior is for
an individual to postpone reproduction until the benefits of waiting one more year (in terms
of fecundity) no longer outweigh the costs (in terms of survival). In general, an individual
70

Figure 5.2: Contour plot showing analytically calculated ESS values as a function of mortality
cost of reproduction (m) and annual survival of a non-reproducing individual (σs). Lines
indicate boundaries between i values where θ ∗ j = 1 and θ ∗ i = 0 ∀ i = j. For these simulations
the fecundity function was given by φi = 2i/(3 + i).
should increase the number of years between reproduction attempts as the cost of skipping
reproduction decreases (σs increases) and the cost of reproducing (m) increases (Figure 5.2).
The exact form and values of the fecundity function Φ will affect if and where the transitions
in the ESS strategy occur. A clear tradeoff between reproduction and survival has rarely been
demonstrated empirically (Reznick, 1985). However, in species where reproduction involves
an ‘accessory’ activity, this activity can incur a survival cost. For example, in species that
must migrate to reproduce, migrating individuals often incur an extra mortality cost (e.g.
Atlantic salmon; Jonsson et al., 1991).
5.6 Empirical Comparisons
Although our model makes specific predictions about expected breeding behavior, compar-
ing these predictions to empirical observations in a quantitative way requires being able to
estimate survival and fecundity life history parameters (σs, σr(i) and φ(i)), which is often
71

quite difficult. An alternative approach is to compare model predictions and empirical ob-
servations qualitatively by looking at trends in behavior with respect to a parameter. This
approach is often easier and has the potential to give more insight.
For example, in Atlantic salmon (Salmo salar), reproducing individuals have a higher
mortality (due to migration) than non-reproducing individuals. Our results predict that
as the mortality cost of reproduction increases, individuals should increase the number of
years they skip between breeding attempts. Jonsson et al. (1991) compared salmon from
two populations, one with lower mortality during migration (those that migrated up smaller
rivers) and one with higher mortality (larger rivers). Individuals in the first population re-
produced (migrated) annually whereas those in the second population reproduced biennially.
In Northwestern salamanders (Ambystoma gracile), individuals living at high altitudes expe-
rience a shorter summer and require a longer period of recovery following reproduction than
salamanders at lower altitude. From our model, we would expect females at lower altitude
to reproduce more frequently than those at high altitude, which matches observed behavior
(Eagleson, 1976).
In our model we assume that fecundity rates are fixed across all individuals and years,
such that if any individual reproduces after i years its fecundity will be exactly φi. In reality
there is variation in how individuals experience their environment. An equivalent strategy in
this case would be to reproduce after a certain state (body condition, level of energy stores,
etc.) has been reached instead of waiting a fixed number of years. This appears to be the
strategy that many species with intermittent breeding use, including birds (e.g. blue petrels,
Halobaena caerulea; Chastel et al. 1995), snakes (e.g. diamond-backed rattlesnakes, Crotalus
atrox and asp vipers, Vipera aspis; Tinkle 1962; Naulleau and Bonnet 1996), sea turtles (e.g.
green, Chelonia mydas and leatherback, Dermochelys coriacea; Solow et al. 2002; Caut et al.
2008), and fish (e.g. Atlantic salmon, Salmo salar; Thorpe 1994).
72

Figure 5.3: The a) equilibrium population size, N and the b) ESS reproduction behavior,
θ ∗ i , as a function of fecundity φ. For large values of φ the fixed point equilibrium becomes
unstable and the population bifurcates to a two-cycle, which selects for intermediate values
of θi. Simulations were run with n = 4, σs = 0.9, m = 0.9, φi = φ for all i.
5.7 Fluctuating Population Size
For very high fecundity (φi values), the non-trivial equilibrium given by (5.3) becomes un-
stable. The equilibrium population size undergoes a period-doubling bifurcation first to a
2-cycle, and then to periods of higher order and chaotic behavior for even higher fecundity
values (Figure 5.3). With these fluctuations, the population size is no longer constant and
the vector Θ ∗ must be calculated in terms of the average growth rate, where the average
is taken across all the population sizes that the system visits (see Appendix C / Shaw and
Levin 2011: Appendix for detailed methods). Since the distribution of population sizes can-
73

not be expressed analytically, it must be simulated. For simulations we used Ricker-type
density-dependence of the form
DD = exp
−β
n
i=1
θiφiNi
(5.14)
where β is a constant (Ricker, 1975). To determine the values of the ESS vector Θ, we
evolved each θ ∗ sequentially (e.g. first θ1, then θ2, etc).
In our simulations, we define the ESS value of θi to be the value that when adopted by
the population resists invasion by both individuals with a slightly higher and slightly lower
value of θi for 5 sequential invasion attempts. In most cases, no single value of θi met this
criteria – usually the resident value of θi in the population oscillated among several very
similar values of θi. If an ESS value of θi was not found within 100 sequential attempts, the
ESS value of θi was recorded as the average value of the residential type over the last 40
attempts. In the following figures the ESS values of θi are shown with one standard deviation
bars.
This fluctuation in population size leads to a fluctuation in the strength of density depen-
dence, which in turn causes variable offspring survival. This selects for intermittent breeding
even in cases where we might otherwise expect annual breeding – e.g. when there is neither
a fecundity nor survival benefit for postponing reproduction (φi = φi+1 and σr(i) = σr(i+1);
Figure 5.3). A similar result was discussed by Ellner (1987) in the context of population
fluctuations selecting for dormancy.
5.8 Stochastic Environments
Rarely do organisms live in constant environments. To determine how environmental stochas-
ticity influences the evolved reproductive behavior in our model, we allowed fecundity to vary
randomly across years. We assumed that at each time t the environment was randomly in
one of two possible states with probability p and 1 − p respectively. One state represents a
74

‘bad’ year where Φ = Φlo (Φ being the vector of fecundities of all n classes) and the other
state represents a ‘good’ year where Φ = Φhi. We considered two different forms of what
constitutes a ‘bad’ year:
Form 1) Φlo = a (fecundities of all reproducing individuals are low but non-zero), and
Form 2) Φlo = 0 (all reproduction fails or all newborns die).
With a stochastic environment, the population size is no longer constant and we use the
methods described above for the fluctuating population size to calculate the ESS.
In the stochastic version of the model we found the same basic patterns as in the deter-
ministic version: namely that an increasing cost of reproduction (m) and a decreasing cost of
skipping reproduction (increased σs), both select for individuals to skip more years between
reproduction attempts. However, unlike in the deterministic version, there were often con-
ditions under which the ESS behavior was a probabilistic strategy (where 0 < θi < 1). This
can also be interpreted as a situation where individuals with different strategies (in terms of
the number of skipped years between reproduction events) coexisting within a population.
These intermediate values of θi are due to two mechanisms that act in the stochastic version
of the model, described below.
5.8.1 Mixed strategies in response to mixed conditions
The first mechanism occurs when an environment dominated by good years selects for a
different evolved Θ ∗ than an environment dominated by bad years. For example, consider the
case where good years (with Φhi) select for individuals to wait 4 years between reproduction
attempts (θ ∗ 4 = 1), whereas bad years (with Φlo) select for individuals to reproduce annually
(θ ∗ 1 = 1, e.g. if in bad years everyone has reduced but equal fecundity then there is no
benefit to postponing reproduction, Form 1 above). In this case, the evolved Θ ∗ depends on
the relative frequency of good and bad years (Figure 5.4). Figure 5.4a shows the evolved θ ∗ i
values as a function of the probability of a bad year – an environment with only bad years
(p = 1) selects for θ ∗ 1 = 1, an environment with only good years (p = 0) selects for θ ∗ 4 = 1,
75

Figure 5.4: The ESS reproduction behavior in the stochastic model under different probabilities
of a bad year (p). Panel a) shows the evolved individual strategy in terms of θ ∗ i
(probability that an individual who has skipped i years will now reproduce) as a function
of p. Panels b-d) show the evolved individual strategy as the frequency of years between
reproduction attempts, ψ(i), for a given value of p (each ones represents a vertical ‘slice’ of
panel a). Simulations were run with n = 5, σs = 0.9, m = 0.9, Φhi = 4i/(3 + i) and Φlo = 1.
and an environment with both good and bad years (0 < p < 1) selects for intermediate θ
values. A perhaps more intuitive way of viewing this result is by looking at an individual’s
strategy as a frequency distribution of years between reproduction attempts, which can be
expressed as
ψ(i) = θi
i−1
(1 − θj) . (5.15)
j=1
76

Each panel in figure 5.4b-d shows the evolved ψ(i) values for a different probability of a bad
year.
5.8.2 Mixed strategies to spread the risk
The second mechanism that selects for intermediate values of θi occurs when the fecundity
in bad years is so low that the population is at risk of extinction, Form 2 of stochasticity
above (Φlo is so low that it violate inequality (5.5), the lower stability condition of the non-
trivial equilibrium). In this case, there is selection for individuals to ‘spread the risk’ of
extinction by skipping a variable number of years between reproduction events, resulting in
intermediate values of θi (Figure 5.5). This occurred even if the fecundity of all individuals
was the same (φi = φi+1), which has the counterintuitive effect of selecting for individuals to
postpone reproduction when there is no fecundity benefit for doing so. Figure 5.5a shows the
evolved θ ∗ i values as a function of the fecundity of a bad year and each panel 5.4b-d shows
the ψ(i) values (frequency of years between reproduction attempts) for a different fecundity
in a bad year. Here, as the severity of a bad year increases (Φlo decreases), the variance in
ψ(i) increases. When there is no risk of extinction Φlo = 1, there is no selection to spread
the risk and the ESS is just θ ∗ 1 = 1.
Although we can make specific predictions about the expected breeding behavior in
stochastic environments, being able to compare these predictions to empirical data requires
a system where the variation in environmental conditions is well-characterized. Nevoux et al.
(2010) compared reproduction strategies in two populations of Black-browed albatross (Tha-
lassarche melanophrys) one where individuals bred in a more variable environment (South
Georgia, Atlantic Ocean) and the other breed at less variable site (Kerguelen, Indian Ocean).
The authors found that individuals in the more variable environment skipped breeding more
often.
77

Figure 5.5: ESS reproduction behavior in the stochastic model under different fecundities
in bad year (Φlo): panel a) shows the evolved values of θ ∗ i (probability that an individual
who has skipped i years will now reproduce) as a function of Φlo and panels b-d) show the
frequency of years between reproduction attempts, ψ(i), for a given value of Φlo (each ones
represents a vertical ‘slice’ of panel a). Simulations were run with n = 5, σs = 0.9, m = 0.9,
Φhi = 3 for all φi, and p = 0.4.
5.9 Discussion
Intermittent breeding, also referred to as low frequency reproduction, is a behavior where
a sexually mature adult skips one or more breeding opportunities between reproduction
attempts. This behavior is commonly exhibited by long-lived species where reproduction
comes with a high accessory cost in terms of time, energy, or survival. In this paper, we
present a model to understand how life-history tradeoffs can favor intermittent breeding, and
we use our model to determine how many breeding opportunities an individual should skip.
We find that generally the best (ESS) reproductive strategy is the one that maximizes the
78

atio between growth and mortality. The conditions under which the ESS strategy involved
skipping breeding attempts (intermittent breeding) depend on the type of accessory cost
(time, energy or survival) associated with reproduction.
In constant environments, our model predicts that there should be a pure ESS in behavior
(all individuals in a population skip exactly the same number of years between reproduction
attempts; θi = 0 or 1 ∀ i). While this may be true in some biological populations, in most
cases there is at least some variation in individual strategies, both across individuals and
across years for a single individual. We have shown that including uncertainty in environ-
mental conditions or fluctuations in population size both select for strategy variation within
a population (mixed ESS; 0 < θ ∗ i < 1). Additionally, a number of other factors that we did
not include in our model also could potentially select for individual variation – for example
variation in individual condition or experience.
As with all models, we have made a number of simplifying assumptions that could be
relaxed to include more biological realism (at the cost of added complexity). Here we assume
that in stochastic environments individuals cannot anticipate whether a particular year will
be good or bad. It may be the case that individuals can determine from conditions prior
to the breeding season whether it is likely to be a good or bad year and adjust their deci-
sion to reproduce accordingly. In the case where individuals can guess the environmental
conditions perfectly each year, we expect that individuals would no longer act to ‘spread
the risk’ but instead would only postpone reproduction if the benefits outweigh the costs,
as in the deterministic model. We also assume that that non-reproducing individuals only
gain a benefit as a function of the years since they last bred. However, in species where
non-reproducing individuals grow in body size, the benefit of skipping is cumulative across
reproduction attempts. Accounting for this extra benefit in our model would involve adding
age or stage structure on top of the condition structure, making the model quite unwieldy.
However, this relationship could be explored in a model of a different form.
The work presented here fits with the broader literature on general tradeoffs between
79

growth and reproduction. Past studies have examined what conditions favor indeterminate
growth, where individuals both grow and reproduce for a period in their lives, over determi-
nate growth (bang-bang strategy) where individuals have a single switch from 100% growth
to 100% reproduction (see Perrin and Sibly, 1993, for a review). For example, Cohen (1971;
1976) developed a series of models to determine when plants should invest in growth or
seed production. He found that the optimal strategy was determinate growth, except when
either a plant’s lifespan is uncertain, or when somatic growth comes with an additional re-
production or survival advantage (e.g. increased survival or attractiveness with size). If we
consider intermittent breeding to be equivalent to indeterminate growth, this suggests that
the approaches that have been previously used to understand when organisms should have
determinate or indeterminate growth can also be used to understand how indeterminate the
growth should be (i.e. how many opportunities to skip between reproduction attempts, as
we do here). There are also parallels between our results and other areas of research such
as age of first reproduction and seed dormancy (see Discussion in Shaw and Levin 2011 /
Chapter 4).
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Chapter 6
Rainfall-driven migration timing in
the Christmas Island red crab
(Gecarcoidea natalis) 5
6.1 Abstract
Current climate models project changes in both temperature and precipitation patterns
across the globe in the coming years. Migratory species, which move to take advantage of
seasonal climate patterns, are likely to be affected by these changes. Indeed a number of
studies have shown a relationship between changing temperature and the migration timing of
various species, although few studied have examined the effects of precipitation. Here we ex-
plore the relationship between rainfall and migration timing in a tropical species, Gecarcoidea
natalis (Christmas Island red crab). We find that the timing of the annual crab breeding
migration is closely related to the amount of rain that falls during a ‘migration window’ prior
to potential spawning dates, which is in turn correlated with SOI, an atmospheric ENSO
index. Since reproduction in this species is conditional on successful migration, any changes
5 Authors: Allison K. Shaw and Kathryn A. Kelly; Status: Manuscript in preparation for submission.
81

in migration patterns could have detrimental consequences for the survival of the species.
6.2 Introduction
Current climate projections predict that temperature and precipitation extremes will increase
in most tropical and mid- and high-latitude areas across the globe (Solomon et al., 2007).
Since animal migration is driven by seasonal availability of resources such as food, potential
mates or breeding sites, and favorable climate (Dingle and Drake, 2007), any systematic
change in these resources, due to a change in temperature or precipitation, has the potential
to impact both the motivation for migration (e.g. Pulido and Berthold, 2010) and the ability
of individuals to successfully complete migration (e.g. Báez et al., 2011). In order to predict
how animal migrations will be affected by changing climate in the future, we first have to
understand the existing relationships between migration patterns and climatic variables.
Large-scale anomalies in climatic factors can be characterized by indices such as the El
Niño-Southern Oscillation (ENSO) or North Atlantic Oscillation (NAO). For species where
long-term data are lacking, we can use an organism’s response to events on the order of
years to decades (such as an ENSO event) as a baseline for predicting how it will respond to
longer-term climate change (Trathan et al., 2007). One of the most easily detectable shifts in
migratory patterns is a change in timing, and a number of studies on animal migration have
documented changes in migration timing with respect to temperature (e.g. North American
and Western European birds, sockeye salmon, and several British anuran species – Mysak
1986; Beebee 1995; Jenni and Kéry 2003; Marra et al. 2005; Van Buskirk et al. 2009) or
the North Atlantic Oscillation (e.g. North American and European birds, veined squid, and
flounder – Sims et al. 2001; Forchhammer et al. 2002; Lehikoinen et al. 2004; Sims et al.
2004; Jonzen et al. 2006; Macmynowski et al. 2007; Van Buskirk et al. 2009).
The majority of these studies focus on migratory species living in temperate regions of the
Northern Hemisphere, whereas relatively little is known about the impact of climate change
82

on migratory species in either the Southern Hemisphere (e.g. Australia – Gibbs, 2007), or
the tropics. While temperature dominates as the driver for migration timing in high-latitude
regions, precipitation is more likely to influence migration timing in the tropics (e.g. Boyle
et al., 2010). Since current climate projections show an increase in the precipitation extremes
(Solomon et al., 2007), it is vital that we understand the role of precipitation in the timing
of animal migrations.
Land crabs (family Gecarcinidae) are terrestrial crustaceans that are widely distributed
across the world’s tropics (Hartnoll, 1988). In these species, adults are terrestrial but eggs
require seawater to develop, and so adults undergo regular migrations from their inland
burrows to drop their eggs in the ocean (Wolcott, 1988). Water regulation is crucial, and
migration timing in most species of land crab coincides with the wet season (e.g. Cardisoma
guanhumi – Gifford 1962; Cardisoma hirtipes – Gibson-Hill 1947; Epigrapsus notatus – Liu
and Jeng 2005; Gecarcoidea lalandii – Liu and Jeng 2007; Gecarcoidea natalis – Hicks 1985;
Johngarthia lagostoma – Hartnoll et al. 2010; and Johngarthia malpilensis – López-Victoria
and Werding 2008). Despite this seemingly close link between migration and climate, to our
knowledge no studies have analyzed patterns of land crab migration timing with respect to
climate variability.
Here we present such an analysis for migrations of Gecarcoidea natalis, the Christmas
Island red crab, by looking at the relationship between the timing of red crab migrations with
respect to both rainfall and ENSO. Past studies on red crabs have noted that the start of
migration is related to a combination of the start of the wet season and timing with respect
to the lunar cycle (Hicks, 1985; Adamczewska and Morris, 2001a). Once the migration
starts, the crabs need approximately 3-4 weeks to complete the shoreward migration, mate,
and incubate eggs before the spawning date, which occurs a few days before the new moon.
Therefore we expected that the amount of rainfall just prior to the potential migration start
date (3-5 weeks prior to the new moon, which we refer to as the “migration window”, Figure
6.1) would determine whether crabs migrate in that lunar cycle, or wait until the next one.
83

ENSO has been found to have a strong impact on precipitation in nearby regions (e.g. India,
Sri Lanka, Indonesia, New Guinea, and continental Australia – McBride and Nicholls 1983;
Rasmusson and Carpenter 1983; Ropelewski and Halpert 1987), and is the most important
indicator of precipitation for the region around Christmas Island (Dai and Wigley, 2000),
although to our knowledge no one has explicitly looked at the impact of ENSO on Christmas
Island rainfall. Our goal was to look at relationship between climate variables and the timing
of red crab migrations, which we achieved in three steps. We looked at 1) the correlation
between ENSO and rainfall, 2) the relationship between rainfall and migration timing, and
finally 3) the ability to infer migration timing from ENSO.
6.3 Materials and Methods
6.3.1 Study System
Gecarcoidea natalis, the Christmas Island red crab, is a land crab native to Christmas Island,
Australia (10 ◦ S, 105 ◦ E). Adult crabs spend most of the year living in individual burrows. At
the start of the wet season (around November), they leave their burrows and migrate to the
island’s shore to reproduce. The migration is closely timed with the lunar cycle since females
must release their eggs at dawn on the high tides a few days before the new moon (Figure 6.1;
Adamczewska and Morris 2001a). Once the wet season begins, the migration starts about
three to four weeks before the next potential spawning date. The downward migration takes
one to two weeks, depending on when exactly the wet season starts in relation to the lunar
cycle and whether the crabs are therefore rushed (Hicks, 1985; Adamczewska and Morris,
2001a). Upon arrival at the shore, male crabs dig mating burrows and defend them against
other males (Hicks, 1985). Females arrive, mate, and then seal themselves inside the burrows
where they incubate their eggs for about 12-13 days before releasing them on the spawning
date (Hicks, 1985).
Informal records suggest that red crab migrations occur annually, although no formal
84

Figure 6.1: Crab migration activity with respect to the lunar cycle: spawning occurs a
few days before the new moon and juvenile crabs return to land approximately one month
later, females incubate their eggs two weeks before the spawning date, migration and mating
occurs before this. We designate the period 3-5 weeks before the new moon the “migration
window”.
record of migratory activity (e.g. timing, location, abundance) is available. Here, we as-
semble data on migration dates from 36 years (see Table 6.1) by drawing on a number
of sources, including published scientific papers on red crabs, bulletins published by Parks
Australia each year during the migration (available via the Christmas Island Tourism As-
sociation: http://www.christmas.net.au), and issues of the local newspaper, the Islander
(available at: http://www.shire.gov.cx).
6.3.2 Climate Data
We obtained daily rainfall data (in mm) for Christmas Island from 1973 (the earliest year
available) to 2011 from the Australian government Bureau of Meteorology
http://www.bom.gov.au/climate/data/). From the many climate indices that describe the
ENSO state, we selected the Southern Oscillation Index (SOI), an atmospheric (rather than
oceanic) index, based on the difference in sea level pressure between the Pacific and Indian
Oceans. A positive SOI value corresponds to the cold phase of ENSO (also known as La
Niña) and a negative SOI value corresponds to the warm phase of ENSO (El Niño). Monthly
SOI data are available from the Australian government Bureau of Meteorology
(http://www.bom.gov.au/climate/current/soihtm1.shtml) and moon phase dates are avail-
able from NASA (http://eclipse.gsfc.nasa.gov/phase/phasecat.html).
85

Table 6.1: Compiled data on G. natalis migration dates including the migration year, the first
date of noted migratory activity, approximate spawning date and source. For comparison are
the dates of new moons during the same period. ‘NR’ indicates no record, ‘None’ indicates
the migration never occurred and spawning dates marked with * are inferred from rest of
the migration cycle that year.
# Year Start of
Migration
Activity
Spawning
Date
Source New
Moon
1
New
Moon
2
1 1919-20 21-Nov 14-Dec Gibson-Hill 1947 22-Nov 22-Dec
2 1920-21 13-Nov 3-Dec Gibson-Hill 1947 10-Nov 10-Dec
3 1921-22 1-Nov 22-Nov Gibson-Hill 1947 30-Oct 29-Nov
4 1922-23 22-Nov 9-Dec Gibson-Hill 1947 19-Nov 18-Dec
5 1923-24 13-Dec 1-Jan Gibson-Hill 1947 8-Dec 6-Jan
6 1924-25 NR 19-Nov Gibson-Hill 1947 28-Oct 26-Nov
7 1925-26 NR 11-Dec Gibson-Hill 1947 16-Nov 15-Dec
8 1926-27 3-Dec 25-Dec Gibson-Hill 1947 5-Dec 3-Jan
9 1927-28 21-Nov late-Dec* Gibson-Hill 1947 24-Nov 24-Dec
10 1928-29 22-Nov 3-Jan Gibson-Hill 1947 12-Dec 11-Jan
1929-30 1-Nov NR Gibson-Hill 1947 1-Nov 1-Dec
11 1930-31 23-Nov 5-Dec Gibson-Hill 1947 20-Nov 20-Dec
12 1931-32 9-Nov 2-Dec Gibson-Hill 1947 9-Nov 9-Dec
13 1932-33 5-Nov 23-Nov Gibson-Hill 1947 29-Oct 28-Nov
14 1933-34 8-Nov 8-Dec Gibson-Hill 1947 17-Nov 17-Dec
15 1934-35 9-Nov 30-Nov Gibson-Hill 1947 7-Nov 6-Dec
16 1935-36 1-Nov 21-Nov Gibson-Hill 1947 27-Oct 26-Nov
17 1936-37 14-Nov 6-Dec Gibson-Hill 1947 14-Nov 13-Dec
18 1937-38 3-Dec 25-Dec Gibson-Hill 1947 2-Dec 1-Jan
19 1938-39 25-Nov 15-Dec Gibson-Hill 1947 22-Nov 21-Dec
20 1939-40 10-Nov 2-Dec Gibson-Hill 1947 11-Nov 10-Dec
21 1979-80 NR 11-Dec Hicks 1985 11-Nov 11-Dec
22 1980-81 30-Oct 2-Dec Hicks 1985 7-Nov 7-Dec
1980-81 30-Dec Hicks 1985 7-Dec 6-Jan
23 1981-82 6-Oct 20-Oct Hicks 1985 28-Sep 27-Oct
1981-82 22-Nov Hicks 1985 27-Oct 26-Nov
1981-82 21-Dec Hicks 1985 26-Nov 26-Dec
24 1982-83 12-Nov 12-Dec Hicks 1985 15-Nov 15-Dec
1982-83 7-Jan Hicks 1985 15-Dec 14-Jan
1982-83 2-Feb Hicks 1985 14-Jan 13-Feb
25 1986-87 26-Nov late-Dec* O’Dowd and Lake
1989
1-Dec 31-Dec
26 1988-89 20-Oct False start Green 1997 10-Oct 9-Nov
1988-89 3-Nov 3-Dec Green 1997 9-Nov 9-Dec
86

Table 6.1 (cont’d)
# Year Start of
Migration
Activity
Spawning
Date
Source New
Moon
1
New
Moon
2
27 1989-90 12-Dec late-Jan* Green 1997 28-Dec 26-Jan
28 1993-94 17-Nov 12-Dec Adamczewska and
Morris 2001a
13-Nov 13-Dec
29 1995-96 5-Nov 17-Dec Adamczewska and
Morris 2001a
22-Nov 22-Dec
30 1997-98 None None Max Orchard, 30-Nov 29-Dec
31 2006-07 26-Nov mid-Dec*
pers. comm.
Morris et al. 2010 20-Nov 20-Dec
32 2007-08 7-Nov ear-Dec Morris et al. 2010 9-Nov 9-Dec
2007-08 ear-Jan The Islander 9-Dec 8-Jan
33 2008-09 28-Oct 25-Nov personal
tionobserva-
28-Oct 27-Nov
2008-09 22-Dec personal
tionobserva-
27-Nov 27-Dec
34 2009-10 27-Oct 11-Dec Migration Bulletin 16-Nov 16-Dec
35 2010-11 28-Oct 30-Nov Migration Bulletin 6-Nov 5-Dec
36 2011-12 14-Nov 21-Dec Migration Bulletin 25-Nov 24-Dec
6.3.3 Analysis
We looked at the relationship between climate variables and the timing of red crab migrations
in three steps: by determining 1) the correlation between SOI and rainfall, 2) the relationship
between rainfall and migration timing, and finally 3) the ability to infer migration timing
from SOI.
Since the distribution of rainfall was highly non-normal and seasonal, we removed the
seasonal cycle and converted it to deciles (e.g. Miralles-Wilhelm et al., 2005), before com-
paring rainfall to SOI (which has no significant seasonal signal). We first calculated the
summed rainfall for each of the five two-week intervals during the wet season (between Oc-
tober 15th and December 31st) of each year for which we had rainfall data (1973-2011). We
then subtracted the temporal mean rainfall of each interval from the sums (removing the
seasonal cycle) to create wet season rainfall anomalies. We converted the summed rainfall
87

for each two-week interval to deciles by first ranking all the rainfall anomalies to define decile
cutoffs. We correlated rainfall deciles with the SOI (a monthly index interpolated to match
the two-week intervals). We then regressed rainfall onto SOI to get coefficients for a rainfall
estimate.
To determine the relationship between the start of the annual red crab migration and
rainfall, we summed the amount of rainfall that occurred in each migration window (defined
as the 3-5 week period prior to the new moon, Figure 6.1) that occurred between mid-October
and late-December, and compared it to whether the red crabs started their migration that
lunar cycle. If the wet season starts early enough, there can be several waves of migration,
and spawnings during multiple lunar cycles. However, much of the data we assembled only
reported the date of the first wave of migration and spawning. So in this analysis we only
focus on predicting the date of the first migration each year, and not whether migration
occurred during subsequent lunar cycles.
To determine if migration timing could be inferred from SOI, we calculated an expected
migration date from the SOI values as follows. For each year for which we had crab mi-
gration dates (approximately 1919-1939 and 1976-2011), we interpolated the SOI values to
each migration window during the wet season. We used this value with the regression coeffi-
cients calculated above to estimate an expected rainfall anomaly decile for the window. The
decile was then converted to the expected rainfall anomaly using the decile cutoffs and then
converted to expected rainfall by adding the seasonal rainfall value for that window. We de-
fined the expected migration date as the first migration window where the estimated rainfall
exceeded the rainfall threshold (see Results) determined in the first step of our analysis.
88

Rain decile
10
8
6
4
2
0
1972 1977 1982 1987 1992 1997 2002 2007 2012
Year
Figure 6.2: ENSO and rainfall. The SOI-estimated rainfall decile during the October-
December wet season (solid line) reproduces the variability of the actual rainfall decile
(dashed line), but with smaller amplitude.
6.4 Results
6.4.1 ENSO and Rainfall
The Southern Oscillation Index (SOI) was significantly correlated with the wet season rainfall
anomaly decile values (ρ = 0.35 with p < 0.01), in that a positive SOI value (La Niña
phase) corresponded to more rainfall than average and a negative SOI value (El Niño phase)
corresponded to less rainfall than average. The rainfall deciles derived from the regression
against SOI reproduced the anomalies of the actual rainfall deciles, but with much smaller
amplitudes (Figure 6.2). The average rainfall increased across the wet season from mid-
October to late December (averages for the five two week periods were 30.7mm, 64.6mm,
65.1mm, 100.7mm, and 97.3mm). The rainfall anomalies were highly non-normal (the decile
cutoffs were -97, -75, -63, -54, -31, -26, -10, 11, 38, 116, and 481). The rainfall/SOI regression
was given by RAIN = 0.09 ∗ SOI + 4.86.
6.4.2 Rainfall and Migration
We found a clear relationship between the amount of rainfall during the migration window
(3-5 weeks before a new moon) and the tendency of red crabs to start their migration during
89

Figure 6.3: Rainfall and migration. Tendency of red crabs to start their migration (yes or
no) as a function of the amount of rainfall (in mm) that fell during the migration window
(3-5 weeks before the new moon). There appears to be a threshold effect with migration
primarily occurring above approximately 20mm of rainfall (dotted line).
this period: crabs always started their migration if there was at least 20mm of rainfall during
the migration window (Figure 6.3). Of the 16 years for which we have data on both crab
migration dates and rainfall, in 12 years crabs migrated during the first lunar cycle from
October onward for which there was at least 20mm of rainfall in the migration window, one
year (2009) was borderline, and in 3 years (1982, 2006, and 2007) the crabs started their
migration on very little rainfall.
These exceptions seem to be driven by sporadic rainfall during these four years. In 2009
there was 20.4mm of rainfall in the migration window corresponding to the 18-Oct new
moon, which must have been too early in the season, since the crabs waited until the next
migration window with enough rainfall (67mm for 16-Dec) before migrating. In 1982, 40mm
of rain fell between September 4th and 8th, then no more than 1-2mm of rainfall any week
until early December. However the crabs migrated in late November (on 2.2mm during the
migration window), to spawn in mid-December. In 2006, 17mm of rain fell on November
90

8th-9th then almost no rain fell until mid-December (although data is missing for Nov 19-
20th and 28-29th), and the crabs migrated in late November (on 2mm of rainfall during the
migration window). In 2007, 20mm of rain fell over a one-week period in mid-September,
then there was almost no rain until early December, but the crabs migrated in late November
(on 5.8mm of rainfall during the migration window).
6.4.3 ENSO and Migration
The expected migration dates, calculated based on SOI values and the rainfall/SOI regression
coefficients, matched the actual migration dates in 24 of the 36 years (67%) for which we
have data (Figure 6.4, blue circles). Of the 12 years in which the expected migration date
did not match, in 9 years the SOI-inferred migration date was early (red X’s above 20mm
line: 1923, 1926, 1928, 1937, 1986, 1989, 1997, 2010, and 2011) and in 3 years it was late
(red X’s below 20mm line: 1980, 1981 and 1982). In all except three years (1981, 1989 and
1997), the SOI-inferred date was off by only a single lunar cycle from the actual migration
date. In 1981 there was a minor migration in October, a major migration in November,
and the SOI-inferred date was December. In 1989, there was a small amount of rainfall in
November (the SOI-inferred migration date), then a dry spell, followed by heavy rainfall in
late December and early January (the actual migration date). In 1997, the wet season was
abnormally dry (this year corresponds to the strongest El Niño event of the century; Yu and
Rienecker 1999) and the crabs never migrated. In two of the years where the SOI-inferred
date was late, the crabs migrated on relatively little rainfall (21.2m in 1980 and 2.2mm in
1982, which corresponds to the second largest El Niño event on record).
6.5 Discussion
In this paper we analyze the timing of Christmas Island red crab migrations with respect
to climate indices: rainfall and SOI (an atmospheric ENSO index). We find that rainfall
91

Figure 6.4: ENSO and migration. SOI-inferred migration dates match the actual migration
dates for 24 of 36 years for which we have data. Each black line corresponds to a different year
and shows the SOI-estimated rainfall (in mm) for each migration window between October
and January. Data from 1919-1939 are shown in the top panel and data from 1979-2011 in
the bottom panel. The point at which crabs actually migrated each year is marked in color:
blue circles indicate migration dates that match those predicted by SOI and those with red
X’s indicate migration dates that did not match.
92

during what we refer to as the “migration window” (3-5 weeks before the new moon) is
highly predictive of migration behavior: if at least 20mm of rain falls in the window, the
crabs migrate; otherwise they wait. We also find that SOI is correlated with rainfall anomalies
on Christmas Island. To our knowledge, this is the first study to analyze rainfall patterns
on the island with respect to ENSO, although this finding is consistent with the strong
impact that ENSO has been found to have on surrounding regions (e.g. India, Sri Lanka,
Indonesia, New Guinea, and continental Australia – McBride and Nicholls 1983; Rasmusson
and Carpenter 1983; Ropelewski and Halpert 1987; Dai and Wigley 2000). However, this
relationship translates into only a mediocre ability of SOI to infer the timing of red crab
migrations (67% correct).
Overall, these findings suggest that future changes in precipitation patterns could have a
large impact on red crab migrations on Christmas Island. Since the average rainfall increases
throughout the wet season, an increased variance in precipitation as predicted by climate
models (Solomon et al., 2007) could mean that the amount of rainfall needed to trigger the
crab migrations occurs later in the wet season. It’s unclear what effect migrating later (e.g.
in December) versus earlier (e.g. October) would have for red crabs, but if the rain does
not come until much later (e.g. January or February), the crabs will skip their migration
that year (as occurred in 1997-8). Furthermore, changes in crab migration behavior have the
potential to impact other species, such as whale sharks which migrate to Christmas Island
to feed on red crab larvae (Meekan et al., 2009).
If El Niño events become more regular (as has been predicted by some climate models,
Timmermann et al. (1999), and the wet season is consistently too dry for migration to oc-
cur (as in 1997), this could have severe consequences at the species level. Other migratory
species, such as blackcaps (Sylvia atricapilla; Pulido and Berthold, 2010) and black wilde-
beest (Connochaetes gnou; von Richter, 1974), have been observed to stop migrating as a
response to changing conditions. However in those cases, a non-migratory population is vi-
able, whereas in red crabs, individuals must migrate in order to reproduce. This means that
93

individuals consistently unable to migrate due to dry weather will be consistently unable to
reproduce, and the consequences could be devastating for the species. Even if there is enough
rain to trigger migration, if the wet season is overall drier, this could increase dehydration
risk, increasing mortality during migration and, according to recent theoretical work, this
should select for individual crabs to skip migration more often and will result in fewer crabs
migrating in any given year (Shaw and Levin 2011/Chapter 4).
Although we found a clear relationship between ENSO and rainfall and between rainfall
and migration timing, the relationship between ENSO and migration timing was less clear.
This seems to be owing to the short duration and localized intensity of rainfall; despite
the clear relationship between ENSO and the overall wet season timing, inferring specific
rainfall events that trigger migration is difficult. This is reflected in our finding that the SOI-
estimated rainfall decile anomalies are relatively small compared to the actual anomalies and
the seasonal mean values. This means that SOI is probably not a useful tool for determining
when crab migrations are most likely to occur in a given year. In fact, assuming that crabs
will migrate to spawn on the lunar cycle closest to the average historical spawning date
(December 14th) matches the actual crab migration date 22 of 36 (61%) times (compared
to 24 of 36 or 67% for SOI-inferred dates). In a number of years, crabs migrated in a cycle
for which there was little recorded rainfall in the corresponding migration window. In all
of these years, there had been some rainfall earlier on in the season. Given these results,
it is likely that migration is not triggered only by the quantity of rain that falls during the
migration window, but is instead triggered by a related factor, such as soil moisture. Soil
moisture effectively integrates rainfall over a longer period. In future years, soil moisture
could be monitored in real time to estimate when the migration start date is approaching.
Here we have looked for a relationship between the timing of red crab migrations and
climate variables because timing is the one aspect of the migration for which we were able
to find the most data. It is quite likely that climate variables affect other aspects of the mi-
gration as well. Studies on other migratory species have documented a relationship between
94

ENSO and the abundance (whale sharks and Sábalo fish – Wilson et al. 2001; Smolders et al.
2002), location (bluefin tuna, Pacific hake, and black turtles – Mysak 1986; Smith et al. 1990;
Quiñones et al. 2010) and the survival (black-throated blue warblers – Sillett et al. 2000) of
migrants, as well as an individual’s probability of migrating in a given year (leatherback sea
turtles – Saba et al. 2007). While red crabs are constrained by their need to migrate to the
island’s shore, which shore they choose could vary. Indeed there is some tendency for crabs
migrate to different sides of the island in different lunar cycles within a season (pers obs;
Hicks, 1985). One of the main risks migrating crabs face during migration is dehydration
(Adamczewska and Morris, 2001b), so it seems quite likely that climate variables like rainfall
would be related to abundance and survival of migrants as well.
A number of studies have also found a relationship between ENSO and the recruitment
of juveniles in species that migrate to breed (western rock lobster, mullet, Japanese eel,
barramundi, and anchovy – Pearce and Phillips 1988; Garcia et al. 2001; Kimura et al.
2001; Milton et al. 2005; Hsieh et al. 2009), as red crabs do. It has been suggested that
monsoon rains may affect larvae survival of marine-breeding decapods by altering the salinity
of surrounding water (Adiyodi, 1988). It seems unlikely that this would be the case for red
crabs, since spawning occurs early on in the wet season. However, there is a high variance
in the number of juveniles that return from sea each year after the migration with many
juveniles returning some years and none detected other years (Gibson-Hill, 1947), suggesting
that other oceanic conditions (e.g. temperature and currents, which may be related to ENSO
themselves) may also influence juvenile survival and return.
Here we have demonstrated a relationship between climate variables and the migration
timing of a tropical species. Our results indicate that the changing precipitation patterns
predicted by current climate models will impact migration patterns, which could have par-
ticularly serious consequences for this species, given its dependence on migration for repro-
duction.
95

Chapter 7
Variation in Christmas Island red
crab (Gecarcoidea natalis) migratory
direction 6
7.1 Abstract
Advances in animal-attached technology have made it easier to remotely monitor the be-
haviour and movement of migratory organisms. Here, I attached GPS/ accelerometer tags
to individual Christmas Island red crabs (Gecarcoidea natalis) in order to study their be-
haviour during migration in 2008-09. The GPS data indicate that individuals red crabs
from the same location migrate in completely different directions, contrasting with a pre-
vious study on the same species. The accelerometer data indicate that individual crabs
change their behavioural patterns drastically with the onset of the wet season, a finding that
complements previous observations on annual crab activity levels.
6 Authors: Allison K. Shaw; Status: Manuscript in revision for Australian Journal of Zoology (Short
Communication).
96

7.2 Introduction
Migration is a behavioural phenomenon displayed by a variety of organisms, in which in-
dividuals move to take advantage of seasonally available resources such as potential mates,
food, or suitable climate (Dingle and Drake, 2007). Although migration has attracted the
attention of researchers for over a century, most studies focus on migration timing or mi-
grant behaviour at a single location while we know little about what goes on throughout
the migration. This is due in part to the difficulties of following individuals throughout
their entire migratory journey (Wilcove and Wikelski, 2008). However, the ongoing devel-
opment of animal-attached technology now makes it possible to study individual movement
and behaviour from a distance (Wikelski et al., 2007; Wilson et al., 2008).
Here I consider migratory behaviour of the Christmas Island red crab (Gecarcoidea na-
talis), a land crab native to Christmas Island, Australia. Adult crabs are fully terrestrial
and spend most of the year living in individual burrows, distributed across the entire island.
Their activity patterns seem to be directly driven by water regulation: red crabs are only
active during the wet season and the beginning of the dry season, and remain almost entirely
inside their burrows during the end of the dry season, rarely emerging from their burrows
below humidity levels of 85% (Green, 1997). Red crab larvae require marine water to de-
velop (Wolcott, 1988), so at the start of the wet season (between October and December),
adult crabs leave their burrows and migrate to the islands shore to reproduce (Gibson-Hill,
1947). The migration is closely timed with the lunar cycle, with the main constraint being
the spawning date (Hicks, 1985): females release their eggs at dawn on the high tides during
the last quarter of the lunar cycle (Adamczewska and Morris, 2001a). Once the wet season
begins, the migration starts about three to four weeks before the next potential spawning
date. I attached GPS/accelerometer tags to red crabs prior to migration to study their
migratory behaviour.
97

7.3 Materials and Methods
I attached tags with both GPS tracking and accelerometer technology, developed by the
company E-obs (http://www.e-obs.de), to 31 red crabs in order to record individual be-
haviour and movement during the course of the migration. Crabs were caught and tagged
as they were first observed outside of their burrows, which for most individuals was only
once the wet season started. The onset of the wet season was marked by heavy rain the
night of October 28th, which triggered the emergence of many crabs from their burrows,
and the subsequent migration. Each crab that I caught was sexed, and then weighed with a
spring balance. I only attached tags to individuals weighing at least 250 g, to minimise the
weight burden (each tag weighed 25 g), and I chose individuals at approximately an even
sex ratio. Tags were attached using fast-acting epoxy glue. I tagged 15 crabs on October
29th, 10 on October 30th, and 4 on October 31st, all of which were captured in the same
area (Figure 7.1). Additionally, two crabs that were active earlier in the month were tagged
on October 18th and October 25th, one of which was captured in the same study site and
one was captured at a different location, across the island.
This location of the main study site was chosen as one where the expected migratory
route of the crabs would take them in a southeast direction, through a relatively accessible
region of the island, and end near Greta beach, one of the few spawning locations on the
island that is accessible by foot. The expected migratory route was based on the fact that
crabs from near the study site area had been observed by Parks Australia staff to migrate
southeast in past years, and that the road just southeast of the study site was set up with
crab fencing in anticipation of crabs migrating in that direction again (crab fencing is set up
along sections of the islands roads where the most crabs are expected to cross, to minimise
crab mortality from vehicles).
Each tag was set to record a GPS location every four hours, and acceleration on each
of the three axes every two minutes. The GPS and accelerometer data were stored on each
tag and downloaded directly from recovered tags, or downloaded to a base station receiver
98

Figure 7.1: Map and location of Christmas Island with location. Black lines indicate roads,
grey lines indicate 50 m contour lines, and the black rectangle delineates the region shown
in Figure 7.2.
(if brought within range of the tag). After tagging individual crabs, I went out twice daily
(during morning and evening peak activity times) to locate tagged individuals and download
data, by walking and driving transects across the areas where individuals were last observed
and where they were expected to be.
All work was conducted on Christmas Island between October 2008 and January 2009, un-
der a permit from Parks Australia (RESEARCH – SHAW – RED CRABS – 0908). GPS and
acceleration data from the tags were entered into Movebank (www.movebank.org), a global
repository of animal movement data. Monthly rainfall data was downloaded from the Aus-
tralian government Bureau of Meteorologys website (http://www.bom.gov.au/climate/data/).
99

Parks Australia staff provided geographical data (in ArcGIS form) of physical characteristics
on the island including the locations of roads, contour lines, cleared areas, and locations of
past yellow crazy ant (Anoplolepis gracilipes) colonies that were eradicated by Parks be-
tween 2000 and 2007. The yellow crazy ant is an invasive species that forms high-density
supercolonies that can kill not only red crabs with burrows in the same area, but also any
crabs that move through the area during the migration (Abbott, 2006). Yellow crazy ants
have killed about one third of the red crab population (O’Dowd et al., 2003) but their overall
impact on red crab migratory behaviour is currently unknown. A number of measures have
been taken to control yellow crazy ant populations, such as an aerial distribution of toxic
bait in 2002 and ongoing hand-distribution of bait (Green and O’Dowd, 2009).
7.4 Results
Of the 30 tagged individuals from the main study site, three lost their tags immediately,
and a fourth tag was never relocated (and perhaps was not turned on properly). All of
the remaining 26 tagged individuals migrated out of the tagging area. These individuals
migrated in a variety of different directions (southwest, west, northwest, and northeast; Fig-
ure 7.2, solid lines), although none migrated in the expected migratory direction (southeast
towards Greta beach; Figure 7.2, dashed line). Since tagged individuals were moving in
several directions and traveling longer distances than anticipated, across the islands rough
terrain, simultaneously tracking them all proved impossible. Despite searching continuously
for tagged individuals during peak crab activities times (morning and evening) throughout
the majority of the migratory season, I was not able to track the full migration of any tagged
individual. However, I obtained clear initial migratory directions for at least 6 individuals
(Figure 7.2).
The accelerometers on the tagged red crabs provide a measure of individual activity
level. Individuals displayed a clear diurnal activity pattern with heightened activity between
100

Figure 7.2: Map showing the release site of tagged individuals and their subsequent migration
trajectories (solid lines) – see Figure 7.1 for location within island. The release site was
chosen as one where the expected migration trajectory (dotted line) would end near Greta
beach. Grey solid lines indicate 50 m contours, grey double dashed lines are roads, hashed
regions are cleared areas, and grey regions are locations of past yellow crazy ant (Anoplolepis
gracilipes) colonies that were eradicated by Parks between 2000 and 2007.
approximately 6am and 6pm. Both of the individuals tagged prior to the onset of the wet
season had an abrupt change in behavioural patterns around October 28-29th, coinciding
with the first rainfall and onset of the wet season (Figure 7.3).
7.5 Discussion
The tag GPS data indicate that individuals red crabs from the same initial location migrate
in completely different directions. This finding contrasts with a previous study that used tags
with radio transmitters to monitor red crabs during their migration and found that, although
individuals did not always migrate to the nearest coast, all tracked individuals from a starting
population migrated along similar routes (Figures 7-8 in Adamczewska and Morris 2001a).
While we cannot rule out the possibility that the tags somehow interfered with the crabs
101

Figure 7.3: Individual crab activity level, as measured by the tag accelerometer, changed
drastically with the onset of the wet season (starting with a burst of rainfall on the night of
October 28th). Raw acceleration data for an individual crab along each of 3 axes a) heave
(dorsal-ventral axis), b) surge (anterior-posterior axis), and c) sway (lateral axis), units are
in g (where 1 g=9.81 ms −2 ); and d) daily recorded rainfall data (mm). (Accelerometer data
from October 29-30th is missing due to a recording error).
navigation ability, future studies could test this by, for example, spray painting hundreds of
crabs from the same area and determining their general direction (as in Adamczewska and
Morris 2001a).
Furthermore, the tag GPS data show that no tagged individuals migrated towards Greta
Beach, the expected migratory direction based on consultation with Parks Staff. One possible
explanation for this unexpected behaviour is that, several months prior to this study, a yellow
crazy ant supercolony that has been between the study site and the coast (Figure 2, grey
area) was eradicated by Parks Australia (Parks Staff, pers. comm.). Although no ants were
present during the 2008-09 migration, the supercolony would have been active during the red
102

crab migration in the previous year, and could have influenced red crab choice of migratory
direction. Although further studies are needed to confirm this finding, the potential for
yellow crazy ants to influence red crab migratory behaviour suggests that impact on the red
crab population may be more severe than previously expected. Even if populations of red
crabs are maintained on Christmas Island, the species may still go extinct if adults are not
able to migrate successfully in order to reproduce.
The tag accelerometer data indicate that individual crabs change their behavioural pat-
terns drastically with the onset of the wet season. A number of previous studies have observed
that crab activity above ground increases drastically with the start of the wet season and
that crab activity is generally correlated with rainfall and humidity (Hicks, 1985; Green,
1997; Adamczewska and Morris, 2001a). However, this study is the first to my knowledge
to demonstrate that an individual crab shifts its behaviour with the start of the wet season.
Furthermore, the two crabs that displayed this behaviour were both individuals that had
been active before the wet season started, meaning that the shift from inactivity within the
burrow to activity outside of it alone cannot account for this change in behaviour. Future
studies could use accelerometer tags to monitor how individual activity levels change during
the migration, compared to humidity and rainfall, by carefully tracking a few individuals
throughout their entire migration.
In this study, all tagged crabs migrated, while previous studies have observed that ap-
proximately half of adult crabs migrate in a given migration wave (Hicks, 1985; Green, 1997).
Given that I only attached tags to individuals that were active outside their burrows at the
start of the wet season, this suggests that activity level at the start of a migration wave is
correlated with tendency to migrate, and those individuals that skip migration are slower
to become active. This implies that individual crabs decide early on whether to attempt
migration, presumably basing their decision either on internal cues (e.g. body condition) or
external cues that can be sensed within their burrows (e.g. soil moisture) – hypotheses that
could be tested in future studies.
103

Appendix A
Motives for migration: Mammal
migration data
104

Table A.1: All species listed as migratory in the three databases checked, their migration
patterns (locomotion method if migratory, unclear, unknown, or none observed), their migration
pattern if migratory (refuge, tracking, breeding), and the motivation for movement
if known.
Family Species
Name)
(Common
Artiodactyla
Antiloca- Antilocapra ameripridaecana
(Pronghorn)
Bovidae Addax nasomaculatus
(Addax)
Bovidae Ammotragus
(Aoudad)
lervia
Bovidae Antidorcas marsupi-
alis (Springbok)
Bovidae Bison bison (American
Bison)
Migration
(if known)
Pattern Motivation
Walking [1] Refuge [1] Snow [1]
Walking [2] Tracking?
[2]
Walking [3] Unknown
None [4]
Walking [5] Refuge?/
Tracking?
[5]
Rainfall? [2]
Bovidae Bos mutus (Wild Yak) Walking [6] Unknown
Bovidae Bos javanicus
teng)(Ban-
Walking [7] Tracking [7]
Bovidae Bos sauveli (Kouprey) Unknown
Bovidae Capra caucasica Unknown
(Western Tur)
Bovidae Capra
(Markhor)
falconeri Unknown
Bovidae Capra sibirica Walking [8] Refuge [8] Sodium/ for-
(Siberian Ibex)
age, snow [8]
Bovidae Connochaetes gnou Walking Tracking?
(Black Wildebeest) (historically)
[9]
[9]
Bovidae Connochaetes tau- Walking Tracking Vegetation
rinus
Wildebeest)
(Common [10] [10] [10]
Bovidae Damaliscus lunatus Walking Refuge?/ Water [11]
(Topi)
[11] Tracking?
[11]
Bovidae Damaliscus pygargus Unknown
(Blesbok/bontebok)
Bovidae Eudorcas thomsonii Walking [7] Refuge?/
(Thomson’s Gazelle)
Tracking?
Bovidae Gazella cuvieri (Cu- Walking Unknown
vier’s Gazelle) [12]
105

Family Species
Name)
(Common
Bovidae Gazella dorcas (Dorcas
Gazelle)
Bovidae Gazella gazella
(Mountain Gazelle)
Bovidae Gazella leptoceros
(Slender-horned
Gazelle)
Bovidae Gazella subgutturosa
(Goitered Gazelle)
Bovidae Hemitragus jemlahicus
Tahr)
(Himalayan
Bovidae Naemorhedus goral
Bovidae
(Himalayan Goral)
Nanger dama (Dama
Gazelle)
Bovidae Nanger granti
Migration
(if known)
Walking
[13]
Unknown
Unknown
Walking
(histori-
cally) [14]
Walking
[15]
Unknown
Unknown
Pattern Motivation
Tracking
[13]
Food/water
[13]
Refuge [14] Snow [14]
Unknown
Walking Unknown
(Grant’s Gazelle) [16]
Bovidae Oreamnos americanus Walkng [17] Refuge/
(Mountain Goat)
Tracking
[17]
Bovidae Ovis ammon (Argali) Walking
[18]
Refuge [18] Snow [18]
Bovidae Ovis canadensis Walking Refuge [19] Snow [19]
(Bighorn Sheep) [19]
Bovidae Ovis dalli (Thinhorn Walking Refuge [20] Snow [20]
Sheep)
[20]
Bovidae Pantholops hodgsonii Walking Breeding Calf preda-
(Chiru)
[21] [21] tion/insects
[21]
Bovidae Procapra gutturosa Walking Tracking Primary pro-
(Mongolian Gazelle) [22] [22] ductivity [22]
Bovidae Saiga tatarica (Mon- Walking Refuge [23] Snow [23]
golian Saiga) [23]
Cameli- Camelus ferus (Bac- Unknown
daetrian Camel)
Cameli- Vicugna vicugna None [7]
dae (Vicuña)
Cervidae Alces alces (Eurasian Walking Refuge [24] Snow [24]
Elk)
[24]
106

Family Species
Name)
(Common
Cervidae Capreolus pygargus
Cervidae
(Siberian Roe Deer)
Cervus elaphus (Red
Deer)
Cervidae Hippocamelus antisen-
sis (Taruca)
Cervidae Hippocamelus bisulcus
(Patagonian Huemul)
Cervidae Odocoileus hemionus
(Mule Deer)
Cervidae Odocoileus virginianus
(White-tailed Deer)
Cervidae Rangifer
(Reindeer)
tarandus
Cervidae Rucervus eldii (Eld’s
Deer)
Suidae Phacochoerus
africanus
Warthog)
(Common
Suidae Sus barbatus (Bearded
Pig)
Suidae Sus
Boar)
scrofa (Wild
Carnivora
Canidae Canis
ote)
latrans (Coy-
Canidae Lycaon pictus
Canidae
(African Wild Dog)
Vulpes corsac (Corsac
Fox)
Felidae Puma
(Cougar)
concolor
Felidae Acinonyx
(Cheetah)
jubatus
Felidae Panthera uncia (Snow
Leopard)
Herpestidae
Liberiictis kuhni
(Liberian Mongoose)
Migration
(if known)
Pattern Motivation
Walking
[25]
Refuge [25] Snow [25]
Walking [7] Unknown
Walking [7] Unknown
Walking
(histori-
cally) [26]
Walking
[27]
Walking
[28]
Walking
[29]
Walking
[30]
Unknown
Walking
[31]
Unknown
[32]
None [33]
Unknown
Unknown
Walking
[34]
Walking
[35]
Walking
[36]
Unknown
107
Unknown
Some tracking,
others
refuge [27]
Refuge [28]
Some snow,
others rainfall
[27]
Refuge [29] Predation
[29]
Tracking Water [30]
[30]
Refuge [31] Avoid deep
water [31]
Tracking
[34]
Tracking
[35]
Refuge?/
Tracking?
[36]
Mule deer
[34]
Migratory
prey [35]
Climate?
Prey? [36]

Family Species
Name)
(Common
Musteli- Lontra felina (Marine
dae otter)
Musteli- Lontro provocax
dae
Odobenidae
(Southern river otter)
Odobenus rosmarus
rosmarus
Walrus)
(Atlantic
Migration
(if known)
None [37]
None [38]
Swimming
[39]
Otariidae Callorhinus ursinus Swimming
(Northern fur seal) [40]
Otariidae Eumetopias jubatus Swimming
(Steller sea lion) [41]
Otariidae Otaria flavescens None [42]
(South American sea
lion)
Otariidae Zalophus californi- Swimming
anus
lion)
(California sea [43]
Phocidae Cystophora cristata Swimming
(Hooded seal) [44]
Phocidae Erignathus barbatus
(Bearded seal)
Phocidae Hydrurga leptonyx
Phocidae
(Leopard seal)
Lobodon carcinophaga
(Crabeater seal)
Phocidae Mirounga angustirostris
(Northern
Phocidae
Elephant Seal)
Ommatophoca
(Ross seal)
rossii
Phocidae Pagophilus groenlandicus
(Harp seal)
Phocidae Phoca fasciata
bon seal)
(Rib-
Phocidae Phoca largha (Spotted
seal)
Phocidae Phoca vitulina
bour seal)
(Har-
Pattern Motivation
Unknown
Breeding Temperature
[40]
Breeding
Breeding?
[43]
Breeding?/
Refuge?
Unclear [45] Refuge?
[45]
Unclear [7,
46]
Unclear [47]
Swimming
[48]
Swimming
[49]
Swimming
[50]
Swimming
[52]
Swimming
[53, 54]
None [55]
108
Whelping
grounds
and molting
grounds [44]
Double migration: 1
breeding + 1 refuge [48]
Breeding?/
Refuge?
Tracking?
[51] Breeding?
Unknown
Unknown

Family Species
Name)
(Common
Phocidae Pusa caspica (Caspian
seal)
Phocidae Pusa sibirica (Baikal
Pinnipedia
seal)
Arctocephalus australis
(South American
fur seal)
Halichoerus grypus
Migration
(if known)
Swimming
[56]
Swimming
[57]
None [7]
Pinnipe-
Unclear [58]
dia (Grey seal)
Pinnipe- Monachus monachus None [59]
dia (Mediterranean monk
seal)
Ursidae Ursus arctos (Grizzly
bear)
None [33]
Ursidae Ursus thibetanus (Hi- Walking
Cetacea
malayan black bear) [60]
Balaeni- Balaena mysticetus Swimming
dae (Bowhead whale) [61]
Balaenidae
Balaenidae
Balaenidae
Balaenopteridae
Balaenopteridae
BalaenopteridaeBalaenopteridaeBalaenopteridae
Eubalaena australis
(Southern right
whale)
Eubalaena glacialis
(North Atlantic right
whale)
Eubalaena japonica
(North Pacific right
whale)
Balaenoptera acutorostrata
(Common
Minke whale)
Balaenoptera
bonaerensis (Antarctic
Minke whale)
Balaenoptera borealis
(Sei whale)
Balaenoptera edeni
(Bryde’s whale)
Balaenoptera musculus
(Blue whale)
Swimming
[63]
Swimming
[63]
Swimming
[63]
Swimming
[65]
Swimming
[67]
Swimming
[66]
Unclear [68,
69]
Swimming
[70]
109
Pattern Motivation
Breeding
Unknown
Tracking
[60]
Refuge/
Tracking
[61, 62]
Breeding
[64]
Breeding
[63]
Breeding
[63]
Breeding
[66]
Breeding
[66]
Breeding
[66]
Breeding
[71]
Ice [62] /
prey [61]
Food, calf
survival [66]
Food, calf
survival [66]
Food, calf
survival [66]
Food, calf
survival [71]

Family Species
Name)
(Common
Balaenop- Balaenoptera physalus
teridae
Balaenopteridae
Delphinidae
Delphinidae
Delphinidae
DelphinidaeDelphinidae
DelphinidaeDelphinidaeDelphinidae
Delphinidae
Delphinidae
Delphinidae
Delphinidae
Delphinidae
(Fin whale)
Megaptera novaengliae
(Humpback
whale)
Cephalorhynchus
commersonii (Com-
merson’s dolphin)
Cephalorhynchus eutropia
(Chilean dol-
phin)
Cephalorhynchus
heavisidii (Heaviside’s
dolphin)
Delphinus delphis
(Common dolphin)
Globicephala melas
melas (Long-finned
pilot whale)
Grampus griseus
(Risso’s dolphin)
Lagenodelphis hosei
(Fraser’s dolphin)
Lagenorhynchus acutus
(Atlantic white-
sided dolphin)
Lagenorhynchus
albirostris (White-
beaked dolphin)
Lagenorhynchus
australis (Peale’s
dolphin)
Lagenorhynchus cruciger
(Hourglass dol-
phin)
Lagenorhynchus
obscurus (Dusky
dolphin)
Orcaella brevirostris
(Irrawaddy dolphin)
Migration
(if known)
Swimming
[71]
Swimming
[61]
Swimming
[72]
Unknown
[73]
Unknown
[73]
Swimming
[74]
Swimming
[73]
Swimming
[73]
Unknown
[73]
Swimming
[73]
Swimming
[73]
Swimming
[73]
Unclear [73]
Swimming
[73]
Swimming
[73]
110
Pattern Motivation
Breeding
[71]
Breeding
[66]
Tracking?
[73]
Tracking?
[74]
Tracking?
[75]
Breeding?
[73]
Tracking?
[73]
Unknown
Breeding?
[73]
Tracking?
[73]
Refuge?/
Tracking?
[73]
Food, calf
survival [71]
Food, calf
survival [66]
Maybe fish
[73]
Prey, Loligo
pealei [75]
Temperature
[73]
Prey [73]
Possibly anchovy
[73]
Water level?
prey? [73]

Family Species (Common
Name)
Delphinidae
Delphinidae
Orcaella heinsohni
(Australian snubfin
dolphin)
Orcinus orca (Killer
Whale/ Orca)
Delphini- Sotalia fluviatilis (Tudaecuxi/
Buoto dolphin)
Delphini- Sousa chinesis (Indodae
Pacific
dolphin)
humpbacked
Delphini- Sousa teuszii (Atdaelantic
dolphin)
hump-backed
Delphini- Stenella attenuata
dae (Pantropical
dolphin)
spotted
Delphini- Stenella clymene
dae (Clymene dolphin)
Delphini- Stenella coeruleoalba
dae (Striped dolphin)
Delphini- Stenella longirostris
dae (Spinner dolphin)
Delphini- Tursiops aduncus (Indaedian
Ocean bottlenose
dolphin)
Delphini- Tursiops truncatus
dae (Bottlenose dolphin)
Eschrich- Eschrichlius robustus
tiidae (Grey whale)
Iniidae Inia geoffrensis (Amazon
river dolphin)
Mono- Delphinapterus leucas
dontidae (Beluga)
Monodontidae
Neobalaenidae
Monodon monoceros
(Narwhal)
Caperea marginata
(Pygmy right whale)
Migration
(if known)
Unclear [76]
Swimming
[73, 77]
Unknown
[73]
Unclear [73]
Swimming
[73]
Swimming
[73]
Unknown
[73]
Swimming
[73]
Swimming
[73]
Unknown
[73]
Swimming
[81]
Swimming
[61]
Swimming
[82]
Swimming
[66]
Swimming
[73]
Unclear [69]
111
Pattern Motivation
Tracking,
Refuge?
Unknown
[73]
Unknown
[73]
Unknown
Unknown
Unknown
Pinnipeds
[77, 78], penguins
[78],
salmon [79],
herrings [80]
Breeding Food, calf
Tracking?
survival [66]
Migrating
[82] fish [82]
Unknown Food [83],
Ice, maybe
Breeding/
molt [61]
Calf sur-
Refuge [61] vival?
Ice [84]?
[61]

Family Species (Common
Name)
Phocoenidae
Phocoenidae
PhocoenidaePhocoenidaePhocoenidae
Neophocaena asiaeorientalis(Narrowridged
finless por-
poise)
Neophocaena phocaenoides
porpoise)
(Finless
Phoceona dioptrica
(Spectacled porpoise)
Phocoena phocoena
(Harbour porpoise)
Phocoena spinipinnis
(Burmeister porpoise)
Phocoeni- Phocoenoides dalli
dae (Dall’s porpoise)
Physeter- Physeter macroidaecephalus
whale)
(Sperm
Platanist- Platanista gangetica
idae (Ganges Susu)
Ponto- Pontoporia blainvillei
poriidae (La Plata dolphin)
Ziphiidae Berardius arnuxii
(Arnoux’s
whale)
beaked
Ziphiidae Berardius bairdii
(Baird’s
whale)
beaked
Ziphiidae Hyperoodon ampullatus
(Northern
bottlenose whale)
Ziphiidae Mesoplodon grayi
(Gray’s
whale)
beaked
Chiroptera
Embal- Diclidurus albus
lonuridae (Northern ghost bat)
Embal- Taphozous nudiventris
lonuridae (Naked-rumped tomb
bat)
Migration
(if known)
Unknown
Swimming
[73]
Unknown
[73]
Swimming
[73]
Swimming
[73]
Unclear [73,
85]
Swimming
[86]
Swimming
[66]
Unknown
[73]
Swimming
[73]
Swimming
[73]
Swimming
[73]
Unknown
[73]
Unclear [87]
Pattern Motivation
Unknown Temperature?
[73]
Unknown Ice,
[73]
food?
Unknown Temperature?,
[73]
prey?
Tracking?
[86]
Tracking?
[66]
Refuge?
[73]
Unknown
Unknown
Flying [88] Unknown
112
Pack ice [73]

Family Species (Common
Name)
Hipposideridae
MolossidaeMolossidae
Molossidae
Molossidae
Molossidae
Molossidae
Molossidae
Hipposideros commersoni
(Commerson’s
leaf-nosed bat)
Nyctinomops macrotis
(Big free-tailed bat)
Otomops madagascariensis(Madagascar
free-tailed
bat)
Otomops martiensseni
(Large-eared free-
tailed bat)
Tadarida australis
(White-striped free-
tailed bat)
Tadarida brasiliensis
(Mexican free-tailed
bat)
Tadarida insignis
(East Asian free-
tailed bat)
Tadarida latouchei
(La Touche’s freetailed
bat)
Tadarida teniotis (Eu-
Migration
(if known)
Unknown
Flying [33] Refuge [33]
Unknown
Unclear [89,
90]
Flying [91] Refuge/
Tracking
Flying [33,
93]
Unknown
Unknown
Pattern Motivation
[91, 92]
Unknown
Temperature,humidity
[92]
Molossi-
None [94,
daeropean free-tailed bat) 95]
Natalidae Natalus stramineus Unknown
(Mexican funnel-eared
bat)
Nycteri- Nycteris thebaica Flying [96] Unknown
dae (Common
bat)
slit-faced
Phyllo- Choeronycteris mexi- Flying [33] Refuge/ Blooming
stomidaecana (Mexican long-
Tracking plants [33]
tongued bat)
[33]
Phyllo- Leptonycteris nivalis Flying [33, Unknown Maternity
stomidae (Big long-nosed bat) 97, 98]
colonies?
[33]
Phyllo- Leptonycteris Flying [33] Unclear [99, Food [99,
stomidae yerbabuenae (South-
100, 101] 100]
ern long-nosed bat)
113

Family Species (Common
Name)
Phyllostomidae
Pteropodidae
Pteropodidae
Pteropodidae
PteropodidaePteropodidae
PteropodidaePteropodidaeRhinolophidae
RhinolophidaeRhinolophidae
Rhinolophidae
Rhinolophidae
Rhinolophidae
Rhinolophidae
Sturnira lilium (Little
yellow-shouldered
bat)
Balionycteris maculata
(Spotted-winged
fruit bat)
Eidolon helvum
(Straw-coloured fruit
bat)
Nanonycteris veldkampi
(Veldkamp’s
bat)
Pteropus alecto (Cen-
tral flying fox)
Pteropus poliocephalus
(Grey-headed flying
fox)
Pteropus scapulatus
(Little red flying fox)
Rousettus egyptiacus
(Egyptian rousette)
Rhinolophus blasii
(Peak-saddle
shoe bat)
horse-
Rhinolophus capensis
(Cape horseshoe bat)
Rhinolophus euryale
(Mediterranean
horseshoe bat)
Rhinolophus ferrumequinum
(Greater
horseshoe bat)
Rhinolophus hipposideros
(Lesser
horseshoe bat)
Rhinolophus megaphyllus
(Eastern
horseshoe bat)
Rhinolophus mehelyi
(Mehely’s horseshoe
bat)
Migration
(if known)
Unclear
[102]
Unknown
Pattern Motivation
Refuge?
[102]
Flying [103] Tracking
[103, 104]
Flying [106] Tracking
[106]
Fruit [104,
105, 106]
Fruit [106]
Unclear
[107]
Flying [108] Tracking Fruit, mating
[108, 109]
Flying [91,
107]
Unclear
[110]
None [95]
None [111]
Flying [95,
112]
Unclear
[112, 113]
Unclear
[112]
None [11]
Unknown
Breeding?/
Refuge?
Breeding?/
Refuge?
[113]
Temperature
[113]
Refuge Caves [112]
Flying [112] Refuge? Caves [112]
114

Family Species (Common
Name)
Vespertilionidae
Vespertilionidae
VespertilionidaeVespertilionidaeVespertilionidaeVespertilionidae
VespertilionidaeVespertilionidaeVespertilionidaeVespertilionidae
Vespertilionidae
Vespertilionidae
VespertilionidaeVespertilionidaeVespertilionidaeVespertilionidaeVespertilionidae
Barbastella barbastellus
(Western
barbastelle)
Corynorhinus
rafinesquii
(Rafinesque’s bigeared
bat)
Eptesicus fuscus (Big
brown bat)
Eptesicus nilssonii
(Northern bat)
Eptesicus serotinus
(Serotine)
Lasionycteris noctivagens
bat)
(Silver-haired
Lasiurus borealis
(Eastern red bat)
Lasiurus
(Hoary bat)
cinereus
Lasiurus seminolus
(Mahogany bat)
Miniopterus natalensis
(Natal long-
fingered bat)
Miniopterus schreibersii
(Schreiber’s long-
fingered bat)
Myotis auriculus
(Southwestern myotis)
Myotis austroriparius
(Southeastern myotis)
Myotis bechsteinii
(Bechstein’s myotis)
Myotis blythii (Lesser
mouse-eared myotis)
Myotis brandtii
(Brandt’s myotis)
Myotis capaccinii
(Long-fingered bat)
Migration
(if known)
Unclear [94,
95]
None [33]
Flying [33]
Unclear [94]
Refuge
114]
[33,
Unclear [94,
95]
Flying [33] Refuge
Flying [33] Refuge
Flying [33] Refuge
Unclear [33]
Pattern Motivation
Flying [103] Refuge [103] Hibernacula
caves [103]
Flying [94,
95]
Flying [33] Refuge [33]
None [33]
None
95]
[94,
Flying [115] Unknown
Refuge [94] Winter caves
[94, 95]
Flying [116] Refuge [94] Winter
roosts [94]
Flying [94] Refuge [94] Winter
roosts [94]
115

Family Species
Name)
(Common
Vesper- Myotis dasycneme
tilionidae
Vespertilionidae
Vespertilionidae
(Pond myotis)
Myotis daubentonii
(Daubenton’s myotis)
Myotis emarginatus
(Geoffroy’s bat)
Migration
(if known)
Pattern Motivation
Flying [94] Refuge [94] Winter
roosts [94]
Flying [116] Refuge [116] Winter
roosts [94,
Flying [94,
95]
Refuge/
Tracking
[94]
116]
Winter
roosts,
swarming
caves [94]
Vesper- Myotis evotis (Long- Unclear [33]
tilionidaeeared myotis)
Vesper- Myotis grisescens Flying [33] Refuge [33] Winter caves
tilionidae (Gray myotis)
[33]
Vesper- Myotis keenii (Keen’s Unknown
tilionidae myotis)
[33]
Vesper- Myotis myotis Flying [94, Refuge/ Winter
tilionidae (Greater mouse-eared 95] Tracking roosts,
bat)
[94] swarming
caves [94]
Vesper- Myotis mystacinus Flying [94, Refuge [94] Winter
tilionidae (Whiskered myotis) 95]
roosts [94]
Vesper- Myotis nattereri (Nat- Flying [94] Refuge/ Winter
tilionidaeterer’s bat)
Tracking roosts,
[94] swarming
caves [94]
Vesper- Myotis septentrionalis None [33]
tilionidae (Northern
myotis)
long-eared
Vesper- Myotis sodalis (Indi- Flying [33] Refuge [33] Hibernation
tilionidaeana bat)
caves [33]
Vesper- Myotis yumanensis Unclear [33]
tilionidae (Yuma myotis)
Vesper- Nyctalus lasiopterus Flying [94] Unclear
tilionidae (Giant noctule)
Vesper- Nyctalus leisleri Flying [94, Refuge [94]
tilionidae (Lesser noctule) 95]
Vesper- Nyctalus noctula Flying [94] Refuge
tilionidae (Noctule)
Vesper- Nycticeius humeralis Flying [33] Refuge [33]
tilionidae (Evening bat)
Vesper- Pipistrellus kuhlii None [94]
tilionidae (Kuhl’s pipistrelle)
116

Family Species (Common
Name)
Vespertilionidae
Vespertilionidae
Pipistrellus nathusii
(Nathusius’ pip-
istrelle)
Pipistrellus pipistrellus
pipistrelle)
(Common
Pipistrellus savii
(Savi’s pipistrelle)
Plecotus auritus
(Brown big-eared bat)
Plecotus austriacus
Migration
(if known)
Pattern Motivation
Flying [94] Refuge [94]
Unclear [95]
Vesper-
Unclear [94,
tilionidae
95, 116]
Vesper-
Unclear [94,
tilionidae
95]
Vesper-
None [94,
tilionidae (Gray big-eared bat) 95]
Vesper- Vespertilio murinus Flying [94, Refuge [94]
tilionidae (Particoloured bat) 95]
Perissodactyla
Equidae Equus burchelli Walking Tracking Water
(Plains zebra) [117]
Equidae Equus grevyi (Grevy’s Walking Tracking Water [118]
zebra)
[118] [118]
Equidae Equus hemionus (Kulan)
Unknown
Equidae Equus kiang (Tibetan Unclear Tracking?
wild ass)
[119] [119]
Rhino- Ceratotherium simum Unknown
cerotidae
Primates
(White rhinoceros) [7, 120]
Cebidae Callithrix penicillata Unknown
(Black-tufted-ear
marmoset)
Homini- Gorilla beringei None [121]
dae beringei
gorilla)
(Mountain
Homini- Gorilla beringei Unknown
dae graueri (Eastern
Homini-
lowland gorilla)
Gorilla gorilla diehli Unknown
dae (Cross River gorilla)
Homini- Gorilla gorilla gorilla Unknown
dae (Western lowland gorilla)
117

Family Species
Name)
(Common
Proboscidea
Elephant- Elephas maximus
idae
Elephantidae
Rodentia
CricetidaeCriceti-
(Asian elephant)
Loxodonta africana
(African elephant)
Migration
(if known)
Unknown
Unknown
Lagurus lagurus Unknown
(Steppe lemming)
Myopus schisticolor Unknown
dae (Wood lemming)
Sciuridae Tamias dorsalis (Cliff Walking
Sirenia
chipmunk)
[122]
Dugong- Dugong dugon Swimming
idae (Dugong)
[123, 124]
Trichechi- Trichechus inunguis Swimming
dae (Amazonian manatee) [125]
Trichechi- Trichechus manatus Swimming
dae latirostris
manatee)
(Florida [126]
Trichechi- Trichechus manatus Unclear
dae manatus
manatee)
(Antillean [127]
Trichechi- Trichechus senegalen- Unclear
daesis (West African [126, 127]
manatee)
Table References
Pattern Motivation
Tracking
[122]
Refuge [123, Temperature
124] [123, 124]
Refuge [125] Predation
[125]
Refuge [126] Temperature
[126]
Refuge?
[127]
Refuge?
[126]
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129

Appendix B
Migration or residency: Extra figures
& details
130

Table B.1: All model parameters and values.
FIXED PARAMETERS
Parameter Meaning Simulation value
N Number of individuals 4, 096
rR Repulsion radius 0.00125 = 1BL
rA Attraction/alignment radius 6 rR = 0.0075
ρ Initial density of individuals 2/(r2 dt Simulation delta-time
R ) = 1.28x106
0.1
s Speed 0.00125 = 1BL
∆y Distance per step s dt = 0.1BL
y0 Starting y-coordinate 0.2
θmax Maximum turn angle allowed per step 2 dt = 0.2 radians
G Number of generations 500
T Number of steps per generation 5, 000
C Number of copies of each generation 25
µ Standard deviation of mutation Gaussian 0.01
H Direction of historical movement [0 1]
R Direction of resource-based movement Location-dependent
S Direction of social-based movement Location-dependent
VARIED PARAMETERS
Parameter Meaning Simulation value
ψ Global trend Varied (as indicated)
pq Patch quality Varied (as indicated)
pw Patch width Varied (as indicated)
σ Standard deviation of H Varied (as indicated)
EVOLVED PARAMETERS
Parameter Meaning Simulation value
ωH Weight given to historical direction Evolved (0 ≤ ωH ≤ 1)
ωS Weight given to social direction Evolved (0 ≤ ωS ≤ 1)
ωR Weight given to resource direction Evolved (0 ≤ ωR ≤ 1)
131

Figure B.1: Individuals can easily evolve the correct direction of H de novo. This shows the
result of a test simulation where individuals were not given the vector H as [0 1] but instead
started with random directions for the vector H and evolved this direction over the course
of the simulation in addition to evolving the ω-values.
132

Figure B.2: The information usage strategies and movement behavior that evolved in environments
(a) with different values of ψ and constant values of pq (10) and pw (8 BL), under
the (b) cumulative (c) end-point and (d) minimum fitness functions. In the ternary plots,
values of ωH, ωS, and ωR are indicated by dashed, dotted, and solid lines, respectively. See
Figure 3.2 for alternative version and more details. Note that the scale on the x-axes in the
bottom row are different than top two for migration distance.
133

Figure B.3: The information usage strategies and movement behavior that evolved in environments
(a) with different values of pq and constant values of ψ (0.2) and pw (8 BL), under
the (b) cumulative (c) end-point and (d) minimum fitness functions. See Figure 3.2 and B.2
captions for more details. Note that the scale on the x-axes in the bottom row are different
than top two for migration distance.
134

Figure B.4: The information usage strategies and movement behavior that evolved in environments
(a) with different values of pw (in BL) and constant values of ψ (0.2) and pq (10),
under the (b) cumulative (c) end-point and (d) minimum fitness functions. See Figure 3.2
and B.2 captions for more details. Note that the scale on the x-axes in the bottom row are
different than top two for migration distance.
135

B.1 Appendix: Analytic Model
We can understand the selection for residency or migration in our simulations by constructing
a simple analytic model. Consider a resource distribution, R(y, t), that consists of a linear
trend of slope ψ in the y direction plus some amount of patchiness that varies in space and
time, δ(y, t), where E δ(y, t) = 0. The resource value at each location at each time is given
by
R(y, t) = ψy + δ(y, t) . (B.1)
For simplicity, we assume that the distribution of resource patches is uncorrelated in space
and time. Individuals start at position y0 and have one of two behaviors: 1) they are resident
and stay at the same y location, but can look for locally good resource patches or 2) they
are migrant and can move at most ∆y per step in the y direction, for a total of T steps
during a season. (Note that this does not assume anything about the information used by
individuals, only what types of movement they have.)
B.1.1 Conditions favoring migration
Under a cumulative fitness function, an individual’s fitness is the sum of the value of the
resource it passes through at every time step over the course of the generation. The fitness
of a resident is given by
φR =
T
R(y0, t) (B.2a)
t=1
= T ψy0 +
136
T
δ(y0, t) . (B.2b)
t=1

Let δres be the average quality of resource patch that a resident encounters (where resident
individuals are able to locate better than average resources; δres > 0) and the resident fitness
is
The fitness of a migrant is given by
φM =
φR ≈ T ψy0 + T δres . (B.2c)
T
R(y0 + t∆y, t) (B.3a)
t=1
= T ψy0 + ψ∆y
T
t +
t=1
T
δ(y0 + t∆y, t) . (B.3b)
Assuming migrants are too busy migrating to locate good resource patches, and just get the
average patch quality (0), then
t=1
T (T + 1)
φM ≈ T ψy0 + ψ∆y
2
. (B.3c)
We can expect that migration should evolve under conditions where migrants have higher
fitness than residents, i.e. when
(T + 1)
ψ∆y
2
> δres . (B.4)
Alternatively, under an end-point fitness, an individual’s fitness is equal to the resource
value at its final location after T steps. In this case, the fitness of a resident is given by
137

and the fitness of a migrant is given by
Migration will be favored if
φR = R(y0, T ) (B.5a)
≈ ψy0 + δres
(B.5b)
φM = R(y0 + T ∆y, T ) (B.6a)
≈ ψy0 + ψT ∆y . (B.6b)
ψT ∆y > δres . (B.7)
Migration will occur under a broader range of ecological conditions (in terms of ψ and δ) for
an end-point fitness than for a cumulative fitness, since ψ∆yT > ψ∆y
T +1.
To compare the
2
above predictions with our simulation results, we need to estimate a value for δres. Figure B.5
shows the results if we set δres to be approximately 0.5 of a standard deviation of the resource
distribution as generated in the simulation model, which are quite a good approximation of
the simulation results shown in Figure B.2b-c and B.3b-c.
Note that in this analytic model (where we consider the resource mean) we cannot draw
meaningful conclusions under the minimum fitness function (where fitness depends on the
resource variance). Similarly to draw any conclusions with respect to patch width pw, we
would need to include spatial correlation of resource patches.
138

Figure B.5: Migratory distance as a function of seasonality ψ (a-b), and patch quality pq
(c-d) as predicted by the simple analytic model under the cumulative (a, c) and end-point
(b, d) fitness functions.
B.1.2 Transition between residency and migration
In our simulation results, we see a sharp transition in migratory distance, i.e. individuals
should either be residents and not move much, or be migrants and migrate as far as possible
during the time allowed. In reality, animals display a range of migratory distances. We
can use the analytic model described above to determine the optimal migration distance
as follows. Consider an individual that spends with a strategy intermediate between full
residency and full migration, that spends γ of the time being a migrant and 1−γ of the time
being a resident. Assuming a cumulative fitness function and combining equations (B.2c)
and (B.3c), the fitness of this type is given by
φ(γ) =
T
t=1
T (T + 1)
R(y0 + t∆yγ, t) = T ψy0 + ψ∆yγ + (1 − γ)T δres
2
139
(B.8)

We determine the value of γ that optimizes fitness by taking the partial derivative
∂φ
∂γ
setting it to zero, and solving, to get
γ ∗ = 1 if
γ ∗ = 0 if
= ψ∆y T (T + 1)
2
− T δres
(B.9)
ψ∆y(T + 1)
> δres
2
(B.10a)
ψ∆y(T + 1)
< δres .
2
(B.10b)
This demonstrates that, under the assumptions of our model, an individual should either be
fully resident or fully migratory, and fitness is never optimized by an intermediate amount
of migration.
However, consider the alternative version of an intermediate migratory strategy, where
an individual first spend T1 migrating and then spend T2 = T − T1 as a resident. In this
scenario, the individual’s fitness is:
T1
T2
φ = R(y0 + t∆y, t) + R(y0 + T1∆y, t) (B.11a)
t=1
≈ T ψy0 + ψ∆y
t=1
− 1
2 T 2 1 + 1
2 T1
+ T T1
+ (T − T1) δres
We determine the value of T1 that optimizes fitness by taking the partial derivative
∂φ
∂T1
= ψ∆y −T1 + 1
+ T − δres
2
(B.11b)
(B.12)
setting it to zero, and solving, to get T1 = T + 1 1 − 2 ψ∆y δres. Here we can see that for in
140

the extreme for very high patchiness (δres >> ψ) that T2 ≈ T , meaning that an individual
should spend all of its time being a resident. In the other extreme, when patchiness is very
low (δres

Appendix C
Partial migration: ESS calculation
details
142

To determine under what conditions an individual should skip a breeding opportunity, we
calculate θ ∗ (the ESS value of θ) as follows.
Without stochasticity, the population size is constant and θ ∗ can be found analytically
(Metz et al., 1992; Ferriere and Gatto, 1995; Caswell, 2001; McGill and Brown, 2007). The
growth rate of a mutant type (with θ = θM) in a resident population (with θ = θR) is given
by
G(θM, θR) = max(λJ) (C.1)
where λJ are the eigenvalues of the Jacobian, J, for a mutant in a resident population given
by
⎡
J ¯N(θR)
⎢
= ⎣ θMσr + θMφ1 DDR σr + φ2 DDR
(1 − θM)σs
0
⎤
⎥
⎦ (C.2)
where ¯ N(θR) = [ ¯ N1(θR), ¯ N2(θR)] is the resident population size and DDR is the resident
density-dependence at equilibrium, given by equation (4.4). The ESS is the value θ ∗ such
that
G(θ ∗ , θ ∗ ) > G(θM, θ ∗ )
or
G(θ ∗ , θ ∗ ) = G(θM, θ ∗ ) and G(θ ∗ , θM) > G(θM, θM) (C.3)
for all values of θM. If θ ∗ = 1, then all sexually mature adults reproduce every season. Any
value of θ ∗ < 1 indicates partial migration, where at least a fraction of the population forgoes
reproduction and migration in a given season.
With stochasticity, the population size is no longer constant and the value of θ ∗ must
be calculated in terms of the average growth rate, where the average is taken across all the
143

population sizes that the system visits (Metz et al., 1992; Ferriere and Gatto, 1995; Caswell,
2001; McGill and Brown, 2007). The average growth rate of a mutant type (with θ = θM)
in a resident population (with θ = θR) is given by
where
Gavg(θM, θR) = |G(θM, θR)| 1
T (C.4)
G(θM, θR) = max(λJ ′) (C.5)
and λJ] are the eigenvalues of the composite Jacobian, J ′ , for a mutant in a resident popu-
lation given by
J ′
= J N(θR, 1) ∗ J N(θR, 2) ∗ · · · ∗ J N(θR, T ) . (C.6)
Here, J N(θR, t) is the Jacobian for a mutant in a resident of population size N(θR, t) given
by equation (C.2) and T is the number of points in the resident population’s attractor (if
the attractor is chaotic or stochastic, take T → ∞), and N(θR, 1), N(θR, 2), · · · , N(θR, T )
are the resident population sizes at each attractor point. The ESS is the value θ ∗ such that
Gavg(θ ∗ , θ ∗ ) > Gavg(θM, θ ∗ )
or
Gavg(θ ∗ , θ ∗ ) = Gavg(θM, θ ∗ ) and Gavg(θ ∗ , θM) > Gavg(θM, θM) (C.7)
for all values of θM. This method produces the same results as equation (C.3) above if the
resident goes to a fixed-point (T = 1).
If the distribution of population sizes can be described in closed form, the entire cal-
culation could be done analytically. Benaïm and Schreiber (2009, section 5.1) analyze an
144

unstructured model with density-dependence in a correlated environment, but are only able
to get a closed form description of the distribution of population sizes when the correlation
is close to perfect. In our case, the environment (as defined by both the random fecundity
values, which are not correlated, and resident population size, which is correlated) is only
partially correlated, therefore a closed form solution is likely impossible. However, it may
be possible to derive an analytic expression for the viability of a population in a stochas-
tic environment essentially a stochastic version of equation (4.3) – by assuming a different
form of stochasticity (gamma-distributed noise) and following the methodology of Roerdink
(1988) and Benaïm and Schreiber (2009).
Since we could not describe the distribution of resident population in closed form in the
stochastic version of our model, we had to find the ESS value of θ via iterative simulations as
follows. First we picked a value of θ as θR and simulated the resident population for 100 steps
from a random initial condition. We then simulated the resident population for 10, 000 more
steps to generate a distribution of resident population sizes, N(θR, 1), N(θR, 2), · · · , N(θR, T ).
If the resident population was not viable (decayed to a population size less than one), the
process was started over with a different value of θR. If the resident population was viable,
we then calculated the growth rate of several different mutant types (with θM values near
θR) analytically, according to equations (C.4-C.6). If any mutant had a higher growth rate
than the resident type, then the mutant type with the highest average growth rate according
to (C.4) was saved as the new resident type (new value for θR). The process was repeated
from the beginning until a resident type, θ ∗ , was found that resisted invasion by a mutant
(grew faster than all mutant types) for 5 sequential iterations. This was considered to be
the ESS value of θ.
145

Appendix D
Intermittent breeding: Stability
analysis
146

Using logic similar to Levin and Goodyear (1980), we can determine the stability of the
equilibria of model (5.1), which is governed by the Jacobian
where
⎡
H1
⎢ u1 ⎢
J = ⎢ 0
⎢ .
⎣
H2
0
u2
.
H3
0
0
.
. . .
. . .
. . .
.. .
Hn
⎥
0 ⎥
0 ⎥
. ⎥
⎦
0 0 . . . un−1 0
Hi = vi + θi φi DD + K N 1
∂DD
The eigenvalues, λ, of J are the roots of the characteristic equation, given by
λ n − H1 λ n−1 − H2 u1 λ n−2 − H3 u1 u2 λ n−3 − . . . − Hn u1 u2 . . . un−1 = 0 . (D.1)
Since li = i−1
j=1 uj, this can be rewritten as
λ n
1 −
n
i=1
λ −i liHi
∂Ni
⎤
eq
.
= 0 . (D.2)
At the trivial equilibrium, Hi = vi + θi φi, which is positive for all i. In this case, J is a
non-negative irreducible matrix, so by the Perron-Frobenius theorem we know that it has a
positive real dominant eigenvalue, and to find it we solve
1 =
n
λ −i li Hi . (D.3)
i=1
147

The right hand side (RHS) of (D.3) is a monotonically decreasing function of λ. If λ = 0,
the RHS is infinite, and if λ = 1, the RHS becomes
=
n
i=1
li vi +
n
i=1
li θi φi
(D.4)
= 1 − L + K . (D.5)
Therefore the dominant eigenvalue of J, the value of λ that satisfies (D.3), will be less than
1 as long as 1 − L + K < 1 or equivalently K < L. This is the stability condition for the
trivial equilibrium.
At the non-trivial eqiulibrium, DD = L/K. Since DD(0) = 1 and ∂DD/∂Ni ≤ 0, we
require that L < K in order for the non-trivial equilibrium to exist biologically (N i ≥ 0).
This is one of the stability conditions for the non-trivial equilibrium. There is an additional
set of stability requirements, which are harder to derive analytically since for the non-trivial
equilibrium,
Hi = vi + θiφiDD + KN 1
∂DD
∂Ni
eq
, (D.6)
which is no longer always positive and therefore we cannot use the Perron-Frobenius theorem.
When these stability conditions are violated the system goes through a series of period-
doubling bifurcations.
148

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