Ecological Monographs, 84(3), 2014, pp. 355–372
Ó 2014 by the Ecological Society of America
Competition, predation, and migration: individual choice patterns
of Serengeti migrants captured by hierarchical models
J. GRANT C. HOPCRAFT,
1,2,8
J. M. MORALES,
3
H. L. BEYER,
4
MARKUS BORNER,
1,2
EPHRAIM MWANGOMO,
5
A. R. E. SINCLAIR,
6
HAN OLFF,
7
AND DANIEL T. HAYDON
1
1
Boyd Orr Centre for Population and Ecosystem Health, College of Medical Veterinary and Life Sciences,
University of Glasgow, Glasgow G12 8QQ United Kingdom
2
Frankfurt Zoological Society, Box 14935, Arusha, Tanzania
3
Laboratorio ECOTONO, INIBIOMA, Universidad Nacional del Comahue, Quintral 1250, (8400) Bariloche, Argentina
4
ARC Centre of Excellence for Environmental Decisions, Centre for Biodiversity and Conservation Science,
University of Queensland, Brisbane, Queensland 4072 Australia
5
Tanzania National Parks, P.O. Box 3134, Arusha, Tanzania
6
Centre for Biodiversity Research, University of British Columbia, 6270 University Boulevard,
Vancouver, British Columbia V6T 1Z4 Canada
7
Centre for Ecological and Evolutionary Studies, University of Groningen, P.O. Box 11103, 9700 CC Groningen, The Netherlands
Abstract. Large-herbivore migrations occur across gradients of food quality or food
abundance that are generally determined by underlying geographic patterns in rainfall,
elevation, or latitude, in turn causing variation in the degree of interspecific competition and
the exposure to predators. However, the role of top-down effects of predation as opposed to
the bottom-up effects of competition for resources in shaping migrations is not well
understood. We studied 30 GPS radio-collared wildebeest and zebra migrating seasonally in
the Serengeti-Mara ecosystem to ask how predation and food availability differentially affect
the individual movement patterns of these co-migrating species. A hierarchical analysis of
movement trajectories (directions and distances) in relation to grass biomass, high-quality
food patches, and predation risk show that wildebeest tend to move in response to food
quality, with little attention to predation risk. In contrast, individual zebra movements reflect
a balance between the risk of predation and the access to high-quality food of sufficient
biomass. Our analysis shows how two migratory species move in response to different
attributes of the same landscape. Counterintuitively and in contrast to most other animal
movement studies, we find that both species move farther each day when resources are locally
abundant than when they are scarce. During the wet season when the quality of grazing is at
its peak, both wildebeest and zebra move the greatest distances and do not settle in localized
areas to graze for extended periods. We propose that this punctuated movement in high-
quality patches is explained by density dependency, whereby large groups of competing
individuals (up to 1.65 million grazers) rapidly deplete the localized grazing opportunities.
These findings capture the roles of predation and competition in shaping animal migrations,
which are often claimed but rarely measured.
Key words: center of attraction and repulsion; correlated random walk; forage quality; GPS radio-
collar data; homing; landscape of fear; MCMC simulation; predator-sensitive foraging; Serengeti-Mara
ecosystem; wildebeest, Connochaetes taurinus; zebra, Equus burchelli.
INTRODUCTION
The global decline of terrestrial mammal migrations
has raised serious concerns about the persistence of this
unique landscape-scale biological process (Harris et al.
2009). Because migrations rely on large contiguous
habitats across regional environmental gradients, the
collapse of migratory systems around the world is an
indication that these remaining wild areas are succumb-
ing to increased human pressure, particularly habitat
loss and landscape fragmentation (Bolger et al. 2008).
By moving large distances, migrants are able to escape
the limitations of local food supply, resulting in
superabundant populations that have unusually large
impacts on ecosystems (Fryxell et al. 1988; Hopcraft et
al., in press). For example, the seasonal movement of
1.24 million wildebeest in the Serengeti (Conservation
Information Monitoring Unit 2010) affects virtually
every dynamic in the ecosystem, including fire frequency
and tree–grass competition (Dublin et al. 1990, Holdo et
al. 2009a), biodiversity of grasses and animals (Ander-
son et al. 2007b), food web structure (de Visser et al.
2011), and the socioeconomic status of local people
(Sinclair and Arcese 1995b, Sinclair et al. 2008). The
profound impacts that migrations have on ecosystems
necessitates an improved understanding of how and why
Manuscript received 29 July 2013; revised 28 October 2013;
accepted 5 November 2013; final version received 17 December
2013. Corresponding Editor: C. C. Wilmers.
8
E-mail: grant.hopcraft@glasgow.ac.uk
355
animals move. Progress in this field requires discerning
the key factors that influence the choice patterns of
individual animals within a population (Alerstam 2006,
Schick et al. 2008, Morales et al. 2010).
Animal migrations are typically determined by
seasonal access to high-quality food patches, which
generally occur across gradients of soil fertility,
rainfall, elevation, or latitude (Fryxell and Sinclair
1988, Alerstam et al. 2003). However, individual
animals must also balance access to essential resources
(especially food), while at the same time minimizing the
exposure to risk—especially from predation and
anthropogenic threats ( Fryxell et al. 2008). For
instance, North American el k (Cervus elaphus)move
across an elevation gradient that determines the
seasonal quality and quantity of forage (Frair et al.
2005, Hebblewhite et al. 2008), but local movement
decisions are influenced by proximity to r isks such as
predation from wolves, or disturbance from roads and
clear-cut logging ( Hebblewhite and Merrill 2007, 2009,
Frair et al. 2008). Similarly, the movement of Thom-
son’s gazelle (Eudorcas thomsoni) in the Serengeti i s
closely related to periodic greening of the energy-rich
short-grass sward ( Fryxell et al. 2004, 2005). Popula-
tions of saiga (Saiga tart arica) migrate large distances
over the Central Asian steppe along a latitudinal
gradient of productivity determined by seasonal pre-
cipitation and frost (Singh et al. 2010). Mongollian
gazelle ( Procapra gutturosa)alsomoveinrelationto
latitudinal gradients of frost, but their movements tend
be more variable than those of saiga, despite living in
similar environments ( Ito et al. 2006, Olson et al. 2010,
Mueller et al. 2011). Wildebeest (Connochaetes taur-
inus) in the Serengeti migrate over an opposing rainfall
and soil fertility gradient (Holdo et al. 2009b)where
high soil fertility areas attract large herds during t he
wet season and high-rainfall areas are a refuge during
the dry season (P ennycuick 1975, Maddock 1979,
Boone et al. 2006). However, it is not well understood
how individual animals weigh the costs and the benefits
of moving in response to food and predation in such a
way that leads to an annual migration.
Animal migrations represent the sum total of a
sequential series of complex movements: at the finest
scale, minute-by-minute choices sum to daily displace-
ments, which in turn sum to monthly and seasonal
trajectories. Therefore, the fine-scale movements of
migrants are nested within the coarser scale movements
and these aggregate to an annual migration (Bo
¨
rger et
al. 2011). Because the resources that migrants track are
in a constant state of flux (such as standing biomass),
understanding the factors that explain daily movement
provides evidence for the drivers of annual migrations.
However, the role of predation in shaping mammal
migrations has received relatively little attention, with
the notable exception of elk in North America (Frair et
al. 2005, Hebblewhite and Merrill 2007, 2009). Preda-
tion risk for large herbivores in savannas is correlated
with vegetation and topography that allow predators to
ambush their prey, leading to somewhat predictable
patterns across the landscape (Hopcraft et al. 2005,
2010).
Until now, no studies have compared the movement
patterns of two sympatric migratory species to ascertain
if the same landscape variables, such as those related to
food vs. predation, influence the movement of both
species equally. This comparative approach is potential-
ly powerful because not only does it allow us to
investigate how different environmental conditions
affect the same individuals as they migrate between
distinct landscapes, but also it allows us to compare how
these distinct landscapes affect individuals of different
species (a natural paired factorial experiment). For
instance, both wildebeest and plains zebra (Equus
burchelli) have similar and associated migrations in the
Serengeti-Mara ecosystem (Hopcraft et al., in press) and
yet these species are taxonomically unr elated (i.e.,
bovids vs. equids), with quite different digestive phys-
iologies (the annual migratory cycle and maps can be
viewed in Appendix A). Ruminants, such as wildebeest,
are more efficient at digesting moderate-quality plant
material than are hindgut fermenters, such as zebra
(Foose 1982, Demment and Soest 1985 ). Hindgut
fermenters offset their lower digestive efficiency by
processing greater quantities of forage faster, which
enables species such as zebra to gain sufficient energy
from low-quality grass (Bell 1970, Ben-Shahar and Coe
1992). The maximum abundance of wildebeest in the
Serengeti seems to be regulated by the availability of
dry-season forage rather than predation (Mduma et al.
1999), whereas evidence suggests the Serengeti zebra
population might be limited by predation, especially on
juvenile age classes, rather than by the overall food
supply (Sinclair 1985, Grange et al. 2004). Therefore, it
is possible that zebra might be choosing where and how
to move during the migration based on factors related to
predation, whereas wildebeest might make choices based
on food availability. We conjecture that these two
species might make choices as to how to move based on
very different attributes of the same habitat.
The development of state-space models that link the
basic components of animal movement (such as the turn
angle and the displacement distance between consecutive
time intervals) with potentially complex covariates have
advanced our ability to understand individual choice
patterns. For instance, these models have been used to
understand animal movement as a function of the
spatial environment that an animal is moving through,
such as rainfall and vegetation quality (Morales et al.
2004, Patterson et al. 2008, McClintock et al. 2012), or
the social context (e.g., group size) within which an
individual is embedded (Haydon et al. 2008). Further-
more, these methods enable us to discern the external
environmental variables that attract, repulse, or have
negligible effect on the local movement decisions, and
hence on trajectories of individual animals. The appli-
J. GRANT C. HOPCRAFT ET AL.356
Ecological Monographs
Vol. 84, No. 3
cation of these more mechanistic ‘‘spatially informed’’
and ‘‘socially informed’’ methods to the study of
migrations significantly advances predictive ecology,
while their hierarchical nature facilitates fine-scale
analysis of individual responses that captures many of
the subtle individual differences in how animals weigh
the costs and benefits of moving through a complex
landscape.
The objective of this study is to determine how food
quality, food abundance, and predation risk influence
the distance and direction that migratory Serengeti
herbivores choose to travel each day, and how these
determinants d iffer b etween wildebeest and zebra.
Because each tracked animal can be considered different
to others, but not statistically independent, we used a
hierarchical approach to model movement data from
free-ranging wildebeest and zebra to determine which
landscape variables best describe their movement.
Hierarchical models account for the inherent variance
between unique animals that is nested within the overall
variance structure of the sampled population (Schick et
al. 2008, Bestley et al. 2012). Based on the physiological
differences between wildebeest and zebra and the factors
regulating their overall abundance in the ecosystem, we
hypothesize that (1) food quality affects the movement
of individual wildebeest more than zebra, (2) the
exposure to risk affects zebra movement more than
wildebeest, and (3) food quantity affects both species
most during the dry season, when resources are most
limiting. By contrasting the movement trajectories of
these two sympatric species, we illustrate how research
on individual choice patterns through hierarchical
modeling expands our overall understanding of the
drivers of animal migrations.
M
ATERIALS AND METHODS
The ecosystem and data
The movement trajectories of migratory wildebeest
and zebra were studied in the Serengeti-Mara ecosystem,
which lies on the border of Kenya and Tanzania in East
Africa. The ecosystem extends from 1830
0
to 3830
0
S and
34800
0
and 35845
0
E, and is defined by the extent of the
wildebeest migration ( Fig. 1). S emiarid grassla nds
dominate the south, with mixed Acacia and Commiphora
woodlands spread over the central and northern areas
which are interspersed with large, treeless glades (Reed
et al. 2008, Sinclair et al. 2008). The average annual
rainfall increases from ;450 mm in the southeast to
.1400 mm in the northwest (Fig. 1a), and falls primarily
in the wet season (November to May). The ecosystem is
described in detail by Sinclair et al. (2008).
We analyzed data from 17 female migratory wilde-
beest fitted with GPS radio collars between the years
2000 and 2008 (except 2002 during a transition period
between funders) and 13 female zebra from 2005 to 2008
(see Appendix A for summary of collar statistics and
Appendix B for details on animal capture, handling, and
FIG. 1. (a) The greater Serengeti-Mara ecosystem lies between Kenya and Tanzania and coincides with a strong regional
rainfall gradient. (b) Wildebeest and zebra move seasonally between open grassed plains in the southeast to woodland and open
savanna areas in the west and north. Grass samples (triangles) and vegetation measurements (points along transects) were
distributed across the rainfall gradient and in different habitat types.
August 2014 357SERENGETI MIGRANTS: INDIVIDUAL MOVEMENT
GPS collars). In order to avoid the complications of
fine-scale movement (Yackulic et al. 2011), we selected
only the GPS locations at 18:00 hours ( just before
sunset when animals tend to congregate for the night;
J. G. C. Hopcraft, personal observation), as we were
interested in establishing the factors that influence the
sequential movement between days that sum to the
annual migration.
Models
The objective of this study is to understand how
different environmental variables related to local food
abundance, food quality, predation risk, and anthropo-
genic factors affect the daily movement decisions of
zebra and wildebeest. Our approach is to estimate the
parameters for a spatially informed correlated random
walk, based on the approach introduced by Morales et
al. (2004) to model elk movement. However, we extend
this approach in two way s. Rather than modeling
switches between discrete behavioral states (such as
migratory vs. encamped), we model the parameters
governing the distributions of daily steps (i.e., the
displacement distance between consecutive daily loca-
tions) and turn angles (i.e., the absolute angle between
straight lines linking three consecutive daily locations) as
continuous logit or log-linked functions of environmen-
tal variables. We also adapted the approach to capture
individual variation between collared animals by making
the models hierarchical (see Supplement for the code
and details in Statistical analysis).
We used a Weibull distribution to describe the daily
step lengths. This is a nonnegative continuous distribu-
tion defined by a scale parameter a and a shape
parameter b and has the following form:
WðxÞ¼abx
b1
expðax
b
Þ: ð1Þ
The Weibull distribution is flexible, reducing to an
exponential distribution when b ¼ 1, having an
exponential tail for b 1 and a fat tail when b , 1.
Furthermore, a Weibull distribution with shape param-
eter b equal to 2 is the theoretical expectation for
displacements under a simple diffusion model, thus this
distribution is well-suited for analyzing daily displace-
ment distances ( Moral es et al. 2004). The mean
displacement distance (d ) as described by the Weibull
distribution is given by:
d ¼
1
a
1=b
C
1 þ b
1
ð2Þ
where C is the Gamma function. Note that as the scale
parameter (a) increases, the mean displacement decreas-
es for a given value of beta.
We used the wrapped Cauchy distribution to model
turning angles (Morales et al. 2004). The wrapped
Cauchy i s a cir cular distribution defined b y the
parameters q and l and takes the following form:
CðUÞ¼
1
2p
1 q
2
1 þ q
2
2q cosðU lÞ
ð3Þ
where 0 U 2p and 0 q 1.
The parameter l describes the mean direction in
radians. The parameter q describes the concentration
around the mean such that as q approaches 1, the
distribution becomes increasingly concentrated around
the mean. When q approaches 0, the distribution is
uniform in the circle, corresponding to an equal
probability of movement in all directions.
The step lengths and turning angles of individual
animals were linked to features of the landscape by
modeling the scale parameter of the Weibull distribution
a, and the variability and mean direction of turning
angles (q and l) as continuous functions of various
landscape features that will be described in detail.
Landscape features that cause animals to reduce their
displacement distances (i.e., increase a) and increase the
variability in turning angles (reduce q), resulting in an
area-restricted search type of movement pattern, can be
differentiated from the landscape features that cause
animals to increase their daily step lengths (i.e., decrease
a) and reduce turning angle variability (increase q
toward 1), resulting in strong directional movement and
a rapid exit from an area. We transformed turns to
absolute values so that left-hand turns were equivalent
to right-hand turns; therefore, l could only range from 0
to p (0 implies directional persistence, whereas p
indicates a complete turn in the opposite direction).
Observation error was minimal at the scale of our
analysis and therefore not included in the model: the
average daily displacement was ;4 km, whereas GPS
locations have approximately 610 m error and locations
were recorded at 18:00 hours local time every day 63
minutes. Only data from sequential days were included
in the analysis.
Landscape variables
GIS layers were constructed for eight predictor
variables estimating food quality, food abundance,
predation, and human disturbance at a spatial resolu-
tion of 1 km
2
(Table 1). The proximity of each animal’s
GPS locations to each of these landscape variables was
calculated across all observations (except NDVI, nor-
malized difference vegetation index). We tested for
nonlinear relations by also including a quadratic
function of the distance to each variable. The role of
food quality was estimated from (1) the animal’s
proximity to high-nitrogen grass patches, (2) the 16-
day mean NDVI value at the time and location of
observation (i.e., the average greenness of the vegeta-
tion), and (3) the difference between the current 16-day
mean NDVI and the previous 16-day mean NDVI
values (p ositive values indicate greening, whereas
negative values indicate drying). All of the NDVI layers
were calculated from remote-sensing observations by
NASA’s MODIS satellite platform. Grass nitrogen was
J. GRANT C. HOPCRAFT ET AL.358
Ecological Monographs
Vol. 84, No. 3
measured at 148 randomly selected sites across the
Serengeti (Fig. 1) within all combinations of soil and
vegetation types and across the rainfall gradient.
Because the concentration of nitrogen in the grass is
inversely correlated with the mean NDVI (see Appendix
C), we regression kriged (Hengl et al. 2007, Bivand et al.
2008) the data from the 148 points with a 9-year mean
NDVI layer (2000–2009) to generate an accurate
estimate of the spatial distribution of grass nitrogen
across the ecosystem (details provided in Appendix C).
We estimated the Euclidean distance of the location of
each animal at each time step to patches of high-
nitrogen grass (defined as areas within the upper 25th
percentile of grass nitrogen).
Grass biomass is positively correlated with soil
moisture and rainfall, and negatively correlated with
grass quality (Breman and De Wit 1983, McNaughton
et al. 1985, Olff et al. 2002, Anderson et al. 2007a).
Therefore we used the topographic wetting index
combined with the long-term average rainfall over a
46-year period to estimate the biomass of grass available
to the migrants (see Appendix C). Because animals
might only require periodic access to areas with
abundant grass biomass to supplement their diet (e.g.,
daily or seasonal foraging forays), the distance to high-
biomass sites (defined as areas within the upper 25th
percentile of grass biomass) was estimated for each
animal at each time step.
Landscape features such as dense thickets or drainage
beds conceal predators or provide predictable locations
where predators might encounter prey (Hebblewhite et
al. 2005, Hopcraft et al. 2005, Balme et al. 2007,
Kauffman et al. 2007, Valeix et al. 2009, Anderson et al.
2010). For instance, drainage beds are often associated
with erosion embankments and confluences that help
predators such as lions to catch prey (Hopcraft et al.
2005). Therefore, we used the distance to thick, woody
cover and the distance to drainage beds to estimate the
risk of predation. Most drainages in Serengeti are
ephemeral freshets and do not necessarily contain water;
access to surface water is determined separately. The
amount of woody cover available for stalking predators
was measured systematically at 1-km intervals along
1882 km of transects over the entire ecosystem (Fig. 1)
and the mean horizontal vegetative cover that could
conceal a predator was assigned to each of the 27
physiognomic vegetation classes identified by Reed et al.
(2008) and was mapped at a resolution of 1 km
2
(see
Appendix C). We estimated the distance of each animal
at every GPS location to the nearest thick cover (defined
as cells above the 85th percentile of horizontal cover).
Access to water might be important for wildebeest
and zebra and could influence their daily movement
trajectories (Kgathi and Kalikawe 1993), so the distance
to pooled or flowing water was estimated for all animals
during the dry season only. During this time, water can
only be found in the largest river systems (i.e., classes 1
and 2 of the RiversV3 layer in the Serengeti GIS
Database; see Gereta and Wolanski 1998). During the
wet season when migrants are on the plains, pools of
rainwater are plentiful everywhere and access to
drinking water is essentially unlimited, so we did not
include proximity to water in the analysis of movement
on the plains.
Exposure to human distur bance such as illegal
hunting was estimated by measuring the proximity to
human settlements and scaled by the density of people.
Areas adjacent to high-density villages have large values
and a high probability of illegal hunting (Hofer et al.
2000), whereas areas distant from low-density villages
have small values (see Appendix C).
Statistical analysis
All landscape variables were standardized to zero
mean and unit variance to facilitate cross-seasonal and
cross-species comparisons. The parameters a, q, and l of
the Weibull and wrapped Cauchy distributions that are
used to characterize movement were modeled as
functions of landscape variables (Table 1) through log
and logit links, respectively:
TABLE 1. Explanatory variables included in the models predicting the parameters a, q, and l for
the Weibull and wrapped Cauchy models of animal displacement and turn angles.
Term Definition
x
1
Standardized Euclidean distance of the ith individual at time t to patches of high
grass nitrogen (patches in the upper 25th percentile of grass nitrogen).
x
2
Standardized 16-day mean NDVI value at the location of the ith individual at time t.
x
3
Standardized difference between the current 16-day mean NDVI value and the
previous 16-day mean NDVI value at the location of the ith individual at time t.
x
4
Standardized Euclidean distance of the ith individual at time t to patches of high
grass biomass (patches in the upper 25th percentile of grass biomass).
x
5
Standardized Euclidean distance of the ith individual at time t to patches of thick
woody cover (patches in the upper 85th percentile of woody cover).
x
6
Standardized Euclidean distance of the ith individual at time t to drainage beds.
x
7
Standardized Euclidean distance of the ith individual at time t to pooled or flowing
water (included in the analysis of movement in the woodlands, but not on the
plains).
x
8
Standardized log of the Euclidean distance of the ith individual at time t to human
settlements, weighted by population size of the settlement.
August 2014 359SERENGETI MIGRANTS: INDIVIDUAL MOVEMENT
