vol. 173, no. 4 the american naturalist april 2009
Opposing Rainfall and Plant Nutritional Gradients Best
Explain the Wildebeest Migration in the Serengeti
Ricardo M. Holdo,
Robert D. Holt,
and John M. Fryxell
1. Department of Zoology, University of Florida, Gainesville, Florida 32611; 2. Department of Zoology, University of Guelph, Guelph,
Ontario N1G 2W1, Canada
Submitted June 20, 2008; Accepted October 9, 2008; Electronically published February 25, 2009
Online enhancements: appendixes, video.
abstract: Multiple hypotheses have been proposed to explain the
annual migration of the Serengeti wildebeest, but few studies have
compared distribution patterns with environmental drivers. We used
a rainfall-driven model of grass dynamics and wildebeest movement
to generate simulated monthly wildebeest distributions, with wil-
debeest movement decisions depending on 14 candidate models of
adaptive movement in response to resource availability. We used
information-theoretic approaches to compare the ﬁts of simulated
and observed monthly distribution patterns at two spatial scales over
a 3-year period. Models that included the intake rate and nitrogen
(N) concentration of green grass and the suppressive effect of tree
cover on grass biomass provided the best model ﬁts at both spatial
scales tested, suggesting that digestive constraints and protein re-
quirements may play key roles in driving migratory behavior. The
emergence of a migration was predicted to be dependent on the
ability of the wildebeest to track changes in resource abundance at
relatively large scales (180–100 km). When movement decisions are
based solely on local resource availability, the wildebeest fail to mi-
grate across the ecosystem. Our study highlights the potentially key
role of strong and countervailing seasonally driven rainfall and fer-
tility gradients—a consistent feature of African savanna ecosystems—
as drivers of long-distance seasonal migrations in ungulates.
Keywords: Connochaetes taurinus, dynamic model ﬁtting, emergent
behaviors, resource landscapes, spatial autocorrelation.
Long-distance ungulate migrations constitute one of the
great spectacles of nature and have been documented
across a wide range of ecosystems (Craighead et al. 1972;
Fryxell and Sinclair 1988; Williamson et al. 1988; Fancy
et al. 1989; Berger 2004). By moving seasonally between
geographic locations that differ in terms of food intake,
survival, and fecundity, many species have evolved an ef-
fective life-history strategy for exploiting heterogeneous
* Corresponding author; e-mail: rholdo@uﬂ.edu.
Am. Nat. 2009. Vol. 173, pp. 431–445. 䉷2009 by The University ofChicago.
0003-0147/2009/17304-50552$15.00. All rights reserved.
environments (Fryxell et al. 1988; Berger 2004). The wil-
debeest (Connochaetes taurinus) migration in the Seren-
geti/Mara ecosystem of Tanzania and Kenya represents an
iconic example of ungulate migration and constitutes one
of the most thoroughly documented animal migrations in
one of the most intensively studied ecosystems on Earth
(Pennycuick 1975; Maddock 1979; Fryxell et al. 1988;
Mduma et al. 1999; Wilmshurst et al. 1999b; Wolanski and
Gereta 2001; Sinclair 2003; Musiega and Kazadi 2004;
Boone et al. 2006). Surprisingly, however, we still lack a
satisfactory mechanistic explanation of the Serengeti mi-
gration. The Serengeti wildebeest, by virtue of their large
numbers, are widely regarded as ecosystem engineers (Sin-
clair 1979, 2003; Holdo et al. 2007), so understanding
exactly which variables determine their migratory patterns
and how these might evolve over time (e.g., as a result of
global climate change) becomes of particular importance.
In the Serengeti migration, up to 1.4 million wildebeest,
plus large numbers of zebra (Equus burchelli) and Thom-
son’s gazelles (Gazella thomsoni), move seasonally between
dry and wet season ranges over a 30,000-km
area. It is
clear that this migration is ultimately driven by the marked
and strongly seasonal rainfall gradient that runs from the
southeastern short-grass plains to the tall-grass woodland
and savanna habitats in the north, center, and west of the
ecosystem (Pennycuick 1975; McNaughton 1979a; Sinclair
1979; Boone et al. 2006). This gradient imposes a con-
straint: at the end of the wet season, migrant species leave
the plains as the latter dry up and green grass and surface
water become conﬁned to the wetter, northern reaches of
the ecosystem (McNaughton 1979a). These constraints
compel wildebeest and other migratory species to move
north. What is less clear is what the proximate factors are
that drive the wildebeest into the plains at the onset of
the wet season to begin with, since rainfall (the main de-
terminant of forage production) is higher in the woodlands
than in the plains throughout the year. Several explana-
tions have been postulated to explain this movement onto
the plains, including higher forage abundance and quality,
432 The American Naturalist
Figure 1: Map of the Serengeti ecosystem showing key protected areas
and geographic features (water bodies are shown in dark gray, and topo-
graphical features in lighter shades of gray). SNP pSerengeti National
Park, NCA pNgorongoro Conservation Area, MMGR pMasai Mara
Game Reserve (GR), MGR pMaswa GR, IGR pIkorongo GR, and
GGR pGrumeti GR.
surface water nutrient content, and escape from predation
(Jarman and Sinclair 1979; Fryxell et al. 1988; Murray
1995; Wolanski and Gereta 2001). So far, however, few
studies have systematically tested any of these hypotheses
by confronting wildebeest movement models with data.
Recently, Wilmshurst et al. (1999a) showed that wil-
debeest show a signiﬁcant preference for grass patches of
short to medium height at the landscape scale. Because
energy intake shows a hump-shaped response as a function
of grass height (Wilmshurst et al. 1999b, 2000), wildebeest
movement patterns follow an energy maximization strat-
egy, a ﬁnding supported at a more restricted spatial scale
for Thomson’s gazelles, another migratory species (Fryxell
et al. 2004). Also in a recent article, Boone et al. (2006)
used evolutionary programming (EP) to show that sim-
ulated wildebeest evolve migratory pathways that resemble
those observed in nature when moving across a landscape
containing information on rainfall and the normalized dif-
ference vegetation index (NDVI), an index of plant pro-
ductivity, suggesting that seasonal ﬂuctuations in primary
productivity can account for the migration (Boone et al.
2006). A potential difﬁculty with the analysis of Boone et
al. (2006), however, is that the wildebeest in the EP model
evolve to move toward areas that experience high rates of
change in NDVI in the plains during the wet season, but
these are also areas of lower absolute NDVI and, by in-
ference, lower peak green biomass than the woodlands.
Boone et al. (2006) suggest that changes in NDVI measure
new forage production, but it could be argued that these
changes track (rather than explain) wildebeest grazing pat-
terns, given that wildebeest grazing can more than double
grass primary production in the Serengeti plains (Mc-
Naughton 1985). In addition, NDVI generally does not
distinguish between woody and herbaceous green biomass
(Lu et al. 2003; Boone et al. 2006), so it quantiﬁes different
resources in the treeless plains and the woodlands, which
consist of a tree-grass mixture (Sinclair 1979). Wildebeest
in the EP model also move toward areas of high relative
rainfall (measured as monthly rain expressed as a pro-
portion of the annual total), even though absolute rainfall
has been shown to be the best predictor of primary pro-
duction in the Serengeti (Sinclair 1975; McNaughton
1985). These derived variables allow the EP model to gen-
erate a reasonable approximation to the migration, but
they do not necessarily pinpoint the resources that drive
the migration and movement in general across the
Like Boone et al. (2006), in this article we focus pri-
marily on forage availability as the main driver of wil-
debeest spatial distribution patterns, but we expand on
their approach by teasing apart the effects of forage quality
and nutrient content, tree-grass competition, and abiotic
factors such as terrain characteristics and water availability
on habitat selection and assume that movement decisions
respond to seasonally ﬂuctuating environmental condi-
tions. Following Wilmshurst et al. (1999a), we incorporate
realistic functional responses and digestive constraints into
a mechanistic model of food intake. We ﬁt a series of
competing models for wildebeest movement driven by en-
vironmental variables to wildebeest distribution data, us-
ing geostatistical methods to allow the data to identify the
model providing the best ﬁt to the observed distribution
patterns. Finally, we use our model to conduct atheoretical
investigation of the spatial scale of resource tracking used
by wildebeest, as reﬂected by the size of local movement
neighborhoods, to infer the minimum conditions under
which migration can occur within an adaptive movement
framework. We believe the approach we take here provides
a useful linkage among herbivore foraging decisions, land-
scape patterns, competitive interactions, and emergent
Material and Methods
The Serengeti ecosystem (ﬁg. 1) can be broadly divided
into two main habitat types: the treeless, short-grass plains
Wildebeest Migration in the Serengeti 433
Figure 2: Environmental variables used to model wildebeest distribution patterns in the Serengeti ecosystem (deﬁned by the extent of the wildebeest
migration), shown at 10-km resolution. A, Rainfall (varies monthly in the model; shown here as 1969–1972 annual mean); B, Percent tree cover;
C, Flow accumulation (shown here unweighted by rainfall) in km
;D, Terrain roughness, expressed as the standard deviation of elevation across
pixels, E, Plant N concentration; and F, Plant Na concentration. The total area covered represents 30,700 km
. The boundary of Serengeti
National Park is shown inset for reference.
in the southeastern portion of the ecosystem (“plains”
hereafter) and the tall-grass savanna and woodland
(“woodlands”) in the north and west (ﬁg. 2B). Wildebeest
are the dominant herbivores in this system, with a pop-
ulation that has ﬂuctuated between 1 and 1.4 million an-
imals over the past quarter-century. The Serengeti is char-
acterized by strong climatic and edaphic gradients and
discontinuities. A marked precipitation gradient runs in a
southeast to northwest direction, ranging from less than
400 mm in the rain shadow of the Ngorongoro volcano
to more than 1,200 mm near the shores of Lake Victoria
(ﬁg. 1). In addition to this gradient, there is substantial
regional heterogeneity in soil properties. The plains soils
are shallow, nutrient-rich volcanic ashes with an almost
continuous hardpan layer that impedes tree growth (Sin-
clair 1979). In the north, soils tend to be dystrophic, with
a lower clay content than in the plains (Sinclair 1979). For
the purposes of our analysis, the Serengeti ecosystem is
regarded as the area bounded by the wildebeest migration,
as deﬁned by Maddock (1979), covering a surface area of
Approach and Data Sources
A basic assumption of our model is that wildebeest move-
ments track real-time environmental conditions and re-
source availability and that we can use observed distri-
butions against the template of alternative resources to
make inferences about movement rules. The resources and
environmental drivers we included here as candidates for
informing movement decisions are forage biomass, intake,
and quality; water availability; and tree cover (which affects
forage biomass). We focused on plant nitrogen (N) and
sodium (Na) as key indicators of forage quality because
of the importance previously attached to crude protein
and Na for Serengeti herbivores (Sinclair 1977; McNaugh-
ton 1988; Murray 1995). We also included an index of
topographic roughness as a covariate, because this may
inﬂuence access to resources. To ﬁnd the combination of
environmental drivers that best predict wildebeest distri-
bution patterns, we ﬁt a wildebeest movement model to
detailed monthly wildebeest distribution data spanning a
3-year period over the entire Serengeti.
The main data set underpinning our analysis is a set of
monthly distribution maps of the Serengeti wildebeest
population based on monthly aerial surveys conducted
between August 1969 and August 1972, known as the
“recce” data (Norton-Grifﬁths 1973; Maddock 1979;
Boone et al. 2006). To this date, the recce data constitute
the only time series showing seasonal shifts in the spatial
distribution of the entire wildebeest herd in the Serengeti
and thus the only comprehensive data source detailed
enough to analyze the migration at the population level.
Given the importance attributed to the migration, it is
surprising both that such data have not been collected
since and that the recce data have not been analyzed in
The collection of the wildebeest recce data has been
described in detail elsewhere (Norton-Grifﬁths 1973; Mad-
dock 1979). For this study, we adopted two spatial scales:
434 The American Naturalist
the ﬁne-scale resolution (10 km) used by Maddock (1979)
and a coarse-scale (25 km) resolution. We conducted the
analysis at the coarse resolution (25 km) to examine
whether misregistration of spatial information might lead
to erroneous rejection of particular models at the ﬁner
scale. Misregistration occurs when two maps show similar
spatial patterns but do not “line up” (Costanza 1989), and
it occurs more frequently at ﬁner spatial scales. Details on
the development of wildebeest distribution maps and the
geographical information system (GIS) layers of the en-
vironmental drivers are given in appendix A in the online
edition of the American Naturalist.
Wildebeest Movement Model
The wildebeest movement model is a discrete-time, spa-
tially explicit simulation model of grass and wildebeest
dynamics. The model is implemented across a lattice fol-
lowing the boundaries of the ecosystem as deﬁned by the
recce data (ﬁg. 2), at both ﬁne (10 km) and coarse (25
km) resolutions. Both within-cell daily dynamics—grass
growth and decay (determined by monthly rainfall) and
herbivory—and between-cell weekly dynamics—wilde-
beest movement—occur in the model, which is described
in detail by Holdo et al. (2009) and summarized in ap-
pendix B in the online edition of the American Naturalist.
The model generates maps of wildebeest distribution pat-
terns, which can then be compared to observed distri-
bution patterns. Wildebeest emigration from a cell at each
time step is governed by the value of a resource variable
Zwithin the cell (Z
) in relation to its mean value evaluated
within a surrounding neighborhood of radius r(Z
cording to the equation
(following Fryxell et al. 2004), where V
(see eq. [B9])
represents the emigration of wildebeest W
from cell ij,
) is the expected value of Z
across the neighborhood,
and Jcontrols the shape of the migration function. An
increasingly strong dispersal response occurs as Jin-
creases. The variable rrepresents a circle of radius rsur-
rounding each cell, deﬁned as the “resource tracking
neighborhood.” We assume that at any given time, wil-
debeest track resources across the landscape up to a dis-
tance rand then disperse within this local neighborhood.
Wildebeest that emigrate from a cell distribute themselves
proportionately throughout the subset of target cells
within the resource tracking neighborhood that are of
greater value than the cell they have left, as assumed by
Fryxell et al. (2004). Wildebeest distributions are updated
with a weekly rather than daily time step because of con-
straints imposed by the high computational burden of the
movement submodel. We show later that using a daily
time step does not alter our conclusions.
One of our primary objectives en route to developing
a movement model was to ﬁnd the functional form of Z
that maximizes the ﬁt between the model and the wil-
debeest distribution data. We selected 14 candidate models
that differed in terms of the combination of variables de-
ﬁning Z: green grass biomass Gand intake I, tree cover
T(ﬁg. 2B), surface water availability or ﬂow accumulation
F(ﬁg. 2C), terrain roughness R(ﬁg. 2D), and grass ni-
trogen N(ﬁg. 2E) and sodium Na (ﬁg. 2F) concentrations
(table 1). Of these variables, some were directly obtainable
from GIS layers of the ecosystem (ﬁg. 2), whereas others
(such as green grass biomass and intake) were derived
variables generated by the movement model. We used the
model ZpGas a “null” or base model, given that green
grass abundance is known to be one key driver of habitat
choice in the Serengeti (McNaughton 1979a). The inclu-
sion of green grass intake instead of green grass biomass
in several models allowed digestive constraints on green
grass intake imposed by the presence of dry grass biomass
and digestive capacity limitations to be incorporated in
the model. In several of the candidate models, we included
as terms of Z(table 1). This allowed
the simultaneous inclusion of the effects of grass biomass
(or intake) and quality (in terms of nutrient concentra-
tion) in the resource function; the model with ZpIN
implies that wildebeest maximize intake of green grass
multiplied by a power function of its N concentration.
The use of the exponent ballowed relatively ﬂexible (i.e.,
nonlinear) functional forms to be ﬁtted without having to
estimate a large number of parameters (cf. Pacala et al.
1994). It also allowed us to evaluate the comparative
strength of grass biomass or intake versus grass nutrient
concentration in informing movement decisions; for ex-
ample, when , wildebeest will respond dispropor-b11
tionately to grass N in comparison to grass biomass. We
also used power functions when testing the effects of ﬂow
accumulation and terrain roughness on habitat choice (ta-
ble 1). To incorporate the effect of tree-grass competition,
we also included the term e
in some of the models; for
example, the model I,T,N, with ZpIe
intake, grass N, and suppressive effects of tree cover on
the amount of area occupied by grass (table 1).
Fitting the Dynamic Model to Distribution Data
The dynamic model generated maps of predicted wilde-
beest abundance (Y) across the Serengeti at monthly in-
tervals between August 1969 and August 1972. We used
the 33 months that matched the survey ﬂights from the
recce data to obtain mean wildebeest abundances Y
Wildebeest Migration in the Serengeti 435
Table 1: Candidate models and ordinary least squares (OLS) and autoregressive
(AR) model ﬁts for wildebeest movement models in the Serengeti ecosystem between
1969 and 1972
in model Zp
OLS 25 km AR 25 km OLS 10 km
GG 0 226.8 126.3 638.6
1 123.9 117.2 548.5
1 55.3 71.6 232.2
2 44.3 56.5 107.5
II 0 103.1 58.1 283.0
1 72.4 72.2 162.8
1 25.8 53.9 143.9
2 21.9 48.0 .0
2 78.0 80.9 107.5
4 26.6 53.5 42.7
4.0 .0 .4
4 12.2 46.3 4.1
3 2.6 3.8 135.4
I,F I ⫹gF
2 56.6 22.0 144.5
Note: Zrefers to the resources or environmental covariates that drive movement across the
landscape in each model (see eq. ). The quantity p(see eq. ) equals the number of movement
model parameters (Greek letters in function Z; it excludes k, the number of autocorrelation function
parameters). Variable deﬁnitions: Gpgreen grass biomass; Ipgreen grass intake; Tptree cover;
Npgrass N concentration; Na pgrass Na concentration; Fpﬂow accumulation; Rpterrain
Corrected Akaike Information Criterion value relative to best model.
(where iand jare cell coordinates and sis the season) for
the three distinct annual seasons. We then compared these
modeled abundances with the observed wildebeest abun-
. This is a regression problem in which either
the original data or the ﬁtted residuals can exhibit spatial
and/or temporal autocorrelation, potentially leading to
problems of inference and parameter bias (Haining 1990,
pp. 40–41; Hoeting et al. 2006; Ives and Zhu 2006; Dor-
mann 2007). Taking account of both spatial and temporal
autocorrelation in this case would require computationally
intensive Monte Carlo methods that are beyond the scope
of this study (Ver Hoeff et al. 2001). We minimized the
problem of temporal autocorrelation by using seasonal
rather than monthly distributions, thereby sacriﬁcing some
information. We tested for spatial autocorrelation by com-
puting Moran’s Ias a function of lag distance (Legendre
and Legendre 1998, p. 714; Lichstein et al. 2002) for the
ﬁtted residuals after ﬁrst ﬁtting the model to data using
ordinary least squares (OLS) methods, and we then re-
peated the analysis using an autoregressive (AR) approach.
We assumed a lognormal distribution for wildebeest abun-
dances because this transformation improved the distri-
butional properties of the data and the residuals. Our pro-
cedure for calculating OLS and AR likelihoods is given in
appendix C in the online edition of the American
Following the estimation of the log likelihoods for each
model, we used a modiﬁed version of the corrected Akaike
Information Criterion (AIC
) to compare the goodness of
ﬁt of competing models (Hoeting et al. 2006):
AIC p⫺2ᐉ⫹2ns ,(2)
where is the log likelihood, nis the number of cells inᐉ
the lattice, sis the number of seasons (and thus ns gives
the total number of observations), pis the number of
parameters ﬁt to the movement model, and kis the num-
ber of parameters associated with the autocorrelation func-
tions, equal to 0 in the OLS models.
To test the robustness of our model ﬁts to uncertainty
in the environmental data layers and model parameters,
we conducted an error analysis by running all of the
models with alternative realizations of the input GIS layers
and some key parameters (Pacala et al. 1996; Holdo 2007).
In particular, many of our environmental covariates (as
interpolated maps) were generated from observations col-
lected at a limited number of sites, and there was, there-
fore, considerable uncertainty associated with under-
sampled regions; this uncertainty can propagate through
the model (Kyriakidis 2001). To keep the error analysis
manageable, we focused the analysis on those layers and
parameters that were most likely to draw contrasts between
alternative models. For example, rainfall-driven grass
436 The American Naturalist
Video 1: Representation of movement model I,T,Nat ﬁne scale. Figure
is the initial frame from a movie of the simulated migration, which is
available in the online edition of the American Naturalist.
growth is common to all models, so we kept the monthly
rainfall layers and grass growth parameters at their default
values. Of primary interest to us were the effects of plant
nutrients, tree cover, surface water, and intake versus bio-
mass as explanatory factors in the migration, so we in-
corporated uncertainty in plant Nand Na,treecoverT,
and four dynamic model parameters associated with intake
, and daily voluntary intakes DVI
described in app. B) in the error analysis. We did not model
uncertainty in ﬂow accumulation because of the large
computational burden associated with producing these
monthly maps. For each of 1,000 random realizations of
these input maps and parameters, we ﬁt all 14 models to
the data and computed AIC
values. We used the 25-km
resolution and OLS because of the prohibitive computa-
tional burden imposed by using either the AR approach
or the OLS analysis at 10-km resolution. The resampling
procedure we used to generate input maps and parameters
is outlined in appendix D in the online edition of the
Finally, to compare the performance of our model to
that of the only other model of the wildebeest migration
produced to date (the EP model of Boone et al. 2006), we
reﬁt our best overall 10-km model at the higher 5-km
resolution used in EP. Although our model-ﬁtting pro-
cedure (see below) differed from that used by Boone et
al. (2006), we used their classiﬁcation system to compare
model ﬁts. In the EP model, the raw census data (see app.
A) were used to produce a binary classiﬁcation of lattice
cells as occupied (≥250 animals) or unoccupied (!250
animals). Unlike our seasonal approach, 12 monthly dis-
tribution maps averaged over the entire census period
(1969–1972) were produced and compared with the maps
generated by the model. An index of ﬁt is provided by the
mean number of cells (averaged across all months) that
are occupied in both model and data as a fraction of the
total number of cells occupied in either model or data.
In addition to testing model ﬁts with AIC
, we con-
ducted a graphical comparison of the ability of competing
models to generate a migration. We deﬁned the term “mi-
gration distance” (d
) as the distance between the cen-
troids of the entire wildebeest herd averaged through the
wet and dry seasons (deﬁned as the December–April and
August–November seasons). We calculated the migration
distance for the actual wildebeest distribution (the ob-
served value of d
) and for each of the candidate models.
We then graphically compared the observed and modeled
values of d
Resource Tracking Neighborhood
The default scenario in the model comparison is to assume
that wildebeest can track resources and disperse over a
radius ; that is, wildebeest can make movement de-rr⬁
cisions based on the entire landscape and are therefore
“omniscient.” To investigate how migration and overall
model ﬁt are affected by the size of the resource-tracking
neighborhood, we reﬁt the best overall candidate model
to the data with ﬁxed values of rranging between 10 km
(a neighborhood that would include only adjacent cells)
and 200 km and plotted d
and the log likelihood proﬁle
as functions of r.
OLS Model Fits
In the OLS analysis, different models provided the best
ﬁts to the data at 10- and 25-km resolutions. At the coarse
resolution, the model with the lowest AIC
therefore the best ﬁt) included terms for intake, tree cover,
plant N, and ﬂow accumulation (model I,T,N,F), whereas
at the ﬁne resolution, model I,T,N(intake, tree cover, and
plant N) provided the best overall ﬁt (table 1; video 1).
In both cases, green biomass intake Iwas a better predictor
of wildebeest distribution patterns than green biomass G,
and the inclusion of plant N in the function Zimproved
ﬁt over simpler models (table 1). Although the inclusion
of tree cover did improve model ﬁt at the 25-km resolution
over simpler models when ﬂow accumulation (F) was ex-
cluded from the analysis, this covariate provided a mar-
ginal improvement to model ﬁt only when water avail-
ability was taken into account at this scale (table 1). At
the 10-km resolution, tree cover greatly improved ﬁt over
simpler models, and ﬂow accumulation had little explan-
Wildebeest Migration in the Serengeti 437
Table 2: Maximum likelihood estimates (MLEs) and multivariate 95% conﬁdence
intervals (lower and upper bounds) for best-ﬁt model parameters
Model ZLattice (km) Parameter
MLE Lower Upper
25 b3.34 2.20 4.99
g9.50 1.49 99.94
d.34 .01 1.30
25 b3.09 1.62 4.31
g32.14 .82 99.93
d.50 .11 1.39
1.94 1.26 4.73
1.39 .57 4.97
10 q.031 .026 .033
b2.99 2.76 3.50
See table 1 for a list of parameters.
Parameter in the AR likelihood function (see app. C in the online edition of the American
atory power (table 1). At both spatial resolutions, neither
plant Na nor terrain roughness Rimproved model ﬁts.
The error analysis strongly supported the conclusions
of the analysis conducted with the default layers and pa-
rameters (table D1). In most cases (particularly for the
best models), model ranks obtained in the default case
were preserved when error in the environmental layers
and parameters was included. In addition to generating
conﬁdence limits for our AIC
values, we compared the
rank of any given model with the rank of the next-best
model for each realization of the error analysis, and we
found that our model rankings had very strong support
(table D1). For example, the inclusion of tree cover and
nitrogen consistently improved model ﬁt, and intake mod-
els strongly outperformed biomass models (table D1). To
test whether surface water and tree cover may be somewhat
confounded with each other, we examined the bivariate
correlations between these and other input layers (table
E1 in the online edition of the American Naturalist). Gen-
erally, the correlations among the environmental variables
were weak, including that between tree cover and ﬂow
accumulation. The only notable relationships were be-
tween plant N and Na, which showed a moderate positive
correlation, and plant N and rainfall, which were quite
strongly negatively correlated (table E1).
An examination of the maximum likelihood estimates
(MLEs) for the dynamic model parameters (table 2)
showed that variation in plant N concentration across the
landscape (ﬁg. 2E) is more inﬂuential than tree cover (ﬁg.
2B) or water availability (ﬁg. 2C) in affecting wildebeest
distribution patterns in the model. An approximate in-
dication of the inﬂuence of a particular variable is given
by comparing the ratio of Zwith the variable in question
set at its maximum and minimum values (with parameters
set to their MLEs) across the ecosystem. This ratio can
then be compared across variables. Using this approach,
the estimated value of b, the power term in the function
, suggests a 40-fold difference in the “attrac-
tiveness” of areas with the lowest and highest plant N
content, whereas the estimated value of q(which controls
the effect of tree cover on grass biomass) produces a ratio
about half as large (see table 2 for parameter estimates).
Similarly, the estimated values of parameters gand d,
which determine the inﬂuence of ﬂow accumulation on
habitat choice (table 2), result in a twofold variation in
the value of this term in the resource function Z(table
2). The multivariate conﬁdence bounds for each of the
parameters estimated, drawn from the Metropolis sam-
pling distributions, are shown in ﬁgure E2. In addition to
showing conﬁdence bounds, these plots indicate relation-
ships among the parameters. Figure E2Aand E2Bshows
that the coefﬁcient gand exponent dfor the ﬂow accu-
mulation term F(where ZpIN
; see table 2) in
the I,N,Fmodel appear to be strongly correlated, but nei-
ther of these parameters is correlated with the bexponent
of the nitrogen term N. This suggests that a simpler model
lacking a dparameter (i.e., ) would have provided
an equally good ﬁt, but it also suggests that the contri-
butions of Nand Fin the model are independent and not
confounded. Figure E2Dalso suggests that the effects of
tree cover (parameter q) and N(parameter b) are inde-
pendent, which was to be expected given the weak cor-
relation between these two environmental covariates across
In terms of migration distance (d
), some models were
far more successful in generating a seasonal migration than
others (ﬁg. 3A). The simplest model (G) performed par-
ticularly poorly, and replacing green biomass with green
biomass intake (I) substantially lengthened the migration
distance generated by the model (ﬁg. 2A). Generally, mod-
els that included a plant N term resulted in migration
438 The American Naturalist
Figure 3: A, Observed and modeled migration distance d
of the wil-
debeest herd, deﬁned as the distance between the centroids of the herd
averaged separately for the wet (December–April) and dry (August–
November) seasons. The seasonal values are means computed over the
period August 1969–August 1972. The observed value is compared with
that of 14 candidate models, identiﬁed by the environmental variables
that they include (see table 1 for model descriptions). B, Observed and
simulated (based on the best movement model I,T,N, which incorporates
green grass intake, grass N content, and tree cover) monthly locations
of the “center of mass” of the Serengeti wildebeest population averaged
over the 1969–1972 time period.
distances that most closely match the value of d
from the data (ﬁg. 3A).
The predicted seasonal wildebeest distributions for the
best 10-km resolution OLS model (I,T,N) are shown
alongside the observed distributions in ﬁgures 3Band 4.
The ﬁts between model and data were best at the extremes
of the migration (December–April and August–Novem-
ber) and poorer during the transition period (May–July).
During this transition period, wildebeest tend to move
toward the central woodlands and western corridor of the
Serengeti. Even in the best model, wildebeest tend to per-
sist in the southern portion of the ecosystem during this
period (ﬁgs. 3B, 4).
AR Model Fits
Since signiﬁcant spatial autocorrelation was detected in
model residuals in even the best-ﬁtting models for both
the 10- and 25-km resolutions (ﬁg. E1), we used an au-
toregressive approach in addition to the OLS analysis. As
outlined in appendix C, we used an iterative procedure to
estimate the model and covariance function parameters.
At the ﬁne resolution, this convergence was unsuccessful
for several of the candidate models, especially those pro-
viding poor ﬁts in the OLS analysis, so we report results
only at 25-km resolution. The autoregressive approach
identiﬁed the same model (I,T,N,F) that provided the best
ﬁt in the OLS case (table 1), suggesting that even after
correcting for the effects of spatial autocorrelation the
same variables emerge as the drivers of the wildebeest
migration and distribution patterns. The MLE for the au-
tocorrelation distance parameter (v
in app. C) was of the
order of 50 km (table 2; ﬁg. E2).
When the best overall model was run with different re-
source tracking neighborhood radii (r), we found that
model ﬁt, in terms of both model likelihood and migration
distance, improved monotonically up to a distance of 80–
100 km, with no appreciable improvement in ﬁt for larger
neighborhoods (ﬁg. 5). This implies that wildebeest in the
dynamic model need to be able to track landscape con-
ditions over relatively large distances in order to replicate
the movement patterns that are actually observed. The plot
of migration distance in particular (ﬁg. 5B) suggested that
when wildebeest move only within local neighborhoods
(!80 km), there is little or no emergent pattern of long-
distance movement, and the simulated population tends
to get “trapped” within certain portions of the landscape.
To test whether this effect was an artifact of our weekly
movement iteration or our choice of spatial scale, we re-
peated the simulation (i) with a daily movement step and
(ii) at a spatial resolution of 5 km and had similar results
in both cases (ﬁg. 5A), suggesting that the perception ra-
dius threshold effect is not generated by the model struc-
ture or choice of spatial resolution but rather reﬂects the
spatial scale of seasonal environmental change and how it
needs to be tracked to be exploited effectively. Note that
although wildebeest are unlikely to be able to move across
the entire landscape in a single day (the maximum daily
distance recorded in the literature is 50 km; Talbot and
Wildebeest Migration in the Serengeti 439
Figure 4: Observed wildebeest distribution patterns (individuals km
) in the Serengeti ecosystem versus modeled output from the best-ﬁt ordinary
least squares simulation model (I,T,N) at 10-km resolution. The distributions (both actual and modeled) represent seasonal means derived from
monthly layers spanning the period August 1969–August 1972.
Talbot 1963), our results show that increasing the fre-
quency of movements in our model without increasing
the size of the perception window does not increase the
ability of modeled wildebeest to track environmental gra-
dients efﬁciently enough to allow long-distance migration.
Grass Intake and Nutritional Quality
Explain the Migration
Our model suggests that green grass intake and protein
content both play a key role in determining the movement
and distribution patterns of migratory wildebeest in the
Serengeti. Green grass intake is a much better predictor
of the wildebeest migration than is grass biomass, and
maximizing this quantity rather than biomass helps to
explain not only local movement patterns but also long-
Previous studies on both wildebeest and Thomson’s ga-
zelle movements in the Serengeti suggested that ungulates
follow energy-maximizing rather than simply biomass-
maximizing strategies (Wilmshurst et al. 1999a; Fryxell et
al. 2004). Because the quality of grasses (as measured by
protein, ﬁber, and/or energy content) generally declines and
intake increases as a function of grass height or biomass,
energy intake is often optimized in areas of intermediate
grass height or biomass (Wilmshurst et al. 1999a; Fryxell et
al. 2004). Although a single variable (biomass) may in some
cases sufﬁce to model both quantity and quality of forage
intake (Fryxell et al. 2004), here we partitioned grasses
into high- and low-quality (green and dry grass, respec-
tively) compartments. This allowed us to treat food quan-
tity and quality independently, which can be important in
distinguishing between growing and senescing swards that
may have equal biomass but differ in quality. Despite dif-
ferences in model details, however, our conclusions are
consistent with the previous ﬁnding (Wilmshurst et al.
1999a) that what is being optimized by the wildebeest is
440 The American Naturalist
Figure 5: A, Ordinary least squares likelihood proﬁle (assuming weekly and daily movement intervals at 10-km resolution and weekly movement
at 5-km resolution), and B, migration distance d
(assuming weekly movement at 10-km resolution, the model default) for the best overall model
(I,T,N) as a function of the radius of the resource tracking neighborhood in the simulation model.
the rate of intake of the high-quality compartment. This
intake rate is not simply a monotonic function of biomass,
because (i) new green grass growth is inhibited by the
accumulation over time of dry grass due to senescence,
and (ii) digestive constraints on intake are imposed by the
inevitable consumption of some dry grass in a green-dry
grass mixture. This means that as the season progresses,
areas with abundant dry grass will tend to be avoided
because they reduce green grass intake. Green grass intake
thus follows an approximately unimodal relationship with
total grass biomass and may serve as a proxy for energy
An added aspect of food quality that we explicitly con-
sidered is grass crude protein or N concentration. Whereas
the intake variable incorporates a seasonally varying com-
ponent of food quality (in addition to quantity), our use
of landscape-level variation in plant N (or protein) content
adds an additional spatial component that is ﬁxed over
time. This plant N gradient is strongly correlated with a
soil N gradient (McNaughton 1985; Ruess and Seagle
1994) that is opposite of the rainfall gradient in the Ser-
engeti: the nutrient-rich plains of the southeastern portion
of the Serengeti lie on volcanic soils and are at the low
end of the rainfall spectrum, whereas the sandier woodland
soils of the central and northern Serengeti receive more
rainfall but are less fertile (Sinclair 1979). Our results sug-
gest that this N gradient (or some other variable that is
correlated with N) further helps to explain the differences
in plant quality that drive the Serengeti migration. In par-
ticular, the high N content of grasses in the plains may be
the key factor driving the movement of the migratory
grazers into this habitat at the onset of the rains. When
the rainy season begins, green grass biomass rapidly in-
creases throughout the ecosystem, but the higher quality
of the food supply in the plains compared with the wood-
lands may explain why the wildebeest leave the woodlands
en masse at this time. As this supply dries up, green grass
persists only in the woodlands, and the wildebeest are
forced to move northward (McNaughton 1979b). The mi-
gration thus permits exploitation of an N-rich resource
pulse that arises predictably each year.
The EP model of Boone et al. (2006) used a different
approach to reach a broadly similar conclusion: the wil-
debeest migration is driven by a combination of rainfall
and NDVI that together comprise an index of forage avail-
ability. We note that in the EP model, when two areas have
equal NDVI, wildebeest do not choose areas with higher
rainfall (and thus grass production) at any given time, but
rather areas in which the ratio of current rainfall to total
annual rainfall for a site is highest (Boone et al. 2006). In
the wet season, this ratio is highest in the plains, so the
wildebeest move there, but it is difﬁcult to see in practice
how assessing this ratio provides a plausible mechanism
to explain movement onto the plains. The comparison
between our model and that of Boone et al. (2006) in-
dicated a better ﬁt (27.4% vs. 13.4% of blocks with wil-
debeest present or observed in agreement) of our model
at a 5-km resolution (ﬁg. 6). This suggests that the in-
corporation of digestive constraints and plant protein con-
tent provide more reliable information about the resources
that wildebeest seek than NDVI. We show here that in-
corporating additional factors such as plant N concentra-
tion helps account more fully for the seasonal movement
into the plains, and the drive to exploit areas of high
protein intake (when available) could provide a concrete
mechanism to explain the migration. Given that Serengeti
ungulates tend to enter a period of protein deﬁciency to-
ward the end of the dry season (Sinclair 1977), it would
Wildebeest Migration in the Serengeti 441
Figure 6: Monthly wildebeest distributions from the recce data (A) and predicted by the best-ﬁt ordinary least squares model (I,T,N) at 5-km
resolution (B), with ﬁlled cells representing mean values of ≥250 individuals calculated over the period August 1969–August 1972.
not be surprising if high-protein areas were rapidly sought
out at the onset of the wet season.
Tree-Grass Competition, Water Availability,
and Other Factors
Our conclusions regarding the potential importance of the
suppressive effect of tree cover on grass biomass in de-
termining wildebeest movement patterns are somewhat
scale dependent. There is a negative correlation between
tree and grass cover in savannas (Scholes and Archer
1997). All else being equal, the presence of trees in the
woodlands and their absence in the plains should therefore
result in a greater amount of grass biomass per unit area
in the latter, and this difference could play a role in at-
tracting wildebeest to the plains at times when grass is
available. Our results do show that including tree cover
in the model increases the modeled migration distance
(ﬁg. 3A) compared with simpler grass biomass or intake
models, so tree-grass competition does play some role in
facilitating the migration. These results are less apparent
at the broader spatial scale, although it is possible that
heterogeneity in tree cover is more important in deter-
mining wildebeest distribution patterns at ﬁner scales, and
loss of information that results from aggregating data at
the broader spatial scale masks these effects. An alternative
possibility is that at a local scale, woody cover is correlated
with risk factors (e.g., predation).
Conversely, the distribution of water supplies helps to
explain wildebeest distribution patterns at the broader
scale (25 km) but not at 10 km. The value of our water
availability index (ﬂow accumulation) varies widely over
442 The American Naturalist
ﬁne spatial scales, depending on the idiosyncratic location
of major rivers. Two very dry cells could differ greatly in
terms of their proximity to water but would be treated
identically in our model. This is more likely to lead to
poor ﬁts at the ﬁner scale, since at the broader scale this
heterogeneity becomes diluted. Regardless of these scale
differences, however, the quantitative contribution of ﬂow
accumulation to model ﬁt is minor. In the resource func-
tion Zwe use in the model, food and water are combined
additively (table 1). Our parameter estimates suggest far
greater variation in the effect of the food term than in the
water term (table 2), so the latter is likely to be inﬂuential
only at the end of the dry season, when the food term
tends to zero and water is scarce.
Past work has suggested than Na can play an important
role in the behavioral ecology of Serengeti ungulates (Mc-
Naughton 1990; Tracy and McNaughton 1995; Wolanski
and Gereta 2001). Ungulates often experience Na deﬁcien-
cies, especially during pregnancy and lactation (Michell
1995), and select habitats and foods that offset these de-
ﬁciencies (Belovsky and Jordan 1981; Holdo et al. 2002),
so we hypothesized that the distribution of plant Na across
the landscape might inﬂuence wildebeest migratory move-
ments. In the end, this was not supported by our model.
We note, however, that our model ﬁt is poor during the
transition period when wildebeest typically move into the
western corridor (ﬁg. 4), where soil and plant Na levels
appear to be high (McNaughton 1988). It is also at this
time that lactation demands are high and Na stress likely
to be particularly important (Michell 1995). The lack of
ﬁt could thus be due to uncertainty in our plant Na GIS
layer, leading to poor spatial agreement between the animal
distribution and plant Na layers. Unlike N, which shows
quite a consistent southeast to northwest gradient across
the Serengeti, Na appears to show a more complex spatial
pattern, with pockets of high Na within a low-Na matrix
(ﬁg. 2F). As a consequence, the unbalanced sampling on
which the maps are based results in greater uncertainty in
Na than N mapping (since most cell values in the lattice
are based on interpolated quantities). Further sampling of
soil and plant nutrients across the landscape may clarify
this issue and shed light on the reasons for the preference
of wildebeest for the western corridor at the beginning of
the dry season.
Spatial Scale of Resource Tracking
A key ﬁnding of our model is that the size of the local
neighborhood that wildebeest track and move within is as
important as the overall spatial distribution of resources
and seasonality in determining the migration. In our
model, migratory behavior is an emergent property that
arises from an adaptive movement framework when wil-
debeest are able to track resources in a neighborhood with
a radius of at least 80 km and thus compare conditions
at this scale with conditions in their current location for
making movement choices. If their ability to track re-
sources remains highly localized, the model predicts that
they would not undertake the long-distance movements
that are necessary to generate the migration.
That wildebeest can respond in real time to environ-
mental cues to modify their migratory behavior has long
been known. Early studies of the Serengeti migration
showed that wildebeest and other species respond to both
intra- and interannual ﬂuctuations in the spatial distri-
bution of resources, most likely forage or surface water
linked to rainfall events (Swynnerton 1958; Grzimek and
Grzimek 1960; Talbot and Talbot 1963; Pennycuick 1975;
McNaughton 1979a). These researchers noted that migra-
tion routes and the timing of movement are highly variable
from year to year (Swynnerton 1958; Talbot and Talbot
1963; Pennycuick 1975), prompting McNaughton (1979a,
p. 57) to prefer the term “nomadic” rather than “migra-
tory” to describe wildebeest movements. It must be
pointed out, however, that factors other than large-scale
perception may drive wildebeest to move out of local re-
source patches. We assumed in our model that the average
wildebeest makes adaptive “decisions” based on immediate
comparisons among sites, but our results could also ﬁt
models with behavioral components involving memory
and genetically encoded movements.
We can outline several possibilities. At one extreme, only
real-time environmental cues and/or social information
drive the migration. It has long been noted that wildebeest
appear able to track stochastic rainfall events (and thus
ﬂushes of green grass) over large distances (Talbot and
Talbot 1963; McNaughton 1979b). Moreover, a combi-
nation of environmental and social cues picked up by
animals in a widely dispersed herd could give rise to an
“effective range” of perception that is greater than the local
neighborhood of any given individual (Grunbaum 1998;
Couzin et al. 2005; Couzin 2007). Couzin et al. (2005)
and Grunbaum (1998) provided a theoretical framework
for such an expanded effective range of perception, show-
ing that when social information from even a few indi-
viduals is conveyed to the group, collective behavior
emerges that effectively tracks resources across the land-
scape. By combining local environmental information and
direct perception of long-distance cues with social cues
from the larger herd, wildebeest may be able to move
effectively up “noisy” resource gradients, leading to an
emergent seasonal migration. For an isolated individual,
this task may be impossible when conditions are variable
(Couzin 2007). Although our model does not directly in-
clude social cues, it strongly suggests that extended per-
Wildebeest Migration in the Serengeti 443
ception neighborhoods are a prerequisite for effective
landscape-level exploitation of resources by wildebeest.
At the other extreme, the timing of and route taken
during the migration are better understood as evolved
traits resulting from selective pressure imposed by a long-
term moving average in spatiotemporal patterns of re-
source availability (Boone et al. 2006). This seems unlikely
to us, given the demonstrated correlation between time
spent in wet and dry season ranges and rainfall abundance
across years (Pennycuick 1975). A third hybrid possibility
is that the migration is the result of simultaneous short-
term responses to local environmental conditions coupled
with navigation-driven movements (stemming from past
experience or genetically coded behavior) acting at larger
spatial scales (Bailey et al. 1996; Fritz et al. 2003; Mueller
and Fagan 2008). The latter coarse-scale driver would per-
mit wildebeest to explore areas beyond their local neigh-
borhoods. This would have a synergistic effect on social
information mechanisms and extend the effective percep-
tion range of the herd, allowing wildebeest to move up
noisy environmental gradients with greater efﬁciency.
Large-scale environmental trends, being more predictable
than small-scale ﬂuctuations, may become internalized
over time by migrating herbivores, either through indi-
vidual experience or as a selective force (Boone et al. 2006),
and used as a tool for moving up noisy resource gradients.
The poor ﬁt of the wildebeest distribution to environ-
mental factors during the transition period (May–July),
when wildebeest move to the western corridor for the rut
(Talbot and Talbot 1963), may be explained by a switch
from environmental cues to a navigational mode during
this period (Mueller and Fagan 2008). This switch could
allow wildebeest to ﬁnd the rutting site at the appropriate
time. Memory (the past experience of an individual or
herd) has been identiﬁed as an important mechanism in
the movement behavior of large herbivores (Bailey et al.
1996; Dalziel et al. 2008) and may well play a role during
this period and cause a deviation from the short-term
resource-optimization strategy that operates at other times.
Further research is required to infer the extent to which
individually detected environmental versus social cues, and
opportunistic versus learned or genetically determined be-
havior (and the scales over which they operate), drive the
movement decisions of individual animals (Alerstam et al.
2003). Speciﬁcally, the simultaneous collection of data re-
lating to environmental factors, movement (as opposed to
the resulting distributional patterns), and social context
(behavior of members of the same or other species) would
provide a basis for teasing apart the contribution of social
cues after controlling for environment, for example; also,
a study of navigational skills and cues would provide a
basis for understanding the contribution of memory to
migratory patterns in wildebeest. It would be of particular
interest to understand the contribution of social cues and
memory and genetic factors in driving ﬂuid “nomadic”
migrations such as that of the wildebeest versus other types
of large-scale movement behavior (e.g., strict to-and-fro
migration) more typical of migratory systems (Alerstam
et al. 2003; Mueller and Fagan 2008).
The two key elements in our model that unequivocally
give rise to a seasonal wildebeest migration are the coun-
tervailing rainfall and fertility gradients that cut across the
Serengeti. Rainfall acts as a seasonal “switch” that controls
the availability (and to some extent, the quality) of grass
biomass: the length of the growing season is positively
correlated with the amount of rainfall received across the
ecosystem (McNaughton 1985; Boone et al. 2006), so the
dry plains have forage available only for a few months of
the year, but that forage is of high nutritional value when
available. Such opposing rainfall and fertility gradients are
a common feature of African savanna ecosystems (Bell
1982; Ruess and Seagle 1994) and may thus play a role in
driving ungulate migrations elsewhere on the continent,
such as the white-eared kob (Kobus kob) migration of the
Sudan (Fryxell and Sinclair 1988) or the wildebeest mi-
gration of the Kalahari (Williamson et al. 1988). Given
strong enough gradients over short enough distances to
make seasonal migrations feasible, our model results sug-
gest that the rainfall-fertility correlation provides the nec-
essary conditions for a migration to emerge. The necessity
of a minimum “resource tracking window” threshold is a
key insight into our understanding of how complex emer-
gent phenomena such as migrations have at least the po-
tential to be explained by the application of simple rules
within an adaptive movement framework. Our results do
not refute the existence of genetically programmed factors
as contributing factors driving the migration but rather
suggest that they may not be strictly necessary to explain
We would like to thank S. J. McNaughton for making soil
and plant nutritional data available to the National Center
for Ecological Analysis and Synthesis Biocomplexity in the
Serengeti Working Group and M. Coughenour for facil-
itating data interpretation and providing Shuttle Radar
Topography Mission data. We also thank M. Norton-
Grifﬁths for providing permission to use canopy cover data
and T. Sinclair and K. Metzger for facilitating access to
these data sets. Many other data sets have been compiled
and maintained by the Tanzania Wildlife Research Institute
(TAWIRI). B. Bolker provided valuable assistance and dis-
444 The American Naturalist
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models to spatial data sets, M. Barﬁeld provided comments
on an earlier version of the manuscript, and I. Couzin
provided valuable insights on the role of social cues in
driving movement behavior. We also thank three anony-
mous reviewers for their comments. We would like to
acknowledge the support of the National Science Foun-
dation Biocomplexity Program (DEB-0308486) and the
University of Florida Foundation.
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