Journal of Ecology 2008, 96, 1011–1022
doi: 10.1111/j.1365-2745.2007.01341.x
A mechanistic simulation model of seed dispersal by
animals
Blackwell Publishing Ltd
Heidrun Will* and Oliver Tackenberg
Institute of Ecology, Evolution and Diversity, University of Frankfurt, D-60323 Frankfurt (Main), Germany
Summary
1. In order to investigate seed dispersal by animals on a landscape scale, we developed the spatially
explicit, individual-based mechanistic model SEED (Simulation of Epi- and Endozoochorous Seed
Dispersal). The purpose of the model is to predict patterns and densities of seeds dispersed by
animals (especially mammals) within a simulated landscape.
2. The model was parameterized for sheep, cattle and deer as vectors but may be applied to other
animals if data for parameterization is available. The model data base currently includes parameter
values for about 100 plant species.
3. Seed attachment to and seed detachment from the fur, as well as seed excretion after passage
through the gut, are explicitly simulated by drawing randomly from distributions that were determined by standardized experiments. Animal movement is simulated as a correlated random walk,
but to increase reality of the model, radio-tracking data of animals can also be used.
4. A sensitivity analysis of SEED was conducted to identify the relative importance of plant and
animal traits. The analysis highlighted where the main gaps in our knowledge of seed dispersal processes lie. Even though in our study endozoochorous dispersal had the higher potential for longdistance dispersal compared to epizoochory, there is only scarce knowledge about seed production
and especially about the proportion of seeds eaten by an animal, parameters which were shown to
be of major importance for dispersal.
5. A comparison of variation in plant and animal traits, respectively, showed that dispersal kernels
depend more on changes in the animal vector than on the comparably little variation a particular
plant species can exhibit. For this reason, animal movement is, from all the dispersal-relevant
parameters, the one for which more exact data is most urgently needed.
6. Synthesis. The newly developed simulation model will help to understand, quantify and predict
long-distance seed dispersal by animals. The possibility to incorporate real landscapes and
movement data from very different animals makes the model generalizable and possibly applicable
to a wide range of scientific and applied questions.
Key-words: animal dispersal, animal movement, long-distance dispersal, mammals, mechanistic
model, plant traits, plant–animal interactions, seed dispersal, seed shadow, zoochory
Introduction
Seed dispersal is a key process in ecology, determining,
among other things, colonization, local and meta-population
dynamics, and the spatial structure of plant communities
(Nathan & Muller-Landau 2000). Long-distance dispersal
events, although typically rare, are especially crucial to
population spread, to the maintenance of genetic connectivity,
and hence to the regional survival of plant species (Cain et al.
2000).
*Correspondence author. E-mail: [email protected]
Against the background of changing land use, alien species
introduction and, in particular, climate change, it is extremely
important to better understand dispersal processes at different
spatial scales. Accurate measures of seed dispersal are essential
to assess its importance for different plant species and their
response to environmental changes. Yet, long-distance dispersal is extremely difficult to quantify empirically. Dispersal
models have long been used to quantify dispersal processes
(Levin et al. 1984). Classical diffusion models, however,
generally underestimated long-distance dispersal events, as
was shown by historical records and molecular analyses (Cain
et al. 1998; Godoy & Jordano 2001). Mixed dispersal models
© 2008 The Authors. Journal compilation © 2008 British Ecological Society
1012
H. Will & O. Tackenberg
with fat tails are also of limited use. They are indeed able to
predict long-distance dispersal as inferred from historical
records (Clark 1998), but disregard the fact that seed dispersal
by animals can basically not be modelled as a decreasing
function of distance. Instead, it requires the inclusion of
habitat preferences, behaviour and movement patterns of the
animals (Vellend et al. 2003; Russo et al. 2006).
Spatially explicit mechanistic models are a promising tool
for the study of long-distance dispersal and have achieved
considerable progress in quantifying wind dispersal processes
(Nathan et al. 2001; Tackenberg 2003; Soons et al. 2004;
Katul et al. 2005; Kuparinen 2006). Zoochorous dispersal,
however, is influenced by a large variety of – sometimes interrelated – plant and animal traits, which represent a serious
obstacle in developing dispersal models for zoochory. Empirical
data for many of the relevant factors are scarce and general
rules often not known. Consequently, few attempts have been
made to model seed dispersal by animals (Pakeman 2001;
Westcott et al. 2005; Morales & Carlo 2006; Russo et al. 2006;
Couvreur et al. 2007). With the exception of Pakeman (2001),
all of these studies simulated either only endo- or only
epizoochory by one specific animal vector within one specific
landscape. Pakeman (2001) took data for several animals into
account, but made very simplified assumptions about animal
movement.
To our knowledge, no study has hereto combined an
explicit simulation of animal movement with empirically
based routines for epi- and endozoochorous seed dispersal.
Recent studies of attachment and detachment of plant seeds
to and from animal fur (Couvreur et al. 2005; Tackenberg
et al. 2006; Will et al. 2007) filled an important knowledge
gap and made it possible to develop a model for epi- as well as
endozoochory which operates at the landscape scale and is
based on parameters empirically determined for different
plant and animal species.
Here, we present the spatially explicit, individual-based
mechanistic simulation model SEED (Simulation of Epi- and
Endozoochorous Seed Dispersal). The focus of our model lies
on dispersal via large mammals. Due to their comparatively
large home ranges and relatively long food retention times in
the gut (Warner 1981), they are potentially very effective
long-distance dispersal agents. We show that the mechanistic
model presented is a valuable tool not only to characterize
seed rain patterns, but also to better understand the processes
associated with seed dispersal and their relative importance.
Our model is the first to simulate both epi- and endozoochorous dispersal within the same modelling framework and
based on empirical trials. Using wild as well as domestic
animals as vectors, it is possible to run simulations for various
real and artificial landscapes within time scales relevant for longdistance dispersal. Suitable for studying many aspects of seed
dispersal, the model will be particularly useful for ecologists
and conservationists looking at plant species responses to
habitat fragmentation, climate change, invasive species and
restoration issues. Evolutionary ecologists will also gain from
the model as trade-offs between certain plant traits (e.g. those
that facilitate either epi- or endozoochory) can be studied.
Modelling approach
The model predicts patterns and densities of animal-dispersed
seeds within a simulated landscape. It is designed to show how
certain plant and animal traits relate to the shape and scale of
animal-generated dispersal kernels. It was parameterized for
sheep, cattle and deer as vectors, but may be applied to other
animals so long as data for parameterization are available.
The model data base currently includes parameter values for
about 100 plant species (see Table 1 and Table S1 in Supplementary Material).
Here, we first outline the basic model concepts, discuss the
position of the model within the context of current knowledge
on seed dispersal processes and highlight how it advances our
understanding of these processes. We next introduce the individual components of the model and show how the resulting
dispersal kernels and spatial patterns change when more
factors enter incrementally into the model (Fig. 1). We will
then proceed with a short overview of the most important
model processes. A detailed model description is included in
Appendix S1 in the Supplementary Material.
(1) D E T A C H M E N T A N D D E F E C A T I O N
Plant seed retention in animal fur is probably one of the
dispersal processes that has been studied longest (e.g. Agnew
& Flux 1970 and Bullock & Primack 1977; more recent studies
include Fischer et al. 1996; Couvreur et al. 2005; Mouissie
et al. 2005). Several studies have shown that seed retention in
the fur or seed detachment from the fur, respectively, depends
on fur type, seed mass and seed morphology (Couvreur
et al. 2004; Mouissie et al. 2005; Römermann et al. 2005b;
Tackenberg et al. 2006). Until now, however, our knowledge
of seed retention capabilities was restricted to relatively few
plant species. Besides, data from different studies were often
not comparable due to differing study designs or, in the case
of field experiments, due to experimental conditions that were
hard to control or to repeat. To parameterize our model, we
experimentally determined detachment curves for more than
100 plant species according to the protocol in Tackenberg
et al. (2006). To our knowledge, no previous study has compiled
such curves for as many species following one standardized
protocol. The parameters of the observed detachment curves
were determined for each measured plant species by maximum
likelihood fit to a gamma distribution. These parameters are
shape, scale and the proportion of retained seeds, i.e. those
seeds that did not detach from the fur during the time span
of the experiment and that are hereafter referred to as ‘stuck’
(F. Schurr, pers. comm.).
Excretion curves for endozoochory were derived from
feeding experiments with sheep and cattle (Bonn 2005). They
were assumed to be identical for different plant species,
whereas survival rates (see next section) were determined
separately for each species. Excretion curves are mathematically similar to the detachment curves from the fur and were
also derived by maximum likelihood fit to a gamma distribution.
The main difference between detachment (fur) and excretion
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022
Simulation model of seed dispersal by animals
1013
Table 1. Overview of model parameters. For each parameter, a typical value is given. Plant species parameters are known for approximately 100
species; animal species parameters for sheep, cattle and deer (partial). Table S1 in Supplementary Material lists the values known for each plant
species
Parameter
Unit
Common value
Range
Reference for method
Seed attachment fur
Seed exposure
Seed surface structure
Height of infructescence
Animal height (min., max.)
Seed production
–
–
m
m
m–2
Enclosed
0.8
0.5
0.3–0.8
1 000 000
Enclosed to fully exposed
0–1
0.09–1.5
0.3–1.5
276–18 780 889
Will et al. (2007)
Will et al. (2007)
Bonn et al. (2000)
Grzimek (1988)
Sera & Sery (2004)
%
50
0–100
Römermann et al. (2005b)
%
m–2
10
1 000 000
0–100
276–18 780 889
Estimation
Sera & Sery (2004)
Gut passage
Parameters of excretion curve:
Shape
Scale
Prop. of seeds digested
1.8–7
6–21
0 –100
Bonn (2005);
Römermann et al. (2005a)
%
5
8
96
Animal movement
Speed
Turning angle
m min–1
°
5
180
4 –13
0–360
Estimation
Estimation
Landscape
Plant cover
Landscape size
Number of attractive sites
Size of attractive sites
Position of attractive sites
%
km2
–
m2
–
25
10 × 10 km
15
20 000
random
1–100
1–100
0-any
1-any
–
Seed detachment fur
Retention after one hour (determining
the parameters of the retention curve)
Seed ingestion
Proportion of seeds eaten
Seed production
(gut) curves is that the latter start with a lag phase (with no
seeds being excreted), followed by a steady increase in the
number of excreted seeds. A peak of seed numbers is reached
some time after ingestion and following his peak the curve
steadily declines to zero (Fig. 1a). Although gut passage rates
have already been investigated for a relatively long time
(e.g. Warner 1981; Jones & Simao Neto 1987; Gardener et al.
1993; Ramos et al. 2006; Varela & Bucher 2006), only a few
studies have simulated endozoochorous seed dispersal based
on empirically determined gut passage rates. The most
prominent exceptions (Westcott et al. 2005; Russo et al. 2006)
designed their models so as to reflect the specific environment
and dispersing animal under study (tropical forest, a large
bird and a monkey species, respectively), whereas our model
aims at a more general simulation of seed dispersal – including
different dispersal vectors in various kinds of landscapes.
(2) A T T A C H M E N T , I N G E S T I O N A N D S U R V I V A L
Unlike detachment and excretion curves, the proportion of
seeds that actually attach to the fur of a passing animal was
not known until recently. Will et al. (2007) developed a
general linear model of seed attachment to sheep wool. This
model predicts the proportion of attaching seeds (from all
seeds in the infructescence) after one passing event. Accord-
5
6
7
Arbitrarily determined or
based on real landscapes (maps)
ing to this study, attachment depends on seed exposure and
seed surface structure and may differ markedly between plant
species. For the current study, we also developed mathematical
models to predict attachment to cattle and deer fur (see
Appendix S1). By combining seed attachment with seed
detachment, we were able to calculate dispersal kernels in
relation to all seeds passed by the animal (Fig. 1b).
Unfortunately, exact data on the amount of seeds of a given
plant species eaten by a certain animal were not available.
To substitute missing data, the proportion of seeds eaten by
the animal is determined through a constant uptake rate
depending on the distance travelled, i.e. 10% of all seeds the
animal passed while taking one step.
The number of endozoochorously dispersed seeds, however,
is not only reduced because only a certain proportion of seeds
are eaten. During gut passage, there might be an additional
loss of seeds due to digestion (in the study described by Bonn,
2005, only 3.6% of all viable seeds survived gut passage, i.e.
germinated from the dung). To account for this fact, the
excretion curve, like the detachment curve, also contains a
third plant species-specific parameter for all the seeds that are
not deposited due to chewing or digestion-related destruction.
Based on our data and the assumptions of the proportion
of seeds eaten, it is possible to assess the relative proportions
of epi- and endozoochory (Fig. 1b). Previous studies usually
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022
1014 H. Will & O. Tackenberg
Fig. 1. (a)–(d) Stepwise inclusion of additional model parameters and processes. In each of the four figures, one or two additional model
parameters are included. Black dots () denote epizoochorously, grey dots () endozoochorously dispersed seeds. Plant parameters refer to
Achillea millefolium. Animal parameters refer to red deer; radio-tracking data for one individual of this species was incorporated into the model
(recorded during the summer and autumn of 2004 in the north-east German lowlands). Graph (a) shows the proportion of seeds that detached
or were excreted at a certain point of time, with 100% corresponding to all seeds being dispersed by the respective dispersal type. Complementing
this simulation with the processes of attachment, ingestion, and also with species survival rate, leads to a shift in the relative position of the
dispersal kernels to each other (b). 100% in (b) and the following figures refers to all seeds of the plant species the animal passed. Including
animal movement (c) transforms the relatively smooth dispersal kernels of (a) and (b) into multimodal kernels with peaks representing areas with
prolonged residence time. The map in (d) shows grasslands (encircled areas) as habitats of A. millefolium and in light grey places where epi- and
endozoochorously dispersed seeds can be found. An analysis of the spatial pattern reveals that although seeds are dispersed for much longer
distances endozoochorously, the probability of an endozoochorously dispersed seed to arrive in an unsuitable habitat is much higher in
comparison to epizoochory.
focused on one dispersal type and consequently were not able
to point out the relative proportion of seeds dispersed in
either way, although this proportion may alter achieved
dispersal distances considerably (compare Fig. 1a and b). To
draw definite conclusions more data is needed on the actual
proportion of seeds an animal eats. We provide the tool, but
the final answer to this question is left open until we can
parameterize the model adequately in this respect.
(3) A N I M A L M O V E M E N T
The detachment and excretion curves described above are
plotted against time. By including animal movement, we are
able to plot dispersed seeds against distance (Fig. 1c). The
behaviour of the dispersing animal often leads to multimodal
curves because many animals tend to linger in certain areas of
their range, while moving relatively fast and straight through
other areas (Morales et al. 2004; Russo et al. 2006). To address
animal movement as realistically as possible, our model
offers the possibility to use radio-tracking data to simulate
seed dispersal based on observed animal movement. As these
data are scarce, we also implemented animal movement as
a correlated random walk. For many animals, correlated
random walk models have been shown to represent animal
movement appropriately, even with relatively few descriptive
parameters being included (Bovet & Benhamou 1988;
Turchin 1991; Byers 2001).
(4) L A N D S C A P E
–
SPATIAL COMPONENT
One of the outstanding features of the model is the spatially
explicit simulation of seed dispersal that allows predictions of
seed dispersal within specific (artificial or real) landscapes
(Figs 1d and 4). The inclusion of the second dimension is
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022
Simulation model of seed dispersal by animals
1015
Table 2. Scheduling of processes. Every time step, the routines listed are processed in the given order. ‘Distractible CRW’ means that the animals
may turn in wider angles (90° to the left and right, respectively). ‘Focused CRW’ is more straight ahead; the animals may only choose turning
angles half as wide as in the ‘distractible mode’
Process
Animal movement
Description
FLM (patchy landscape)
CLM (uniform landscape)
If animals are on patch: each animal makes one step
individually according to a ‘distracted’ correlated
random walk.
Each animal makes one step individually according to
a correlated random walk (‘distracted’ if on attractive site,
‘focused’ if not on attractive site)
If animals are between two patches: all animals make
one step collectively following a straight line to the
next patch
Seed attachment
Seed ingestion
Seed excretion
Seed detachment
Seeds attach to the fur of an animal – a new fur seed parcel is initialized.
Seeds are ingested – a new gut seed parcel is initialized.
Seeds leave a gut parcel and are added to the seeds in the current grid cell.
Seeds leave a fur parcel and are added to the seeds in the current grid cell.
particularly valuable when investigating the influence of
animal movement or the effect of habitat fragmentation. Only
at the spatial level it is possible to see whether seeds of a
specific plant species are actually dispersed to a new suitable
habitat. Again, the results of the previous step may be considerably altered since the dispersal type with the longest
dispersal distances may also have the greatest probability of
dispersing a seed to an unsuitable habitat (Fig. 1d).
when the animal passes a plant. For every group of seeds that
attached at the same time to the same animal, epizoochorous
dispersal is simulated as successive dropping down from the
fur. Animals also ingest seeds when they pass a palatable
plant. As before, dispersal is simulated for every group of
seeds that was eaten at the same time by the same animal as
successive defecating events (Table 2).
Example model runs
Model overview
The model comprises two simulation modes which may be
treated as two distinct, but closely related models. Both
(sub)models simulate the processes of seed attachment,
ingestion, detachment and excretion in exactly the same way.
They differ only in their landscape type and, accordingly, in
the way animals move. Here, we refer to the first model as
CLM (Continuous Landscape Model) and to the second as
FLM (Fragmented Landscape Model). The landscape of the
FLM represents isolated habitat patches. The plant species
for which dispersal is simulated occurs exclusively within the
patches. The landscape of the CLM is one (large) area which
may contain sites which are especially attractive for the
animals. In contrast to the FLM, the considered plant species
is uniformly distributed within the landscape.
Animal movement is simulated in different ways. In the
FLM, animals move according to a correlated random walk
on habitat patches but take the shortest possible route when
moving from one patch to another. That means movement is
individual within patches and collective (within a group)
when moving between patches. In the CLM, animal movement is always simulated as a correlated random walk with
its parameters depending on site attractiveness. Additionally, it is possible to use radio-tracking data of wild animals
to simulate animal movement according to empirical
observations.
In both the fragmented and continuous landscape model, a
certain proportion of seeds attach to the fur of an animal
(1) F R A G M E N T E D L A N D S C A P E M O D E L
To illustrate the effects of differing plant and animal traits
and to demonstrate a possible model application, we simulated
seed dispersal to isolated grassland sites for three herbaceous
species (Daucus carota L., Festuca ovina L. s.s. and Galium verum
L. s.s.). The five considered patches of calcareous grassland,
at most 4 km away from each other, are located within a low
mountain range in Central Bavaria. The movement of the
simulated flock is identical to the trail a local shepherd took
according to her own account in autumn 2005. The real flock
consisted of about 750 sheep. We used this animal species and
flock size for our model runs, but also performed the same
simulation for cattle to show the effects of fur type and gut
passage rate. Seed production for the three plant species was
taken from Sera & Sery (2004), plant species frequency and
cover was chosen according to Witschel (1980).
(2) C O N T I N U O U S L A N D S C A P E M O D E L
Additionally, the model was run in the continuous landscape
mode for the common herb Achillea millefolium L. as plant
species and with movement data from the animal sensitivity
analysis (varied animal traits: movement speed (1–30 m min–1)
and turning angle (0° to 360 °). The aim of this second example
run is to show the proportion of variation originating from
plant and animal traits, respectively. The plant traits varied
were attachment (0–6.25%), detachment (after 1 h on the
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022
1016
H. Will & O. Tackenberg
shaking machine: 15–85% of applied seeds had detached), gut
passage rate and survival after ingestion (0.4 –10.7%). The
ranges of all parameter values are based on empirical trials
where infructescences or seeds of A. millefolium were tested.
To compare variation within one plant species and variation
between all plant species, the same animal movement data
were also used to run the model with the plant parameter set
from the main sensitivity analysis (below).
SENSITIVITY ANALYSIS
To explore the behaviour of the model, we performed a sensitivity analysis where variables related to plants and animals,
respectively, were tested separately. This separation was
introduced because results of the main (plant related)
sensitivity analysis should be independent of animal movement and hence independent of the process where the least
empirical information is incorporated into the model. Since
all response variables in the main sensitivity analysis are
related to dispersal time, it is possible to connect them to
animal movement afterwards. By knowing which distance the
animal covered after a certain time, we can calculate the
distance a median time seed and a 95th percentile time seed,
respectively, is transported.
Response variables for the main sensitivity analysis were:
the number of seeds that detached or were excreted more than
one week after having attached or been eaten, the median
and the 95th percentile of the dispersal time curve . Values for
the varied parameters (seed production, seed attachment,
seed ingestion, shape and scale for both fur detachment and
gut excretion curves, and the proportion of seeds attaching to
the fur for very long or being digested) were obtained by Latin
Hypercube sampling (McKay et al. 1979). Values of the
parameters were sampled evenly from 19 intervals within the
ranges given in Table 1. Sampling was repeated 10 times. For
each randomly sampled parameter combination, a dispersal
simulation was performed with 10 animals over four months.
Altogether, 190 simulations were run, resulting in an equal
number of values for the response variables. The importance
of the tested parameters for the response variables was
estimated by stepwise multiple rank regressions (Conover &
Iman 1981). To obtain a measure for the relative importance of
the significant parameters for the respective response variable,
the standardized regression coefficients were calculated as the
absolute ratio of the coefficient and the corresponding standard error.
Tested animal variables were animal speed and turning
angles. Since the focus of the animal sensitivity analysis lay
on movement, beeline distance covered within 1 week and
3 months, respectively, were chosen as response variables.
Movement speed was tested in 1 ms–1 steps between 1 and 30,
and turning angles in 45° steps between 0° and 360°. A turning angle of 0° means absolutely straight movement (no turning at all), an angle of 180° means that the animal can turn
between –90° and 90°. If the turning angle is 360°, the animal
can turn between –180° and 180°, i.e. it can take every possible
direction.
Results
EXAMPLE RUNS
(1) Fragmented landscape model
Daucus carota had the highest proportion of seeds dispersed
to the fifth patch (0.4% with sheep and 0.02% with cattle),
whereas seeds of Festuca ovina arrived at this site in the
highest numbers (1.23 million with sheep and 140 276 with
cattle) (Fig. 2). Both species may be regarded as successful
long-distance dispersers. Their strategy, however, differs.
Whereas D. carota possesses hooked seeds (which aid in
epizoochorous dispersal), F. ovina produces exceedingly high
numbers of seeds, thereby ensuring dispersal to distant sites
despite relatively poor attachment and retention in sheep
fur. Up to 24 times more seeds were dispersed in the fur of
sheep than in cattle fur; epizoochorous dispersal distances
were also larger with sheep compared to cattle. Median
endozoochorous dispersal distances were higher for cattledispersed seeds because cattle excrete most of the seeds
later than sheep (averaged over the three species, sheep
excreted 36% of all seeds on the third patch, whereas cattle
excreted 46% on this patch). For cattle, endozoochory contributed more to the arrival at the last patch (four times
more endozoochorously dispersed seeds), whereas 94% of
the sheep-dispersed seeds on the last patch arrived there via
epizoochory.
(2) Continuous landscape model
Seeds were dispersed for significantly longer median and
mean distances by endo- than by epizoochory (P < 0.001 for
both Achillea millefolium and all plant species, Fig. 3). Looking
only at A. millefolium, mean (and 95th percentile) dispersal
distance for endozoochory and epizoochory were 2125 m
(4514 m) and 153 m (874 m), respectively. For all plant species,
the difference between both dispersal types was somewhat
smaller, but endozoochory still had a considerably greater
potential for long-distance dispersal (mean distance: 2870 m
endo-, and 450 m epizoochory; 95th percentile distance:
6314 m endo-, and 1644 m epizoochory). Dispersal distance
spectra varied largely with each plant as well as with varying
animal traits. However, the resulting variation in dispersal
distances was larger when animal traits were varied. Slow
moving animals with large turning angles disperse seeds for
considerably shorter distances than fast moving animals with
small turning angles (Fig. 4). Dispersal distances are also
larger when there is no spatial restriction due to a small animal
home range.
SENSITIVITY ANALYSIS
The median epizoochorous dispersal distance as well as the
95th percentile are mainly influenced by the shape of the seed
detachment curve (t = 22.26 and 13.18, respectively, Table 3).
Seed attachment to fur is less relevant (t = 3.92 and 3.01,
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022
Simulation model of seed dispersal by animals 1017
Fig. 2. Proportion and absolute number of seeds dispersed to five grazing sites. The map above gives an overview of the spatial location of the
five calcareous grassland sites which were grazed by a large flock of sheep in 2005 in the order indicated by the boxed numbers. Each site was
grazed for one day. For dispersal simulations, it was assumed that seeds only attached or were eaten at the first (darker painted) site. In addition
to sheep (s), the simulation was also run for a flock of cattle (c) to show the effect of different fur types and gut passage rates. Grey columns
represent epizoochorous, black columns endozoochorous dispersed seeds. The proportion of dispersed seeds refers to the total number of seeds
available at the first site.
respectively). Both the median and the 95th percentile
endozoochorous dispersal distance are strongly influenced by
the scale and shape of the seed excretion curve; for the 95th
percentile, however, the scale of this curve is of somewhat
greater importance than the shape (t = 14.96 and 9.24,
respectively). Shape and scale of the seed excretion curve are
– in contrast to the fur detachment curve – not significant
parameters for the number of seeds dispersed in the gut for
more than 1 week. Instead, the proportion of seeds digested is
much more important for this response variable than the proportion of long-attaching seeds (‘stuck’) for epizoochorous
dispersal.
For the beeline distance one animal covers within 1 week or
1 month, turning angles are slightly more important than
movement speed if the (probably unrealistic) case of no
turning (straight walking) is included (Fig. 5). If only turning
angles greater than 0° are included, movement speed is of
greater significance for the distances covered (distance
covered within 1 week (1 month): t = 41.55 (32.93) for speed
and t = –31.47 (–25.08) for turning angles).
Discussion
SENSITIVITY ANALYSIS: WHICH ARE THE MOST
IMPORTANT PARAMETERS?
For further refinement of the model, it will be crucial to gather
more empirical data on relevant plant and animal traits. Since
data collection is often very costly and time consuming, a
concentration on the most important parameters would be
advisable. Also, any grazing management regime based on
predictions from SEED will be more efficient if centred on
sensitive parameters that are easy to manipulate.
For a real plant individual or population, the actual
number of seeds that is dispersed for a minimum distance will
be more relevant than the median or maximum distance itself,
since a minimum seed density is needed to make probable a
successful germination and establishment (Augspurger &
Kitajima 1992). For the number of seeds dispersed, the most
important parameters for epizoochory are the scale of seed
detachment, seed attachment, and seed production (in this
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022
1018
H. Will & O. Tackenberg
Fig. 3. (a)–(c) Results of the example model
run for Achillea millefolium L. vs. all plants.
All left graphs show results for epizoochory
(a, c, e); endozoochorous seed dispersal is
displayed in the right graphs (b, d, f ). The
upper graphs (a, b) show dispersal curves
with standard deviations (grey shading) averaged over 15 (endozoochory, right) and 20
(epizoochory, left) model runs with varying
attachment, detachment, gut passage rate,
and survival after ingestion. For these curves,
animal movement speed and turning angle
were constant (15 m min–1, 180°). The middle
graphs (c, d) are based on the same (constant)
animal parameters but plant parameters were
varied over the scale of all plant species for
which data is known (190 model runs). The
lower graphs (e, f ) show curves averaged over
240 model runs with varying movement speed
and turning angles. In these simulations, plant
traits were constant (average traits of A.
millefolium: attachment 1.5%, detachment:
shape 5.67, scale 0.13, stuck in fur 6%, gut
passage: shape 4.57, scale 9.67, and 3%
survival).
Fig. 4. Pattern of epizochorously dispersed seeds for varying animal movement. The graphs show seed dispersal patterns resulting when one
animal moves always with the same speed (15 m min–1) but with turning angles varying from (a) 45° (–22.5° to 22.5°) to (b) 180° (–90° to 90°)
and (c) 360° (–180° to 180°). The more directed the animal walks the larger is the total area covered with seeds, with seed density declining. The
total number of dispersed seeds was always the same.
order); for endozoochory these parameters are survival
rate, proportion of seeds eaten, and seed production. While
focusing only on the significance of dispersal-aiding attributes of diaspores, the importance of seed production has
been recognized only a few times (Eriksson & Jakobsson
1999; Bruun & Poschlod 2006; Tackenberg & Stöcklin 2007).
Given our results, it should not be neglected, at least if the
over-all dispersal success (including recruitment) is considered.
The high importance of seed attachment, ingestion
(proportion of seeds eaten) and survival rate was expected.
However, data on seed ingestion and gut passage survival are
scarce and it would be of great value if more feeding experiments were conducted for a range of plant and animal species.
The need for more feeding experiments is also expressed by
the significance of gut passage shape and scale for the median
and 95th percentile of the dispersal curve.
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022
Simulation model of seed dispersal by animals 1019
Table 3. Results of sensitivity analysis. For each parameter varied in the sensitivity analysis, the regression coefficients (RC) in rank-based
multiple regressions with the following response variables are given: number of seeds attaching to the fur or being transported in the gut for more
than 1 week (number), median (median) and 95th percentile (perc.) of the dispersal time curve for fur and gut separately, and beeline distance
covered within 1 week and 1 month, respectively (dweek, dmonth). NS = not significant, 0° included/excluded = including or excluding absolutely
straight movement with no turning at all.
Variable
Epizoochorous dispersal
Seed production
Seed attachment to fur
Seed detachment (shape)
Seed detachment (scale)
Proportion of seeds ‘stuck’
Endozoochorous dispersal
Seed production
Proportion of seeds eaten
Gut passage rate (shape)
Gut passage rate (scale)
Proportion of seeds digested
RC number
RC median
RC perc
9.71
10.05
9.64
11.17
–2.35
NS
3.92
22.26
5.37
NS
NS
3.01
13.18
9.38
NS
9.13
11.62
NS
NS
–11.97
NS
4.66
11.40
13.96
NS
NS
4.03
9.24
14.96
NS
RC dmonth
RC dweek
Animal movement
0° included
0° excluded
0° included
0° excluded
Movement speed
Turning angles
27.30
–31.55
41.55
–31.47
23.16
–27.50
32.93
–25.08
Fig. 5. Effect of speed and turning angle on
beeline distance covered after one week.
Since simulations were run within a simulated
landscape of 10 × 10 km and animals started
in the centre of the area, the maximum
distance to the start point is approximately
7 km. Covered distances increase linearly
with speed. The relationship between turning angles and covered distances, however,
is clearly non-linear: Changes in narrow
turning angles (for example from 20° to 40°)
have a much stronger effect on distance than
changes in wide turning angles (for example
from 320° to 340°).
Interestingly, even for the absolute number of seeds dispersed for a minimum time, the scale of fur detachment
turned out to be the most significant parameter. For the
median and (less so) for the 95th percentile of the dispersal
curve, shape is more relevant than scale, but both parameters
are decisive for the dispersal distance spectrum. Further
research should therefore focus on more detailed studies,
preferably also in the field, of seed detachment from the fur.
ANIMAL MOVEMENT
When comparing variability within the traits of one plant
species and variability within the traits of animals potentially
dispersing this species, it is evident that dispersal failure or
success depends much more on changes in the animal vector
than on the comparably little variation a specific plant species
can exhibit. Even well-adhering seeds, for example, cannot be
dispersed far when attaching to the fur of an animal that is
either very slow-moving or that possesses a very small home
(and movement) range. Conversely, it is possible for a large
and heavy seed that is retained in the fur for short time spans
to be dispersed for long distances when the dispersing animal
moves fast and relatively straight. The influence of the animal
is still more pronounced when considering endozoochorous
dispersal since the rate at which single seeds pass through the
digestive tract of animals depends on many factors (such as
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022
1020
H. Will & O. Tackenberg
animal species, animal age, health, movement, and food
quality and quantity), few of which are related to the seed (or
the plant species) itself.
For this reason, more exact data on animal movement is,
from all the dispersal-relevant parameters, most urgently
required. Russo et al. (2006) have also shown that the incorporation of spatially explicit information on disperser behaviour
is indispensable in order to provide a realistic description
of plant seed shadows. The compilation of published home
range sizes for a number of (larger) animal species alone
would improve model predictions regarding the spatial extent
of seed dispersal. Regarding the spatial pattern of dispersed
seeds, we need more information on animal movement, especially on movement speed and the alternation of exploratory
moves (with little turns) and encamped activity (with lots of
turns in short succession), an alternation that has been found
in elk movement (Morales et al. 2004). It would also be valuable
to know how these movement patterns relate to grazing
activity and dung excretion. For many animals it is known
that dung excretion mainly occurs at resting places, leading to
a more concentrated dropping of seeds than from the fur
(Kohler et al. 2006).
ABILITIES AND LIMITATIONS OF THE MODEL
One great advantage of SEED is the explicit simulation of
seed attachment to and seed detachment from the fur, as well
as seed excretion after passage through the gut. All of these
processes are modelled based on empirical trials. The plant
traits determining both seed attachment and detachment potentials have been identified in previous studies
(Römermann et al. 2005b; Tackenberg et al. 2006; Will et al.
2007). Using SEED, it is now possible to estimate the relative
importance of both processes and the relevant plant traits,
respectively.
Another strength of SEED is the joint utilization of both
plant- and animal-related parameters. There have been quite
a number of successful attempts to model animal movement
in space (Bovet & Benhamou 1988; Turchin 1991; Zollner &
Lima 1999; Byers 2001; Morales et al. 2004; Frair et al. 2005;
Morales et al. 2005; Van Dyck & Baguette 2005; Vuilleumier
& Metzger 2006). Nevertheless, only few studies have tried to
amend models of animal movement with routines for seed
dispersal (exceptions are, for example, Westcott et al. 2005,
Morales & Carlo 2006, Russo et al. 2006 and Couvreur et al.
2007). However, all of these studies simulated either only
frugivory or only epizoochory by one specific animal vector
within one specific landscape. The current study adds to these
models the possibility of simulating both epi- and endozoochorous dispersal by different animals within the same
modelling framework and based on empirical trials. Moreover,
it is possible to run simulations for different real landscapes
within long-distance dispersal-relevant time scales.
Admittedly, the great level of spatial and temporal detail
comes at a cost because the processing of especially adhesive
seed dispersal over longer periods of time can be quite computing power-intensive. Another drawback of the model is
derived from one of its advantages: since attachment, detachment, and excretion curves are empirically based, simulations
can only be run for a certain plant species when either its
relevant traits are known (attachment) or when detachment
curves were experimentally measured. Also, a certain animal
vector can only be included when typical movement features
and gut passage rates are known. For many plant species and
a few animal species, however, these data are already available
and are included in the model’s data base.
POSSIBLE FIELDS OF APPLICATION
Model results could be used as the basis for plant demographic studies, for example for predicting the dynamics and
spatial distributions of seedling populations. SEED is also well
suited to comparing spatial occurrences of metapopulations
with predictions of seed dispersal between fragmented
populations. In some cases, habitat fragmentation (resulting
in the formation of metapopulations) may increase the
extinction risk for a plant species (Levin et al. 2003). SEED
may be applied to test whether zoochorous seed transport can
lead to dispersal rates allowing metapopulation persistence.
It is also possible to reconstruct the re-immigration of plant
species into former habitats following deglaciation. Many
plant species showed considerable movement speeds while
travelling from refugia into recently deglaciated areas (Cain
et al. 1998). It was often hypothesized that these speeds could
only have been achieved by travelling via animals (Pakeman
2001; Vellend et al. 2003). Scaled up to a continental (spatial)
and century-long (temporal) scale, SEED could be used to
test this hypothesis by comparing historical range expansion
rates to those predicted by the model. To increase reality of
the model, radio-tracking data of wild animals wearing GPS
collars can be easily added to investigate the effect of actual
movement patterns on dispersal kernels. This might be especially relevant for seed dispersal research in tropical forests
where wild animals are still more important dispersal vectors
than in anthropogenically modified landscapes.
Further applications of the model may also include nature
conservation issues, such as the dispersal of invasive species
and the (often dispersal-limited) restoration of species-rich
grasslands. Management or restoration scenarios could be
included into and tested with SEED to aid in the decisionmaking process of planning authorities. The SEED data base
can be easily extended to include further plant or animal species
as soon as dispersal-relevant data is available for them. The
data base can be used to compare different plant species with
respect to their zoochorous dispersal potential or to test the
relative importance of plant and/or animal traits or of dispersal
mechanisms (epi- or endozoochory) for different plant species.
Conclusion
Currently, seed dispersal by wind is probably the best-studied
dispersal mechanism and there are a number of mechanistic
wind dispersal models that have been proven to realistically
simulate dispersal curves (Nathan et al. 2001; Tackenberg
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022
Simulation model of seed dispersal by animals 1021
2003; Soons et al. 2004; Schurr et al. 2005). By developing a
model for seed dispersal by animals, we add to the network of
models aiming to understand, quantify and predict longdistance dispersal (Nathan 2005). Moreover, SEED offers the
possibility to incorporate movement data from very different
animals, thus being generalizable and possibly applicable to a
wide range of scientific and applied investigations.
Acknowledgements
We thank Stefanie Kahmen, Robert Will and Frank Schurr for help with model
development and implementation, Christine Römermann for her efforts in data
collection, and Siegfried Rieger for providing radio-tracking data for red deer.
Angela Moles and two anonymous referees made valuable comments that
helped in improving earlier versions of this manuscript. The German Research
Foundation (DFG) kindly supported the project (TA 311/2–1,2).
References
Agnew, A.D.Q. & Flux, J.E.C. (1970) Plant dispersal by hares (Lepus capensis
L.) in Kenya. Ecology, 51, 735–737.
Augspurger, C.K. & Kitajima, K. (1992) Experimental studies of seedling
recruitment from contrasting seed distributions. Ecology, 73, 1270–
1284.
Bonn, S. (2005) Dispersal of plants in the Central European landscape. Dispersal
processes and assessment of dispersal potential exemplified for endozoochory.
PhD Thesis, University of Regensburg, Regensburg.
Bonn, S., Poschlod, P. & Tackenberg, O. (2000) ‘Diasporus’: a database for
diaspore dispersal: concept and applications in case studies for risk assessment. Zeitschrift für Ökologie und Naturschutz, 9, 85–98.
Bovet, P. & Benhamou, S. (1988) Spatial analysis of animals’ movements using
a correlated random walk model. Journal of Theoretical Biology, 131, 419–
433.
Bruun, H.H. & Poschlod, P. (2006) Why are small seeds dispersed through
animal guts: large numbers or seed size per se? Oikos, 113, 402–411.
Bullock, S.H. & Primack, R.B. (1977) Comparative experimental study of seed
dispersal on animals. Ecology, 58, 681–686.
Byers, J.A. (2001) Correlated random walk equations of animal dispersal
resolved by simulation. Ecology, 82, 1680–1690.
Cain, M.L., Damman, H. & Muir, A. (1998) Seed dispersal and the Holocene
migration of woodland herbs. Ecological Monographs, 68, 325–347.
Cain, M.L., Milligan, B.G. & Strand, A.E. (2000) Long-distance seed dispersal
in plant populations. American Journal of Botany, 87, 1217–1227.
Clark, J.S. (1998) Why trees migrate so fast: confronting theory with dispersal
biology and palaeorecord. American Naturalist, 152, 204–224.
Conover, W.J. & Iman, R.L. (1981) Rank transformations as a bridge between
parametric and nonparametric statistics. American Statistician, 35, 124–
129.
Couvreur, M., Vandenberghe, B., Verheyen, K. & Hermy, M. (2004) An experimental assessment of seed adhesivity on animal furs. Seed Science Research,
14, 147–159.
Couvreur, M., Verheyen, K. & Hermy, M. (2005) Experimental assessment of
plant seed retention times in fur of cattle and horse. Flora, 200, 136–147.
Couvreur, M., Verheyen, K., Vellend, M., Lamoot, I., Cosyns, E., Hoffmann, M.
& Hermy, M. (2007) Epizoochory by large herbivores: merging data with
models. Basic and Applied Ecology, doi: 10.1016/j.baae.2006.12.002.
Eriksson, O. & Jakobsson, A. (1999) Recruitment trade-offs and the evolution
of dispersal mechanisms in plants. Evolutionary Ecology, 13, 411–423.
Fischer, S.F., Poschlod, P. & Beinlich, B. (1996) Experimental studies on the
dispersal of plants and animals on sheep in calcareous grasslands. Journal of
Applied Ecology, 33, 1206–1222.
Frair, J.L., Merrill, E.H., Visscher, D.R., Fortin, D., Beyer, H.L. & Morales,
J.M. (2005) Scales of movement by elk (Cervus elaphus) in response to
heterogeneity in forage resources and predation risk. Landscape Ecology, 20,
273 –287.
Gardener, C.J., McIvor, J.G. & Jansen, A. (1993) Passage of legume and grass
seeds through the digestive tract of cattle and their survival in faeces. Journal
of Applied Ecology, 30, 63–74.
Godoy, J.A. & Jordano, P. (2001) Seed dispersal by animals: exact identification
of source trees with endocarp DNA microsatellites. Molecular Ecology, 10,
2275–2283.
Grzimek, B. (1988) Grzimeks Enzyklopädie der Säugetiere. Kindler, München.
Jones, R.M. & Simao Neto, M. (1987) Recovery of pasture seed ingested by
ruminants. 3. The effects of the amount of seed in the diet and of diet quality
on seed recovery from sheep. Australian Journal of Experimental Agriculture,
27, 253–256.
Katul, G.G., Porporato, A., Nathan, R., Siqueira, M., Soons, M.B., Poggi, D.,
Horn, H.S. & Levin, S.A. (2005) Mechanistic analytical models for longdistance seed dispersal by wind. American Naturalist, 166, 368–381.
Kohler, F., Gillet, F., Reust, S., Wagner, H.H., Gadallah, J.-M.G. & Buttler, A.
(2006) Spatial and seasonal patterns of cattle habitat use in a mountain
wooded pasture. Landscape Ecology, 21, 281–295.
Kuparinen, A. (2006) Mechanistic models for wind dispersal. Trends in Plant
Science, 11, 296–302.
Levin, S.A., Cohen, D. & Hastings, A. (1984) Dispersal strategies in patchy
environments. Theoretical Population Biology, 26, 165–191.
Levin, S.A., Muller-Landau, H.C., Nathan, R. & Chave, J. (2003) The ecology
and evolution of seed dispersal: a theoretical perspective. Annual Review of
Ecology, Evolution and Systematics, 34, 575–604.
McKay, M.D., Beckman, R.J. & Conover, W.J. (1979) A comparison of three
methods for selecting values of input variables in the analysis of output from
a computer code. Technometrics, 21, 239–245.
Morales, J.M. & Carlo, T.A. (2006) The effects of plant distribution and
frugivore density on the scale and shape of dispersal kernels. Ecology, 87,
1489–1496.
Morales, J.M., Fortin, D., Frair, J.L. & Merrill, E.H. (2005) Adaptive models
for large herbivore movements in heterogeneous landscapes. Landscape
Ecology, 20, 301–316.
Morales, J.M., Haydon, D.T., Frair, J., Holsinger, K.E. & Fryxell, J.M. (2004)
Extracting more out of relocation data: building movement models as
mixtures of random walks. Ecology, 85, 2436–2445.
Mouissie, A.M., Lengkeek, W. & van Diggelen, R. (2005) Estimating adhesive
seed-dispersal distances: field experiments and correlated random walks.
Functional Ecology, 19, 478–486.
Nathan, R. (2005) Long-distance dispersal research: building a network of
yellow brick roads. Diversity and Distributions, 11, 125–130.
Nathan, R. & Muller-Landau, H.C. (2000) Spatial patterns of seed dispersal,
their determinants and consequences for recruitment. Trends in Ecology and
Evolution, 15, 278–285.
Nathan, R., Safriel, U.N. & Noy-Meir, I. (2001) Field validation and sensitivity
analysis of a mechanistic model for tree seed dispersal by wind. Ecology, 82,
374–388.
Pakeman, R.J. (2001) Plant migration rates and seed dispersal mechanisms.
Journal of Biogeography, 28, 795–800.
Ramos, M.E., Robles, A.B. & Castro, J. (2006) Efficiency of endozoochorous
seed dispersal in six dry-fruited species (Cistaceae): from seed ingestion to
early seedling establishment. Plant Ecology, 185, 97–106.
Römermann, C., Tackenberg, O. & Poschlod, P. (2005a) Dispersability traits –
internal animal dispersal (endozoochory). The LEDA Traitbase Collecting
and Measuring Standards of Life History Traits of the Northwest European
Flora (eds I.C. Knevel, R.M. Bekker, D. Kunzmann, M. Stadler & K.
Thompson), pp. 129–131. LEDA Traitbase Project, Groningen.
Römermann, C., Tackenberg, O. & Poschlod, P. (2005b) How to predict attachment potential of seeds to sheep and cattle coat from simple morphological
seed traits. Oikos, 110, 219–230.
Russo, S.E., Portnoy, S. & Augspurger, C.K. (2006) Incorporating animal
behavior into seed dispersal models: implications for seed shadows. Ecology,
87, 3160–3174.
Schurr, F.M., Bond, W.J., Midgley, G.F. & Higgins, S.I. (2005) A mechanistic
model for secondary seed dispersal by wind and its experimental validation.
Journal of Ecology, 93, 1017–1028.
Sera, B. & Sery, M. (2004) Relation between number and weight of seeds and
reproductive strategies of herbacaeous plants. Folia Geobotanica, 39, 27–
40.
Soons, M.B., Heil, G.W., Nathan, R. & Katul, G.G. (2004) Determinants of
long-distance seed dispersal by wind in grasslands. Ecology, 85, 3056–3068.
Tackenberg, O. (2003) Modeling long-distance dispersal of plant diaspores by
wind. Ecological Monographs, 73, 173–189.
Tackenberg, O., Römermann, C., Thompson, K. & Poschlod, P. (2006) What
does diaspore morphology tell us about external animal dispersal? Evidence
from standardized experiments measuring seed retention on animal-coats.
Basic and Applied Ecology, 7, 45–58.
Tackenberg, O. & Stöcklin, J. (2007) Wind dispersal of alpine plant species: a
comparison with lowland species. Journal of Vegetation Science, doi:
10.3170/2007–8–18338.
Turchin, P. (1991) Translating foraging movements in heterogeneous environments into the spatial distribution of forages. Ecology, 72, 1253–1266.
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022
1022
H. Will & O. Tackenberg
Van Dyck, H. & Baguette, M. (2005) Dispersal behaviour in fragmented
landscapes: routine or special movements? Basic and Applied Ecology, 6,
535–545.
Varela, O. & Bucher, E.H. (2006) Passage time, viability, and germination of
seeds ingested by foxes. Journal of Arid Environments, 67, 566–578.
Vellend, M., Myers, J.A., Gardescu, S. & Marks, P.L. (2003) Dispersal of
Trillium seeds by deer: implications for long-distance migration of forest
herbs. Ecology, 84, 1067–1072.
Vuilleumier, S. & Metzger, R. (2006) Animal dispersal modelling: handling
landscape features and related choices. Ecological Modelling, 190, 159–170.
Warner, A.C.I. (1981) Rate of passage of digesta through the gut of mammals
and birds. Nutrition Abstracts and Reviews Series B, 51, 789–820.
Westcott, D.A., Bentrupperbäumer, J., Bradford, M.G. & McKeown, A. (2005)
Incorporating patterns of disperser behaviour into models of seed dispersal
and its effects on estimated dispersal curves. Oecologia, 146, 57–67.
Will, H., Maussner, S. & Tackenberg, O. (2007) Experimental studies of
diaspore attachment to animal coat: predicting epizoochorous dispersal
potential. Oecologia, 153, 331–339.
Witschel, M. (1980) Xerothermvegetation und Dealpine Vegetationskomplexe in
Südbaden. Landesanstalt für Umweltschutz Baden-Württemberg,
Karlsruhe.
Zollner, P.A. & Lima, S.L. (1999) Search strategies for landscape-level interpatch movements. Ecology, 80, 1019–1030.
Received 18 July 2007; accepted 19 November 2007
Handling Editor: Angela Moles
Supplementary material
The following supplementary material is available for this
article:
Appendix S1. Technical model documentation.
Table S1. SEED plant data base.
Figure S1. Model flow chart.
This material is available as part of the online article from:
http://www.blackwell-synergy.com/doi/abs/10.1111/j.13652745.2007.01341.x
(This link will take you to the article abstract.)
Please note: Blackwell Publishing is not responsible for the
content or functionality of any supplementary materials
supplied by the authors. Any queries (other than missing
material) should be directed to the corresponding author for
the article.
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Ecology, 96, 1011–1022