A mechanistic simulation model of seed dispersal by animals

Authors


Correspondence author. E-mail: will@bio.uni-frankfurt.de

Summary

  • 1In 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.
  • 2The 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.
  • 3Seed 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.
  • 4A 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 long-distance 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.
  • 5A 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.
  • 6Synthesis. 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.

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).

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 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 long-distance 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).

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 Thumbnail image of

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.

Figure 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 (inline image) denote epizoochorously, grey dots (inline image) 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.

(1) detachment and defecation

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 (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) attachment, ingestion and survival

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. According 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 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) animal movement

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) landscape – 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 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).

Figure 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.

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 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).

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’
ProcessDescription
FLM (patchy landscape)CLM (uniform landscape)
Animal movementIf 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 attachmentSeeds attach to the fur of an animal – a new fur seed parcel is initialized.
Seed ingestionSeeds are ingested – a new gut seed parcel is initialized.
Seed excretionSeeds leave a gut parcel and are added to the seeds in the current grid cell.
Seed detachmentSeeds leave a fur parcel and are added to the seeds in the current grid cell.

Example model runs

(1) fragmented landscape model

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) continuous landscape model

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 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 cattle-dispersed 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.

Figure 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.

(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.

Figure 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).

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, 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.

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.
VariableRC numberRC medianRC perc
Epizoochorous dispersal
 Seed production9.71   NS   NS
 Seed attachment to fur10.053.923.01
 Seed detachment (shape)9.6422.2613.18
 Seed detachment (scale)11.175.379.38
 Proportion of seeds ‘stuck’–2.35   NS   NS
Endozoochorous dispersal
 Seed production9.13   NS   NS
 Proportion of seeds eaten11.624.664.03
 Gut passage rate (shape)NS11.409.24
 Gut passage rate (scale)NS13.9614.96
 Proportion of seeds digested–11.97   NS   NS
Animal movementRC dweekRC dmonth
0° included0° excluded0° included0° excluded
Movement speed27.3041.5523.1632.93
Turning angles–31.55–31.47–27.50–25.08

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).

Figure 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°).

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 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.

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 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 decision-making 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 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 long-distance 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).

Ancillary

Advertisement