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Keywords:

  • agents;
  • animals;
  • dispersal;
  • distance;
  • gut;
  • mechanistic;
  • models;
  • process;
  • seed passage

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. The state of play of animal seed-dispersal models
  5. Towards a new generation of process-based animal seed-dispersal models
  6. Modelling seed passage through animals
  7. Detachment of seeds from the outsides of animals
  8. Modelling animal movement
  9. Priorities and options
  10. Acknowledgements
  11. References

1. Animals are the most important dispersal vector for a vast number of terrestrial plants.

2. Whereas our understanding of dispersal by wind has taken enormous conceptual strides in recent years, our ability to predict dispersal patterns by animals remains crude by comparison despite the large volume of research on this topic.

3. We review published models of dispersal by animals, discuss component processes that have been modelled in other contexts and indicate approaches that could usefully be taken in the future.

4. The current problem restricting progress is that few animal dispersal models include the processes most likely to cause dispersal to change over time or space. Thus, they are context-specific, predicting only under the conditions from which data were collected.

5. The key to deeper understanding is to ask ‘What determines the behaviour of the vector; and what determines the influence of the vector on the trajectory of a seed’ (rather than what is the behaviour of the vector in a case study and how far does it move seeds in that study). This leads naturally to process-based models with the ability to predict over a range of scenarios.

6. Priority processes for a more mechanistic approach include: animal movement within a landscape; linking gut throughput, defecation, feeding rate and other behaviours; and detachment from an animal’s surface. Models of gut throughput are probably already sufficient to include them in a dispersal model. Perhaps the best way to achieve progress would be to initiate an international working group of experts in modelling and the particular biological processes.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. The state of play of animal seed-dispersal models
  5. Towards a new generation of process-based animal seed-dispersal models
  6. Modelling seed passage through animals
  7. Detachment of seeds from the outsides of animals
  8. Modelling animal movement
  9. Priorities and options
  10. Acknowledgements
  11. References

The past decade has seen considerable advances in our understanding of the movement achieved by plant propagules (seeds, fruits or other structures) dispersing by wind (e.g. Katul et al. 2005; Bohrer et al. 2008). The key to this has been the development of models that incorporate ever greater realism of the processes acting on the dispersal vector, namely air, as it moves over and through vegetation. As a result, we are able to simulate a dispersing propagule’s trajectory under various sets of conditions, thus overcoming the problem that empirical observations are context-specific (Schupp 2007). Our ability to predict dispersal by animals, using models, is far less developed.

Models are a useful indirect way of estimating where seeds might go to, from a given origin. They aid us in developing and testing our theoretical understanding of the processes affecting dispersal, using tools such as sensitivity analysis. In formulating the model, we bring together a wide array of field observations on dispersal vectors and plant propagules, allowing the identification of anomalies and gaps in knowledge. In some situations, for example where dispersal is over very long distances, they may be the only effective way to estimate dispersal distances.

In this paper, we review the current state-of-the-art of predicting dispersal distances by animals, give examples of recent conceptual advances, and indicate where existing models of component processes can be put together to build models that should considerably improve our understanding. It provides a discussion of an approach to research and is not an exhaustive review of the entire literature on seed dispersal by animals. Moreover, the review draws largely on the modelling literature and uses examples of empirical results to illustrate particular points or to show how a model might be constructed. Thus, some areas (such as modelling movement through a gut) will be covered in more detail than areas which, though they may have attracted considerable empirical research, have not been modelled in a mechanistic way (such as seed detachment from animal coats or empirically measured times to pass through the gut).

The state of play of animal seed-dispersal models

  1. Top of page
  2. Summary
  3. Introduction
  4. The state of play of animal seed-dispersal models
  5. Towards a new generation of process-based animal seed-dispersal models
  6. Modelling seed passage through animals
  7. Detachment of seeds from the outsides of animals
  8. Modelling animal movement
  9. Priorities and options
  10. Acknowledgements
  11. References

Ecologists and natural historians have long studied the components of dispersal by animals: watching feeding behaviour and interactions between feeding animals, estimating fruit crops and feeding rates, examining the contents of faeces, the viability of defecated seeds, and so on. The result is a large phenomenological database on these components, for particular plants and particular animals. Direct measurement of the overall outcome of the plant–animal interactions, i.e. the final positions of seeds relative to their parents, has always been problematic: seeds may land over large areas through which the animals pass, they may be deliberately placed underground and there are usually multiple plants from which each seed deposited on the ground could have originated. Recording individual seed trajectories is also difficult: animals are difficult to follow within dense vegetation, each animal may eat from many plants of that species, seeds may take hours or even days to pass through the animal, and thus even if an individual animal’s faeces can be identified, the plant of origin may be highly uncertain.

The distance moved by a seed from its source is a function of (i) the time taken between removal from a plant to deposition on the ground and (ii) the distance away that the animal moves in that time. Thus, to predict dispersal locations the simplest models combine equations describing just two processes: locomotion; and release from the animal (depending on the method of dispersal, this may be defecation, physical detachment, regurgitation, spitting or dropping: Fig. 1). Since there is variation in both quantities, the equations are probability distributions (Murray 1988; Mouissie, Lengkeek & van Diggelen 2005; Cousens, Dytham & Law 2008), either discrete or continuous. They may be based on empirical data or on theoretical assumptions. Although they are often referred to as ‘mechanistic’ models – they are based on two component mechanisms – they are perhaps better referred to as quasi-mechanistic, since the equations describe the outcomes of one or both of these processes rather than the ways that they work.

image

Figure 1.  Hypothetical animal illustrating the main ways in which plant propagules are dispersed.

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Probability distributions of gut throughput are almost invariably obtained from caged animals eating from artificial sources (e.g. Sun et al. 1997; Holbrook & Smith 2000), while seed removal from hides has been measured using dummies (Mouissie, Lengkeek & van Diggelen 2005; Römermann, Tackenberg & Poschlod 2005) and tame (Fischer, Poschlod & Beinlich 1996) or caged animals (Sorensen 1986). When incorporated into models, these distributions are invariably regarded as fixed, determined by plant species propagule traits and animal species behaviour (Dennis & Westcott 2007; Will & Tackenberg 2008). No consideration of the underlying physiological or physical processes is incorporated and times to deposition vary neither with behaviour of the animal nor its environment.

Animal displacement sub-models come in a number of forms. For discrete models, spatial and temporal distributions of animals, obtained by visual means or by telemetry, can be used to calculate a table of probabilities of being in a particular displacement distance category at a particular time interval (Murray 1988; Holbrook & Smith 2000; Cousens, Dytham & Law 2008). These make no underlying assumptions about the way that animals move through their environment or the reasons that movement varies. Different rates of movement, during different times of the day and inactive periods when sleeping, have been incorporated by changing the displacement probability function periodically or by calculating the weighted probability from different times of day (Westcott et al. 2005; Russo, Portnoy & Augspurger 2006). For simple assumptions of movement, such as a random walk, it is possible to obtain analytically an equation for the probability of an animal being a given distance from the seed source at a given time (Morales & Carlo 2006). More realistic models of animal movement usually require simulation models. For example, movement data can be analysed to derive the parameters for correlated random walk models (Mouissie, Lengkeek & van Diggelen 2005; Will & Tackenberg 2008), namely frequency distributions of step length and direction of movement relative to the previous direction: stochastic simulations from the model can then generate time-dependent displacement probabilities. Slightly more complex correlated random walk models can include frequency distributions of perching times (Russo, Portnoy & Augspurger 2006) or other activities.

All of the models that we have described so far are gross simplifications, in comparison to the behaviour of real animals. Animals do not undergo random walks: movement decisions are largely made on the basis of motivational factors, such as hunger, thirst, reproductive state and fear. Moreover, the component probability functions in the models, whether discrete or continuous, have parameters that have been quantified under a particular set of conditions. Predictions from the models are thus context-specific and their use under other circumstances could well be unreliable. This problem is widely recognized amongst researchers. To overcome context-specificity, we need to predict how environmental factors will affect both an animal’s trajectory and the likelihood of a seed being deposited at any point in the future. This requires process-based models for movement and retention time rather than simple empirical models.

Towards a new generation of process-based animal seed-dispersal models

  1. Top of page
  2. Summary
  3. Introduction
  4. The state of play of animal seed-dispersal models
  5. Towards a new generation of process-based animal seed-dispersal models
  6. Modelling seed passage through animals
  7. Detachment of seeds from the outsides of animals
  8. Modelling animal movement
  9. Priorities and options
  10. Acknowledgements
  11. References

It is relatively easy to make theoretical dispersal calculations on the basis of empirical observations of animal movement. It is much more difficult to predict what an animal would do in a totally different environment. Moreover, a significant simplification of all the previous models is that animal movement and seed deposition are independent: i.e. the rate of gut throughput does not depend on current or previous behaviour, such as whether it undergoes a long-distance migration or whether the animal has eaten a large meal.

More mechanistic models of dispersal by animals, that can predict dispersal in different sets of conditions, are achievable – though they will be more onerous to construct and may require co-option of additional research skills. As with modelling dispersal by wind, the key is to determine and incorporate the variety of processes affecting the functioning of the dispersal vector (Table 1) and thus its effect on plant propagules. For example, the behaviour of animals with respect to the spatial and temporal distribution and abundance of resources can be quantified and built into models (Levey, Tewksbury & Bolker 2008). The wealth of studies of animal behaviour can be used to construct ‘time and motion’ rules: how long does an animal spend in each activity (not just feeding) and where does it go to next? These rules could also be driven by the motivation of the animal, dictated by its physiological state. The issue of diversity of species remains – we are unlikely to have data for every aspect of physiology and behaviour on every species – but we can identify (or hypothesize) functional types of dispersers with characteristic behaviours (Dennis & Westcott 2007), often based on a few well-studied species (e.g. Levey et al. 2005) and learn from modelling with these. For instance, feeding behaviours of small facultative frugivorous birds that flock are likely to be affected by similar environmental characteristics (e.g. vegetation cover that reduces predation) and follow qualitatively similar rules. These will differ from ground dwelling mammalian frugivores or large avian dispersers.

Table 1.   Examples of processes and factors determining dispersal distance
  1. All of these will be dependent on the distribution and abundance of food species, competing animals, predators and other resources in space and time. The interactions between the processes can be critical. The level of detail required in a model, since any process can be further divided into another level of component processes, will depend on the questions being addressed, the species involved and the judgement of the researcher.

Animal movement
 Phenology of food species
 Feeding duration at a given source
 Carrying food elsewhere
 Food selection (free choice or otherwise)
 Activities other than feeding – movement between locations, drinking, displaying, mating, nest building, tending of young, fighting, other social interactions, sleeping/resting, avoidance of predators
 Weather conditions
Seed detachment
 Strength of physical bond between propagules and animal
 Self-propulsion mechanisms, (e.g. seeds that corkscrew into fleece)
 Position on the animal
 Availability of force that will detach the propagules (height of vegetation, mutual grooming)
 Relative heights of source plant and animal (modified by time of year and age of animal)
 Moulting
 Rainfall
 Bathing/wallowing
Gut throughput
 Food handling
 Ingestion
 Regurgitation
 Satiety and other physiological drivers
 Animal behaviour, – e.g. time relative to migration event
 Gut structure and function (including digestion/fermentation)
 Size of seeds
 Physical and chemical properties of any covering structures
 Defecation

Two examples serve to illustrate where considerable advances have been made through very modest increases in model complexity. Levey et al. (2005) and Levey, Tewksbury & Bolker (2008) used a correlated random walk model with perching time as an additional variable. Simulations were made on a landscape of habitat grid cells: in calculating the next move, angle, step length and perching time probabilities were varied with habitat type, distance to habitat edge, orientation of the nearest edge and the previous move. This enabled predictions to be made about the effects of habitat heterogeneity, patch shape and size, and corridors on seed dispersal. Morales & Carlo (2006) and Carlo & Morales (2008) assumed that their birds only moved between food trees, that they somehow knew the fruit crop size of each tree, could assess the distances between these trees and could fly directly to a given tree. Each tree was assigned an ‘attractivity’, which was used to calculate a probability that it would be chosen as the next destination. Times spent in each tree and gut passage rates were taken from fixed probability functions. Fruit ingestion was determined using an hyperbolic functional response constrained by gut fullness. Using the model, they predicted the effects of bird abundance, fruit removal behaviour and plant spatial distribution on dispersal distances, albeit based on some arguable assumptions.

These two models have only begun to scratch the surface of what could be learned from models with even greater realism. None of the models discussed so far attempt to predict gut passage in a biologically based way, for example, and yet we know that gut passage is affected by gut content and the behavioural activities taking place (Murray et al. 1994; French 1996). We also know that many activities, other than feeding, determine animal movement. There is thus considerable opportunity to develop mechanistic sub-models for these processes that will influence ingestion rates and seed shadows.

Modelling seed passage through animals

  1. Top of page
  2. Summary
  3. Introduction
  4. The state of play of animal seed-dispersal models
  5. Towards a new generation of process-based animal seed-dispersal models
  6. Modelling seed passage through animals
  7. Detachment of seeds from the outsides of animals
  8. Modelling animal movement
  9. Priorities and options
  10. Acknowledgements
  11. References

A fully mechanistic model for seed passage would need to consider three phases: (I) various pre-swallowing (‘pre-deglutition’) processes, (II) gut transit and (III) defecation. Of all the component processes affecting dispersal, gut transition is the one that has been modelled most often; yet, these models have rarely been used in predicting dispersal distances. For phases I and III, we will describe the factors that would need to be considered in formulating models.

The pre-deglutition phase of seed throughput can be characterized by the ‘bite-chew-swallow’ (mammal) or ‘bite-swallow-chew’ (avian) approach to understanding the rate of intake of any food chosen from an environment (Cohen, Pastor & Moen 1999). It has been demonstrated by a number of authors that the ‘bite-chew-swallow’ version of food intake can be analysed using queuing theory (Gross & Harris 1974). These analyses suggest that the animal’s strategy to maintain intake of nutrients is to ‘bite-swallow’– an approach that would not lead to substantial disruption of the plant propagule. However, as the animal approaches the point when feeding ceases (either by fulfilling nutrient requirements or the patch has been depleted of food), there is more time available for ‘bite-chew-swallow’. In this context, the distribution of propagules by gut throughput may well be linked to habitat conditions and the animal’s ability to acquire food. Inevitably, the description of ‘bite-swallow-chew’ for a bird conjures an interesting image. The ‘chew’ component is the disruption of the food component in the gut (specifically the proventriculus) and, in many species, is not an action undertaken in the beak of the bird.

The processes of food handling, including chewing, dictate to some extent the viability of the propagule. Food handling may include moving fruits away from the parent plant prior to ingestion (which could be incorporated into an animal movement model) and discarding the seeds while ingesting the flesh. Separation of seeds from fruit tissues by a range of birds and mammals prior to swallowing (Overdorff & Strait 1998) will limit dispersal but reduce gut transit times for any seeds swallowed. Similarly, regurgitation of seeds, such as that seen in many large-seeded fruits consumed by birds, will reduce the time between intake and deposition (Levey 1986).

Highly frugivorous bird species often have highly modified guts which increase gut passage rates (Murphy et al. 1993), thus dispersal distances for obligate and facultative frugivores will differ and be dependent upon the size of the animal. For animals that are usually seed predators, models will need to be more complicated as seed handling with beaks or teeth will kill a proportion of seeds but others may be left uningested or may pass through the gut unaffected. For herbivorous mammals and avian consumers such as parrots, the integration of chewing (including beak processing) to gut passage models has been poorly developed. If we include a sub-model that considers the processes of seed handling (including the potential disruption of the seed source), there are a series of ‘trade-offs’ between rate of eating, quantity ingested and handling time of the food (Walsh 1996; Cohen, Pastor & Moen 1999). The likelihood that the propagule is damaged during handling can be described by an arbitrary probability distribution, one based on a simple assumption (Van Soest 1995), or using an approach based on survival analysis (Hosmer & Lemeshow 1999).

Researchers in production agriculture have developed a variety of models for the passage of indigestible components of rations through the gut (i.e. phase II), that could be applied to seed dispersal. These can be divided into three main groups based on the functionality and structure of the digestive tract of the species; the monogastric (including avian and reptilian), the pre-gastric fermenter (e.g. ruminants) and the post-gastric fermenter (e.g. horses, elephants), though inevitably there are a number of ‘variations on a theme’. In the simplest models (monogastric), food is ingested into the mouth of the animal and is disrupted to a greater or lesser extent by handling, before swallowing and transit into the intestine via temporary storage in the upper tract (Van Soest 1995). The food is likely to be modified by chemical or enzymatic processes before the indigestible fraction is voided (Wahaj et al. 1998; Traveset, Rodríguez-Pérez & Pías 2008). In the more complex models (pre- and post-gastric fermenters) differences arise from the monogastric model insofar as flow of digesta through various gut compartments, that can retain selectively different particle sizes, have differing chemical and physical environments, and retain food residues for variable periods of time.

The approaches taken to develop a passage model (post lower oesophageal sphincter) for a seed in an animal are relatively simple, as the model will depend on: the digestible and indigestible fractions of the digesta; the relationship between the rates of digestion and passage; the number of individual structural segments of the digestive tract; and the effect of the liquid phase on the mobility of solid digesta (Van Soest 1995). If the seed transits successfully through the ‘pre-oral’ and ‘oral’ phases of eating, the seed will move through the gut along with other indigestible material in the food ingested. The rate of seed movement therefore equates to the proportion of the undigested residues from a given meal that passes a given point in the gut in a set period of time. Clearly, meal size, foraging behaviour, diet selection and free-choice have an influence on this process: for instance, the passage rates of animals fed ad libitum are generally faster than those offered rations at maintenance level of feeding, although starved and hungry animals may have quick passage rates (French 1996; Hill et al. 2009). The use of liquid and solid phase markers in experimental studies allows the identification of differential flow of liquid or solid phases (known as ‘compartments’), which can also be modelled (Dhanoa et al. 1985).

Three kinetic models have been used to predict the rate of passage (or retention) of digesta. These models seem to be universal, but the choice and application of the models have to be considered carefully in light of structural and functional differences of the digestive tract of individual species. The simplest model is a one-pool exponential model that assumes all particles have an equal opportunity to leave the digesta pool, irrespective of how long the particle has resided there (Hill et al. 2009). In essence, it is an ‘age-independent’ model. The model is useful under conditions where the food ingested is relatively uniform in its structure. A modification of this model is the ‘one-pool age-dependent model’, in which the probability of a particle passing through the gut increases with the time (age) that the particle is retained. It accurately models the passage of particles within the digestive tract as the particle structure, shape, functional specific gravity and buoyancy can change reflecting the rate and extent of digestion. In many species of herbivorous animal, two-pool models for estimation of passage are more appropriate (Udén et al. 1982; Reese et al. 1995). These models are, in essence, based on age-dependent models that predict the change in nutrient absorption between pools (sites of digestion). The most important aspect of these models is the ability to change the rate of flow of digesta between pools, as well as the particle distribution. All these models suffer from a lack of precision in their estimates as they rely on good measures of pool size (the mass of food residing in the digesta pool) at individual sites along the gut. Recently, flux models have become popular to estimate passage rate of food in the digestive tract (Reese et al. 1995). However, they require good estimates of gut volume and flow from the site of digestion, and they represent the whole diet rather than single components of the diet. The latter point is important if the animal is free-ranging and has the ability to select a ration by free-choice or preference.

Most dispersal models implicitly assume continuous seed deposition: however, animals do not defecate randomly or continuously. In phase III, the processes that control defecation are closely controlled by hind gut physiology. They can also be determined by animal behaviour, such as the voiding of the hind gut prior to flight by birds and hence the aggregation of deposition around perches. Conceptually, it should be straightforward to produce a model in which defecation is discrete, though we are not aware of this yet being done.

Detachment of seeds from the outsides of animals

  1. Top of page
  2. Summary
  3. Introduction
  4. The state of play of animal seed-dispersal models
  5. Towards a new generation of process-based animal seed-dispersal models
  6. Modelling seed passage through animals
  7. Detachment of seeds from the outsides of animals
  8. Modelling animal movement
  9. Priorities and options
  10. Acknowledgements
  11. References

The rates of seed attachment to and detachment from the surface of an animal are probably the most difficult components of dispersal to model mechanistically. The number of seeds attaching to an animal will depend on the number of propagules available at that time, their ripeness (determining the force required to detach them from the plant), and their height of presentation relative to the stature of the animal. The strength of attachment will depend on the morphology of the propagule and of the hairs/wool/feathers of the animal, as well as on any substances they exude and the properties of any mud that they are in. Time will also be relevant, as propagules can work their way further into the coat and the coat may be moulted seasonally. Some parts of the animal are difficult to self-groom, so seeds will stay on those parts of the body for longer (Sorensen 1986); the height and structure of the vegetation, or water depth, relative to the stature of the animal (which will clearly be age-dependent) also determines the forces applied to the propagules as the animal moves, as does the angle of the body surface relative to the direction of movement.

At present, therefore, dispersal models for externally transported seeds rely on probability distributions fitted to observed detachment data, rather than models of the processes involved in detachment. Thus it is difficult to achieve context-independence. Distribution parameters estimated from observations under discrete sets of conditions allow us to produce models for animals with different types of coat, or plants with different types of propagule (perhaps through classifying species to functional types: Römermann, Tackenberg & Poschlod 2005; Tackenberg et al. 2006). So far, however, there has been little attention to parameter variation in response to factors that vary spatially or temporally. For example, cold and rainfall can affect coat architecture.

The exponential model for duration of attachment, the most commonly used function, assumes that there is a constant probability of any propagule detaching from any position on the animal (Mouissie, Lengkeek & van Diggelen 2005). Since the probability of detachment might be considered to be itself a sum of body position-specific probabilities, the gamma distribution (Will & Tackenberg 2008) might be more appropriate. In fact, those propagules which reside on the animal for longer are likely to be better attached, so the proportional rate of detachment of a propagule cohort may decrease considerably over time (at least until the animal moults). Once again, conceptually it is possible to build these factors into a more mechanistic model.

Modelling animal movement

  1. Top of page
  2. Summary
  3. Introduction
  4. The state of play of animal seed-dispersal models
  5. Towards a new generation of process-based animal seed-dispersal models
  6. Modelling seed passage through animals
  7. Detachment of seeds from the outsides of animals
  8. Modelling animal movement
  9. Priorities and options
  10. Acknowledgements
  11. References

The majority of published dispersal models assume that movement following the ingestion of a seed is unaffected by any particular activity. A correlated random walk takes fixed parameters (describing ‘typical’ behaviour) and predicts the animal’s trajectory from mean and variance of step lengths and turn angles. It is relatively straightforward (though by no means trivial) to make the pattern of movement more mechanistic than this. ‘Behavioural states’ can be assigned to the moving animal (Morales et al. 2004), modifying its step lengths or angles according to (i) where it is currently within the landscape (habitat quality –Levey et al. 2005; Revilla et al. 2004; specific habitat factors, such as elevation, slope, aspect, dominant species –Creel et al. 2005), (ii) the distribution of resources and other animals in the landscape (food and its abundance; perches; sleeping sites; nests, as in the case of ants; suitable seed deposition sites, in scatterhoarders; proximity of other seed-eaters or predators; locations of the edges of favourable or unfavourable habitat patches - Levey et al. 2005; Morales et al. 2004; Haddad 1999), (iii) its physiological status (how hungry it is, thus making a feedback loop to gut throughput models; age; gender - Creel et al. 2005; presence of young; whether it is moulting or breeding season - Dubowy 1997; whether it is about to migrate) and (iv) physical conditions such as time of day, temperature and wind speed. The changes in animal movement parameters can be determined from separate observations in each habitat type, or from analysis of trajectories through the entire landscape over time [using techniques such as nonlinear vector autoregression (Creel et al. 2005) or artificial neural networks (Dalziel, Morales & Fryxell 2008)]. Multi-agent modelling shells could also be used as development platforms (e.g. Ginot, Le Page & Souissi 2002).

To obtain parameters for probabilities of movement from one place to another and from one behavioural state to another requires more than simply observing where an animal travels when leaving a food source in the field: to avoid context-specificity, we need to base our model on a knowledge of the factors that determine what the animal does next, how (perhaps just in probabilistic terms) the animal ‘decides’ which activity to do next, how it decides which direction to go in (to known locations, or purely nomadic) and for how long. This may not be easy, but it is essential if we are to have models that will predict for different landscapes. Home ranges can be modelled more simply, either by including a rule specifying a fixed range size, or by one animal recognizing the position of another’s territory edge (e.g. perches where other birds sing, or where other animals have scent-marked (Moorcroft, Lewis & Crabtree 1999) and changing movement parameters accordingly.

Rather than following this very detailed, but still empirical, approach of specifying behavioural states, it would be possible to model animal movement in response to food in a way that links behaviour to physiology in a more mechanistic way. There is often an interaction between intensive searching mode (ISM) and extensive searching mode (ESM) (Fontin 2002). In the former, the animal commonly responds to food aggregation by an area-restricted search, by increasing path sinuosity and reducing travel speed, to ensure their nutrient requirements are fulfilled. If this is the case, there may be an increased probability of defecation within that environment as the animal is resident for a longer period. The switch to ESM may reflect food depletion (in quantity and/or quality) within an environment, with the response being to reduce sinuosity and increase travel speed, hence reducing the likelihood of defecation within the food-source environment (Walsh 1996). Food search patterns inform pre-deglutition process models insofar as they provide a method to predict the probability that the mouth is full (or there is an increase in the ratio of bite rate to swallowing). Daily energy intake and expenditure may also determine the time available for activities other than feeding (Dubowy 1997).

Individual animal movement steps can be initiated by optimal decision theory based on energy benefit and factors such as predation risk (Weber, Ens & Houston 1998). Elk movement has been modelled as a state-dependent game, in which food resources vary spatially and seasonally, and elk position in the landscape is determined from the optimal trajectory that maximizes individual fitness in terms of energy acquisition (Noonburg et al. 2007). The outcome depended, in part, on the abundance of other animals competing for food. Another elk model (Morales et al. 2005) has used artificial neural networks to model animal decisions (foraging vs. exploration), based on gut fullness, body fat, time of day, time of year, food biomass and risk of predation.

As we have pointed out, the spatial context is critical to predicting animal movement. Many animal movement simulations in the past explored theoretical issues, by running simulations within artificial, unstructured landscapes. However, modern software can be modified to work from a cell-based or rasterized landscape, and the development of input and output routines for transfer of real data from a GIS (Geographic Information System) is straightforward (Parrott 2005). Outputs can then be transferred back to the GIS for spatial analysis, generation of the output dispersal distributions, and subsequently for running of multigenerational models. The position of the animal in the landscape and the positions of others can be mapped on to a GIS landscape, while distributions of habitat patches and boundaries (either as a cellular grid or as a vector-based landscape –Vuilleumier & Metzger 2006), can be determined from GIS layers.

Mechanistic modelling of interactions between the landscape and its inhabitants demands an approach which recognizes the importance of individual animals (Parry, Evans & Morgan 2006). ‘Agent-based modelling’ treats each animal as an individual agent whose (stochastic) behaviour is described quantitatively by a set of rules relating to key activities; these agents are then allowed to move at the same time through a two-dimensional arena in a pattern dictated by those rules. Although seldom applied in the context of seed dispersal, individual based animal movement models using autonomous agent techniques (Dumont & Hill 2001; Pitt, Box & Knowlton 2003) appear to be an excellent platform for linking animal behaviour to seed dispersal issues.

Priorities and options

  1. Top of page
  2. Summary
  3. Introduction
  4. The state of play of animal seed-dispersal models
  5. Towards a new generation of process-based animal seed-dispersal models
  6. Modelling seed passage through animals
  7. Detachment of seeds from the outsides of animals
  8. Modelling animal movement
  9. Priorities and options
  10. Acknowledgements
  11. References

There are so many more unknowns, compared with wind dispersal, that prediction of dispersal by animals may appear like a Holy Grail. It is certainly very complicated and species-dependent, but it can be modelled much more mechanistically than at present. Such an approach has the potential to advance our understanding of seed dispersal patterns considerably. Consideration of functional groups of dispersers makes the problem more tractable: we do not have to study every vector in minute detail to better understand dispersal as a process. The key to success is for researchers to ask ‘What determines the behaviour of the vector; and what determines the influence of the vector on the seed trajectory’ (rather than what is the behaviour of the vector and how far does it move seeds). This leads naturally to process-based models with the ability to predict over a range of scenarios.

Of course, not every model has to include the same level of detail on every process and the development of the ‘ultimate’ mechanistic model may not warrant the investment. However, it is not always easy to tell which processes do not justify detailed modelling, because we may not be aware of interactions that emerge when they are combined with other processes (for example between food availability, gut passage rate, habitat structure and animal behaviour). Having developed a complex model, it is then possible to derive a simpler model in the clear knowledge of the trade-off in capability that this entails. It can also be argued that science would greatly benefit from the production of an algorithm for a complex model of the system and from the exercise of obtaining the information required to build it, even if that modelling does not then occur (Cousens 2001).

Clearly, our ability to model seed dispersal by animals in a mechanistic way is dependent on our ability to model the component processes and hence the availability of appropriate data. From this perspective, the areas most in need of a mechanistic approach are animal movement within landscapes, the links between gut throughput, defecation, feeding rate (and other behaviours) and the retention of seeds on the outside of animals. However, we already have well-developed process models for gut throughput, so this could be the component most easily introduced into existing dispersal models. One way of making more rapid progress on mechanistic models would be to initiate a joint international working group, bringing together modellers with experts in the individual processes to build the models together.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. The state of play of animal seed-dispersal models
  5. Towards a new generation of process-based animal seed-dispersal models
  6. Modelling seed passage through animals
  7. Detachment of seeds from the outsides of animals
  8. Modelling animal movement
  9. Priorities and options
  10. Acknowledgements
  11. References
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