State-dependent ideal free distributions

Summary The standard ideal free distribution (IFD) states how animals should distribute themselves at a stable competitive equilibrium. The equilibrium is stable because no animal can increase its fitness by changing its location. In applying the IFD to choice between patches of food, fitness has been identified with the net rate of energetic gain. In this paper we assess fitness in terms of survival during a non-reproductive period, where the animal may die as a result of starvation or predation. We find the IFD when there is a large population that can distribute itself between two patches of food. The IFD in this case is state-dependent, so that an animal's choice of patch depends on its energy reserves. Animals switch between patches as their reserves change and so the resulting IFD is a dynamic equilibrium. We look at two cases. In one there is no predation and the patches differ in their variability. In the other, patches differ in their predation risk. In contrast to previous IFDs, it is not necessarily true that anything is equalized over the two patches.     

Competitive foraging in mallards: “Ideal free’ ducks

Mallards (Anas platyrhynchos L.) distribute themselves between two patches of food in a close approximation to the distribution predicted by the ideal free model. However an important assumption of this model is violated since the despotic behaviour of some individuals results in different birds receiving unequal payoffs. The distribution of the birds between the food patches is influenced by the distribution of these despots. Evidence is presented to suggest that the ducks initially use the frequency of supply of food items at a patch to assess its profitability, but they can, over a longer time scale, use other cues.     

Unequal competitor ideal free distribution in fish?

Key predictions of unequal competitor ideal free distribution models were tested using a continuous input situation. Ten individually identifiable cichlid fish competed for food items at either end of their tank. Their distribution fitted the predictions of the equal competitor, continuous input ideal free model almost perfectly. However, examination of individual intakes revealed significant variation in individual success and relative competitive ability between patches. Contrary to expectations, fish did not exclusively use the patch where their intake was higher, although individuals experiencing greater differences in intake rate between patches were more selective. We found no evidence for a truncated distribution or even a correlation between competitive ability and patch quality. Changing the input regime to reduce competition did not produce a decrease in the range of intake rates between individuals. This study indicates the value of future empirical and theoretical work on how relative competitive ability varies with the nature of the foraging environment.     

Distribution of a naturally fluctuating ungulate population among heterogeneous plant communities: ideal and free?

1. Herbivore distribution is often assumed to follow the ideal free distribution (IFD) model. This assumes that organisms are omniscient about forage quality and availability within the area available to them and are free to move, with negligible cost, throughout this environment. If this were the case we would expect that, at lowest densities, all animals would be found in the best habitat patches, with less desirable habitats being occupied stepwise as population density increases. We test this using data from a naturally fluctuating population of feral Soay sheep. 2. We show that, although the distribution of individuals is correlated positively with food quality, in line with patterns reported for hill sheep in Scotland, their distribution does not conform to the predictions of the IFD model. We argue that it is the dynamic nature of their food resource that causes this departure from the predictions of the IFD model and make the case that the IFD model, in its unmodified form, is inappropriate for use in modelling distribution among patches containing dynamic resources.     

Physiological Ecology Meets the Ideal-free Distribution: Predicting the Distribution of Size-structured Fish Populations Across Temperature Gradients

We describe a habitat selection model that predicts the distribution of size-structured groups of fish in a habitat where food availability and water temperature vary spatially. This model is formed by combining a physiological model of fish growth with the logic of ideal free distribution (IFD) theory. In this model we assume that individuals scramble compete for resources, that relative competitive abilities of fish vary with body size, and that individuals select patches that maximize their growth rate. This model overcomes limitations in currently existing physiological and IFD-based models of habitat selection. This is because existing physiological models do not take into account the fact that the amount of food consumed by a fish in a patch will depend on the number of competitors there (something that IFD theory addresses), while traditional IFD models do not take into account the fact that fish are likely to choose patches based on potential growth rate rather than gross food intake (something that physiological models address). Our model takes advantage of the complementary strengths of these two approaches to overcome these weaknesses. Reassuringly, our model reproduces the predictions of its two constituent models under the simple conditions where they apply. When there is no competition for resources it mimics the physiological model of habitat selection, and when there is competition but no temperature variation between patches it mimics either the simple IFD model or the IFD model for unequal competitors. However, when there are both competition and temperature differences between patches our model makes different predictions. It predicts that input-matching between the resource renewal rate and the number of fish (or competitive units) in a patch, the hallmark of IFD models, will be the exception rather than the rule. It also makes the novel prediction that temperature based size-segregation will be common, and that the strength and direction of this segregation will depend on per capita resource renewal rates and the manner in which competitive weight scales with body size. Size-segregation should become more pronounced as per capita resource abundance falls. A larger fish/cooler water pattern is predicted when competitive ability increases more slowly than maximum ration with body size, and a smaller fish/cooler water pattern is predicted when competitive ability increases more rapidly than maximum ration with body size.     

Predator hunting modes and predator–prey space games

Predators and prey are often engaged in a game where their expected fitnesses are affected by their relative spatial distributions. Game models generally predict that when predators and prey move at similar temporal and spatial scales that predators should distribute themselves to match the distribution of the prey's resources and that prey should be relatively uniformly distributed. These predictions should better apply to sit-and-pursue and sit-and-wait predators, who must anticipate the spatial distributions of their prey, than active predators that search for their prey. We test this with an experiment observing the spatial distributions and estimating the causes of movements between patches for Pacific tree frog tadpoles (Pseudacris regilla), a sit-and-pursue dragonfly larvae predator (Rhionaeschna multicolor), and an active salamander larval predator (Ambystoma tigrinum mavortium) when a single species was in the arena and when the prey was with one of the predators. We find that the sit-and-pursue predator favors patches with more of the prey's algae resources when the prey is not in the experimental arena and that the prey, when in the arena with this predator, do not favor patches with more resources. We also find that the active predator does not favor patches with more algae and that prey, when with an active predator, continue to favor these higher resource patches. These results suggest that the hunting modes of predators impact their spatial distributions and the spatial distributions of their prey, which has potential to have cascading effects on lower trophic levels.     

Interspecific Competition Models Derived from Competition Among Individuals

This paper demonstrates how discrete-time models describing population dynamics of two competing species can be derived in a bottom-up manner by considering competition for resources among individuals and the spatial distribution of individuals. The competition type of each species is assumed to be either scramble, contest, or an intermediate between them. Individuals of two species are distributed over resource sites or patches following one of three distribution functions. According to the combination of competition types of the two species and the distribution of individuals, various interspecific competition models are derived. Furthermore, a general interspecific competition model that includes various competition models as special cases is derived for each distribution of individuals. Finally, this paper examines dynamics of some of the derived competition models and shows that the likelihood of coexistence of the two species varies greatly, depending on the type of spatial distribution of individuals.     

The effect of travel costs on the ideal free distribution in stickleback

The ideal free distribution (IFD) theory, which predicts that a population of individuals will match the distribution of a patchily distributed resource, is widely used in ecology to describe the spatial distribution of animals. While many studies have shown general support of its habitat matching prediction, others have described a systematic pattern of undermatching, where too many animals feed at patches with fewer resources, and too few animals feed in richer patches. These results have been attributed to deviations from several of the assumptions of the IFD. One possible variable, the cost of travelling between patches, has received little attention. Here, we investigated the impact on resource matching when travel costs were manipulated in a simple laboratory experiment involving two continuous input patches. This experiment allowed us to control for extraneous variables and decouple time costs from energetic costs of travel. Two experiments examined the impact of varying travel costs on movement rates between foraging patches and how these travel costs impact conformity to the IFD. Our data demonstrated that there was less movement between patches and greater discrepancies from the IFD predictions as the cost of travel increased.     

Transition from a random to an ideal free to an ideal despotic distribution: the effect of individual difference in growth

Individual differences in growth can lead to a monopolistic form of food competition. We studied the long-term transition in the mode of competition and the distribution of individuals between food patches of the cloned salmonid fish, Oncorhynchus masou ishikawae, in the laboratory. This transition was accompanied by growth depensation, i.e., the increase over time in the variance of size between individuals resulting from the differences in individual growth rates. The 120-cm experimental tanks were divided into two compartments (patches) between which an opaque partition was placed. Fish were able to move freely between the patches and therefore were able to assess the patch quality using long-term memory, but they were not able to see the food input in the other patch directly. The distribution between the two food patches, the amount of food gained, and the growth and the agonistic behavior of four groups of six individuals were observed over 4 weeks. We found that (1) within-group variation in body weight increased with time; (2) on average, the better patch was used by more individuals than predicted by a random distribution but fewer individuals than predicted by an ideal free distribution, and (3) the distribution and pattern of resource use by the fish changed over the 4-week experimental period from a random distribution to an ideal free distribution and finally to an ideal despotic distribution. We suggest that growth depensation causes the long-term change in the spatial distribution and pattern of resource use by competitors. Received: December 19, 2000 / Accepted: March 19, 2001     

Foraging behaviour and dispersion of eastern grey kangaroos (Macropus giganteus) in an ideal free framework

Ideal free distribution (IFD) theory predicts that animals in competitive situations should distribute themselves among available habitat patches according to the density of conspecifics and its regulatory effect on resources. To investigate the applicability of IFD models to free-ranging herbivores, we quantified the dispersion and foraging behaviour of eastern grey kangaroos Macropus giganteus among habitat patches of differing suitability, within and outside a reservoir catchment in southern Victoria, Australia. Kangaroo densities within the catchment had a regulatory effect on resource density, while surrounding farmland maintained a higher standing crop despite higher densities of competitors. This difference was slight in autumn, however, when the system was apparently close to equilibrium. Gross bite rates of individuals foraging in farmland were lower than for individuals foraging within the catchment, and vigilance behaviour occurred more frequently in farmland habitat than any other, decreasing time devoted to feeding. Interference competition occurred in only 1.9% of focal samples, although competitive differences based on phenotype were observed. Although resource gains by individual kangaroos are likely to be influenced by other factors, including resource dynamics, predation risk and phenotypic differences, IFD theory provides a valuable analytical framework for this herbivore foraging system.     

Taking the rough with the smooth: foraging for particulate food in continuous time

This paper describes the development of the general dynamical model of foraging developed by Ollason (1980, Theoret. Popul. Biol. 18, 44-65) to predict foraging for particulate food in three different types of environment. In an environment containing particles of different types of food, the model predicts the selection of an approximately optimal diet; in an environment in which the particles occur in patches, the model predicts a time budget of patch occupancy that approximates to the optimal time budget; and in an environment containing patches of particles that regenerate by the addition of particles of food at constant rates, the model predicts that animals will dispose themselves among the patches approximately as predicted by the ideal free distribution. Where the predictions of the model depart from the predictions of optimal foraging theory, they are qualitatively similar to the observed departures of the behaviour of real animals from the predictions of optimal foraging theory. The model provides a general representation of the foraging decisions of animals whether they feed strictly continuously or discontinuously on particles of food, and does so without explicit reference to optimization processes.     

The sociality of solitary foragers: a model based on resource dispersion

Under versions of what may broadly be called the Resource Dispersion Hypothesis (RDH) several authors have concluded that territory size and group size are limited respectively, and independently, by the dispersion and richness of patches of food. This paper presents a model that shows how the frequency distribution of resources available per unit time within a territory may permit the formation of groups even in the absence of any functional advantage to any individual from the presence of another. In this model, animals (called primary occupants) occupy territories containing sufficient resources to meet or exceed their requirements for a critical proportion of feeding periods. The availability of these resources is described in terms of their mean richness and their heterogeneity, and plots of these parameters indicate the circumstances within which individuals may share the minimum territory with the primary occupants. The model shows how, under plausible conditions of resource dispersion, a territory that provides almost total food security for two occupants could also provide, at no cost to the original occupants, substantial food security for an additional group member, even if it never used the same food patches as the originals. It is not therefore, as is sometimes supposed, a necessary condition for the RDH that members of a group often forage simultaneously in the same patch. Thus the model describes ecological circumstances whereby groups could evolve amongst species whose members neither forage communally, nor even meet frequently.     

Animal response to nested self-similar patches: a test with woolly bears

To gain insight into how animals respond to resource patchiness at different spatial scales, we envision their responses in environments comprised of nested, self-similar patches. In these environments, all resources reside within the smallest patches, and resource density declines as a constant exponent of patch size. Accordingly, we use simple mathematical formulations to describe a self-similar environment and a null model of how animals should respond to this environment if they do not perceive resource distribution. We then argue that animals that can perceive resource distribution should partition space by reducing the relative time searching between patches as patch size increases. On an experimental landscape, we found that woolly bear caterpillars Grammia geneura could partition space in this manner, but the range of patch sizes over which they did so tended to increase with resource aggregation. Nevertheless, scaling efficiency (i.e. the scaling of search time versus the scaling or resource density) was similar in all distributions when averaged over all patch sizes. These disparate patterns with similar outcomes resulted from differences in caterpillars' abilities to discriminate spatially among patches of different sizes via their movement pathways, and differences in their use of speed to detect resource items. Our work is relevant to the characterization of resource availability from an animal's perspective, and to the linking of optimal foraging theory to the modeling of search behavior.     

Clutch-size behavior and coexistence in ephemeral-patch competition models

Systems of patchy, ephemeral resources often support surprisingly diverse assemblages of consumer insects. Aggregation of consumer individuals over the landscape of patches has been suggested as one mechanism that can stabilize competition among consumer species. One mechanism for larval aggregation is the laying of eggs in clutches by females traveling among patches to distribute their total fecundity. We use simulation models to explore the consequences, for coexistence of competitors, of larval aggregation that arises from clutch laying. Contrary to some previous treatments, we find that clutch laying can be strongly stabilizing and under certain conditions can be sufficient to allow competitors to coexist stably. We extend these models by considering clutch size as a variable that responds to the abundance of resource patches. Such a relationship might be expected because females should lay their eggs in fewer but larger clutches when the cost of travel among patches is high (because patches are rare). When females adjust clutch size in response to resource abundance, coexistence can be easiest when resource patches are scarce and most difficult when resources are abundant.     

Decrease in Alarm Call Response Among Tufted Capuchins in Competitive Feeding Contexts: Possible Evidence for Counterdeception

Animal signals function to elicit behaviors in receivers that ultimately benefit the signaler, while receivers should respond in a way that maximizes their own fitness. However, the best response may be difficult for receivers to determine when unreliable signaling is common. “Deceptive” alarm calling is common among tufted capuchins (Cebus apella nigritus) in competitive feeding contexts, and responding to these calls is costly. Receivers should thus vary their responses based on whether a call is likely to be reliable. If capuchins are indeed able to assess reliability, I predicted that receivers will be less likely to respond to alarms that are given during competitive feeding contexts than in noncompetitive contexts, and, within feeding contexts, that individuals inside or adjacent to a food patch will be less likely to respond to alarms than those further from the resource. I tested these predictions in a group of wild capuchins by observing the reactions of focal animals to alarm calls in both noncompetitive contexts and experimental feeding contexts. Antipredator escape reactions, but not vigilance reactions, occurred significantly less often in competitive feeding contexts than in noncompetitive contexts and individuals adjacent to food patches were more likely to respond to alarm calls than were those inside or further from food patches. Although not all predictions were fully supported, the findings demonstrate that receivers vary their behavior in a way that minimizes the costs associated with “deceptive” alarms, but further research is needed to determine whether or not this can be attributed to counterdeception.     

Frequency-dependent conspecific attraction to food patches

In many ecological situations, resources are difficult to find but become more apparent to nearby searchers after one of their numbers discovers and begins to exploit them. If the discoverer cannot monopolize the resources, then others may benefit from joining the discoverer and sharing their discovery. Existing theories for this type of conspecific attraction have often used very simple rules for how the decision to join a discovered resource patch should be influenced by the number of individuals already exploiting that patch. We use a mechanistic, spatially explicit model to demonstrate that individuals should not necessarily simply join patches more often as the number of individuals exploiting the patch increases, because those patches are likely to be exhausted soon or joining them will intensify future local competition. Furthermore, we show that this decision should be sensitive to the nature of the resource patches, with individuals being more responsive to discoveries in general and more tolerant of larger numbers of existing exploiters on a patch when patches are resource-rich and challenging to locate alone. As such, we argue that this greater focus on underlying joining mechanisms suggests that conspecific attraction is a more sophisticated and flexible tactic than currently appreciated.     

Density-dependent habitat selection in migratory passerines during stopover: what causes the deviation from IFD?

We studied the distribution of migratory warblers (genus: Sylvia) in poor and high quality habitat patches at a stopover site in the northern Negev, Israel. The purpose of our study was to test predictions based on the ideal free distribution (IFD) model by using a natural ecosystem which has a high turnover of individuals moving between unfamiliar foraging patches. We trapped birds in two groves of Pistacia atlantica embedded within a coniferous forest. The fruit-density ratio between these groves was 45:1. We compared bird density, body condition and habitat matching (the ratio between bird density and resource density) at the two sites. To analyse the data we integrated two approaches to density-dependent habitat selection: the isodar method and the habitat matching rule. As predicted by the IFD model, we found that habitat suitability decreased with bird density with a high correlation between warbler densities in the two habitat patches. Contrary to IFD predictions, warbler density in the poor patch was higher than expected by the habitat-matching rule. This habitat under-matching, had a cost: in the rich habitat the average energy gain per individual bird was higher than in the poor habitat. Further analysis suggests that the apparent habitat under-matching is not due to interference or differences in warbler competitive abilities. Therefore, we suggest that this migratory bird community is not at equilibrium because the birds possess imperfect knowledge of resource distribution. We propose that this lack of knowledge leads to free, but not ideal distributions of migrant birds in unfamiliar stop over sites.     

The Trail Less Traveled: Individual Decision-Making and Its Effect on Group Behavior

Social insect colonies are complex systems in which the interactions of many individuals lead to colony-level collective behaviors such as foraging. However, the emergent properties of collective behaviors may not necessarily be adaptive. Here, we examine symmetry breaking, an emergent pattern exhibited by some social insects that can lead colonies to focus their foraging effort on only one of several available food patches. Symmetry breaking has been reported to occur in several ant species. However, it is not clear whether it arises as an unavoidable epiphenomenon of pheromone recruitment, or whether it is an adaptive behavior that can be controlled through modification of the individual behavior of workers. In this paper, we used a simulation model to test how symmetry breaking is affected by the degree of non-linearity of recruitment, the specific mechanism used by individuals to choose between patches, patch size, and forager number. The model shows that foraging intensity on different trails becomes increasingly asymmetric as the recruitment response of individuals varies from linear to highly non-linear, supporting the predictions of previous work. Surprisingly, we also found that the direction of the relationship between forager number (i.e., colony size) and asymmetry varied depending on the specific details of the decision rule used by individuals. Limiting the size of the resource produced a damping effect on asymmetry, but only at high forager numbers. Variation in the rule used by individual ants to choose trails is a likely mechanism that could cause variation among the foraging behaviors of species, and is a behavior upon which selection could act.     

Learning rules for social foragers: implications for the producer-scrounger game and ideal free distribution theory

In population games, the optimal behaviour of a forager depends partly on courses of action selected by other individuals in the population. How individuals learn to allocate effort in foraging games involving frequency-dependent payoffs has been little examined. The performance of three different learning rules was investigated in several types of habitats in each of two population games. Learning rules allow individuals to weigh information about the past and the present and to choose among alternative patterns of behaviour. In the producer-scrounger game, foragers use producer to locate food patches and scrounger to exploit the food discoveries of others. In the ideal free distribution game, foragers that experience feeding interference from companions distribute themselves among heterogeneous food patches. In simulations of each population game, the use of different learning rules induced large variation in foraging behaviour, thus providing a tool to assess the relevance of each learning rule in experimental systems. Rare mutants using alternative learning rules often successfully invaded populations of foragers using other rules indicating that some learning rules are not stable when pitted against each other. Learning rules often closely approximated optimal behaviour in each population game suggesting that stimulus-response learning of contingencies created by foraging companions could be sufficient to perform at near-optimal level in two population games.     

The dilemma of foraging herbivores: dealing with food and fear

For foraging herbivores, both food quality and predation risk vary across the landscape. Animals should avoid low-quality food patches in favour of high-quality ones, and seek safe patches while avoiding risky ones. Herbivores often face the foraging dilemma, however, of choosing between high-quality food in risky places or low-quality food in safe places. Here, we explore how and why the interaction between food quality and predation risk affects foraging decisions of mammalian herbivores, focusing on browsers confronting plant toxins in a landscape of fear. We draw together themes of plant–herbivore and predator–prey interactions, and the roles of animal ecophysiology, behaviour and personality. The response of herbivores to the dual costs of food and fear depends on the interplay of physiology and behaviour. We discuss detoxification physiology in dealing with plant toxins, and stress physiology associated with perceived predation risk. We argue that behaviour is the interface enabling herbivores to stay or quit food patches in response to their physiological tolerance to these risks. We hypothesise that generalist and specialist herbivores perceive the relative costs of plant defence and predation risk differently and intra-specifically, individuals with different personalities and physiologies should do so too, creating individualised landscapes of food and fear. We explore the ecological significance and emergent impacts of these individual-based foraging outcomes on populations and communities, and offer predictions that can be clearly tested. In doing so, we provide an integrated platform advancing herbivore foraging theory with food quality and predation risk at its core.