Putting competition strategies into ideal free distribution models: habitat selection as a tug of war

When resources are patchily distributed in an environment, behavioral ecologists frequently turn to ideal free distribution (IFD) models to predict the spatial distribution of organisms. In these models, predictions about distributions depend upon two key factors: the quality of habitat patches and the nature of competition between consumers. Surprisingly, however, no IFD models have explored the possibility that consumers modulate their competitive efforts in an evolutionarily stable manner. Instead, previous models assume that resource acquisition ability and competition are fixed within species or within phenotypes. We explored the consequences of adaptive modulation of competitive effort by incorporating tug-of-war theory into payoff equations from the two main classes of IFD models (continuous input (CI) and interference). In the models we develop, individuals can increase their share of the resources available in a patch, but do so at the costs of increased resource expenditures and increased negative interactions with conspecifics. We show how such models can provide new hypotheses to explain what are thought to be deviations from IFDs (e.g., the frequent observation of fewer animals than predicted in "good" patches of habitat). We also detail straightforward predictions made uniquely by the models we develop, and we outline experimental tests that will distinguish among alternatives.     

Choosing where to feed: the influence of competition on feeding behaviour of cod, Gadus morhua L.

Groups of cod, Gadus morhua L, presented with two feeding patches with a food abundance ratio of 2:1, distributed themselves between the patches in a ratio of 2.5:1. This is slightly higher than the 2:1 ratio predicted by the ideal free distribution theory. Large differences were observed in competitive ability between individual fish. A strong correlation was found between feeding success of individuals and time spent in a feeding patch. The more successful competitors caught about 2.5 times as many food items in the rich patch as in the poor patch. The less successful competitors caught an equal amount of food in both patches. All competitors, however, spent significantly more time in the rich patch. These results suggest that hunting success is the most important factor in assessing patch quality. However, it is not the only parameter which cod use in deciding where to feed.     

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.     

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.     

The effects of habitat manipulation on population distribution and foraging behavior in meadow voles

Individuals, free to choose between different habitat patches, should settle among them such that fitness is equalized. Alternatives to this ideal free distribution result into fitness differences among the patches. The concordance between fitnesses and foraging costs among inhabitants of different quality patches, demonstrated in recent studies, suggests that the mode of habitat selection and the resulting fitness patterns may have important implications to the resource use of a forager and to the survival of its prey. We studied how coarse scale selection between habitat patches of different quality and quitting harvest rate in these patches are related to each other and to fine scale patch use in meadow voles (Microtus pennsylvanicus). To demonstrate these relationships, we manipulated habitat patches within large field enclosures by mowing vegetative cover and adding supplemental food according to a 2×2 factorial design. We tracked vole population densities, collected giving‐up densities (GUDs, a measure of patch quitting harvest rate), and monitored the removal of seeds from lattice grids with 1.5 m intervals (an index of fine‐scale space use) in the manipulated habitat patches. Changes in habitat quality induced changes in habitat use at different spatial scales. In preferred habitats with intact cover, voles were despotic and GUDs were low, but increased with the addition of food. In contrast, voles in less‐preferred mowed habitats settled into an ideal free distribution, GUDs were high and uninfluenced by the addition of food. Seed removal was enhanced by the presence of cover but inhibited by supplemental food. Across all treatments, vole densities and GUDs were strongly correlated making it impossible to separate their effects on seed removal rates. However, this relationship broke down in unmowed habitats, where GUDs rather than vole density primarily influenced seed removal by voles. GUDs and seed removal correlated with predation on tree seedlings formerly planted into the enclosures, demonstrating the mechanisms between coarse‐scale habitat manipulations and community level consequences on a forager's prey.     

Foraging on patchily distributed prey by a cichlid fish (Teleostei,Cichlidae): A test of the ideal free distribution theory

Cichlid fish (Aequidens curviceps) distributed themselves and allocated their foraging time between two drift food patches in close approximation to the patch profitability ratio, as predicted by the ideal free distribution theory. The fish thereby achieved similar average feeding rates in the two patches, in two of three patch profitability ratio experiments. However, one major assumption of the ideal free model was violated, since individual fish differed in their competitive abilities for limited food resources, which resulted in unequal payoffs among individuals within each patch. Individual variation in feeding rates, and thus in competitive ability, was not related to despotism, but perhaps rather to individual differences in perceptual ability and in the ability to learn which patch was currently the more profitable. The strategy used by the fish to assess patch profitability included sampling available patches. However, individual fish switched (sampled) patches with varying frequency. Sampling had an associated cost, since high-frequency switchers had lower feeding rates on average than low-frequency switchers. Differences in foraging strategy among the fish therefore contributed to the observed in-equality in individual payoffs within patches.     

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.     

The ideal free distribution and predator-prey populations

The ideal free distribution, a theoretical model of the distribution of competitors between habitat patches, has recently undergone a number of modifications and extensions. These fall into two main categories: those that assume that equilibrium is attained, and those that establish whether it is attained. The modifications suggest ways in which behavioural properties of individuals might affect the distribution of competitors, and clear a path for further empirical tests.     

Habitat choice in predator-prey systems: spatial instability due to interacting adaptive movements

The role of habitat choice behavior in the dynamics of predator-prey systems is explored using simple mathematical models. The models assume a three-species food chain in which each population is distributed across two or more habitats. The predator and prey adjust their locations dynamically to maximize individual per capita growth, while the prey's resource has a low rate of random movement. The two consumer species have Type II functional responses. For many parameter sets, the populations cycle, with predator and prey "chasing" each other back and forth between habitats. The cycles are driven by the aggregation of prey, which is advantageous because the predator's saturating functional response induces a short-term positive density dependence in prey fitness. The advantage of aggregation in a patch is only temporary because resources are depleted and predators move to or reproduce faster in the habitat with the largest number of prey, perpetuating the cycle. Such spatial cycling can stabilize population densities and qualitatively change the responses of population densities to environmental perturbations. These models show that the coupled processes of moving to habitats with higher fitness in predator and prey may often fail to produce ideal free distributions across habitats.     

Temporal resource variability and the habitat-matching rule

Summary The ideal free distribution of competitors in a heterogeneous environment often predicts habitat matching, where the equilibrium number of consumers in a patch is proportional to resource abundance in that patch. We model the interaction between habitat matching and temporal variation in resource abundance. In one patch the rate of resource input follows a Markov chain; a second patch does not vary temporally. We predict patch use by scaling transition rates in the variable patch to the time that consumers require to respond to changes in rates of resource input. If consumers respond very quickly, habitat matching tracks temporal variability. If resource input fluctuates faster than consumers respond, habitat matching averages over the equilibrium of the Markov chain. Tracking and averaging produce the same mean resource consumption for individuals, but long-term mean occupation of the patches differs. When habitat matching tracks temporal variability in resources, consumer density in the variable patch has a lower mean and a higher variance than when habitat matching reflects only average rates of resource input.We tested our model by feeding free-living mallard ducks (Anas platyrynchos) at two artificial patches. The foragers' behavior satisfied the quantitative predictions of the model in each of two experiments.     

Evolutionary stability of ideal free nonlocal dispersal

We study the evolutionary stability of nonlocal dispersal strategies that can produce ideal free population distributions, that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium. We find that the property of producing ideal free distributions is necessary and often sufficient for evolutionary stability. Our results extend those already developed for discrete diffusion models on finite patch networks to the case of nonlocal dispersal models based on integrodifferential equations. The analysis is based on the use of comparison methods and the construction of sub- and supersolutions.     

Evolutionary stability of ideal free nonlocal dispersal

We study the evolutionary stability of nonlocal dispersal strategies that can produce ideal free population distributions, that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium. We find that the property of producing ideal free distributions is necessary and often sufficient for evolutionary stability. Our results extend those already developed for discrete diffusion models on finite patch networks to the case of nonlocal dispersal models based on integrodifferential equations. The analysis is based on the use of comparison methods and the construction of sub- and supersolutions.     

Coexistence in metacommunities: a tree-species model

Simple patch-occupancy models of competitive metacommunities have shown that coexistence is possible as long as there is a competition-colonization tradeoff such as that of superior competitors and dispersers. In this paper, we present a model of competition between three species in a dynamic landscape, where patches are being created and destroyed at a different rate. In our model, species interact according to a linear non-transitive hierarchy, such that species Y(3) outcompetes and can invade patches occupied by species Y(2) and this species in turn can outcompete and invade patches occupied by the inferior competitor Y(1). In this hierarchy, inferior competitors cannot invade patches of species with higher competitive ability. Analytical results show that there are regions in the parameter space where coexistence can occur, as well as regions where each of the species exists in isolation depending on species' life-history traits associated with their colonization abilities and extinction proneness as well as with the dynamics of habitat patches. In our model, the condition for coexistence depends explicitly on patch dynamics, which in turn modulate the limiting similarity for species coexistence. Coexistence in metacommunities inhabiting dynamic landscapes although possible is harder to attain than in static ones.     

Interference and the ideal free distribution: models and tests

We review the assumptions and predictions of five competitivedistribution models that predict how optimal foragers will bedistributed across resource patches when gains are reduced byinterference. This review revealed a number of previously ignoredpredictions and assumptions: in particular, there should beno change in relative patch use as competitor density changes.A new model is proposed in which interference results from thecosts of encounters with other foragers and where the gainson a patch are independent of the costs of interference. Thismodel predicts that as density increases, there will be increasedproportional use of lower-quality patches. Past empirical studiesof interference distributions are reanalyzed; none of the studiesprovides strong support for any of the existing ideal free-distributionmodels. We suggest that previous results are more consistentwith the predictions of our new model.     

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     

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.     

Determinism in a transient assemblage: the roles of dispersal and local competition

Both dispersal and local competitive ability may determine the outcome of competition among species that cannot coexist locally. I develop a spatially implicit model of two-species competition at a small spatial scale. The model predicts the relative fitness of two competitors based on local reproductive rates and regional dispersal rates in the context of the number, size, and extinction probability of habitat patches in the landscape. I test the predictions of this model experimentally using two genotypes of the bacteriophagous soil nematode Caenorhabditis elegans in patchy microcosms. One genotype has higher fecundity while the other is a better disperser. With such a fecundity-dispersal trade-off between competitors, the model predicts that relative fitness will be affected most by local population size when patches do not go extinct and by the number of patches when there is a high probability of patch extinction. The microcosm experiments support the model predictions. Both approaches suggest that competitive dominance in a patchily distributed transient assemblage will depend upon the architecture and predictability of the environment. These mechanisms, operating at a small scale with high spatial admixture, may be embedded in a larger metacommunity process.     

Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species

Patch occupancy theory predicts that a trade-off between competition and dispersal should lead to regional coexistence of competing species. Empirical investigations, however, find local coexistence of superior and inferior competitors, an outcome that cannot be explained within the patch occupancy framework because of the decoupling of local and spatial dynamics. We develop two-patch metapopulation models that explicitly consider the interaction between competition and dispersal. We show that a dispersal-competition trade-off can lead to local coexistence provided the inferior competitor is superior at colonizing empty patches as well as immigrating among occupied patches. Immigration from patches that the superior competitor cannot colonize rescues the inferior competitor from extinction in patches that both species colonize. Too much immigration, however, can be detrimental to coexistence. When competitive asymmetry between species is high, local coexistence is possible only if the dispersal rate of the inferior competitor occurs below a critical threshold. If competing species have comparable colonization abilities and the environment is otherwise spatially homogeneous, a superior ability to immigrate among occupied patches cannot prevent exclusion of the inferior competitor. If, however, biotic or abiotic factors create spatial heterogeneity in competitive rankings across the landscape, local coexistence can occur even in the absence of a dispersal-competition trade-off. In fact, coexistence requires that the dispersal rate of the overall inferior competitor not exceed a critical threshold. Explicit consideration of how dispersal modifies local competitive interactions shifts the focus from the patch occupancy approach with its emphasis on extinction-colonization dynamics to the realm of source-sink dynamics. The key to coexistence in this framework is spatial variance in fitness. Unlike in the patch occupancy framework, high rates of dispersal can undermine coexistence, and hence diversity, by reducing spatial variance in fitness.     

Competitive resource sharing: An experimental test of a learning rule for ESSs

Six sticklebacks (Gasterosteus aculeatus) distributed themselves between two simulated drift food patches in the ratio of patch profitabilities (Milinski 1979). The present study investigated the rule with which each fish decides to stay in one or the other patch, and whether the fish have more difficulties in reaching a decision when the prey is supplied irregularly as is the case under natural conditions. With frame by frame analysis of filmed experiments the hunting success and sampling effort of each individual fish could be determined continuously. The results support the hypothesis that the fish used the relative payoff sum (RPS) learning rule (Harley 1981; Regelmann 1984). There was a close correlation between all decisions of individual fish during a trial, whether to stay or leave a patch, and decisions predicted by the RPS learning rule using the actual experience of the fish. Differences in competitive ability between the fish influenced the dynamics of the distribution in the predicted way, the more successful competitors deciding earlier where to stay than the less successful ones. This had the effect that the good competitors as well as the poor ones were distributed between the patches in the ratio of patch profitabilities. It is also compatible with the RPS learning rule that the fish reached their decision as quickly whether they were supplied with prey regularly or irregularly.