Interference and the ideal free distribution: oviposition in a parasitoid wasp

The interference ideal free distribution (IFD) model of Sutherlandmakes a number of predictions that have yet to be tested andthat have implications for the validity of subsequent extensionsto the theory. We tested these predictions in a study usingdifferent densities of the parasitoid wasp, Venturia canescens,foraging on patches containing different densities of its host,Plodia interpunctella. Our results support a number of the interferenceIFD model's general predictions. Gain rate decreased becauseof increased interference at higher density. Although gain rateson the two patches differed slighdy, this would be expectedallowing for some sampling behavior and perceptual constraints.Early in each experiment when patch assessment is likely tooccur, wasp movement was higher and gain rates lower. However,the more specific prediction of Sutherland's model, that proportionalpatch use should be constant and independent of density, wasnot upheld. Contemporary IFD models use only one of severalequally valid potential relationships between gain rate, interference,and competitor density. The results of this study provide supportfor the additive model developed by Tregenza et al. (companionarticle).     

The effect of travel loss on evolutionarily stable distributions of populations in space

A key assumption of the ideal free distribution (IFD) is that there are no costs in moving between habitat patches. However, because many populations exhibit more or less continuous population movement between patches and traveling cost is a frequent factor, it is important to determine the effects of costs on expected population movement patterns and spatial distributions. We consider a food chain (tritrophic or bitrophic) in which one species moves between patches, with energy cost or mortality risk in movement. In the two-patch case, assuming forced movement in one direction, an evolutionarily stable strategy requires bidirectional movement, even if costs during movement are high. In the N-patch case, assuming that at least one patch is linked bidirectionally to all other patches, optimal movement rates can lead to source-sink dynamics where patches with negative growth rates are maintained by other patches with positive growth rates. As well, dispersal between patches is not balanced (even in the two-patch case), leading to a deviation from the IFD. Our results indicate that cost-associated forced movement can have important consequences for spatial metapopulation dynamics. Relevance to marine reserve design and the study of stream communities subject to drift is discussed.     

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.     

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.     

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.     

Dynamical facilitation of the ideal free distribution in nonideal populations

The ideal free distribution (IFD) requires that individuals can accurately perceive density‐dependent habitat quality, while failure to discern quality differences below a given perception threshold results in distributions approaching spatial uniformity. Here, we investigate the role of population growth in restoring a nonideal population to the IFD. We place a simple model of discrete patch choice under limits to the resolution by which patch quality is perceived and include population growth driven by that underlying quality. Our model follows the population's distribution through both breeding and dispersal seasons when perception limits differ in their likely influence. We demonstrate that populations of perception limited movers can approximate an IFD provided sufficient population growth; however, the emergent IFD would be temporally inconstant and correspond to reproductive events. The time to emergence of the IFD during breeding is shorter under exponential growth than under logistic growth. The IFD during early colonization of a community persists longer when more patches are available to individuals. As the population matures and dispersal becomes increasingly random, there is an oscillation in the observance of IFD, with peaks most closely approximating the IFD occurring immediately after reproductive events, and higher reproductive rates producing distributions closer to the IFD.     

The evolution of patch selection in stochastic environments

A null model for habitat patch selection in spatially heterogeneous environments is the ideal free distribution (IFD), which assumes individuals have complete knowledge about the environment and can freely disperse. Under equilibrium conditions, the IFD predicts that local population growth rates are zero in all occupied patches, sink patches are unoccupied, and the fraction of the population selecting a patch is proportional to the patch's carrying capacity. Individuals, however, often experience stochastic fluctuations in environmental conditions and cannot respond to these fluctuations instantaneously. An evolutionary stability analysis for fixed patch-selection strategies reveals that environmental uncertainty disrupts the classical IFD predictions: individuals playing the evolutionarily stable strategy may occupy sink patches, local growth rates are negative and typically unequal in all patches, and individuals prefer higher-quality patches less than predicted by their carrying capacities. Spatial correlations in environmental fluctuations can enhance or marginalize these trends. The analysis predicts that continually increasing environmental variation first selects for range expansion, then selects for persisting coupled sink populations, and ultimately leads to regional extinction. In contrast, continually increasing habitat degradation first selects for range contraction and may select for persisting coupled sink populations before regional extinction. These results highlight the combined roles of spatial and temporal heterogeneity on the evolution of habitat selection.     

Habitat assessment by parasitoids: consequences for population distribution

The ideal free distribution (IFD) is a stable distribution ofcompetitors among resource patches. For equally efficient competitors,equilibrium is reached when the per capita rate of intake equalizesacross patches. The seminal version of the IFD assumes omniscience,but populations may still converge toward the equilibrium providedthat competitors 1) accurately assess their environment by learningand 2) remain for an optimal (rate-maximizing) time on eachencountered patch. In the companion article (Tentelier C, DesouhantE, Fauvergue X. 2006. Habitat assessment by parasitoids: mechanismsfor patch time allocation. Behav Ecol. Forthcoming), it is shownthat the parasitoid wasp Lysiphlebus testaceipes adapts itsexploitation of aphid host colonies based on previous experience,in a manner consistent with these two conditions. We thereforepredicted that a randomly distributed population of initiallynaive wasps should converge toward the IFD. We tested this predictionby introducing 1300 L. testaceipes females into a 110-m² greenhousecontaining 40 host patches. Just after introduction, the parasitoidrate of gain was positively affected by host number and negativelyaffected by parasitoid number but, as predicted, these effectsvanished in the course of the experiment. Six hours after introduction,the expected rate of gain reached a constant. Surprisingly,this passage through equilibrium was not accompanied by a decreasein the coefficient of variation among gain rates or by a shiftfrom a random to an aggregated distribution of parasitoids.These results challenge our understanding of the link betweenindividual behavior and population distribution.     

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 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.     

Biophysical Constraints on Optimal Patch Lengths for Settlement of a Reef-Building Bivalve

Reef-building species form discrete patches atop soft sediments, and reef restoration often involves depositing solid material as a substrate for larval settlement and growth. There have been few theoretical efforts to optimize the physical characteristics of a restored reef patch to achieve high recruitment rates. The delivery of competent larvae to a reef patch is influenced by larval behavior and by physical habitat characteristics such as substrate roughness, patch length, current speed, and water depth. We used a spatial model, the “hitting-distance” model, to identify habitat characteristics that will jointly maximize both the settlement probability and the density of recruits on an oyster reef (Crassostrea virginica). Modeled larval behaviors were based on laboratory observations and included turbulence-induced diving, turbulence-induced passive sinking, and neutral buoyancy. Profiles of currents and turbulence were based on velocity profiles measured in coastal Virginia over four different substrates: natural oyster reefs, mud, and deposited oyster and whelk shell. Settlement probabilities were higher on larger patches, whereas average settler densities were higher on smaller patches. Larvae settled most successfully and had the smallest optimal patch length when diving over rough substrates in shallow water. Water depth was the greatest source of variability, followed by larval behavior, substrate roughness, and tidal current speed. This result suggests that the best way to maximize settlement on restored reefs is to construct patches of optimal length for the water depth, whereas substrate type is less important than expected. Although physical patch characteristics are easy to measure, uncertainty about larval behavior remains an obstacle for predicting settlement patterns. The mechanistic approach presented here could be combined with a spatially explicit metapopulation model to optimize the arrangement of reef patches in an estuary or region for greater sustainability of restored habitats.     

The energetic equivalence of cover to juvenile coho salmon (Oncorhynchus kisutch): ideal free distribution theroy applied

Cover is often thought to be an important habitat characteristicfor juvenile stream salmonida. In addition to providing protectionfrom predators, cover may be associated with reduced food availability.Thus, an individual's use of cover is likely to reflect a trade-offbetween the conflicting demands of growth and survival. We measuredthe influence of cover on foraging-site selection in groupsof eight juvenile coho salmon (Oncorhynchus kisutch) by examiningtheir distribution across two stream channel patches, one providingaccess to cover but little food (the "poor" patch), the otherproviding more food but no cover (the "good" patch). Becausefish distributions in the absence of cover conformed to an idealfree distribution (IFD) for unequal competitors (i.e., the distributionof competitive abilities matched the distribution of food),we used IFD theory to quantify the energetic equivalence ofcover to the fish. In the presence of cover and a model avianpredator, use of the poor patch increased relative to the predictionsof the IFD model. Using this observed deviation from an IFD,we calculated how much extra food must be added to the goodpatch to return the distribution of fish to the previously observedIFD of unequal competitors. As predicted, adding this amountof food caused the fish to return to their previous distribution,demonstrating that IFD theory can be used to relate energy intakeand risk of predation in a common currency     

Aggregations from using inadvertent social information: a form of ideal habitat selection

Social information in breeding site selection has received extensive study; however, few attempts have been made to link this process to pre‐existing models. We examine the importance of social information to three pertinent models of habitat selection that describe breeding aggregations and spatial patterns: 1) the ideal despotic distribution (IDD) which considers conspecific competition and habitat availability, 2) the perceptual constraints model which accounts for patch selection when animals experience a threshold of undetectable difference in quality, and 3) the “neighbourhood model” which predicts concordance between resources and settlers can be disrupted by conspecific attraction when resources are patchy. These models all predict initial settlers will select a high quality patch first. However, their predictions of subsequent settlement behaviour in remaining patches differ: the IDD predicts subsequent settlers will be distributed regularly, the perceptual constraints model predicts a random distribution, and the neighbourhood model predicts clustering from conspecific attraction. We examined which model best described settlement patterns of bobolink Dolichonyx oryzivorus and savannah sparrow Passerculus sandwichensis, in the context of social information. We observed settlement timing, quantified available resources, and determined where they occurred in the highest (local population “core”) and lowest densities (local population “periphery”). We then assessed whether individuals in the periphery settled in greater concordance with resources or conspecific presence. Core territories were clustered strongly on relevant resources, and these territory holders were older than in the periphery. Peripheral territories were likewise clustered but did not always co‐occur with the best available resources, matching the neighbourhood model prediction that social information may not always direct them to the best sites available. This suggests older individuals used their own experience to locate ideal habitat, whereas younger individuals attempted to aggregate on seemingly ideal habitat by using conspecific location; such information asymmetry due to age can be viewed as an “ideal aggregative distribution”.     

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.     

Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments

In this article, we develop population game theory, a theory that combines the dynamics of animal behavior with population dynamics. In particular, we study interaction and distribution of two species in a two-patch environment assuming that individuals behave adaptively (i.e., they maximize Darwinian fitness). Either the two species are competing for resources or they are in a predator-prey relationship. Using some recent advances in evolutionary game theory, we extend the classical ideal free distribution (IFD) concept for single species to two interacting species. We study population dynamical consequences of two-species IFD by comparing two systems: one where individuals cannot migrate between habitats and one where migration is possible. For single species, predator-prey interactions, and competing species, we show that these two types of behavior lead to the same population equilibria and corresponding species spatial distributions, provided interspecific competition is patch independent. However, if differences between patches are such that competition is patch dependent, then our predictions strongly depend on whether animals can migrate or not. In particular, we show that when species are settled at their equilibrium population densities in both habitats in the environment where migration between habitats is blocked, then the corresponding species spatial distribution need not be an IFD. Thus, when species are given the opportunity to migrate, they will redistribute to reach an IFD (e.g., under which the two species can completely segregate), and this redistribution will also influence species population equilibrial densities. Alternatively, we also show that when two species are distributed according to the IFD, the corresponding population equilibrium can be unstable.     

Use of space and habitats by meadow voles at the home range,patch and landscape scales

Using capture/recapture methods, we examined the spatial usage patterns of Microtus pennsylvanicus within and between experimentally created habitat patches of three sizes (1.0, 0.25 and 0.0625 ha) and between a 20-ha fragmented and a 20-ha continuous habitat landscape. We tested the prediction that home ranges near patch edges would be qualitatively different from those in patch interiors, and that the edge:interior habitat ratio could be used to make predictions concerning the dispersion and spatial use of individuals occupying different sized patches and between landscapes with different habitat structure. We found adult females on patch edges to have larger and more exclusive home ranges, larger body sizes, longer residence times, and to reproduce at a higher frequency than those in patch interiors. These edge effects also appeared to be largely responsible for the greater proportion of larger, reproductive females we found in small than larger patches and in the fragmented than in the continuous habitat (control) landscape. The selection of higher quality edge habitats by dominant females and the relegation of sub-dominants to patch interiors provides an explanation for the observed differences in the distribution and performance of females over patches and between landscapes.     

Foraging on spatially distributed resources with sub‐optimal movement,imperfect information,and travelling costs: departures from the ideal free distribution

Ideal free distribution (IFD) theory offers an important baseline for predicting the distribution of foragers across resource patches. Yet it is well known that IFD theory relies on several over‐simplifying assumptions that are unlikely to be met in reality. Here we relax three of the most critical assumptions: (1) optimal foraging moves among patches, (2) omniscience about the utility of resource patches, and (3) cost‐free travelling between patches. Based on these generalizations, we investigate the distributions of a constant number of foragers in models with explicit resource dynamics of logistic type. We find that, first, when foragers do not always move to the patch offering maximum intake rate (optimal foraging), but instead move probabilistically according to differences in resource intake rates between patches (sub‐optimal foraging), the distribution of foragers becomes less skewed than the IFD, so that high‐quality patches attract fewer foragers. Second, this homogenization is strengthened when foragers have less than perfect knowledge about the utility of resource patches. Third, and perhaps most surprisingly, the introduction of travelling costs causes departures in the opposite direction: the distribution of sub‐optimal foragers approaches the IFD as travelling costs increase. We demonstrate that these three findings are robust when considering patches that differ in the resource's carrying capacity or intrinsic growth rate, and when considering simple two‐patch and more complex multiple‐patch models. By overcoming three major over‐simplifications of IFD theory, our analyses contribute to the systematic investigation of ecological factors influencing the spatial distribution of foragers, and thus help in deriving new hypotheses that are testable in empirical systems. A confluence of theoretical and empirical studies that go beyond classical IFD theory is essential for improving insights into how animal distributions across resource patches are determined in nature.     

The Little Miss Muffet Effect: Quantifying the Effect of Predation Risk on Foraging Patch Choice by Houseflies (<Emphasis Type="Italic">Musca domestica</Emphasis>)

The ability of the ideal free distribution (IFD) to predict patch choice of female houseflies (Musca domestica) was determined by examining their distribution between two patches containing unequal amounts of food. The effect of predation risk was then quantified in energetic terms by examining fly distribution between patches of equal food, with one containing spiders. Results were used to predict how much extra food must be added to the risky patch to offset the risk of predation. Flies were found to conform fairly closely to the IFD. Predation risk had a major effect on their distribution, with fewer flies feeding in the presence of predators as risk increased. Addition of extra food to the risky patch was successful in offsetting the risk of predation. These results suggest that the effect of risk on housefly foraging behavior can be quantified in energy terms, providing a common currency for predicting the effects of resources and predation risk on habitat use.     

Geometry of the ideal free distribution: individual behavioural variation and annual reproductive success in aggregations of a social ungulate

Variation in social environment can mitigate risks and rewards associated with occupying a particular patch. We aim to integrate Ideal Free Distribution (IFD) and Geometry of the Selfish Herd (GSH) to address an apparent conflict in their predictions of equal mean fitness between patches (IFD) and declining fitness benefits within a patch (GSH). We tested these hypotheses in a socio‐spatial context using individual caribou that were aggregated or disaggregated during calving and varied in their annual reproductive success (ARS). We then tested individual consistency of these spatial tactics. We reveal that two socio‐spatial tactics accorded similar mean ARS (IFD); however, ARS for aggregated individuals declined near the periphery (GSH). Individuals near the aggregation periphery exhibited flexibility, whereas others were consistent. The integration of classical theories through a contemporary lens of consistent individual differences provides evidence for an integrated GSH and IFD strategy that may represent an evolutionary stable state.