Consumer–resource matching in a food chain when both predators and prey are free to move

The classical theory of the ideal free distribution (IFD) predicts that the spatial distribution of consumers should follow the distribution of the resources they depend on. Here, we study consumer–resource matching in a community context. Our model for the community is a food chain with three levels. We study whether the primary consumers are able to match resources both under predation risk and in its absence. Both prey and predators have varying degrees of knowledge of the global and local resource distribution. We present two versions of the model. In the "resource maximising" model, the consumers consider the availability of their resource only. In the "balancing" model, individual consumers minimise predation risk per unit of resource that they can gain access to. We show that both models can lead to perfect matching of consumers on resources and predators on consumers, assuming that individuals have full knowledge of the whole environment. However, when the consumers' information and freedom of movement are greater than those of the predators, then the predators generally undermatch the consumers. In the opposite case, we observe overmatching and high consumer movement rates. Furthermore, undermatching of predators on consumers tends to induce overmatching of consumers on resources.     

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.     

Consumers that are not 'ideal' or 'free' can still approach the ideal free distribution using simple patch-leaving rules

1.  The ideal free distribution (IFD) has been widely used to determine whether consumers distribute themselves optimally. However, this theory is based on three assumptions that are clearly violated in many systems. The theory assumes that all individuals know the quality of each available site, are equally free to move between all sites, and have equal competitive abilities.
2.  I examine the utility of this theory to predict the distribution of the invasive European green crab Carcinus maenas , a species that likely violates all of these assumptions. I demonstrate three main findings.
3.  First, understanding how density-dependent interference and size alter individual foraging behaviour is important for understanding the density and biomass distribution of C. maenas in invaded habitats.
4.  Second, once behavioural mechanisms of crab foraging are accurately included in the model, the IFD does a good job of predicting the distribution of C. maenas , even though C. maenas violates the theory's fundamental assumptions.
5.  Third, C. maenas ' distribution can be obtained using simple decision rules and reasonable movement patterns.     

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.     

Microsatellite-based parentage analysis reveals non-ideal free distribution in a parasitoid population

Habitat selection by dispersers is the focus of much theoretical models, most of which are based on the assumption of negative density dependence. The archetype of these models is the ideal free distribution, characterized by an evolutionary stable state where more competitors aggregate in better habitats, so that the fitness benefit of resource abundance is equally offset by the cost of competition in all habitats. In this study, we used parentage analysis on microsatellite genotypes to test the ideal free distribution in a natural population of aphid parasitoids. Parentage analysis was conducted on parasitoids emerging from aphid colonies. We inferred the number of foundress females which had reproduced in each colony, as well as the number of offspring for each foundress. As predicted by the ideal free distribution, the number of offspring per foundress per colony did not depend on the number of hosts per colony. However, contrary to ideal free distribution predictions, it was affected by the number of foundresses per colony. In surprising contrast with the basic assumption of negative density dependence, individual fitness increased with the number of foundresses. Moreover, parentage analysis revealed a very low number of offspring per foundress per colony (mean = 1.8). This observed distribution questions the validity of classical models of habitat choice based on competition. Indeed, our results provide a new illustration reinforcing a growing body of theory and data on positive density dependence. Our results also suggest that the avoidance of hyperparasitism and predation, although generally neglected, may shape the distribution of parasitoids in the field.     

Tracking prey or tracking the prey's resource? Mechanisms of movement and optimal habitat selection by predators

We synthesize previous theory on ideal free habitat selection to develop a model of predator movement mechanisms, when both predators and prey are mobile. We consider a continuous environment with an arbitrary distribution of resources, randomly diffusing prey that consume the resources, and predators that consume the prey. Our model introduces a very general class of movement rules in which the overall direction of a predator's movement is determined by a variable combination of (i) random diffusion, (ii) movement in the direction of higher prey density, and/or (iii) movement in the direction of higher density of the prey's resource. With this model, we apply an adaptive dynamics approach to two main questions. First, can it be adaptive for predators to base their movement solely on the density of the prey's resource (which the predators do not consume)? Second, should predator movements be exclusively biased toward higher densities of prey/resources, or is there an optimal balance between random and biased movements? We find that, for some resource distributions, predators that track the gradient of the prey's resource have an advantage compared to predators that track the gradient of prey directly. Additionally, we show that matching (consumers distributed in proportion to resources), overmatching (consumers strongly aggregated in areas of high resource density), and undermatching (consumers distributed more uniformly than resources) distributions can all be explained by the same general habitat selection mechanism. Our results provide important groundwork for future investigations of predator-prey dynamics.     

The ideal free pike: 50 years of fitness-maximizing dispersal in Windermere

The ideal free distribution (IFD) theory is one of the most influential theories in evolutionary ecology. It predicts how animals ought to distribute themselves within a heterogeneous habitat in order to maximize lifetime fitness. We test the population level consequence of the IFD theory using 40-year worth data on pike (Esox lucius) living in a natural lake divided into two basins. We do so by employing empirically derived density-dependent survival, dispersal and fecundity functions in the estimation of basin-specific density-dependent fitness surfaces. The intersection of the fitness surfaces for the two basins is used for deriving expected spatial distributions of pike. Comparing the derived expected spatial distributions with 50 years data of the actual spatial distribution demonstrated that pike is ideal free distributed within the lake. In general, there was a net migration from the less productive north basin to the more productive south basin. However, a pike density-manipulation experiment imposing shifting pike density gradients between the two basins managed to switch the net migration direction and hence clearly demonstrated that the Windermere pike choose their habitat in an ideal free manner. Demonstration of ideal free habitat selection on an operational field scale like this has never been undertaken before.     

A THURSTONE-COOMBS MODEL OF CONCURRENT RATINGS WITH SENSORY AND LIKING DIMENSIONS

A popular product testing procedure is to obtain sensory intensity and liking ratings from the same consumers. Consumers are instructed to attend to the sensory attribute, such as sweetness, when generating their liking response. We propose a new model of this concurrent ratings task that conjoins a unidimensional Thurstonian model of the ratings on the sensory dimension with a probabilistic version of Coombs' (1964) unfolding model for the liking dimension. The model assumes that the sensory characteristic of the product has a normal distribution over consumers. An individual consumer selects a sensory rating by comparing the perceived value on the sensory dimension to a set of criteria that partitions the axis into intervals. Each value on the rating scale is associated with a unique interval. To rate liking, the consumer imagines an ideal product, then computes the discrepancy or distance between the product as perceived by the consumer and this imagined ideal. A set of criteria are constructed on this discrepancy dimension that partition the axis into intervals. Each interval is associated with a unique liking rating. The ideal product is assumed to have a univariate normal distribution over consumers on the sensory attribute evaluated. The model is shown to account for 94.2% of the variance in a set of sample data and to fit this data significantly better than a bivariate normal model of the data (concurrent ratings, Thurstonian scaling, Coombs' unfolding model, sensory and liking ratings).     

Extension of ideal free resource use to breeding populations and metapopulations

The concept of an ideal and free use of limiting resources is commonly invoked in behavioural ecology as a null model for predicting the distribution of foraging consumers across heterogeneous habitat. In its original conception, however, its predictions were applied to the longer timescales of habitat selection by breeding birds. Here I present a general model of ideal free resource use, which encompasses classical deterministic models for the dynamics in continuous time of feeding aggregations, breeding populations and metapopulations. I illustrate its key predictions using the consumer functional response given by Holling's disc equation. The predictions are all consistent with classical population dynamics, but at least two of them are not usually recognised as pertaining across all scales. At the fine scale of feeding aggregations, the steady state of an equal intake for all ideal free consumers may be intrinsically unstable, if patches are efficiently exploited by individuals with a non-negligible handling time of resources. At coarser scales, classical models of population and metapopulation dynamics assume exploitation of a homogeneous environment, yet they can yield testable predictions for heterogeneous environments too under the assumption of ideal free resource use.     

Children's competition in a natural setting: evidence for the ideal free distribution

Little is known of the foraging abilities of children in modern cultures, especially when children forage in groups. Here we present a test of optimal foraging theory in groups of street children working for money. The children we observed were selling bottles of water to drivers distributed in two lanes at a crossroad of Istanbul, Turkey. As predicted by the ideal free distribution (a model of optimal group foraging), the ratio of children working in the two lanes was sensitive to the ratio of cars (and therefore the ratio of potential buyers) present in each lane. Deviations from the ideal free model arose largely from numerical restrictions on the set of possible ratios compatible with a small group size. When these constraints were taken into account, optimal behavior emerged as a robust aspect of the children's group distribution. Our results extend to human children aspects of group foraging that were previously tested in human adults or other animal species.     

The ideal free distribution of clonal plant's ramets among patches in a heterogeneous environment

The plastic response of clonal plant to different patch quality is not always the same and the degree is different too. So the result of this kind of foraging behaviour is different. In order to make clear whether the ramtes stay in favourable patches and get the quantitative relationship between the ramets distribution among patches and the available resource amount in heterogeneous environment, we develop a theoretical work under ideal free distribution (IFD) theory framework by neglecting some morphological plasticity of the spacer in this article. The results of our general model show that the ramet distribution should obey input matching rule at equilibrium. That means the ratio of ramet number in different patches should be equal to the ratio of available resource amount in these patches. We also use the simulation to predict the distribution pattern under history mattering. The results show that the initial ramets number has significant influence on the final distribution: over matching and under matching both can occur. More initial ramets in favourable patch result in over matching and more initial ramets in unfavourable patch result in under matching. The degree of the deviation from input matching rule is great when the difference of patches is small. These results prove that ideal free distribution theory works the same with animals. The ramets can stay in favourable patches sometimes in spite of the plasticity of the spacer, and the distribution depends on both patch quality and the history factors. But these results are true only when the functional response is type II.     

Threshold elemental ratios of carbon and phosphorus in aquatic consumers

Inadequate supply of one or more mineral elements can slow the growth of animal consumers and alter their physiology, life history and behaviour. A key concept for understanding nutrient deficiency in animals is the threshold elemental ratio (TER), at which growth limitation switches from one element to another. We used a stoichiometric model that coupled animal bioenergetics and body elemental composition to estimate TER of carbon and phosphorus (TER_C:P) for 41 aquatic consumer taxa. We found a wide range in TER_C:P (77–3086, ratio by atoms), which was generated by interspecific differences in body C : P ratios and gross growth efficiencies of C. TER_C:P also varied among aquatic invertebrates having different feeding strategies, such that detritivores had significantly higher threshold ratios than grazers and predators. The higher TER_C:P in detritivores resulted not only from lower gross growth efficiencies of carbon but also reflected lower body P content in these consumers. Supporting previous stoichiometric theory, we found TER_C:P to be negatively correlated with the maximum growth rate of invertebrate consumers. By coupling bioenergetics and stoichiometry, this analysis revealed strong linkages among the physiology, ecology and evolution of nutritional demands for animal growth.     

The information of food distribution realizes an ideal free distribution: Support of perceptual limitation

Previous tests of ideal free distribution (IFD) under continuous input conditions have demonstrated that more profitable patches tend to be relatively underused compared to that predicted by the theory. We tested the hypothesis that competitors’ perceptual constraints of resource distribution cause this deviation from the IFD. A laboratory experiment was conducted to determine whether additional information on food distribution by a light cue that indicates the food input point improves the IFD theory’s fit to the distribution of clone red-spotted masu salmons (Salmonids),Oncorhynchus masou ishikawai, that had been conditioned to the light as a cue indicating the site with a higher input rate. In the treatments without a light cue, the distribution of fish was closer to a random pattern than an IFD. In contrast, in the treatments with light cue, the distribution of fish was closer to the expected value of an IFD rather than to a random pattern, supporting the perception-limit hypothesis. The distribution and the pattern of resource use by fish in the treatments without the light cue were best explained by the perception-limit model. Our results suggest that it is perceptual constraints that cause deviation from the IFD.     

Scale‐dependent role of demography and dispersal on the distribution of populations in heterogeneous landscapes

Both dispersal and local demographic processes determine a population's distribution among habitats of varying quality, yet most theory, experiments, and field studies have focused on the former. We use a generic model to show how both processes contribute to a population's distribution, and how the relative importance of each mechanism depends on scale. In contrast to studies only considering habitat‐dependent dispersal, we show that predictions of ideal free distribution (IFD) theory are relevant even at landscape scales, where the assumptions of IFD theory are violated. This is because scales that inhibit one process, promote the other's ability to drive populations to the IFD. Furthermore, because multiple processes can generate IFDs, the pattern alone does not specify a causal mechanism. This is important because populations with IFDs generated by dispersal or demography respond much differently to shifts in resource distributions.     

Density-dependent habitat selection in muskrats: a test of the ideal free distribution model

Summary Two predictions of the ideal free distribution model, a null hypothesis of habitat selection, were examined using free-ranging muskrats. We rejected the prediction that the proportion of the animals found in each of five habitats was independent of population size. Data on over-winter occupancy of muskrat dwellings tend also to refute the prediction of equal fitness reward among habitats. Habitat type and water-level had a profound effect on the suitability of a site for settlement. We concluded that the observed pattern of muskrat distribution followed more closely an ideal despotic distribution where some individuals benefited from a higher fitness because of resource monopolization. Current theories of density-dependent habitat selection, which assume an ideal free distribution, would not apply to muskrats and possibly to many other mammal species.     

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     

Relationships between survival and habitat suitability of semi‐aquatic mammals

Spatial distribution and habitat selection are integral to the study of animal ecology. Habitat selection may optimize the fitness of individuals. Hutchinsonian niche theory posits the fundamental niche of species would support the persistence or growth of populations. Although niche‐based species distribution models (SDMs) and habitat suitability models (HSMs) such as maximum entropy (Maxent) have demonstrated fair to excellent predictive power, few studies have linked the prediction of HSMs to demographic rates. We aimed to test the prediction of Hutchinsonian niche theory that habitat suitability (i.e., likelihood of occurrence) would be positively related to survival of American beaver (Castor canadensis), a North American semi‐aquatic, herbivorous, habitat generalist. We also tested the prediction of ideal free distribution that animal fitness, or its surrogate, is independent of habitat suitability at the equilibrium. We estimated beaver monthly survival probability using the Barker model and radio telemetry data collected in northern Alabama, United States from January 2011 to April 2012. A habitat suitability map was generated with Maxent for the entire study site using landscape variables derived from the 2011 National Land Cover Database (30‐m resolution). We found an inverse relationship between habitat suitability index and beaver survival, contradicting the predictions of niche theory and ideal free distribution. Furthermore, four landscape variables selected by American beaver did not predict survival. The beaver population on our study site has been established for 20 or more years and, subsequently, may be approaching or have reached the carrying capacity. Maxent‐predicted increases in habitat use and subsequent intraspecific competition may have reduced beaver survival. Habitat suitability‐fitness relationships may be complex and, in part, contingent upon local animal abundance. Future studies of mechanistic SDMs incorporating local abundance and demographic rates are needed.     

Variation in trophic shift for stable isotope ratios of carbon, nitrogen, and sulfur

Use of stable isotope ratios to trace pathways of organic matter among consumers requires knowledge of the isotopic shift between diet and consumer. Variation in trophic shift among consumers can be substantial. For data from the published literature and supplementary original data (excluding fluid-feeding consumers), the mean isotopic shift for C was +0.5±0.13‰ rather than 0.0‰, as commonly assumed. The shift for C was higher for consumers analyzed as muscle (+1.3±0.30‰) than for consumers analyzed whole (+0.3±0.14‰). Among consumers analyzed whole, the trophic shift for C was lower for consumers acidified prior to analysis (−0.2±0.21‰) than for unacidified samples (+0.5±0.17‰). For N, trophic shift was lower for consumers raised on invertebrate diets (+1.4±0.21‰) than for consumers raised on other high-protein diets (+3.3±0.26‰) and was intermediate for consumers raised on plant and algal diets (+2.2±0.30‰). The trophic shift for S differed between high-protein (+2.0±0.65‰) and low-protein diets (-0.5±0.56‰). Thus, methods of analysis and dietary differences can affect trophic shift for consumers; the utility of stable isotope methods can be improved if this information is incorporated into studies of trophic relationships. Although few studies of stable isotope ratios have considered variation in the trophic shift, such variation is important because small errors in estimates of trophic shift can result in large errors in estimates of the contribution of sources to consumers or in estimates of trophic position.