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We present three models representing the trophic and behavioral dynamics of a simple food chain (primary producers, grazers, and predators) at temporal scales shorter than the scale of consumer reproduction, and at the spatial scales typically employed in field experiments. These models incorporate flexible behavioral responses of organisms to their predators and resources in spatially heterogeneous environments that are open to immigration and emigration. The basic models include passive immigration at all trophic levels, producer growth rates and losses to grazer consumption, grazer emigration rate as a behavioral response to producer and predator densities, grazer losses to predator consumption, and predator emigration as a function of grazer density. We model this system as: (1) a set of ordinary differential equations (''well-mixed model''); (2) a set of partial differential equations describing a population of discrete grazers foraging on discrete patches of primary producers (''discrete-grazer model''); and (3) a set of simulation rules describing the movement and foraging of individual grazers and the growth of primary producers on discrete patches in explicit space (''individual-based model''). The ordinary differential-equation models produced similar results to individual-based models with wellmixed producers, and the discrete-grazer and individual-based models produced similar results when grazers possessed a long-term memory of patch reward rates. The well-mixed and discrete-grazer models thus represent specific, limiting cases of the general individualbased model.Multiple equilibria and sustained oscillations are possible but are less likely in the discrete-grazer and individual-based models than in the well-mixed model, because localized foraging of discrete grazers leads to the rapid development of spatial heterogeneity in producer biomass and, hence, to a decrease in overall primary production. All models predict that stable equilibrium densities of all trophic levels increase with enrichment, provided grazers increase their emigration rates as predator density increases. If increasing predator density leads to decreasing grazer-emigration rates, predator and grazer densities increase, but producer biomass may increase or decrease with enrichment. These results contrast with predictions from models that assume ideal free distributions of grazers and/or predators with respect to their resources. Our models also predict that densities at all trophic levels will increase with increasing producer immigration, and that producer density will decline with increasing grazer immigration and increase with increasing predator immigration. Our qualitative findings on enrichment are used to interpret an experiment dealing with the short-term dynamics of a stream community open to grazers and predators.

We developed a mathematical model based on the microalgal–gastropod system studied by Schmitt, in which two coexisting consumers (Tegula eisini and T. aureotincta) feed on a common resource. The two consumers differ in their foraging behavior and their ability to remove microalgae from rock surfaces. T. eisini is a digger, moving slowly and grazing the algae down to almost bare substrate, whereas T. aureotincta is a grazer, moving more quickly and leaving behind a larger fraction of the algal layer. These complementary foraging strategies result in a size‐structured algal resource, with each size class differentially accessible to each of the consumers. Our model recognized three accessibility states for an algal patch: a refuge (recently grazed by the digger and currently inaccessible to either consumer), a low level (exploitable only by the digger), and a high level (exploitable by both consumers). We assumed that all interactions between consumers and resources were linear and examined the relatively short time‐scale dynamics of feeding, algal renewal, and individual consumer growth at fixed densities of consumers. Thus, our model complemented related models that have focused on population dynamics rather than foraging behavior. The model revealed that coexistence of two consumers feeding on a single algal resource can be mediated by differences in the consumers’ foraging modes and the resource structure that these behaviors create. We then estimated model parameters using data from Schmitt’s experimental studies of Tegula. The fits to the experimental data were all very good, and the resulting parameter values placed the system very close to a narrow coexistence region, demonstrating that foraging complementarity in this system facilitates coexistence. The foraging trade‐offs observed here are likely to be common in many consumer–resource systems. Indeed, mechanisms similar to those we discuss have been suggested in many other systems in which similar consumers also coexist. This model not only demonstrates that such an argument is theoretically plausible, but also provides the first application of the model, showing that the observed conditions for the Tegula system fall very close to the appropriate parameter space. Such quantitative tests are critical if we are to rigorously test the models developed to explain patterns of coexistence.

A general consumer-resource model assuming discrete consumers and a continuously structured resource is examined. We study two foraging behaviors, which lead to fixed and flexible patch residence times, in conjunction with a simple consumer energetics model linking resource consumption, foraging behavior, and metabolic costs. Results indicate a single, evolutionarily stable foraging strategy for fixed and flexible foraging in a nonspatial environment, but flexible foraging in a spatial environment leads to consumer grouping, which affects the resource distribution such that no single foraging strategy can exclude all other strategies. This evolutionarily stable coexistence of multiple foraging strategies may help explain a dichotomous pattern observed in a wide variety of natural systems.