Coexistence and community structure in a consumer resource model with implicit stoichiometry

We combine stoichiometry theory and optimal foraging theory into the MacArthur consumer-resource model. This generates predictions for diet choice, coexistence, and community structure of heterotroph communities. Tradeoffs in consumer resource-garnering traits influence community outcomes. With scarce resources, consumers forage opportunistically for complementary resources and may coexist via tradeoffs in resource encounter rates. In contrast to single currency models, stoichiometry permits multiple equilibria. These alternative stable states occur when tradeoffs in resource encounter rates are stronger than tradeoffs in elemental conversion efficiencies. With abundant resources consumers exhibit partially selective diets for essential resources and may coexist via tradeoffs in elemental conversion efficiencies. These results differ from single currency models, where adaptive diet selection is either opportunistic or selective. Interestingly, communities composed of efficient consumers share many of the same properties as communities based on substitutable resources. However, communities composed of relatively inefficient consumers behave similarly to plant communities as characterized by Tilman’s consumer resource theory. The results of our model indicate that the effects of stoichiometry theory on community ecology are dependent upon both consumer foraging behavior and the nature of resource garnering tradeoffs.     

The evolution of resource specialization through frequency-dependent and frequency-independent mechanisms

Levins's fitness set approach has shaped the intuition of many evolutionary ecologists about resource specialization: if the set of possible phenotypes is convex, a generalist is favored, while either of the two specialists is predicted for concave phenotype sets. An important aspect of Levins's approach is that it explicitly excludes frequency-dependent selection. Frequency dependence emerged in a series of models that studied the degree of character displacement of two consumers coexisting on two resources. Surprisingly, the evolutionary dynamics of a single consumer type under frequency dependence has not been studied in detail. We analyze a model of one evolving consumer feeding on two resources and show that, depending on the trait considered to be subject to evolutionary change, selection is either frequency independent or frequency dependent. This difference is explained by the effects different foraging traits have on the consumer-resource interactions. If selection is frequency dependent, then the population can become dimorphic through evolutionary branching at the trait value of the generalist. Those traits with frequency-independent selection, however, do indeed follow the predictions based on Levins's fitness set approach. This dichotomy in the evolutionary dynamics of traits involved in the same foraging process was not previously recognized.     

Optimal foraging, specialization, and a solution to Liem's paradox

Species that appear highly specialized on the basis of their phenotype (e.g., morphology, behavior, and physiology) also sometimes act as ecological generalists. This apparent paradox has been used to argue against the importance of competition as a diversifying evolutionary force. We provide an alternative explanation based on optimal foraging theory. Some resources are intrinsically easy to use and are widely preferred, while others require specialized phenotypic traits on the part of the consumer. This asymmetry allows optimally foraging consumers to evolve phenotypic specializations on nonpreferred resources without greatly compromising their ability to use preferred resources. The evolution of phenotypic specialization on nonpreferred resources can be driven by competition, but the specialists act as ecological generalists whenever their preferred resources are available. Our model identifies at least three different concepts of specialization that need to be distinguished, based on diet, prey utilization efficiencies, and phenotypic adaptations. The relationships among these concepts are complex and often counterintuitive. Specialists should often reject the very resources that they have evolved traits to use. The most extreme phenotypic specializations should occur in the absence of a trade-off between using preferred and nonpreferred resources. Our model may explain why extreme phenotypic-specializations evolve more often in fish communities than in terrestrial vertebrate communities and provides a mechanism whereby species can coexist in stable communities despite common preferences for some resources.     

Evolutionary stability of optimal foraging: Partial preferences in the diet and patch models

In this article the patch and diet choice models of the optimal foraging theory are reanalyzed with respect to evolutionary stability of the optimal foraging strategies. In their original setting these fundamental models consider a single consumer only and the resulting fitness functions are both frequency and density independent. Such fitness functions do not allow us to apply the classical game theoretical methods to study an evolutionary stability of optimal foraging strategies for competing animals. In this article frequency and density dependent fitness functions of optimal foraging are derived by separation of time scales in an underlying population dynamical model and corresponding evolutionarily stable strategies are calculated. Contrary to the classical foraging models the results of the present article predict that partial preferences occur in optimal foraging strategies as a consequence of the ecological feedback of consumer preferences on consumer fitness. In the case of the patch occupation model these partial preferences correspond to the ideal free distribution concept while in the case of the diet choice model they correspond to the partial inclusion of the less profitable prey type in predators diet.     

Quantitative descriptions of resource choice in ecological models

This article reviews the subject of resource choice by consumers. It is concerned with how such choice has been and should be represented in quantitative ecological models. This requires consideration of the dynamics of behavioral change and the fitness consequences of different resource intake rates. The topic is important because of the impact of choice on the functional response of the consumer to each of the resources it consumes. A variety of open questions related to choice are addressed. These include: the relationship between optimal diet choice and switching; the relationship between adaptive choice of two or resources and type-3 functional responses to a single resource; whether switching behavior requires choice and whether choice always results in switching behavior; why partial preferences are observed; whether choice between habitats is fundamentally different from choice within habitats; how between-individual variation in parameters related to resource use alters functional responses measured at the population level. The impacts of choice on stability are discussed briefly. The costs of increased resource use and the type of nutritional interactions between resources are particularly important determinants of adaptive resource choice, and are considered in some detail.     

Evolution of specialization and ecological character displacement of herbivores along a gradient of plant quality

We study the combined evolutionary dynamics of herbivore specialization and ecological character displacement, taking into account foraging behavior of the herbivores, and a quality gradient of plant types. Herbivores can adapt by changing two adaptive traits: their level of specialization in feeding efficiency and their point of maximum feeding efficiency along the plant gradient. The number of herbivore phenotypes, their levels of specialization, and the amount of character displacement among them are the result of the evolutionary dynamics, which is driven by the underlying population dynamics, which in turn is driven by the underlying foraging behavior. Our analysis demonstrates broad conditions for the diversification of a herbivore population into many specialized phenotypes, for basically any foraging behavior focusing use on highest gains while also including errors. Our model predicts two characteristic phases in the adaptation of herbivore phenotypes: a fast character-displacement phase and a slow coevolutionary niche-shift phase. This two-phase pattern is expected to be of wide relevance in various consumer-resource systems. Bringing together ecological character displacement and the evolution of specialization in a single model, our study suggests that the foraging behavior of herbivorous arthropods is a key factor promoting specialist radiation.     

Adaptive feeding across environmental gradients and its effect on population dynamics

This paper analyzes a consumer's adaptive feeding response to environmental gradients. We consider a consumer-resource system where resources are distributed among many discrete resource patches. Each consumer exhibits a feeding morphology allowing it to remove resources from a patch down to some threshold density (or level) before having to seek resources elsewhere. Assuming consumers trade off resource extraction with patch access and predation, we show that for a given environment there often exists a single evolutionarily stable feeding threshold and it is an evolutionary attractor. We then investigate how the population dynamics of the resource and the consumer change as the environment changes. Two cases are considered: (i) all consumers exhibit a fixed feeding threshold that is adaptive for an intermediate environment; and (ii) the consumer population adapts and adopts the evolutionarily stable feeding threshold associated with the current environment. In less harsh environments (i.e., environments where consumers experience a lower risk of predation, or environments where resource patches are more abundant) the adaptive consumer population is predicted to evolve so that resources within a patch are depleted to lower densities. We show that the change in consumer density due to environmental change can be rather different depending on whether or not the population can adapt. In some situations we observe that when the consumer's environment becomes harsher, the consumer population may increase in density before a rapid crash to extinction. This result has implications for monitoring and managing a population.     

Adaptive foraging does not always lead to more complex food webs

Recent modeling studies exploring the effect of consumers’ adaptivity in diet composition on food web complexity invariably suggest that adaptivity in foraging decisions of consumers makes food webs more complex. That is, it allows for survival of a higher number of species when compared with non-adaptive food webs. Population-dynamical models in these studies share two features: parameters are chosen uniformly for all species, i.e. they are species-independent, and adaptive foraging is described by the search image model. In this article, we relax both these assumptions. Specifically, we allow parameters to vary among the species and consider the diet choice model as an alternative model of adaptive foraging. Our analysis leads to three important predictions. First, for species-independent parameter values for which the search image model demonstrates a significant effect of adaptive foraging on food web complexity, the diet choice model produces no such effect. Second, the effect of adaptive foraging through the search image model attenuates when parameter values cease to be species-independent. Finally, for the diet choice model we observe no (significant) effect of adaptive foraging on food web complexity. All these observations suggest that adaptive foraging does not always lead to more complex food webs. As a corollary, future studies of food web dynamics should pay careful attention to the choice of type of adaptive foraging model as well as of parameter values.     

Evolution of cannibalistic traits: scenarios derived from adaptive dynamics

The evolution of cannibalistic traits in consumer populations is studied in this paper with the approach of adaptive dynamics theory. The model is kept at its minimum complexity by eliminating some environmental characteristics, like heterogeneity and seasonalities, and by hiding the size-structure of the population. Evolutionary dynamics are identified through numerical bifurcation analysis, applied both to the ecological (resident-mutant) model and to the canonical equation of adaptive dynamics. The result is a rich catalog of evolutionary scenarios involving evolutionary stable strategies and branching points both in the monomorphic and dimorphic dynamics. The possibility of evolutionary extinction of highly cannibalistic populations is also ascertained. This allows one to explain why cannibalism can be a transient stage of evolution.     

Implications of flexible foraging for interspecific interactions: lessons from simple models

1.  Some types of flexible foraging behaviours were incorporated into ecological thought in the 1960s, but the population dynamical consequences of such behaviours are still poorly understood.
2.  Flexible foraging-related traits can be classified as shifts in general and specific foraging effort, and shifts in general and specific defense.
3.  Many flexible foraging behaviours suggested by theory have received very little empirical attention, and empirical techniques used to compare the magnitudes of behavioural and non-behavioural responses to predation are likely to have overestimated the behavioural components.
4.  Adaptively flexible foraging in theory causes significant changes in the forms of consumer functional responses and generates a variety of indirect interactions. These can alter fundamental ecological processes, such as co-existence of competitors, and top-down or bottom-up effects in food webs.
5.  Many aspects of flexible foraging are still largely unknown, including the issues of how to represent the dynamics of such phenotypically plastic traits, how flexible traits in multiple species interact, what types of adaptive movements occur in metacommunities, and how adaptive behaviours influence evolutionary change.
6.  Population dynamics in large food webs may be less dependent on behavioural flexibility than in small webs because species replacement may preempt some potential types of behavioural change within species.     

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.     

Evolutionarily stable consumer home range size in relation to resource demography and consumer spatial organization

There is a large variation in home range size within species, yet few models relate that variation to demographic and life-history traits. We derive an approximate deterministic population dynamics model keeping track of spatial structure, via spatial moment equations, from an individual-based spatial consumer-resource model; where space-use of consumers resembles that of central place foragers. Using invasion analyses, we investigate how the evolutionarily stable home range size of the consumer depends on a number of ecological and behavioral traits of both the resource and the consumer. We show that any trait variation leading to a decreased overall resource production or an increased spatial segregation between consumer and resource acts to increase consumer home range size. In this way, we extend theoretical predictions on optimal territory size to a larger range of ecological scenarios where home ranges overlap and population dynamics feedbacks are possible. Consideration of spatial traits such as dispersal distances also generates new results: (1) consumer home range size decreases with increased resource dispersal distance, and (2) when consumer agonistic behavior is weak, more philopatric consumers have larger home ranges. Finally, our results emphasize the role of the spatial correlation between consumer and resource distributions in determining home range size, and suggest resource dispersion is less important.     

Predation risk influences food‐web structure by constraining species diet choice

The foraging behaviour of species determines their diet and, therefore, also emergent food‐web structure. Optimal foraging theory (OFT) has previously been applied to understand the emergence of food‐web structure through a consumer‐centric consideration of diet choice. However, the resource‐centric viewpoint, where species adjust their behaviour to reduce the risk of predation, has not been considered. We develop a mechanistic model that merges metabolic theory with OFT to incorporate the effect of predation risk on diet choice to assemble food webs. This ‘predation‐risk‐compromise’ (PR) model better captures the nestedness and modularity of empirical food webs relative to the classical optimal foraging model. Specifically, compared with optimal foraging alone, risk‐mitigated foraging leads to more‐nested but less‐modular webs by broadening the diet of consumers at intermediate trophic levels. Thus, predation risk significantly affects food‐web structure by constraining species’ ability to forage optimally, and needs to be considered in future work.     

Does competition between resources change the competition between their consumers to mutualism? Variations on two themes by Vandermeer

How does competition between resources affect the interaction between consumer species that share those resources? Existing theory suggests that high resource competition can lead to mutualism. However, this is based on an analysis that need only apply near equilibrium, and experimental demonstrations of such mutualism are rare. Two alternative approaches to measuring food web mutualism are examined here. These are based on the population-level effects of adding or removing a consumer species or on the amount of additional mortality that can be applied to one consumer without excluding it. Both measures suggest that mutualism is likely to be confined to two situations: when overlap in resource use by the consumers is very low and when the consumers are inefficient users of their resources. Competition between resources is also likely to increase the occurrence and magnitude of "hypercompetition" between consumers, where the reduction in population size caused by the introduced consumer is greater than that caused by a consumer that is identical to the resident species. Competition between resources can also increase the negative interaction between consumers by destabilizing the dynamics of the system. Such destabilization can cause negative indirect interactions between specialist consumers having no overlap in resource use.     

The effect of the Holling type II functional response on apparent competition

This article analyzes the classical 2-resource-1-consumer apparent competition community module with the Holling type II functional response. Two types of resource regulation (top-down vs. combined top-down and bottom-up) and two types of consumer behaviors (inflexible consumers with fixed preferences for resources vs. adaptive consumers) are considered. When resources grow exponentially and consumers are inflexible foragers, one resource is always outcompeted due to strong apparent competition. Density dependent resource growth relaxes apparent competition so that resources can coexist. As multiple attractors (either equilibria or limit cycles) coexist, population dynamics and community composition depend on initial population densities. Population dynamics change dramatically when consumers forage adaptively. In this case, the results both for top-down, and combined top-down and bottom-up regulation are similar and they show that species persistence occurs for a much larger set of parameter values when compared with inflexible consumers. Moreover, population dynamics will be chaotic when resource carrying capacities are high enough. This shows that adaptive consumer switching can destabilize population dynamics.     

Optimal Foraging and Predator–Prey Dynamics

A system consisting of a population of predators and two types of prey is considered. The dynamics of the system is described by differential equations with controls. The controls model how predators forage on each of the two types of prey. The choice of these controls is based on the standard assumption in the theory of optimal foraging which requires that each predator maximizes the net rate of energy intake during foraging. Since this choice depends on the densities of populations involved, this allows us to link the optimal behavior of an individual with the dynamics of the whole system. Simple qualitative analysis and some simulations show the qualitative behavior of such a system. The effect of the optimal diet choice on the stability of the system is discussed.     

Remarks on branching-extinction evolutionary cycles

We show in this paper that the evolution of cannibalistic consumer populations can be a never ending story involving alternating levels of polymorphism. More precisely, we show that a monomorphic population can evolve toward high levels of cannibalism until it reaches a so-called branching point, where the population splits into two sub-populations characterized by different, but initially very close, cannibalistic traits. Then, the two traits coevolve until the more cannibalistic sub-population undergoes evolutionary extinction. Finally, the remaining population evolves back to the branching point, thus closing an evolutionary cycle. The model on which the study is based is purely deterministic and derived through the adaptive dynamics approach. Evolutionary dynamics are investigated through numerical bifurcation analysis, applied both to the ecological (resident-mutant) model and to the evolutionary model. The general conclusion emerging from this study is that branching-extinction evolutionary cycles can be present in wide ranges of environmental and demographic parameters, so that their detection is of crucial importance when studying evolutionary dynamics.     

Functional responses of adaptive consumers and community stability with emphasis on the dynamics of plant-herbivore systems

A comparatively recent focus in consumer–resource theory has been the examination of whether adaptive foraging by consumers, manifested through the functional response, can stabilize consumer–resource dynamics. We offer a brief synthesis of progress on this body of theory and identify the conditions likely to lead to stability. We also fill a gap in our understanding by analysing the potential for adaptively foraging herbivores, which are constrained by time available to feed and digestive capacity, to stabilize dynamics in a single-herbivore/two-plant resource system. Because foraging parameters of the adaptive functional response scale allometrically with herbivore body size, we parameterized our model system using published foraging data for an insect, a small mammal and a large mammal spanning four orders of magnitude in body size, and examined numerically the potential for herbivores to stabilize the consumer–resource interactions. We found in general that the herbivore–plant equilibrium will be unstable for all biologically realistic herbivore population densities. The instability arose for two reasons. First, each herbivore exhibited destabilizing adaptive consumer functional responses (i.e. density-independent or inversely density-dependent) whenever they selected a mixed diet. Secondly, the numerical response of herbivores, based on our assumption of density-independent herbivore population growth, results in herbivores reaching densities that enable them to exploit their resource populations to extinction. Our results and those of studies we reviewed indicate that, in general, adaptive consumers are unlikely to stabilize the dynamics of consumer–resource systems solely through the functional response. The implications of this for future work on consumer–resource theory are discussed.     

THE ECO‐EVOLUTIONARY RESPONSES OF A GENERALIST CONSUMER TO RESOURCE COMPETITION

This article explores the combined evolutionary and ecological responses of resource uptake abilities in a generalist consumer to exploitative competition for one resource using a simple 2‐resource model. It compares the sizes of ecologically and evolutionarily caused changes in population densities in cases where the original consumer has a strong or a weak trade‐off in its abilities to consume the two resources. The analysis also compares the responses of the original species to competition when the competitor's population size is or is not limited by the shared resource. Although divergence in resource use traits in the resident generalist consumer is expected under all scenarios when resources are substitutable, the changes in population densities of the resources and resident consumer frequently differ between scenarios. The population of the original consumer often decreases as a result of its own adaptive divergence, and this decrease is often much greater than the initial ecological decrease. If the evolving consumer has a strong trade‐off, the overlapped resource increases in equilibrium population density in response to being consumed by a generalist competitor. Some of these predictions differ qualitatively in alternative scenarios involving sustained variation in population densities or nutritionally essential resources.