ALTERNATIVE MODELS OF CHARACTER DISPLACEMENT AND NICHE SHIFT. I. ADAPTIVE SHIFTS IN RESOURCE USE WHEN THERE IS COMPETITION FOR NUTRITIONALLY NONSUBSTITUTABLE RESOURCES

This paper analyzes the influence of the nutritional status of resources on the adaptive response to interspecific competition in a consumer of those resources. The two cases compared are that in which the resources are nutritionally perfectly substitutable (in the sense of Leon and Tumpson [1975]) and that in which the resources are nonsubstitutable. Each nonsubstitutable resource must be consumed at a certain rate for population growth to occur. Evolutionarily stable strategies of resource utilization are found using models of competition for two resources. If competition occurs solely via the consumer species's effects on resource density, the adaptive response in a consumer's resource-acquisition traits is: a) divergence away from its competitor's resource-acquisition traits if resources are perfectly substitutable and b) convergence towards the competitor's resource-acquisition traits if resources are nonsubstitutable. Exceptions to both of these generalizations may occur if competitor population density affects a consumer species's per capita growth rate independently of effects on resource density. Plants and herbivores often use nonsubstitutable resources. The lack of studies of adaptive responses to competition in these organisms may be responsible for the lack of documented examples of competitive convergence.     

The impact of consumer-resource cycles on the coexistence of competing consumers

This article seeks to determine the extent to which endogenous consumer-resource cycles can contribute to the coexistence of competing consumer species. It begins with a numerical analysis of a simple model proposed by Armstrong and McGehee. This model has a single resource and two consumers, one with a linear functional response and one with a saturating response. Coexistence of the two consumer species can occur when the species with a saturating response generates population cycles of the resource, and also has a lower resource requirement for zero population growth. Coexistence can be achieved over a wide range of relative efficiencies of the two consumers provided that the functional response of the saturating consumer reaches its half-saturation value when the resource population is a small fraction of its carrying capacity. In this case, the range of efficiencies allowing coexistence is comparable to that when two competitors have stable dynamics and a high degree of resource partitioning. A variety of modifications of this basic model are analyzed to investigate the consequences for coexistence of different resource growth equations, different functional and numerical response shapes, and other factors. Large differences in functional response shape appear to be the most important factor in producing robust coexistence via resource cycles. If the unstable species has a concave numerical response, this greatly expands the conditions allowing coexistence. If the stable consumer species has a convex (accelerating) functional and/or numerical response, the range of conditions allowing coexistence is also expanded. We argue that large between-species differences in functional response form can often be produced by between-consumer differences in the adaptive adjustments of foraging effort to food density. Consumer-resource cycles can also expand the conditions allowing coexistence when there is resource partitioning, but do so primarily when resource partitioning is relatively slight; this makes the ease of coexistence relatively independent of consumer similarity.     

The effect of density-independent mortality on the coexistence of exploitative competitors for renewing resources

Many ecologists believe that higher mortality imposed on competing species increases the probability that they will coexist. This belief has persisted in spite of many theoretical counterarguments. However, few of those counterarguments have been based on models having explicit representation of the resources for which competition is occurring. This article analyzes a series of consumer-resource models of competition for nutritionally substitutable renewable resources and determines the range of relative resource requirements that allow coexistence. In most cases, if consumers are initially efficient at reducing resource densities, increasing density-independent mortality widens the range of resource requirements of the consumers that allow coexistence, provided the increase in mortality is not too great. The coexistence-promoting effects of mortality occur because a very efficient consumer species usually reduces the diversity of the set of resources it consumes. This lessens the extent to which resource utilization differences between consumer species can be expressed. Mortality, in this case, increases the diversity of resource types, widening the conditions for coexistence. However, sufficiently high mortality will usually reduce the range of parameters allowing coexistence, in agreement with much previous theory. The results presented here also predict maximal diversity at intermediate levels of productivity. Previous empirical studies and theory are reviewed in light of the theory developed here.     

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.     

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.     

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 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.     

Adaptive plasticity in ontogenetic niche shifts stabilizes consumer-resource dynamics

Ontogenetic niche shifts, changes in the diet or habitats of organisms during their ontogeny, are widespread among various animal taxa. Ontogenetic niche shifts introduce stage structure in a population with different stages interacting with different communities and can substantially affect their dynamics. In this article, I use mathematical models to test the hypothesis that adaptive plasticity in the timing of ontogenetic niche shifts has a stabilizing effect on consumer-resource dynamics. Adaptive plasticity allows consumers in one ontogenetic niche to perform an early shift to the next ontogenetic niche if the resource density of the first niche is low. The early shift will reduce predation by the consumer on the scarce resource. On the other hand, adaptive plasticity allows consumers to delay their shift to the next niche if the resource density of the first niche is high. The delayed shift will increase the predation on the abundant resource. As a result, the scarce resource will tend to increase, and the abundant resource will tend to decrease. This causes density-dependent negative feedback in the resource dynamics, which stabilizes the consumer-resource dynamics. To test this hypothesis, I compare three consumer-resource models differing in terms of mechanisms controlling the timing of the ontogenetic niche shift: the fixed-age model assumes that the age at which the ontogenetic niche shift occurs is fixed; the fixed-size model assumes that the size at the shift is fixed; and the adaptive plasticity model assumes that the timing of the shift is such that the individual fitness of the consumer is maximized. I show that only the adaptive plasticity model has a locally stable equilibrium and that the stabilizing effect is due to the density-dependent negative feedback in the resource dynamics. I discuss the ontogenetic niche shifts of lake fish in light of the obtained result.     

Evolution of density-dependent dispersal in a structured metapopulation

We study the evolution of density-dependent dispersal in a structured metapopulation subject to local catastrophes that eradicate local populations. To this end we use the theory of structured metapopulation dynamics and the theory of adaptive dynamics.The set of evolutionarily possible dispersal functions (i.e., emigration rates as a function of the local population density) is derived mechanistically from an underlying resource-consumer model. The local resource dynamics is of a flow-culture type and consumers leave a local population with a constant probability per unit of time κ when searching for resources but not when handling resources (i.e., eating and digesting). The time an individual spends searching (as opposed to handling) depends on the local resource density, which in turn depends on the local consumer density, and so the average per capita emigration rate depends on the local consumer density as well.The derived emigration rates are sigmoid functions of local consumer population density. The parameters of the local resource-consumer dynamics are subject to evolution. In particular, we find that there exists a unique evolutionarily stable and attracting dispersal rate κ^∗ for searching consumers. The κ^∗ increases with local resource productivity and decreases with resource decay rate. The κ^∗ also increases with the survival probability during dispersal, but as a function of the catastrophe rate it reaches a maximum before dropping off to zero again.     

Evolution of niche width and adaptive diversification

Theoretical models suggest that resource competition can lead to the adaptive splitting of consumer populations into diverging lineages, that is, to adaptive diversification. In general, diversification is likely if consumers use only a narrow range of resources and thus have a small niche width. Here we use analytical and numerical methods to study the consequences for diversification if the niche width itself evolves. We found that the evolutionary outcome depends on the inherent costs or benefits of widening the niche. If widening the niche did not have costs in terms of overall resource uptake, then the consumer evolved a niche that was wide enough for disruptive selection on the niche position to vanish; adaptive diversification was no longer observed. However, if widening the niche was costly, then the niche widths remained relatively narrow, allowing for adaptive diversification in niche position. Adaptive diversification and speciation resulting from competition for a broadly distributed resource is thus likely if the niche width is fixed and relatively narrow or free to evolve but subject to costs. These results refine the conditions for adaptive diversification due to competition and formulate them in a way that might be more amenable for experimental investigations.     

Adaptive dynamics of competition for nutritionally complementary resources: character convergence, displacement, and parallelism

Consumers acquire essential nutrients by ingesting the tissues of resource species. When these tissues contain essential nutrients in a suboptimal ratio, consumers may benefit from ingesting a mixture of nutritionally complementary resource species. We investigate the joint ecological and evolutionary consequences of competition for complementary resources, using an adaptive dynamics model of two consumers and two resources that differ in their relative content of two essential nutrients. In the absence of competition, a nutritionally balanced diet rarely maximizes fitness because of the dynamic feedbacks between uptake rate and resource density, whereas in sympatry, nutritionally balanced diets maximize fitness because competing consumers with different nutritional requirements tend to equalize the relative abundances of the two resources. Adaptation from allopatric to sympatric fitness optima can generate character convergence, divergence, and parallel shifts, depending not on the degree of diet overlap but on the match between resource nutrient content and consumer nutrient requirements. Contrary to previous verbal arguments that suggest that character convergence leads to neutral stability, coadaptation of competing consumers always leads to stable coexistence. Furthermore, we show that incorporating costs of consuming or excreting excess nonlimiting nutrients selects for nutritionally balanced diets and so promotes character convergence. This article demonstrates that resource-use overlap has little bearing on coexistence when resources are nutritionally complementary, and it highlights the importance of using mathematical models to infer the stability of ecoevolutionary dynamics.     

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.     

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.     

Cyclicity and variability in prey dynamics strengthens predator numerical response: the effects of vole fluctuations on white stork productivity

Theory predicts that optimality of life-long investment in reproduction is, among other factors, driven by the variability and predictability of the resources. Similarly, during the breeding season, single resource pulses characterized by short periods and high amplitudes enable strong numerical responses in their consumers. However, it is less well established how spatio-temporal dynamics in resource supplies influence the spatio-temporal variation of consumer reproduction. We used the common vole (Microtus arvalis)—white stork (Ciconia ciconia) resource—consumer model system to test the effect of increased temporal variation and periodicity of vole population dynamics on the strength of the local numerical response of storks. We estimated variability, cycle amplitude, and periodicity (by means of direct and delayed density dependence) in 13 Czech and Polish vole populations. Cross-correlation between annual stork productivity and vole abundance, characterizing the strength of the local numerical response of storks, increased when the vole population fluctuated more and population cycles were shorter. We further show that the onset of incubation of storks was delayed during the years of higher vole abundance. We demonstrate that high reproductive flexibility of a generalist consumer in tracking the temporal dynamics of its resource is driven by the properties of the local resource dynamics and we discuss possible mechanisms behind these patterns.     

Adaptive changes in prey vulnerability shape the response of predator populations to mortality

Simple models are used to explore how adaptive changes in prey vulnerability alter the population response of their predator to increased mortality. If the mortality is an imposed harvest, the change in prey vulnerability also influences the relationship between harvest effort and yield of the predator. The models assume that different prey phenotypes share a single resource, but have different vulnerabilities to the predator. Decreased vulnerability is assumed to decrease resource consumption rate. Adaptive change may occur by phenotypic changes in the traits of a single species or by shifts in the abundances of a pair of coexisting species or morphs. The response of the predator population is influenced by the shape of the predator's functional response, the shape of resource density dependence, and the shape of the tradeoff between vulnerability and food intake in the prey. Given a linear predator functional response, adaptive prey defense tends to produce a decelerating decline in predator population size with increased mortality. Prey defense may also greatly increase the range of mortality rates that allow predator persistence. If the predator has a type-2 response with a significant handling time, adaptive prey defense may have a greater variety of effects on the predator's response to mortality, sometimes producing alternative attractors, population cycles, or increased mean predator density. Situations in which there is disruptive selection on prey defense often imply a bimodal change in yield as a function of harvesting effort, with a minimum at intermediate effort. These results argue against using single-species models of density dependent growth to manage predatory species, and illustrate the importance of incorporating anti-predator behavior into models in applied population ecology.     

Is competition needed for ecological character displacement? Does displacement decrease competition?

Interspecific competition for resources is generally considered to be the selective force driving ecological character displacement, and displacement is assumed to reduce competition. Skeptics of the prevalence of character displacement often cite lack of evidence of competition. The present article uses a simple model to examine whether competition is needed for character displacement and whether displacement reduces competition. It treats systems with competing resources, and considers cases when only one consumer evolves. It quantifies competition using several different measures. The analysis shows that selection for divergence of consumers occurs regardless of the level of between‐resource competition or whether the indirect interaction between the consumers is competition (?,?), mutualism (+,+), or contramensalism (+,?). Also, divergent evolution always decreases the equilibrium population size of the evolving consumer. Whether divergence of one consumer reduces or increases the impact of a subsequent perturbation of the other consumer depends on the parameters and the method chosen for measuring competition. Divergence in mutualistic interactions may reduce beneficial effects of subsequent increases in the other consumer's population. The evolutionary response is driven by an increase in the relative abundance of the resource the consumer catches more rapidly. Such an increase can occur under several types of interaction.     

Linking rates of diffusion and consumption in relation to resources

The functional response is a fundamental model of the relationship between consumer intake rate and resource abundance. The random walk is a fundamental model of animal movement and is well approximated by simple diffusion. Both models are central to our understanding of numerous ecological processes but are rarely linked in ecological theory. To derive a synthetic model, we draw on the common logical premise underlying these models and show how the diffusion and consumption rates of consumers depend on elementary attributes of naturally occurring consumer-resource interactions: the abundance, spatial aggregation, and traveling speed of resources as well as consumer handling time and directional persistence. We show that resource aggregation may lead to increased consumer diffusion and, in the case of mobile resources, reduced consumption rate. Resource-dependent movement patterns have traditionally been attributed to area-restricted search, reflecting adaptive decision making by the consumer. Our synthesis provides a simple alternative hypothesis that such patterns could also arise as a by-product of statistical movement mechanics.     

Predation,apparent competition,and the structure of prey communities

It is argued that alternate prey species in the diet of a food-limited generalist predator should reduce each other's equilibrial abundances, whether or not they directly compete. Such indirect, interspecific interactions are labeled apparent competition. Two examples are discussed in which an observed pattern of habitat segregation was at first interpreted as evidence for direct competition, but later interpreted as apparent competition resulting from shared predation. In order to study the consequences of predator-mediated apparent competition in isolation from other complicating factors, a model community is analyzed in which there is no direct interspecific competition among the prey. An explicit necessary condition for prey species coexistence is derived for the case of one predator feeding on many prey species. This model community has several interesting properties: (1) Prey species with high relative values for a parameter $\text{r}\text{a}$ are “keystone” species in the community; (2) prey species can be excluded from the community by “diffuse” apparent competition; (3) large changes in the niche breadth of the predator need not correspond to large changes in predator density; (4) the prey trophic level as a whole is regulated by the predator, yet each of its constituent species is regulated by both the predator and available resources; (5) increased productivity may either increase, decrease, or leave unchanged the number of species in the community; (6) a decrease in density-independent mortality may decrease species diversity. These conclusions seem to be robust to changes in the prey growth equations and to the incorporation of predator satiation. By contrast, adding prey refugia or predator switching to the model weakens these conclusions. If the predator can be satiated or switched, the elements a_ij comprising the community matrix may have signs opposite the long-term effect of j upon i. The effect of natural selection upon prey species coexistence is discussed. Unless r_i, K_i, and a_i are tightly coupled, natural selection within prey species i will tend to decrease the equilibrial abundance of species j.     

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.