The functional responses of adaptive consumers of two resources

This article investigates some aspects of the shape of the functional responses of consumers that utilize two resources. Adaptive variation in consumption behavior is shown to have a major effect on the relationship between amount of resource available and its rate of consumption by an average consumer individual. The effects of adaptive variation are dependent on the nutritional status of the two resources. If the resources are linearly substitutable, increases in the density of resource i will usually increase the quantity, functional response on i divided by density of i, and increases in the density of resource j will decrease this quantity. The result is that the functional response to resource i will generally decrease with the density of resource j, and will increase faster than it would otherwise have increased with the density of resource i. If resources are nonsubstitutable, an adaptive functional response to resource i will increase with the density of resource j, and it will increase more slowly with the density of resource i than it would have without adaptive change. If resources are both complementary and substitutable, the functional response will exhibit ranges of smooth change separated by rapid jumps between values, and different ranges of resource densities will result in a functional response with the characteristics of linearly substitutable or of non-substitutable resources. Adaptive functional response shape is dependent upon the tradeoff involved in raising each functional response. These results have implications for the types of indirect interactions that occur between resources as the result of a common consumer's functional response. They also suggest that the adaptive response of competing consumers to each other will differ depending on the nutritional status of the resources for which they are competing. Implications of these findings for consumer growth isocline shape and several other issues are explored.     

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.     

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.     

Competition between two species for two complementary or substitutable resources

The classical models of interspecific competition are phenomenological, that is, they purport to describe the trajectories followed by the abundances of both competitors, without specifying either mechanisms or the dynamics of what the competition is for, i.e. resources. Yet the conditions for the different outcomes of competition inferred from these models are most often interpreted in terms of resources. Here it is contended that the dynamics of resource supply and exploitation must be explicitly taken into account if these conditions are to be obtained in any accurate form. First, the distinction between perfectly substitutable, imperfectly substitutable and perfectly complementary resources is examined. This leads to an array of models intended to mirror interspecific exploitative competition for two resources for each category considered. Then, the conditions for the coexistence of the two competitors in each case are derived and presented with direct reference to the modes of resource use.     

Character convergence under competition for nutritionally essential resources

Resource competition is thought to drive divergence in resource use traits (character displacement) by generating selection favoring individuals able to use resources unavailable to others. However, this picture assumes nutritionally substitutable resources (e.g., different prey species). When species compete for nutritionally essential resources (e.g., different nutrients), theory predicts that selection drives character convergence. We used models of two species competing for two essential resources to address several issues not considered by existing theory. The models incorporated either slow evolutionary change in resource use traits or fast physiological or behavioral change. We report four major results. First, competition always generates character convergence, but differences in resource requirements prevent competitors from evolving identical resource use traits. Second, character convergence promotes coexistence. Competing species always attain resource use traits that allow coexistence, and adaptive trait change stabilizes the ecological equilibrium. In contrast, adaptation in allopatry never preadapts species to coexist in sympatry. Third, feedbacks between ecological dynamics and trait dynamics lead to surprising dynamical trajectories such as transient divergence in resource use traits followed by subsequent convergence. Fourth, under sufficiently slow trait change, ecological dynamics often drive one of the competitors to near extinction, which would prevent realization of long-term character convergence in practice.     

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.     

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.     

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.     

PREY ADAPTATION AS A CAUSE OF PREDATOR-PREY CYCLES

We analyze simple models of predator-prey systems in which there is adaptive change in a trait of the prey that determines the rate at which it is captured by searching predators. Two models of adaptive change are explored: (1) change within a single reproducing prey population that has genetic variation for vulnerability to capture by the predator; and (2) direct competition between two independently reproducing prey populations that differ in their vulnerability. When an individual predator's consumption increases at a decreasing rate with prey availability, prey adaptation via either of these mechanisms may produce sustained cycles in both species' population densities and in the prey's mean trait value. Sufficiently rapid adaptive change (e.g., behavioral adaptation or evolution of traits with a large additive genetic variance), or sufficiently low predator birth and death rates will produce sustained cycles or chaos, even when the predator-prey dynamics with fixed prey capture rates would have been stable. Adaptive dynamics can also stabilize a system that would exhibit limit cycles if traits were fixed at their equilibrium values. When evolution fails to stabilize inherently unstable population interactions, selection decreases the prey's escape ability, which further destabilizes population dynamics. When the predator has a linear functional response, evolution of prey vulnerability always promotes stability. The relevance of these results to observed predator-prey cycles is discussed.     

Species coexistence in resource-limited patterned ecosystems is facilitated by the interplay of spatial self-organisation and intraspecific competition

The exploration of mechanisms that enable species coexistence under competition for a sole limiting resource is widespread across ecology. Two examples of such facilitative processes are intraspecific competition and spatial self-organisation. These processes determine the outcome of competitive dynamics in many resource-limited patterned ecosystems, classical examples of which include dryland vegetation patterns, intertidal mussel beds and subalpine ribbon forests. Previous theoretical investigations have explained coexistence within patterned ecosystems by making strong assumptions on the differences between species (e.g. contrasting dispersal behaviours or different functional responses to resource availability). In this paper, I show that the interplay between the detrimental effects of intraspecific competition and the facilitative nature of self-organisation forms a coexistence mechanism that does not rely on species-specific assumptions and captures coexistence across a wide range of the environmental stress gradient. I use a theoretical model that captures the interactions of two generic consumer species with an explicitly modelled resource to show that coexistence relies on a balance between species' colonisation abilities and their local competitiveness, provided intraspecific competition is sufficiently strong. Crucially, the requirements on species' self-limitation for coexistence to occur differ on opposite ends of the resource input spectrum. For low resource levels, coexistence is facilitated by strong intraspecific dynamics of the species superior in its colonisation abilities, but for larger volumes of resource input, strong intraspecific competition of the locally superior species enables coexistence. Results presented in this paper also highlight the importance of hysteresis in understanding tipping points, in particular extinction events. Finally, the theoretical framework provides insights into spatial species distributions within single patches, supporting verbal hypotheses on coexistence of herbaceous and woody species in dryland vegetation patterns and suggesting potential empirical tests in the context of other patterned ecosystems.     

Resource competition and adaptive radiation in a microbial microcosm

Theory predicts that competition for shared resources in a monomorphic population generates divergent selection for adaptation to alternative resources. Experimental tests of this hypothesis are scarce. We selected populations of the bacterium Pseudomonas fluorescens in spatially homogeneous microcosms containing a complex mixture of resources. Initially, all populations consisted of two isogenic clones. The outcome of selection was the evolution of a diverse community of genotypes within each population. Sympatric genotypes exhibited differentiation in metabolic traits related to resource acquisition and frequency‐dependent trade‐offs in competitive ability, as we would expect if different genotypes consumed different resources. These results are consistent with the hypothesis of adaptive radiation driven by resource competition. Reconciling the results of this study with those of earlier experiments provides a new interpretation of the ecological causes of adaptive radiation in microbial microcosms.     

Intraspecific competition reduces niche width in experimental populations

Intraspecific competition is believed to drive niche expansion, because otherwise suboptimal resources can provide a refuge from competition for preferred resources. Competitive niche expansion is well supported by empirical observations, experiments, and theory, and is often invoked to explain phenotypic diversification within populations, some forms of speciation, and adaptive radiation. However, some foraging models predict the opposite outcome, and it therefore remains unclear whether competition will promote or inhibit niche expansion. We conducted experiments to test whether competition changes the fitness landscape to favor niche expansion, and if competition indeed drives niche expansion as expected. Using Tribolium castaneum flour beetles fed either wheat (their ancestral resource), corn (a novel resource) or mixtures of both resources, we show that fitness is maximized on a mixed diet. Next, we show that at higher population density, the optimal diet shifts toward greater use of corn, favoring niche expansion. In stark contrast, when beetles were given a choice of resources, we found that competition caused niche contraction onto the ancestral resource. This presents a puzzling mismatch between how competition alters the fitness landscape, versus competition's effects on resource use. We discuss several explanations for this mismatch, highlighting potential reasons why optimality models might be misleading.     

Coexistence and displacement in consumer-resource systems with local and shared resources

Competition for local and shared resources is widespread. For example, colonial waterbirds consume local prey in the immediate vicinity of their colony, as well as shared prey across multiple colonies. However, there is little understanding of conditions facilitating coexistence vs. displacement in such systems. Extending traditional models based on type I and type II functional responses, we simulate consumer-resource systems in which resources are “substitutable,” “essential,” or “complementary.” It is shown that when resources are complementary or essential, a small increase in carrying capacity or decrease in handling time of a local resource may displace a spatially separate consumer species, even when the effect on shared resources is small. This work underscores the importance of determining both the nature of resource competition (substitutable, essential, or complementary) and appropriate scale-dependencies when studying metacommunities. We discuss model applicability to complex systems, e.g., urban wildlife that consume natural and anthropogenic resources which may displace rural competitors by depleting shared prey.     

The evolution of resource use

 The evolution of a consumer exploiting two resources is investigated. The strategy x under selection represents the fraction of time or energy an individual invests into extracting the first resource. In the model, a dimensionless parameter α quantifies how simultaneous consumption of both resources influences consumer growth; α<0 corresponds to hemi-essential resources, 0<α<1 corresponds to complementary resources, α=1 corresponds to perfectly substitutable resources, and α>1 corresponds to antagonistic resources. An analysis of the ecological and evolutionary dynamics leads to five conclusions. First, when α≤1, there is a unique singular strategy x ^* for the adaptive dynamics and it is evolutionarily stable and globally convergent stable. Second, when α=1, the singular strategy x ^* corresponds to the populations exhibiting an ideal free distribution and a population playing this strategy can invade and displace populations playing any other strategy. Third, when α>1, the strategies x=0 and x=1 are evolutionarily stable and convergent stable. Hence, if the populations initially specialize on one resource, evolution amplifies this specialization. Fourth, when α is slightly larger than one (i.e. the resources are slightly antagonistic), there is a convergent stable singular strategy whose basin of attraction is almost the entire strategy space (0,1). This singular strategy is evolutionarily unstable and serves as an evolutionary branching point. Following evolutionary branching, our analysis and numerical simulations suggest that evolutionary dynamics are driven toward an end state consisting of two populations specializing on different resources. Fifth, when α>>1, there is only one singular strategy and it is convergent unstable and evolutionarily unstable. Hence, if resources are overly antagonistic, evolutionary branching does not occur and ultimately only one resource is exploited. Received: 8 June 2002 / Revised version: 28 November 2002 / Published online: 23 April 2003 This work was supported by NSF Grant DMS-0077986 Key words or phrases: Consumer-resource interactions – Adaptive dynamics – Evolutionary branching     

Evolution of species trait through resource competition

To understand the evolution of diverse species, theoretical studies using a Lotka–Volterra type direct competition model had shown that concentrated distributions of species in continuous trait space often occurs. However, a more mechanistic approach is preferred because the competitive interaction of species usually occurs not directly but through competition for resource. We consider a chemostat-type model where species consume resource that are constantly supplied. Continuous traits in both consumer species and resource are incorporated. Consumers utilize resource whose trait values are similar with their own. We show that, even when resource-supply has a continuous distribution in trait space, a positive continuous distribution of consumer trait is impossible. Self-organized generation of distinct species occurs. We also prove global convergence to the evolutionarily stable distribution.     

On the Sympatric Evolution and Evolutionary Stability of Coexistence by Relative Nonlinearity of Competition

If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity. In our analysis, evolution operates on the species'' density-compensation strategies, and we consider a trade-off between population growth rates at high and low resource availability. We confirm previous findings that, irrespective of the particular model of density dependence, there are many combinations of overcompensating and undercompensating density-compensation strategies that allow stable coexistence by relative nonlinearity. However, our analysis also shows that most of these strategy combinations are not evolutionarily stable and will be outcompeted by an intermediate density-compensation strategy. Only very specific trade-offs lead to evolutionarily stable coexistence by relative nonlinearity. As we find no reason why these particular trade-offs should be common in nature, we conclude that the sympatric evolution and evolutionary stability of relative nonlinearity, while possible in principle, seems rather unlikely. We speculate that this may, at least in part, explain why empirical demonstrations of this coexistence mechanism are rare, noting, however, that the difficulty to detect relative nonlinearity in the field is an equally likely explanation for the current lack of empirical observations, and that our results are limited to communities with non-overlapping generations and constant resource supply. Our study highlights the need for combining ecological and evolutionary perspectives for gaining a better understanding of community assembly and biogeographic patterns.     

The evolution of traits affecting resource acquisition and predator vulnerability: character displacement under real and apparent competition

This article investigates some simple models of the evolutionary interaction between two prey species that share a common resource and a common predator. Each prey species is characterized by a trait that determines both the rate of resource capture and vulnerability to a predator. In a simple model of a three-species food chain, such traits usually increase in response to an imposed reduction in resource density. When the per capita growth rates of each of two prey species depend linearly on resource density, such traits will change in opposite directions when the two prey come into sympatry. In addition, the ratio of the effect of the predator on prey fitness to the effect of the resource on prey fitness will diverge from the corresponding ratio in a second prey species when those species coexist in sympatry. These simple predictions need not hold under several alternative assumptions, which may be more common in biological systems. Parallel changes in sympatry may occur if the relationship between resource consumption and prey growth is nonlinear, if the prey species have partial overlap in the set of resources used or in the set of predators that consume them, or if prey experience direct intraspecific competition. The responses to a second prey can also differ significantly from those predicted by the simplest model if separate traits affect vulnerability to predators and resource acquisition rate. It is important to determine whether examples of character displacement previously interpreted as responses to competition for resources might also reflect responses to altered predation risks in sympatry.     

Intraspecific and interspecific competition induces density‐dependent habitat niche shifts in an endangered steppe bird

Interspecific competition is a dominant force in animal communities that induces niche shifts in ecological and evolutionary time. If competition occurs, niche expansion can be expected when the competitor disappears because resources previously inaccessible due to competitive constraints can then be exploited (i.e., ecological release). Here, we aimed to determine the potential effects of interspecific competition between the little bustard (Tetrax tetrax) and the great bustard (Otis tarda) using a multidimensional niche approach with habitat distribution data. We explored whether the degree of niche overlap between the species was a density‐dependent function of interspecific competition. We then looked for evidences of ecological release by comparing measures of niche breadth and position of the little bustard between allopatric and sympatric situations. Furthermore, we evaluated whether niche shifts could depend not only on the presence of great bustard but also on the density of little and great bustards. The habitat niches of these bustard species partially overlapped when co‐occurring, but we found no relationship between degree of overlap and great bustard density. In the presence of the competitor, little bustard's niche was displaced toward increased use of the species' primary habitat. Little bustard's niche breadth decreased proportionally with great bustard density in sympatric sites, in consistence with theory. Overall, our results suggest that density‐dependent variation in little bustard's niche is the outcome of interspecific competition with the great bustard. The use of computational tools like kernel density estimators to obtain multidimensional niches should bring novel insights on how species' ecological niches behave under the effects of interspecific competition in ecological communities.