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.     

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.     

Interspecific Competition Models Derived from Competition Among Individuals

This paper demonstrates how discrete-time models describing population dynamics of two competing species can be derived in a bottom-up manner by considering competition for resources among individuals and the spatial distribution of individuals. The competition type of each species is assumed to be either scramble, contest, or an intermediate between them. Individuals of two species are distributed over resource sites or patches following one of three distribution functions. According to the combination of competition types of the two species and the distribution of individuals, various interspecific competition models are derived. Furthermore, a general interspecific competition model that includes various competition models as special cases is derived for each distribution of individuals. Finally, this paper examines dynamics of some of the derived competition models and shows that the likelihood of coexistence of the two species varies greatly, depending on the type of spatial distribution of individuals.     

Evolutionary games and two species population dynamics

Competition between species has long been modeled by population dynamics based on total numbers of each species. Recently, the evolution of strategy frequencies has been used successfully for competition models between individuals. In this paper, we illustrate that these two views of competition are compatible. It is shown that the rate of intra and interspecific competitions between individuals largely determines the population dynamics. Competition models over a single common resource and predator-prey models are developed from this individual competition approach. In particular, the equilibrium strategies in a co-evolving predator-prey system are shown to be more stable than the predicted strategy cycling of standard evolutionary game theory.     

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.     

Evolution of resource specialisation in competitive metacommunities

Spatial environmental heterogeneity coupled with dispersal can promote ecological persistence of diverse metacommunities. Does this premise hold when metacommunities evolve? Using a two‐resource competition model, we studied the evolution of resource‐uptake specialisation as a function of resource type (substitutable to essential) and shape of the trade‐off between resource uptake affinities (generalist‐ to specialist‐favouring). In spatially homogeneous environments, evolutionarily stable coexistence of consumers is only possible for sufficiently substitutable resources and specialist‐favouring trade‐offs. Remarkably, these same conditions yield comparatively low diversity in heterogeneous environments, because they promote sympatric evolution of two opposite resource specialists that, together, monopolise the two resources everywhere. Consumer diversity is instead maximised for intermediate trade‐offs and clearly substitutable or clearly essential resources, where evolved metacommunities are characterised by contrasting selection regimes. Taken together, our results present new insights into resource‐competition‐mediated evolutionarily stable diversity in homogeneous and heterogeneous environments, which should be applicable to a wide range of systems.     

Interspecific competition in perennial sedentary organisms: An individual-based model

We investigated a mathematical model of the dynamics of the ecological system consisting of two competing perennial species, each of which leads a sedentary life. It is an individual-based model, in which the growth of each individual is described. The rate of this growth is weakened by competition from neighboring individuals. The strength of the competitors' influence depends on their size and distance to them. The conditions, in which the competitive exclusion of one of the competitors and the coexistence of both competitors take place are provided. The influence of the parameters responsible for the strength of competition, the degree of competitive asymmetry, and consideration of the importance of specific elements of the spatial structure of this ecological system on the results of the competition were analyzed. Both species co-exist when they are equal competitors. Permanent coexistence is possible only when interspecific competition is weaker than intraspecific. When interspecific competition is stronger, the coexistence of equal interspecific competitors is random. Both species have equal probability of extinction. If species are not equal competitors, the stronger one wins. This result can be modified by different strengths of intraspecific competition. The weaker interspecific competitor can permanently coexist with stronger one, when its individuals suffer stronger intraspecific competition.     

EVOLUTIONARY DIVERGENCE AND CHARACTER DISPLACEMENT IN TWO PHENOTYPICALLY-VARIABLE,COMPETING SPECIES

Theoretical studies of character displacement lead to the view that evolutionary divergence depends primarily on incomplete utilization of available resources. Those models which incorporate constraints preventing complete utilization of resources, even in the absence of competitors, all predict character displacement. Those models which allow greater flexibility of resource use within a species predict correspondingly less divergence. Indeed, Matessi and Jayakar (1980, 1981) based their conditions for occurrence of character displacement on underutilization of resources. I extend a model used by Slatkin (1980, 1983) and Taper and Case (1985) which allows each species to fully utilize its resources in the absence of competitors. I concentrate on the biologically reasonable case in which the species, though similar, differ in their ecological characteristics. As a result of this greater biological realism, I arrive at a different conclusion regarding the conditions which lead to character displacement. The presence of a variety of biological differences between species—including as a subset those which result from resource underutilization—leads to divergence with respect to a quantitatively inherited character, due to interspecific competitive interactions. The resulting displacement can be large and depends little on the parameters chosen. The only exception, involving a character with very low heritability, occurs when the non-interactive phenotypic differences are much greater than those associated with studies of character displacement in natural populations. Thus, under conditions comparable to those encountered in the field, involving similar yet not identical species, evolutionary divergence is a consequence of interspecific competition.     

病原体感染对物种间资源竞争的影响——基于资源竞争理论

病原体感染对种间竞争的影响可能是因为改变了宿主的资源利用过程,然而竞争模型（Lotka-Volterra）由于参数化竞争系数而忽略了资源的动态变化过程,因此基于此类模型的研究无法揭示病原体对宿主资源利用的影响。基于Tilman的资源竞争理论构建了病原体感染一个物种的资源竞争模型,通过分析宿主物种资源利用效率的变化探讨了病原体对种间竞争的影响。结果表明：（1）病原体降低了宿主对资源的消耗率（消费矢量变短）,抬高了对资源的最低需求（零等倾线上移）,这意味着宿主的竞争力减弱;（2）虽然感染影响了竞争物种的密度,但不会改变共存物种的共存状态;（3）病原体可以使宿主物种的竞争对手更容易入侵,形成共存局面,极大地扩大了竞争物种共存的参数范围,本质上促进了物种多样性维持;（4）病原体的传播率和毒性也复杂地影响了竞争物种共存,传播率越大越能促进物种共存,而中等强度毒性最能促进物种共存。研究结果明确了病原体对物种资源利用模式的潜在改变,强调了病原体在物种共存和生物多样性维持中的重要性。     

Evolutionarily stable range limits set by interspecific competition

A combination of abiotic and biotic factors probably restricts the range of many species. Recent evolutionary models and tests of those models have asked how a gradual change in environmental conditions can set the range limit, with a prominent idea being that gene flow disrupts local adaptation. We investigate how biotic factors, explicitly competition for limited resources, result in evolutionarily stable range limits even in the absence of the disruptive effect of gene flow. We model two competing species occupying different segments of the resource spectrum. If one segment of the resource spectrum declines across space, a species that specializes on that segment can be driven to extinction, even though in the absence of competition it would evolve to exploit other abundant resources and so be saved. The result is that a species range limit is set in both evolutionary and ecological time, as the resources associated with its niche decline. Factors promoting this outcome include: (i) inherent gaps in the resource distribution, (ii) relatively high fitness of the species when in its own niche, and low fitness in the alternative niche, even when resource abundances are similar in each niche, (iii) strong interspecific competition, and (iv) asymmetric interspecific competition. We suggest that these features are likely to be common in multispecies communities, thereby setting evolutionarily stable range limits.     

Predicting stability of mixed microbial cultures from single species experiments: 2. Physiological model

In this paper, we study the equilibria of a physiological model describing the continuous culture in which two microbial populations compete for two substitutable resources. This work is an extension of the stability analysis of the phenomenological model of mixed microbial growth [M.M. Ballyk, G.S.K. Wolkowicz, Exploitative competition in the chemostat for two perfectly substitutable resources, Math. Biosci. 118 (1993) 127-180; S.S. Pilyugin, G.T. Reeves, A. Narang, Predicting stability of mixed microbial cultures from single species experiments: 2. Phenomenological model]. Here, we investigate the influence of the peripheral enzymes that catabolize the substrate uptake on the stability of the mixed culture. We show that, under steady state conditions, an increase in the concentration of one substrate inhibits the uptake of the other substrate(s). We present the criteria for existence, uniqueness, and stability of various types of equilibria. We formulate these criteria in terms of growth isoclines and consumption curves for each of the competing species. Since both types of curves can be obtained from a single species experiment, our approach provides a direct connection between theory and experiment and allows one to infer the dynamics of mixed cultures from the dynamics of single species cultures. By expressing the stability criteria in terms of intracellular properties, the model establishes a link between ecology and molecular biology.     

The contrasting effects of short-term climate change on the early recruitment of tree species

While interspecific competition is prevalent in natural systems, we do not yet understand how it can influence an individual’s phenotype within its lifetime and how this might affect performance. Morphology and swimming performance are two important fitness-related traits in fishes. Both traits are essential in acquiring and defending resources as well as avoiding predation. Here, we examined if interspecific competition could induce changes in morphology and affect the swimming performance of two strains of juvenile Atlantic salmon (Salmo salar). We imposed competitive scenarios on the fish using artificial streams containing different combinations of four interspecific competitors. Exposure to interspecific competitors induced morphological changes over time, through the development of deeper bodies, whereas controls free of interspecific competitors developed more fusiform body shapes. Furthermore, swimming performance was correlated to fusiform morphologies and was weaker for Atlantic salmon in competitive scenarios vs. controls. This implies that interspecific competition has direct effects on these fitness-related traits in Atlantic salmon. To the best of our knowledge, this is the first time that morphology, an important fitness-related trait linked to swimming performance, has been shown to be negatively impacted through interactions with an interspecific competitor.     

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.     

Competition both drives and impedes diversification in a model adaptive radiation

Competitors are known to be important in governing the outcome of evolutionary diversification during an adaptive radiation, but the precise mechanisms by which they exert their effects remain elusive. Using the model adaptive radiation of Pseudomonas fluorescens, we show experimentally that the effect of competition on diversification of a focal lineage depends on both the strength of competition and the ability of the competitors to diversify. We provide evidence that the extent of diversification in the absence of interspecific competitors depends on the strength of resource competition. We also show that the presence of competitors can actually increase diversity by increasing interspecific resource competition. Competitors that themselves are able to diversify prevent diversification of the focal lineage by removing otherwise available ecological opportunities. These results suggest that the progress of an adaptive radiation depends ultimately on the strength of resource competition, an effect that can be exaggerated or impeded by the presence of competitors.     

Clutch-size behavior and coexistence in ephemeral-patch competition models

Systems of patchy, ephemeral resources often support surprisingly diverse assemblages of consumer insects. Aggregation of consumer individuals over the landscape of patches has been suggested as one mechanism that can stabilize competition among consumer species. One mechanism for larval aggregation is the laying of eggs in clutches by females traveling among patches to distribute their total fecundity. We use simulation models to explore the consequences, for coexistence of competitors, of larval aggregation that arises from clutch laying. Contrary to some previous treatments, we find that clutch laying can be strongly stabilizing and under certain conditions can be sufficient to allow competitors to coexist stably. We extend these models by considering clutch size as a variable that responds to the abundance of resource patches. Such a relationship might be expected because females should lay their eggs in fewer but larger clutches when the cost of travel among patches is high (because patches are rare). When females adjust clutch size in response to resource abundance, coexistence can be easiest when resource patches are scarce and most difficult when resources are abundant.     

Competition and coexistence in regional habitats

Habitat heterogeneity plays a key role in the dynamics and structures of communities. In this article, a two-species metapopulation model that includes local competitive dynamics is analyzed to study the population dynamics of two competing species in spatially structured habitats. When local stochastic extinction can be ignored, there are, as in Lotka-Volterra equations, four outcomes of interspecific competition in this model. The outcomes of competition depend on the competitive intensity between the competing pairs. An inferior competitor and a superior competitor, or two strongly competing species, can never stably coexist, whereas two weak competitors (even if they are very similar species) may coexist over the long term in such environments. Local stochastic extinction may greatly affect the outcomes of interspecific competition. Two competing species can or cannot stably coexist depending not only on the competitive intensity between the competing pairs but also on their precompetitive distributions. Two weak competitors that have similar precompetitive distributions can always regionally coexist. Two strongly competing species that competitively exclude each other in more stable habitats may be able to stably coexist in highly heterogenous environments if they have similar precompetitive distributions. There is also a chance for an inferior competitor to coexist regionally or even to exclude a superior competitor when the superior competitor has a narrow precompetitive distribution and the inferior competitor has a wide precompetitive distribution.     

Density-dependent habitat selection: evaluating isoleg theory with a Lotka-Volterra model

Contemporary models of density-dependent habitat selection generally focus on long-term evolutionary consequences of intraspecific or interspecific competition and/or patterns of resource use in patchy environments. A primary goal of such studies often is to elucidate evolutionary stable strategies based on steady-state dynamics of population growth. In contrast, we developed a simulation model to explore short-term movements of interspecific competitors among fine-grained habitats of differing attributes, as might result from field manipulations of habitat quality or population densities. In this model, habitat quality is expressed in terms of mean individual fitness, represented by average per capita growth rate calculated according to the Lotka-Volterra equations describing interspecific competition. This model provides a mechanism for quantifying the effects of habitat quality, patterns of resource use and competition on distributions of individuals. Results demonstrate the heuristic value of this model in corroborating predictions derived from the ideal free distribution and isodar theory, and in generating isolegs to test the predictions of isoleg theory. Results indicate that small changes in model parameters have substantial impacts on patterns of habitat use and co-occurrence between species. The model identifies a variety of conditions under which isolegs for a given type of community organization deviate from predictions of contemporary isoleg theory, potentially expanding the universe of possible interspecific behaviors underlying the development of evolutionary stable strategies.     

Character displacement and niche shift analyzed using consumer-resource models of competition

This paper analyzes the adaptive responses to competition (both character displacement and niche shift) in a two consumer-two resource model. The model includes density dependence that is unrelated to the resources that are explicit in the model. This could be due to another resource dimension, parasites, or interference competition. Competitors adapt by changing their relative consumption rate constants on the two resource types. This model can result in mutually divergent, parallel, or mutually convergent displacement of competitors. Parallel displacement may entail net divergence, net convergence, or no net change. Parallel change with net convergence is most likely when the competitors have similar constraints on the possible values of consumption rate constants, unequal allopatric abundances, and significant intraspecific density dependence. Numerical calculations of displacements are presented for several models and the effect of a number of different possible alterations of the model are discussed. The evolution of resource handling and processing efficiency, and displacement in the presence of additional selective pressures on the character are considered in detail. The results have implications for questions about maximization of population size, the relationship of character displacement and the competition coefficient, and "null" models in the study of competition. Differences between this and previous theoretical works are discussed. It is argued that conditions allowing parallel or convergent displacement are not biologically unlikely, and possible examples are discussed. Data on resource partitioning seem to be more consistent with the results reached here than with previous theory.     

Positive interactions among competitors can produce species-rich communities

Although positive interactions between species are well documented, most ecological theory for investigating multispecies coexistence remains rooted in antagonistic interactions such as competition and predation. Standard resource-competition models from this theory predict that the number of coexisting species should not exceed the number of factors that limit population growth. Here I show that positive interactions among resource competitors can produce species-rich model communities supported by a single limiting resource. Simulations show that when resource competitors reduce each others' per capita mortality rate (e.g. by ameliorating an abiotic stress), stable multispecies coexistence with a single resource may be common, even while the net interspecific interaction remains negative. These results demonstrate that positive interactions may provide an important mechanism for generating species-rich communities in nature. They also show that focusing on the net interaction between species may conceal important coexistence mechanisms when species simultaneously engage in both antagonistic and positive interactions.