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.     

Global dynamics of microbial competition for two resources with internal storage

We study a chemostat model that describes competition between two species for two essential resources based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the monotone dynamical system theory. It is shown that the limiting system of the model basically exhibits the familiar Lotka-Volterra alternatives: competitive exclusion, coexistence, and bi-stability, and most of these results can be carried over to the original model. B. Li’s research was partially supported by NSF grants DMS 0211614 and DMS 0616445. H. L. Smith’s research was supported in part by NSF grant DMS 0414270.     

Species packing in nonsmooth competition models

Despite the potential for competition to generate equilibrium coexistence of infinitely tightly packed species along a trait axis, prior work has shown that the classical expectation of system-specific limits to the similarity of stably coexisting species is sound. A key reason is that known instances of continuous coexistence are fragile, requiring fine-tuning of parameters: A small alteration of the parameters leads back to the classical limiting similarity predictions. Here we present, but then cast aside, a new theoretical challenge to the expectation of limiting similarity. Robust continuous coexistence can arise if competition between species is modeled as a nonsmooth function of their differences—specifically, if the competition kernel (differential response of species’ growth rates to changes in the density of other species along the trait axis) has a nondifferentiable sharp peak at zero trait difference. We will say that these kernels possess a “kink.” The difference in predicted behavior stems from the fact that smooth kernels do not change to a first-order approximation around their maxima, creating strong competitive interactions between similar species. “Kinked” kernels, on the other hand, decrease linearly even for small species differences, reducing interspecific competition compared with intraspecific competition for arbitrarily small species differences. We investigate what mechanisms would lead to kinked kernels in the first place. It turns out that discontinuities in resource utilization generate them. We argue that such sudden jumps in the utilization of resources are unrealistic, and therefore, one should expect kernels to be smooth in reality.     

How Gaussian competition leads to lumpy or uniform species distributions

A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is “lumped” (or “clumped”), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either uniform or lumped species distributions. Here, we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity. In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model. We analyze the origin of this sensitivity and discuss it in the context of recent applications of the model.     

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 signature of competition in ecomorphological traits across the avian radiation

Competition for shared resources represents a fundamental driver of biological diversity. However, the tempo and mode of phenotypic evolution in deep-time has been predominantly investigated using trait evolutionary models which assume that lineages evolve independently from each other. Consequently, the role of species interactions in driving macroevolutionary dynamics remains poorly understood. Here, we quantify the prevalence for signatures of competition between related species in the evolution of ecomorphological traits across the bird radiation. We find that mechanistic trait models accounting for the effect of species interactions on phenotypic divergence provide the best fit for the data on at least one trait axis in 27 out of 59 clades ranging between 21 and 195 species. Where it occurs, the signature of competition generally coincides with positive species diversity-dependence, driven by the accumulation of lineages with similar ecologies, and we find scarce evidence for trait-dependent or negative diversity-dependent phenotypic evolution. Overall, our results suggest that the footprint of interspecific competition is often eroded in long-term patterns of phenotypic diversification, and that other selection pressures may predominantly shape ecomorphological diversity among extant species at macroevolutionary scales.     

Eco‐evolutionary feedback promotes Red Queen dynamics and selects for sex in predator populations

Although numerous hypotheses exist to explain the overwhelming presence of sexual reproduction across the tree of life, we still cannot explain its prevalence when considering all inherent costs involved. The Red Queen hypothesis states that sex is maintained because it can create novel genotypes with a selective advantage. This occurs when the interactions between species induce frequent environmental change. Here, we investigate whether coevolution and eco‐evolutionary feedback dynamics in a predator‐prey system allows for indirect selection and maintenance of sexual reproduction in the predator. Combining models and chemostat experiments of a rotifer‐algae system we show a continuous feedback between population and trait change along with recurrent shifts from selection by predation and competition for a limited resource. We found that a high propensity for sex was indirectly selected and was maintained in rotifer populations within environments containing these eco‐evolutionary dynamics; whereas within environments under constant conditions, predators evolved rapidly to lower levels of sex. Thus, our results indicate that the influence of eco‐evolutionary feedback dynamics on the overall evolutionary change has been underestimated.     

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.     

Evolution of phenotypic clusters through competition and local adaptation along an environmental gradient

We have analyzed the evolution of a quantitative trait in populations that are spatially extended along an environmental gradient, with gene flow between nearby locations. In the absence of competition, there is stabilizing selection toward a locally best-adapted trait that changes gradually along the gradient. According to traditional ideas, gradual spatial variation in environmental conditions is expected to lead to gradual variation in the evolved trait. A contrasting possibility is that the trait distribution instead breaks up into discrete clusters. Doebeli and Dieckmann (2003) argued that competition acting locally in trait space and geographical space can promote such clustering. We have investigated this possibility using deterministic population dynamics for asexual populations, analyzing our model numerically and through an analytical approximation. We examined how the evolution of clusters is affected by the shape of competition kernels, by the presence of Allee effects, and by the strength of gene flow along the gradient. For certain parameter ranges clustering was a robust outcome, and for other ranges there was no clustering. Our analysis shows that the shape of competition kernels is important for clustering: the sign structure of the Fourier transform of a competition kernel determines whether the kernel promotes clustering. Also, we found that Allee effects promote clustering, whereas gene flow can have a counteracting influence. In line with earlier findings, we could demonstrate that phenotypic clustering was favored by gradients of intermediate slope.     

Population dynamics and competition in chemostat models with adaptive nutrient uptake

 The standard Monod model for microbial population dynamics in the chemostat is modified to take into consideration that cells can adapt to the change of nutrient concentration in the chemostat by switching between fast and slow nutrient uptake and growing modes with asymmetric thresholds for transition from one mode to another. This is a generalization of a modified Monod model which considers adaptation by transition between active growing and quiescent cells. Global analysis of the model equations is obtained using the theory of asymptotically autonomous systems. Transient oscillatory population density and hysteresis growth pattern observed experimentally, which do not occur for the standard Monod model, can be explained by such adaptive mechanism of the cells. Competition between two species that can switch between fast and slow nutrient uptake and growing modes is also considered. It is shown that generically there is no coexistence steady state, and only one steady state, corresponding to the survival of at most one species in the chemostat, is a local attractor. Numerical simulations reproduce the qualitative feature of some experimental data which show that the population density of the winning species approaches a positive steady state via transient oscillations while that of the losing species approaches the zero steady state monotonically. Received 4 August 1995; received in revised form 15 December 1995     

Consumer effects on the vital rates of their resource can determine the outcome of competition between consumers

Current competition theory does not adequately address the fact that competitors may affect the survival, growth, and reproductive rates of their resources. Ecologically important interactions in which consumers affect resource vital rates range from parasitism and herbivory to mutualism. We present a general model of competition that explicitly includes consumer-dependent resource vital rates. We build on the classic MacArthur model of competition for multiple resources, allowing direct comparison with expectations from established concepts of resource-use overlap. Consumers share a stage-structured resource population but may use the different stages to different extents, as they do the different independent resources in the classic model. Here, however, the stages are dynamically linked via consumer-dependent vital rates. We show that consumers' effects on resource vital rates result in two important departures from classic results. First, consumers can coexist despite identical use of resource stages, provided each competitor shifts the resource stage distribution toward stages that benefit other species. Second, consumers specializing on different resource stages can compete strongly, possibly resulting in competitive exclusion despite a lack of resource stage-use overlap. Our model framework demonstrates the critical role that consumer-dependent resource vital rates can play in competitive dynamics in a wide range of biological systems.     

Biodiversity,habitat area,resource growth rate and interference competition

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers. This highlights the crucial role that resource growth rates may play in promoting coexistence of consumer species.     

The evolution of traits that determine ability in competitive contests

Summary We analyse mathematical models of the evolution of a trait that determines ability in contest competition. We assume that the value of the competitive trait affects two different components of fitness, one measuring the benefit of winning contests and the other measuring the cost of developing the competitive trait. Unlike previous analyses, we include the population dynamical consequences of larger competitive trait values. Exaggeration of the competitive trait reduces the mean probability of survival during the non-competitive stage of the life cycle. The resulting lower population density reduces competition and, therefore, reduces the advantages of greater competitive ability. Models without population dynamics often predict dimorphism in the competitive trait when resource possession is decided by interactions with many other individuals. If the competition involves a contest with a single other individual, models without population dynamics often predict cycles of increase and collapse in the trait or a continual increase, possibly resulting in extinction. When population dynamics are included, both of these results become less likely and a single stable trait value becomes more likely. Population dynamics also make it possible to have dimorphism when individuals have a single pairwise contest and alternative stable trait values when an individual has many contests. Increases in the value of the resource being contested may increase or decrease the evolutionarily stable size of the trait. Competition between very differently sized species will often decrease size in the larger species (character convergence).     

Species coexistence under resource competition with intraspecific and interspecific direct competition in a chemostat

Competition theory has developed separately for direct competition and for exploitative competition. However, the combined effects of the two types of competition on species coexistence remain unclear. To examine how intraspecific and interspecific direct competition contributes to the coexistence of species competing for a single resource, we constructed a chemostat-type resource competition model. With general functions for intraspecific and interspecific direct competition, we derived necessary and sufficient conditions (except for a critical case that rarely occurs in a biological sense) that determine the number of stably coexisting species. From these conditions, we found that the number of coexisting species is determined just by the invasibility of each species into subcommunities with a smaller number of species. In addition, using a combination of rigorous mathematical theory and a simple graphical method, we can demonstrate how the stronger intraspecific direct competition facilitates species invasion, leading to a larger number of coexisting species.     

Evolutionary disarmament in interspecific competition.

Competitive asymmetry, which is the advantage of having a larger body or stronger weaponry than a contestant, drives spectacular evolutionary arms races in intraspecific competition. Similar asymmetries are well documented in interspecific competition, yet they seldom lead to exaggerated traits. Here we demonstrate that two species with substantially different size may undergo parallel coevolution towards a smaller size under the same ecological conditions where a single species would exhibit an evolutionary arms race. We show that disarmament occurs for a wide range of parameters in an ecologically explicit model of competition for a single shared resource; disarmament also occurs in a simple Lotka-Volterra competition model. A key property of both models is the interplay between evolutionary dynamics and population density. The mechanism does not rely on very specific features of the model. Thus, evolutionary disarmament may be widespread and may help to explain the lack of interspecific arms races.     

Resource storage and competition with spatial and temporal variation in resource availability

This study addresses interspecific competition for a nutrient resource that is stored within individuals in habitats with both temporal and spatial variation. In such environments, population structure is induced by the mixture at any location of individuals with different amounts of stored nutrient, acquired elsewhere in the habitat. Focusing on phytoplankton competing for phosphorus in a partially mixed water column, an individual-based Lagrangian model is used to represent this population structure, and partial differential equations that approximate competitive dynamics are constructed by averaging over this population structure. Although the approximation model overestimates the benefit of resource storage to competitive fitness, both approaches predict that species with high storage capacity are favored by periodic resource pulses that are short lived but large in magnitude. Such storage specialists can competitively exclude or coexist with species that have advantages in maximal nutrient uptake and population growth rates. For very infrequent resource pulses, competitive dynamics become close to neutral. Thus, persistence of diverse species that are differentiated in nutrient storage and uptake capabilities is favored by resource pulses occurring with periods that are many times the average generation time of competitors.     

A discrete stage-structured two-species competition model with sexual and clonal reproduction

In this paper, we analyse a discrete stage-structured model which is a generalization of the two-species competition model studied in [2]. Motivated by plant populations, each species is assumed to reproduce both sexually and clonally. We show that this model has a dynamical behaviour that is similar to that of the classical continuous two-dimensional Lotka-Volterra model under weak nonlinearities of the Beverton-Holt type. By allowing the species to have different competition efficiencies, we show that it is possible to obtain different dynamics including coexistence, bistability and competitive exclusion, in contrast with the model studied in [2], which exhibits only competitive exclusion behaviour.     

Interference competition and species coexistence

Interference competition is ubiquitous in nature. Yet its effects on resource exploitation remain largely unexplored for species that compete for dynamic resources. Here, I present a model of exploitative and interference competition with explicit resource dynamics. The model incorporates both biotic and abiotic resources. It considers interference competition both in the classical sense (i.e. each species suffers a net reduction in per capita growth rate via interference from, and interference on, the other species) and in the broad sense (i.e. each species suffers a net reduction in per capita growth rate via interference from, but can experience an increase in growth rate via interference on, the other species). Coexistence cannot occur under classical interference competition even when the species inferior at resource exploitation is superior at interference. Such a trade-off can, however, change the mechanism of competitive exclusion from dominance by the superior resource exploiter to a priority effect. Now the inferior resource exploiter can exclude the superior resource exploiter provided it has a higher initial abundance. By contrast, when interference is beneficial to the interacting species, coexistence is possible via a trade-off between exploitation and interference. These results hold regardless of whether the resource is biotic or abiotic, indicating that the outcome of exploitative and interference competition does not depend on the exact nature of resource dynamics. The model makes two key predictions. First, species that engage in costly interference mechanisms (e.g. territoriality, overgrowth or undercutting, allelopathy and other forms of chemical competition) should not be able to coexist unless they also engage in beneficial interference mechanisms (e.g. predation or parasitism). Second, exotic invasive species that displace native biota should be superior resource exploiters that have strong interference effects on native species with little or negative cost. The first prediction provides a potential explanation for patterns observed in several natural systems, including plants, aquatic invertebrates and insects. The second prediction is supported by data on invasive plants and vertebrates.     

Coexistence in the chemostat as a result of metabolic by-products

Classical chemostat models assume that competition is purely exploitative and mediated via a common, limiting and single resource. However, in laboratory experiments with pathogens related to the genetic disease Cystic Fibrosis, species specific properties of production, inhibition and consumption of a metabolic by-product, acetate, were found. These assumptions were implemented into a mathematical chemostat model which consists of four nonlinear ordinary differential equations describing two species competing for one limiting nutrient in an open system. We derive classical chemostat results and find that our basic model supports the competitive exclusion principle, the bistability of the system as well as stable coexistence. The analytical results are illustrated by numerical simulations performed with experimentally measured parameter values. As a variant of our basic model, mimicking testing of antibiotics for therapeutic treatments in mixed cultures instead of pure ones, we consider the introduction of a lethal inhibitor, which cannot be eliminated by one of the species and is selective for the stronger competitor. We discuss our theoretical results in relation to our experimental model system and find that simulations coincide with the qualitative behavior of the experimental result in the case where the metabolic by-product serves as a second carbon source for one of the species, but not the producer.     

Evolution as a critical component of plankton dynamics

Microevolution is typically ignored as a factor directly affecting ongoing population dynamics. We show here that density-dependent natural selection has a direct and measurable effect on a planktonic predator-prey interaction. We kept populations of Brachionus calyciflorus, a monogonont rotifer that exhibits cyclical parthenogenesis, in continuous flow-through cultures (chemostats) for more than 900 days. Initially, females frequently produced male offspring, especially at high population densities. We observed rapid evolution, however, towards low propensity to reproduce sexually, and by 750 days, reproduction had become entirely asexual. There was strong selection favouring asexual reproduction because, under the turbulent chemostat regime, males were unable to mate with females, produced no offspring, and so had zero fitness. In replicated chemostat experiments we found that this evolutionary process directly influenced the population dynamics. We observed very specific but reproducible plankton dynamics which are explained well by a mathematical model that explicitly includes evolution. This model accounts for both asexual and sexual reproduction and treats the propensity to reproduce sexually as a quantitative trait under selection. We suggest that a similar amalgam of ecological and evolutionary mechanisms may drive the dynamics of rapidly reproducing organisms in the wild.