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Abstract: This work is devoted to the study of an evolutionary system where similar individuals are competing for the same resources. Mathematically it is a Fisher equation with an integral term describing this non-local competition. Due to this competition, an initially monomorphic population may split into two distinct sub-populations, hence exhibiting a branching capacity. This framework can be applied to various contexts where recognizers are competing for some signals. The pattern formation capacity of this model is investigated analytically and numerically. [Copyright &y& Elsevier]

Abstract: This study explores the evolutionary dynamics of pathogen virulence in a single-infection model with density-dependent mortality. Although virulence is not an adaptation of the pathogen per se, it is generally believed to be an inevitable by-product of a pathogen''s need to propagate and transmit to new hosts: an increase in virulence will parallel an increase in transmission efficacy. The exact characteristics of the trade-off curve defined by this relationship are important with respect to possible evolutionary scenarios. We conduct a critical function analysis, a method that exposes the evolutionary outcome resulting from trade-offs of arbitrary shape, and find that this simple model can display a wide variety of evolutionary dynamics; comprising multiple stable attractors, evolutionary repellors, and most notably, evolutionary branching points. We identify the conditions under which the different evolutionary outcomes are realised. Our analysis furthermore considers the evolution of coexisting strains, and identifies the trade-off characteristics that will support an evolutionarily stable dimorphic state. We find that an evolutionarily stable dimorphism may exist also in the absence of a branching point in the monomorphic state. The analysis reveals that an evolutionarily stable dimorphism will always be attracting and that no further branching is possible under this model. We discuss our results in relation to the dimension of the environmental feedback inherent in the model, and to results from previous studies and models of evolution of virulence. [Copyright &y& Elsevier]

• We study the adaptive dynamics of the colonization rate in an extended competition-colonization model. • The trade-off strength, ownership effect and disturbance intensity qualitatively affect the evolutionary singularity. • Intermediate disturbance promotes evolutionary branching and facilitates the emergence of polymorphisms. • Random mutation scause the transition of coevolutionary trajectories between different basins of attraction. • Branching-extinction evolutionary cycles may be present. We study the adaptive dynamics of the colonization rate of species living in a patchy habitat when there is a trade-off with the competitive strength for individual patches. To that end, we formulate a continuous-time competition-colonization model that also includes ownership effects as well as random disturbance affecting the mortality rate. We find that intermediate disturbance (as measured by the fluctuation intensity of the mortality rate), a strong competition-colonization trade-off, and a weak ownership effect are necessary conditions for evolutionary branching and hence for the emergence of polymorphisms (i.e., coexistence) by small evolutionary steps. Specifically, concerning ownership we find that with low-intermediate disturbance, a weak ownership advantage favours evolutionary branching while ownership disadvantage does not. This asymmetry disappears at the higher-intermediate disturbance. Moreover, at a low-intermediate disturbance, the effect of the strength of the competition-colonization trade-off on evolutionary branching is non-monotonic disappears because the possibility of branching disappears again when the trade-off is too strong. We also find that there can be multiple evolutionary attractors for polymorphic populations, each with its own basin of attraction. With small but non-zero random evolutionary steps and depending on the initial polymorphic condition just after branching, a coevolutionary trajectory may come arbitrarily close to the shared boundary of two such basins and may even jump from one side to the other, which can lead to various kinds of long-term evolutionary dynamics, including evolutionary branching-extinction cycles. [ABSTRACT FROM AUTHOR]

To investigate how complex food-webs can develop through repeated evolutionary diversification, a predator–prey model was analyzed. In the model, each individual has two traits: trait x as a predator and trait y as a prey. These traits constitute a two-dimensional phenotype space, in which the whole group of individuals are represented as a phenotype distribution. Predator–prey interactions among the phenotypes are determined by their relative positions in the phenotype space. Each phenotypic cluster was treated as a species. Each species evolves in y to escape from predation, while it evolves in x to chase their prey. Analytical investigation provided two predictions. First, coupled evolutionary diversifications of y and x may occur when the x of predators have caught up with their prey’s y, which may be repeated. Second, complex food-webs may develop when species’ competitive strengths are kept similar within the communities. If the functional response is close to the ratio-dependent response, the competitive strengths of all species are similar when the relationship between predators and prey corresponds to the ideal free distribution (IFD). These predictions were confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

Tolerance and resistance provide hosts with two distinct defense strategies against parasitism. In resistance the hosts "fight" the parasite directly, whereas in tolerance the hosts fight the disease by ameliorating the damage that infection causes. There is increasing recognition that the two mechanisms may exhibit very different evolutionary behaviors. Although empirical work has often noted considerable variance in tolerance within hosts, theory has predicted the fixation of tolerance due to positive frequency dependence through a feedback with disease prevalence. Here we reconcile these findings through a series of dynamic game theoretical models. We emphasize that there is a crucial distinction between tolerance to the effects of disease-induced mortality and tolerance to the effect of the disease-induced reductions in fecundity. Only mortality tolerance has a positive effect on parasite fitness, whereas sterility tolerance is neutral and may therefore result in polymorphisms. The nature of the costs to defense and their relationship to trade-offs between resistance and tolerance are crucial in determining the likelihood of variation, whereas the co-evolution of the parasite will not affect diversity. Our findings stress that it is important to measure the effects of different mechanisms on characteristics that affect the epidemiology of the parasite to completely understand the evolutionary dynamics of defense. [ABSTRACT FROM AUTHOR]

Abstract: Traditionally, to determine the possible evolutionary behaviour of an ecological system using adaptive dynamics, it is necessary to calculate the fitness and its derivatives at a singular point. We investigate the claim that the possible evolutionary behaviour can be predicted directly from the population dynamics, without the need for calculation, by applying three criteria — one based on the form of the density dependent rates and two on the role played by the evolving parameters. Taking a general continuous time model, with broad ecological range, we show that the claim is true. Initially, we assume that individuals enter in class 1 and move through population classes sequentially; later we relax these assumptions and find that the criteria still apply. However, when we consider models where the evolving parameters appear non-linearly in the dynamics, we find some aspects of the criteria fail; useful but weaker results on possible evolutionary behaviour now apply. [Copyright &y& Elsevier]

Understanding the effect of multiple infections is essential for the prediction (and eventual control) of virulence evolution. Some theoretical studies have considered the possibility that several strains coexist in the same host (coinfection), but few have taken their within-host dynamics explicitly into account. Here, we develop a nested approach based on a simple model for the interaction of parasite strains with their host's immune system. We study virulence evolution by linking the within-host dynamics to an epidemiological framework that incorporates multiple infections. Our model suggests that antigenically similar parasite strains cannot coexist in the long term inside a host. We also find that the optimal level of virulence increases with the efficiency of multiple infections. Finally, we notice that coinfections create heterogeneity in the host population (with susceptible hosts and infected hosts), which can lead to evolutionary branching in the parasite population and the emergence of a hypervirulent parasite strategy. We interpret this result as a parasite specialization to the infectious state of the hosts. Our study has experimental and theoretical implications in a virulence management perspective. [ABSTRACT FROM AUTHOR]

Understanding the mechanisms and processes that generate biological diversity is a fundamental problem in evolution and ecology. In the past decade, the theory of evolutionary branching and adaptive diversification has provided new perspectives for understanding the evolution of diversity caused by ecological interactions. In models of adaptive diversification, the fitness landscapes change dynamically, so that the likelihood of diversification into different phenotypic clusters increases over time. In contrast, in models with static fitness landscapes, the likelihood of diversification decreases as populations climb fitness peaks, because crossing maladaptive fitness valleys becomes increasingly difficult. We used experimental evolution in bacteria to test how the likelihood of diversification changes over time in a bacterial lineage that has diversified in sympatry from a single ancestral strain. By analyzing the "fossil" record of this lineage, and restarting the lineage from different time points in the evolutionary past, we demonstrate that: (i) the lineage has initially undergone a phase of directional adaptation to the competitive environment, and (ii) during this phase, the likelihood of diversification increases significantly over time. These results suggest evolutionary branching caused by frequency-dependent competition as the main mechanism of diversification in our experimental populations. [ABSTRACT FROM AUTHOR]

Abstract: It is well known that two predators with different functional responses can coexist on one prey when the system exhibits nonequilibrium dynamics. In this paper, we investigate under which conditions such coexistence is evolutionarily stable, and whether the two predators may evolve from a single ancestor via evolutionary branching. We assume that predator strategies differ in handling time, and hence in the shape of their Holling type II functional response. Longer handling times are costly in terms of lost foraging time, but allow the predator to extract more nutrients from the prey and therefore to produce more offspring per consumed prey. In the analysis, we apply a new method to accommodate arbitrary trade-off functions between handling time and offspring production. Contrary to previous results obtained assuming a particular trade-off [Kisdi, E. and Liu, S., 2006. J. Evol. Biol. 19, 49–58], we find that evolutionary branching of handling time is possible, although it does not appear to be very likely and can be excluded for a class of trade-offs. Evolutionarily stable coexistence of two predators occurs under less restrictive conditions, which are always satisfied when the trade-off function has two strongly concave parts connected by a convex piece. [Copyright &y& Elsevier]

Cooperation in spatial evolutionary game theory has revealed various interesting insights into the problem of the evolution and maintenance of cooperative behavior. In social dilemmas, cooperators create and maintain a common resource at some cost to themselves while defectors attempt to exploit the resource without contributing. This leads to classical conflicts of interest between the individual and the community with the prisoner's dilemma as the most prominent mathematical metaphor to describe such situations. The evolutionary fate of cooperators and defectors sensitively depends on the interaction structure of the population. In spatially extended populations, the ability to form clusters or collectives often supports cooperation by limiting exploitation to the cluster boundaries but often collectives formation may also inhibit or even eliminate cooperation by hindering the dispersal of cooperators. Another attempt at resolving the conflict of interest allows individuals to drop out of unpromising public enterprises and hence changes compulsory interactions into voluntary participation. This leads to a cyclic dominance of cooperators, defectors and loners that do not participate and gives rise to oscillatory dynamics which again subtly depends on the population structure. Here we review recent advances in the dynamics of cooperation in structured populations as well as in situations where cooperative investments vary continuously. In such continuous games, the evolutionary dynamics driven by mutation and selection can lead to spontaneous diversification and specialization into high and low investing individuals which provides a natural explanation for the origin of cooperators and defectors. [ABSTRACT FROM AUTHOR]

Frequency-dependent disruptive selection is widely recognized as an important source of genetic variation. Its evolutionary consequences have been extensively studied using phenotypic evolutionary models, based on quantitative genetics, game theory, or adaptive dynamics. However, the genetic assumptions underlying these approaches are highly idealized and, even worse, predict different consequences of frequency-dependent disruptive selection. Population genetic models, by contrast, enable genotypic evolutionary models, but traditionally assume constant fitness values. Only a minority of these models thus addresses frequency-dependent selection, and only a few of these do so in a multilocus context. An inherent limitation of these remaining studies is that they only investigate the short-term maintenance of genetic variation. Consequently, the long-term evolution of multilocus characters under frequency-dependent disruptive selection remains poorly understood. We aim to bridge this gap between phenotypic and genotypic models by studying a multilocus version of Levene's soft-selection model. Individual-based simulations and deterministic approximations based on adaptive dynamics theory provide insights into the underlying evolutionary dynamics. Our analysis uncovers a general pattern of polymorphism formation and collapse, likely to apply to a wide variety of genetic systems: after convergence to a fitness minimum and the subsequent establishment of genetic polymorphism at multiple loci. genetic variation becomes increasingly concentrated on a few loci, until eventually only a single polymorphic locus remains. This evolutionary process combines features observed in quantitative genetics and adaptive dynamics models, and it can be explained as a consequence of changes in the selection regime that are inherent to frequency-dependent disruptive selection. Our findings demonstrate that the potential of frequency-dependent disruptive selection to maintain polygenic variation is considerably smaller than previously expected. [ABSTRACT FROM AUTHOR]

Abstract: We investigate symmetry-breaking bifurcation patterns in evolution in the framework of adaptive dynamics (AD). We define weak and strong symmetry. The former applies for populations where only the simultaneous reflection of all individuals is an invariant transformation. The symmetry is strong in populations where reflection of some, but not all, individuals leaves the situation unchanged. We show that in case of weak symmetry evolutionary branching can lead to the emergence of two asymmetric variants, which are mirror images of each other, and the loss of the symmetric ancestor. We also show that in case of strong symmetry, evolutionary branching can occur into a symmetric and an asymmetric variant, both of which survive. The latter, asymmetric branching differs from the generic branching patterns of AD, which is always symmetric. We discuss biological examples for weak and strong symmetries and a specific model producing the new kind of branching. [Copyright &y& Elsevier]

Abstract: This study extends the framework of adaptive dynamics to function-valued traits. Such adaptive traits naturally arise in a great variety of settings: variable or heterogeneous environments, age-structured populations, phenotypic plasticity, patterns of growth and form, resource gradients, and in many other areas of evolutionary ecology. Adaptive dynamics theory allows analysing the long-term evolution of such traits under the density-dependent and frequency-dependent selection pressures resulting from feedback between evolving populations and their ecological environment. Starting from individual-based considerations, we derive equations describing the expected dynamics of a function-valued trait in asexually reproducing populations under mutation-limited evolution, thus generalizing the canonical equation of adaptive dynamics to function-valued traits. We explain in detail how to account for various kinds of evolutionary constraints on the adaptive dynamics of function-valued traits. To illustrate the utility of our approach, we present applications to two specific examples that address, respectively, the evolution of metabolic investment strategies along resource gradients, and the evolution of seasonal flowering schedules in temporally varying environments. [Copyright &y& Elsevier]

Why and how specialist and generalist strategies evolve are important questions in evolutionary ecology. In this paper, with the method of adaptive dynamics and evolutionary branching, we identify conditions that select for specialist and generalist strategies. Generally, generalist strategies evolve if there is a switching benefit; specialists evolve if there is a switching cost. If the switching cost is large, specialists always evolve. If the switching cost is small, even though the consumer will first evolve toward a generalist strategy, it will eventually branch into two specialists. [ABSTRACT FROM AUTHOR]

Abstract: A reaction–diffusion model describing the evolutionary dynamics of a food-web was constructed. In this model, predator–prey relationships among organisms were determined by their position in a two-dimensional phenotype space defined by two traits: as prey and as predator. The mutation process is expressed with a diffusion process of biomass in the phenotype space. Numerical simulation of this model showed co-evolutionary dynamics of isolated phenotypic clusters, including various types of evolutionary branching, which were classified into branching as prey, branching as predators, and co-evolutionary branching of both prey and predators. A complex food-web develops with recursive evolutionary branching from a single phenotypic cluster. Biodiversity peaks at the medium strength of the predator–prey interaction, where the food-web is maintained at medium biomass by a balanced frequency between evolutionary branching and extinction. [Copyright &y& Elsevier]

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

In recent years, the population dynamics of plankton in light- or nutrient-limited environments have been studied extensively. Their evolutionary dynamics, however, have received much less attention. Here, we used a modeling approach to study the evolutionary behavior of a population of plankton living in a mixed water column. Initially, the organisms are mixotrophic and thus have both autotrophic and heterotrophic abilities. Through evolution of their trophic preferences, however, they can specialize into separate autotrophs and heterotrophs. It was found that the light intensity gradient enables evolutionary branching and thus may result in the ecological specialization of the mixotrophs. By affecting the gradient, other environmental properties also acquire influence on this evolutionary process. Intermediate mixing intensities, large mixing depths, and high nutrient densities were found to facilitate evolutionary branching and thus specialization. Later results may explain why mixotrophs are often more dominant in oligotrophic systems while specialist strategies are associated with eutrophic systems. [ABSTRACT FROM AUTHOR]

A population is polymorphic when its members fall into two or more categories, referred to as alternative phenotypes. There are many kinds of phenotypic polymorphisms, with specialization in reproduction, feeding, dispersal, or protection from predators. An individual's phenotype might be randomly assigned during development, genetically determined, or set by environmental cues. These three possibilities correspond to a mixed strategy of development, a genetic polymorphism, and a conditional strategy. Using the perspective of adaptive dynamics, I develop a unifying evolutionary theory of systems of determination of alternative phenotypes, focusing on the relative possibilities for random versus genetic determination. The approach is an extension of the analysis of evolutionary branching in adaptive dynamics. It compares the possibility that there will be evolutionary branching, leading to genetic polymorphism, with the possibility that a mixed strategy evolves. The comparison is based on the strength of selection for the different outcomes. An interpretation of the resulting criterion is that genetic polymorphism is favored over random determination of the phenotype if an individual's heritable genotype is an adaptively advantageous cue for development. I argue that it can be helpful to regard genetic polymorphism as a special case of phenotypic plasticity. [ABSTRACT FROM AUTHOR]

A recent Perspectives article by Gavrilets (2003) on the theory of speciation ignored advances in understanding processes of adaptive speciation, in which the splitting of lineages is an adaptation caused by frequency dependent selection. Adaptive, or sympatric, speciation has been modeled since the 1960s, but the large amount of attention from both empirical and theoretical biologists that adaptive speciation has received in recent years goes far beyond what was described in Gavrilets' paper. Due to conceptual advances based on the theory of adaptive dynamics, adaptive speciation has emerged as a theoretically plausible evolutionary process that can occur in many different ecological settings. [ABSTRACT FROM AUTHOR]

Metapopulation theory for the evolution of specialisation is virtually absent. In this article, therefore, we study a metapopulation model for consumers with a fitness trade-off between two habitats. We focus on effects of habitat abundance, dispersal rate and trade-off strength on the evolution of specialisation under two types of trade-off. Adaptation affects either the intrinsic growth rates r or the carrying capacities K. Depending on dispersal rate and trade-off strength, evolution can result in one generalist, one specialist or two specialist types. Higher dispersal rate and a weaker trade-off favour the evolution of a generalist, for both trade-off structures. However, we also find differences between the two trade-off structures. Our results are qualitatively similar to analyses of two-patch models, suggesting that insights from such simpler models can be extrapolated to metapopulation models. Additional effects, however, occur because in classical metapopulations patch lifetime depends on extinction rate. Counterintuitively, this favours the evolution of specialisation when the trade-off affects r. [Copyright &y& Elsevier]

While it now appears likely that sympatric speciation is possible, its generality remains contentious. If it really is rare, then most natural populations must not fit the assumptions of sympatric speciation theory. A better understanding of these assumptions may help identify when sympatric speciation is or is not likely. This paper investigates two such assumptions: that genetic variation for stringent assortative mating is not limiting and that females are not penalized for mating assortatively. Simulations demonstrate that the speed of sympatric speciation is very sensitive to the population's capacity for stringent assortative mating and is potentially extremely slow. The rapid divergence often thought to be a hallmark of sympatric speciation may only occur in a restricted area of parameter space. [ABSTRACT FROM AUTHOR]

A central goal of evolutionary ecology is to understand the role of different ecological processes in producing patterns of macroevolutionary diversification. Theory and empirical evidence have shown that competition between existing species can promote evolutionary diversification through ecological character displacement and, more recently, that competition may play a role both in producing species and in driving their subsequent evolutionary divergence. However, recent theory and experiments suggest that other ecological interactions, such as facilitation, may also be important in the evolutionary diversification of some taxa. Future research in this area will be invaluable in dissecting the relative roles of different ecological processes in producing and maintaining biodiversity. [ABSTRACT FROM AUTHOR]

Evolutionary branching, which is a coevolutionary phenomenon of the development of two or more distinctive traits from a single trait in a population, is the issue of recent studies on adaptive dynamics. In previous studies, it was revealed that trait variance is a minimum requirement for evolutionary branching, and that it does not play an important role in the formation of an evolutionary pattern of branching. Here we demonstrate that the trait evolution exhibits various evolutionary branching paths starting from an identical initial trait to different evolutional terminus traits as determined by only changing the assumption of trait variance. The key feature of this phenomenon is the topological configuration of equilibria and the initial point in the manifold of dimorphism from which dimorphic branches develop. This suggests that the existing monomorphic or polymorphic set in a population is not an unique inevitable consequence of an identical initial phenotype. [Copyright &y& Elsevier]

Twenty years ago, Bulmer and Bull suggested that disruptive selection, produced by environmental fluctuations, can result in an evolutionary transition from environmental sex determination (ESD) to genetic sex determination (GSD). We investigated the feasibility of such a process, using mutation-limited adaptive dynamics and individual-based computer simulations. Our model describes the evolution of a reaction norm for sex determination in a metapopulation setting with partial migration and variation in an environmental variable both within and between local patches. The reaction norm represents the probability of becoming a female as a function of environmental state and was modeled as a sigmoid function with two parameters, one giving the location (i.e., the value of the environmental variable for which an individual has equal chance of becoming either sex) and the other giving the slope of the reaction norm for that environment. The slope can be interpreted as being set by the level of developmental noise in morph determination, with less noise giving a steeper slope and a more switchlike reaction norm. We found convergence stable reaction norms with intermediate to large amounts of developmental noise for conditions characterized by low migration rates, small differential competitive advantages between the sexes over environments, and little variation between individual environments within patches compared to variation between patches. We also considered reaction norms with the slope parameter constrained to a high value, corresponding to little developmental noise. For these we found evolutionary branching in the location parameter and a transition from ESD toward GSD, analogous to the original analysis by Bulmer and Bull. Further evolutionary change, including dominance evolution, produced a polymorphism acting as a GSD system with heterogamety. Our results point to the role of developmental noise in the evolution of sex determination. [ABSTRACT FROM AUTHOR]

Models of adaptive speciation are typically concerned with demonstrating that it is possible for ecologically driven disruptive selection to lead to the evolution of assortative mating and hence speciation. However, disruptive selection could also lead to other forms of evolutionary diversification, including ecological sexual dimorphisms. Using a model of frequency-dependent intraspecific competition, we show analytically that adaptive speciation and dimorphism require identical ecological conditions. Numerical simulations of individual-based models show that a single ecological model can produce either evolutionary outcome, depending on the genetic independence of male and female traits and the potential strength of assortative mating. Speciation is inhibited when the genetic basis of male and female ecological traits allows the sexes to diverge substantially. This is because sexual dimorphism, which can evolve quickly, can eliminate the frequency-dependent disruptive selection that would have provided the impetus for speciation. Conversely, populations with strong assortative mating based on ecological traits are less likely to evolve a sexual dimorphism because females cannot simultaneously prefer males more similar to themselves while still allowing the males to diverge. This conflict between speciation and dimorphism can be circumvented in two ways. First, we find a novel form of speciation via negative assortative mating, leading to two dimorphic daughter species. Second, if assortative mating is based on a neutral marker trait, trophic dimorphism and speciation by positive assortative mating can occur simultaneously. We conclude that while adaptive speciation and ecological sexual dimorphism may occur simultaneously, allowing for sexual dimorphism restricts the likelihood of adaptive speciation. Thus, it is important to recognize that disruptive selection due to frequency-dependent interactions can lead to more than one form of adaptive splitting. [ABSTRACT FROM AUTHOR]

Understanding mechanisms of evolutionary diversification is central to evolutionary biology. Microbes constitute promising model systems for observing processes of diversification directly in the laboratory. One of the main existing paradigms for microbial diversification is the evolution of cross-feeding polymorphisms, in which a strain specializing on a primary resource coexists with a cross-feeding strain that specializes on a waste product resulting from consumption of the primary resource. Here I propose a theoretical model for the evolutionary dynamics through which cross-feeding polymorphisms can gradually emerge from a single ancestral strain. The model is based on the framework of adaptive dynamics, which has proved to be very useful for studying adaptive processes of divergence under sympatric conditions. In particular, the phenomenon of evolutionary branching serves as a general paradigm for diversification. I show that evolutionary branching naturally occurs in evolutionary models of cross-feeding if (1) there is a trade-off between uptake efficiencies on the primary and secondary resources, and (2) this trade-off has positive curvature. The model also suggests that the evolution of cross-feeding should be more likely in chemostat cultures than in serial batch cultures, which conforms with empirical observations. Overall, the model provides a theoretical metaphor for the evolution of cross-feeding polymorphisms. [ABSTRACT FROM AUTHOR]

Understanding the origin and maintenance of biodiversity is a fundamental problem. Many theoretical approaches have been investigating ecological interactions, such as competition, as potential drivers of diversification. Classical consumer-resource models predict that the number of coexisting species should not exceed the number of distinct resources, a phenomenon known as the competitive exclusion principle. It has recently been argued that including physiological tradeoffs in consumer-resource models can lead to violations of this principle and to ecological coexistence of very high numbers of species. Here, we show that these results crucially depend on the functional form of the tradeoff. We investigate the evolutionary dynamics of resource use constrained by tradeoffs and show that if the tradeoffs are non-linear, the system either does not diversify or diversifies into a number of coexisting species that do not exceed the number of resources. In particular, very high diversity can only be observed for linear tradeoffs., Competing Interests: RC, YI No competing interests declared, MD Reviewing Editor, eLife, (© 2021, Caetano et al.)

Dispersal is one of the fundamental life-history strategies of organisms, so understanding the selective forces shaping the dispersal traits is important. In the Wright's island model, dispersal evolves due to kin competition even when dispersal is costly, and it has traditionally been assumed that the living conditions are the same everywhere. To study the effect of spatial heterogeneity, we extend the model so that patches may receive different amounts of immigrants, foster different numbers of individuals, and give different reproduction efficiency to individuals therein. We obtain an analytical expression for the fitness gradient, which shows that directional selection consists of three components: As in the homogeneous case, the direct cost of dispersal selects against dispersal and kin competition promotes dispersal. The additional component, spatial heterogeneity, more precisely the variance of so-called relative reproductive potential, tends to select against dispersal. We also obtain an expression for the second derivative of fitness, which can be used to determine whether there is disruptive selection: Unlike the homogeneous case, we found that divergence of traits through evolutionary branching is possible in the heterogeneous case. Our numerical explorations suggest that evolutionary branching is promoted more by differences in patch size than by reproduction efficiency. Our results show the importance of the existing spatial heterogeneity in the real world as a key determinant in dispersal evolution., Competing Interests: The authors declare no competing interest., (Copyright © 2020 the Author(s). Published by PNAS.)

Sterilizing pathogens are common, yet studies focused on how such pathogens respond adaptively to fecundity reductions caused in their hosts are rare. Here we assume that the infected hosts, as a result of redistributing energy resources saved by reduced fecundity, have increased longevity and focus on exploring the consequences of such a fecundity-longevity trade-off on sterility virulence evolution in the pathogens. We find that the trade-off itself cannot prevent the evolution of full sterilization. Therefore, we allow for vertical transmission and reveal that the fecundity-longevity trade-off strongly determines the threshold efficiency of vertical transmission above which partial host sterilization evolves. Partial sterilization may appear as an intermediate level of sterility virulence or as a stable dimorphism at which avirulent and highly virulent strains coexist. The fecundity-longevity trade-off significantly contributes to determining the actual outcome, in many cases countering predictions made in the absence of this trade-off. It is known that in well-mixed populations, partial sterilization may evolve in pathogens under a combination of horizontal and vertical transmission. Our study highlights that this is independent of the form of horizontal transmission and the type of density dependence in host demography and that the fecundity-longevity trade-off is an important player in sterility virulence evolution.

Functional connectivity, the realized flow of individuals between the suitable sites of a heterogeneous landscape, is a prime determinant of the maintenance and evolution of populations in fragmented habitats. While a large body of literature examines the evolution of dispersal propensity, it is less known how evolution shapes functional connectivity via traits that influence the distribution of the dispersers. Here, we use a simple model to demonstrate that, in a heterogeneous environment with clustered and solitary sites (i.e., with variable structural connectivity), the evolutionarily stable population contains strains that are strongly differentiated in their pattern of connectivity (local vs. global dispersal), but not necessarily in the fraction of dispersed individuals. Also during evolutionary branching, selection is disruptive predominantly on the pattern of connectivity rather than on dispersal propensity itself. Our model predicts diversification along a hitherto neglected axis of dispersal strategies and highlights the role of the solitary sites-the more isolated and therefore seemingly less important patches of habitat-in maintaining global dispersal that keeps all sites connected., (© 2019 The Author(s). Evolution © 2019 The Society for the Study of Evolution.)

There are many mechanisms that hosts can evolve to defend against parasites, two of which are resistance and tolerance. These defences often have different evolutionary behaviours, and it is important to consider how each individual mechanism may respond to changes in environment. In particular, host defence through tolerance is predicted to be unlikely to lead to variation, despite many observations of diversity in both animal and plant systems. Hence understanding the drivers of diversity in host defence and parasite virulence is vital for predicting future evolutionary changes in infectious disease dynamics. It has been suggested that heterogeneous environments might generally promote diversity, but the effect of temporal fluctuations has received little attention theoretically or empirically, and there has been no examination of how temporal fluctuations affects the evolution of host tolerance. In this study, we use a mathematical model to investigate the evolution of host tolerance in a temporally fluctuating environment. We show that investment in tolerance increases in more variable environments, giving qualitatively different evolutionary behaviours when compared to resistance. Once seasonality is introduced evolutionary branching though tolerance can occur and create diversity within the population, although potentially only temporarily. This branching behaviour arises due to the emergence of a negative feedback with the maximum infected density on a cycle, which is strongest when the infected population is large. This work reinforces the qualitative differences between tolerance and resistance evolution, but also provides theoretical evidence for the theory that heterogeneous environments promote host-parasite diversity, hence constant environment assumptions may omit important evolutionary outcomes., (Copyright © 2019 Elsevier Inc. All rights reserved.)