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Eco-evolutionary modelling involves the coupling of ecological equations to evolutionary ones. The interaction between ecological dynamics and evolutionary processes is essential to simulating evolutionary branching, a precursor to speciation. The creation and maintenance of biodiversity in models depends upon their ability to capture the dynamics of evolutionary branching. Understanding these systems requires low-dimension models that are amenable to analysis. The rapid reproduction rates of marine plankton ecosystems and their importance in determining the fluxes of climatically important gases between the ocean and atmosphere suggest that the next generation of global climate models needs to incorporate eco-evolutionary models in the ocean. This requires simple population-level models, that can represent such eco-evolutionary processes with orders of magnitude fewer equations than models that follow the dynamics of individual phenotypes. We present a general framework for developing eco-evolutionary models and consider its general properties. This framework defines a fitness function and assumes a beta distribution of phenotype abundances within each population. It simulates the change in total population size, the mean trait value, and the trait differentiation, from which the variance of trait values in the population may be calculated. We test the efficacy of the eco-evolutionary modelling framework by comparing the dynamics of evolutionary branching in a six-equation eco-evolutionary model that has evolutionary branching, with that of an equivalent one-hundred equation model that simulates the dynamics of every phenotype in the population. The latter model does not involve a population fitness function, nor does it assume a distribution of phenotype abundance across trait values. The eco-evolutionary population model and the phenotype model produce similar evolutionary branching, both qualitatively and quantitatively, in both symmetric and asymmetric fitness landscapes. In order to better understand the six-equation model, we develop a heuristic three-equation eco-evolutionary model. We use the density-independent mortality parameter as a convenient bifurcation parameter, so that differences in evolutionary branching dynamics in symmetric and asymmetric fitness landscapes may be investigated. This model shows that evolutionary branching of a stable population is flagged by a zero in the local trait curvature; the trait curvature then changes sign from negative to positive and back to negative, along the solution. It suggests that evolutionary branching points may be generated differently, with different dynamical properties, depending upon, in this case, the symmetry of the system. It also suggests that a changing environment, that may change attributes such as mortality, could have profound effects on an ecosystem's ability to adapt. Our results suggest that the properties of the three-dimensional model can provide useful insights into the properties of the higher-dimension models. In particular, the bifurcation properties of the simple model predict the processes by which the more complicated models produce evolutionary branching points. The corresponding bifurcation properties of the phenotype and population models, evident in the dynamics of the phenotype distributions they predict, suggest that our eco-evolutionary modelling framework captures the essential properties that underlie the evolution of phenotypes in populations. [ABSTRACT FROM AUTHOR]

The spread of viruses can be effectively reduced by the publicity of epidemic prevention. Additionally, the interaction between heterogeneous strains has a significant effect on virus evolution. Thus, we first establish an evolutionary dynamics Susceptible-Infected- Recovered (SIR) model which considers the interaction between heterogeneous strains. We utilize adaptive dynamics to investigate the evolutionary outcomes of the trade-off between transmission and virulence. Second, we perform a critical function analysis to generalize the results independent of specific trade-off assumptions and to determine the conditions for evolutionary stability and convergence stability. Last, we investigate the effects of different publicity measures on virulence evolution under two types of interactions, including the case of excess mortality alone and the coexistence of excess mortality and superinfection. Based on the general hypothesis of transmission virulence trade-off, we introduce the cost of host mobility caused by the scope and intensity of publicity. Numerical simulations present a set of evolutionary results, including continuously stable strategies, evolutionary branching points, repellers, and the Garden of Eden. Our results indicate that an excessive publicity scope and intensity can drive the epidemic evolution towards higher virulence. Both types of interactions suggest that continuously increasing the publicity scope under a low publicity intensity can effectively reduce virulence. Furthermore, the concurrent presence of excess mortality and superinfection induces the emergence of a higher virulence. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the consequences of dormancy in the 'rare mutation' and 'large population' regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second 'small mutations' limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011). The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the 'speed of adaptation' of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations. • We study dormancy in the 'rare mutation' regime of stochastic adaptive dynamics. • We first derive the polymorphic evolution sequence, based on prior work. • Our evolutionary branching criterion extends a result by Champagnat and Méléard. • In a classical model dormancy can favour evolutionary branching. • Dormancy also affects several more population characteristics. [ABSTRACT FROM AUTHOR]

In patch- or habitat-structured populations, different processes can favor adaptive polymorphism at different scales. While spatial heterogeneity can generate spatially disruptive selection favoring variation between patches, local competition can lead to locally disruptive selection promoting variation within patches. So far, almost all theory has studied these two processes in isolation. Here, we use mathematical modeling to investigate how resource variation within and between habitats influences the evolution of variation in a consumer population where individuals compete in finite patches connected by dispersal. We find that locally and spatially disruptive selection typically act in concert, favoring polymorphism under a wider range of conditions than when in isolation. But when patches are small and dispersal between them is low, kin competition inhibits the emergence of polymorphism, especially when the latter is driven by local competition for resources. We further use our model to clarify what comparisons between trait and neutral genetic differentiation ( Q ST / F ST comparisons) can tell about the nature of selection. Overall, our results help us understand the interaction between two major drivers of polymorphism: locally and spatially disruptive selection, and how this interaction is modulated by the unavoidable effects of kin selection under limited dispersal. [ABSTRACT FROM AUTHOR]

Evolutionary taxonomic turnovers are often associated with innovations beneficial in various ecological niches. Such innovations can repeatedly occur in species occupying optimum niches for a focal species group, resulting in their repeated diversifications and species flows from optimum to suboptimum niches, at the expense of less innovated ones. By combining species packing theory and adaptive dynamics theory, we develop an equation that allows analytical prediction for such innovation-driven species flows over a niche space of arbitrary dimension under a unimodal carrying capacity distribution. The developed equation and simulated evolution show that central niches (with the highest carrying capacities) tend to attain the fastest innovation speeds to become biodiversity sources. Species that diverge from the central niches outcompete the indigenous species in peripheral niches. The outcompeted species become extinct or evolve directionally toward far more peripheral niches. Because of this globally acting process over niches, species occupying the most peripheral niches are the least innovated and have deep divergence times from their closest relatives, and thus they correspond to living fossils. The extension of this analysis for multiple geographic regions shows that living fossils are also expected in geographically peripheral regions for the focal species group. [ABSTRACT FROM AUTHOR]

Studies of eco‐evolutionary dynamics have integrated evolution with ecological processes at multiple scales (populations, communities and ecosystems) and with multiple interspecific interactions (antagonistic, mutualistic and competitive). However, evolution has often been conceptualised as a simple process: short‐term directional adaptation that increases population growth. Here we argue that diverse other evolutionary processes, well studied in population genetics and evolutionary ecology, should also be considered to explore the full spectrum of feedback between ecological and evolutionary processes. Relevant but underappreciated processes include (1) drift and mutation, (2) disruptive selection causing lineage diversification or speciation reversal and (3) evolution driven by relative fitness differences that may decrease population growth. Because eco‐evolutionary dynamics have often been studied by population and community ecologists, it will be important to incorporate a variety of concepts in population genetics and evolutionary ecology to better understand and predict eco‐evolutionary dynamics in nature. [ABSTRACT FROM AUTHOR]

Most animals undergo ontogenetic niche shifts during their life. Yet, standard ecological theory builds on models that ignore this complexity. Here, we study how complex life cycles, where juvenile and adult individuals each feed on different sets of resources, affect community richness. Two different modes of community assembly are considered: gradual adaptive evolution and immigration of new species with randomly selected phenotypes. We find that under gradual evolution complex life cycles can lead to both higher and lower species richness when compared to a model of species with simple life cycles that lack an ontogenetic niche shift. Thus, complex life cycles do not per se increase the scope for gradual adaptive diversification. However, complex life cycles can lead to significantly higher species richness when communities are assembled trough immigration, as immigrants can occupy isolated peaks of the dynamic fitness landscape that are not accessible via gradual evolution. [ABSTRACT FROM AUTHOR]

Ideal free distribution theory attempts to predict the distribution of well-informed ('ideal') and unconstrained ('free') foragers in space based on adaptive individual decisions. When individuals differ in competitive ability, a whole array of equilibrium distributions is possible, and it is unclear which of these distributions are most likely. In the first part of our study, we show that strong competitors have an intrinsically stronger preference for highly productive habitat patches than poor competitors. This leads to an equilibrium distribution where the average competitive ability on a patch is strongly correlated with the productivity of the patch. In the second part of our study, we consider what happens if differences in competitive ability are heritable and, hence, subject to natural selection. Under constant environmental conditions, selection eliminates such differences: a single strategy prevails that optimally balances the costs and benefits associated with competitive ability. If the productivity of patches changes during the lifetime of individuals, the spatial assortment of competitors of equal competitive ability gives poor competitors a systematic advantage in times of environmental change, while good competitors benefit from equilibrium conditions. Using evolutionary individual-based simulations, we demonstrate that environmental change may then lead to the diversification of competitive ability. • Strong and weak competitors differ systematically in their habitat preferences. • This leads to the spatial assortment of individuals of similar competitive abilities. • In stable environments, selection removes heritable differences in competitiveness. • Fluctuating environments lead to the coexistence of strong and weak competitors. • Weak competitors can persist as they flourish in periods of environmental change. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the evolution of body size of population subject to dispersal and advection. For this purpose, we consider a reaction–diffusion system for competing species with hostile boundary conditions, which models population dynamics in advective environments. First, with the methods of adaptive dynamics, we discuss the stability of evolutionary singular strategy; specifically, evolutionary conditions for continuously stable strategy and evolutionary branching are obtained. Second, by theoretical analysis and numerical simulations, we investigate the influence of dispersal and advection on the evolution trend of body size and high-level polymorphism. Our results show that in environments without advection, the result of evolution mainly depends on competition coefficients, intrinsic growth rates and biological dispersal. In particular, the evolution of the body size will tend to the slow disperser with the increase in the dispersal rate if regardless of the influence of body size on competitiveness and growth rate. But there will be different results in advective environments, the increasing dispersal rate may lead to the evolution of the body size toward a intermediate level. A small or a moderate dispersal rate is likely to stimulate the emergence of evolutionary branching. In addition, our results predict that for hostile boundary conditions, advection can promote evolutionary stability, which prevent the emergence of evolutionary branching. [ABSTRACT FROM AUTHOR]

Niche construction refers to the process in which organisms regulate or influence their environments or other biological organisms through their own movement and metabolism, thus leading to different evolutionary trajectories of organisms in the process of natural selection. These conclusions were drawn based on the two-locus genetic models or mathematical ecological models that built with individual-based model (IBM) or cellular automata (CA) simulation methods. At present, the evolutionary distribution dynamics model is one of the popular methods to analyze the evolutionary invasion. By introducing this approach, we investigated the influence of trait-mediated niche construction on the evolution dynamics of species with intraspecific resource competition. The results confirmed that the niche construction mediated by traits caused obvious changes in the evolutionary trajectory of species. Comparing to the situation without the niche construction, the evolutionary branching reduced and the population density increased when the niche construction center was located in the small trait. While the niche construction acted on the large trait, it could maintain the evolutionary diversity, although the symmetrical evolutionary distribution of classical model was broken. It means that niche construction made significant differences in species traits through the long-term strong positive feedback with their environment. With the increasing of niche-constructing intensity, the species density of dominant traits increased significantly and the number of evolutionary branching decreased. Strong intraspecific competition and weak niche construction would be beneficial to maintain the evolutionary diversity of the species. [ABSTRACT FROM AUTHOR]

This study explores the coevolutionary dynamics of host-pathogen interaction based on a susceptible-infected population model with density-dependent mortality. We assume that both the host’s resistance and the pathogen’s virulence will adaptively evolve, but there are inevitable costs in terms of host birth rate and disease-related mortality rate. Particularly, it is assumed that both the host resistance and pathogen virulence can affect the transmission rate. By using the approach of adaptive dynamics and numerical simulation, we find that the finally coevolutionary outcome depends on the strength of host-pathogen asymmetric interaction, the curvature of trade-off functions, and the intensity of density-dependent natural mortality. To be specific, firstly, we find that if the strengths of host-pathogen asymmetric interaction and disease-related mortality are relatively weak, or the density-dependent natural mortality is relatively strong, then the host resistance and pathogen virulence will evolve to a continuously stable strategy. However, if the strength of host-pathogen asymmetric interaction and disease-related mortality becomes stronger, then the host resistance and pathogen virulence will evolve periodically. Secondly, we find that if the intensities of both the birth rate trade-off function and the density-dependent natural mortality are relatively weak, but the strength of host-pathogen asymmetric interaction becomes relatively strong, then the evolution of host resistance will have a relatively strongly accelerating benefit, the evolutionary branching of host resistance will first arise. However, if the strength of host-pathogen asymmetric interaction is relatively weak, but the intensity of the trade-off function of disease-related mortality becomes relatively strong, then the evolution of pathogen virulence will have a relatively strongly decelerating cost, and the evolutionary branching of pathogen virulence will first arise. Thirdly, after the evolutionary branching of host resistance and pathogen virulence, we further study the coevolutionary dynamics of two-hosts-one-pathogen interaction and one-host-two-pathogens interaction. We find that if the evolutionary branching of host resistance arises firstly, then the finally evolutionary outcome contains a dimorphic host and a monomorphic pathogen population. If the evolutionary branching of pathogen virulence arises firstly, then the finally evolutionary outcome may contain a monomorphic host and a dimorphic pathogen population. [ABSTRACT FROM AUTHOR]

We present a stochastic evolutionary phosphorus–algae–zooplankton model with phosphorus recycling and originally investigate the patterns and outcomes of adaptive changes in algal cell size, under the influence of environmental fluctuations. The threshold that determines whether the stochastic model will ecologically persist or not is first obtained. We then introduce fitness functions with stochastic fluctuations and obtain the evolutionary conditions for continuously stable strategy (CSS) and evolutionary branching, confirmed by numerical simulation. Our results predict that environmental fluctuation could drive algal evolution toward smaller cell size. Algal cell size varies significantly with phosphorus input in the presence of zooplankton, but has no response to the changing phosphorus inflow without zooplankton, and evolutionary branching will never occur without zooplankton. With the existence of zooplankton that has a fixed trait, evolutionary branching occurs with small environmental fluctuation and moderate phosphorus inflow, and the existence of environmental fluctuation could narrow the cell size difference between the newly emerging algal species, while large fluctuation or extreme phosphorus inflow will result in CSS. Moreover, environmental fluctuation potentially benefits algal biodiversity in eutrophic environments, and oligotrophication inhibits algal diversity. For the coevolution of algae and zooplankton, evolutionary cycling could appear, i.e., algal cell size and zooplankton body size can coevolve to a stable limit cycle (the Red Queen dynamics) in an eutrophic environment. In oligotrophic or moderate phosphorus environments, the influence of environmental fluctuation on algal evolution in the coevolution process is similar to the scenario that algae evolves only. [ABSTRACT FROM AUTHOR]

Adaptive radiations are known for rapid niche diversification in response to ecological opportunity. While most resources usually exist prior to adaptive radiation, novel niches associated with novel resources can be created as a clade diversifies. For example, in African lake cichlid radiations some species prey upon other species of the clade (intraclade consumers). Using a trait‐based eco‐evolutionary model, we investigate the evolution of intraclade consumers in adaptive radiations and the effect of this novel trophic interaction on the diversification process of the radiating clade. We find that the evolutionary emergence of intraclade consumers halts the diversification processes of other ecomorphs as a result of increased top‐down control of density. Because high productivity enables earlier evolution of intraclade consumers, highly productive environments come to harbour less species‐rich radiations than comparable radiations in less productive environments. Our results reveal how macroevolutionary and community patterns can emerge from ecological and microevolutionary processes. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of pollution on the body size of prey about a predator-prey evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment. Firstly, an eco-evolutionary predator-prey model incorporating the rapid evolution is formulated to investigate the effects of rapid evolution on the population density and the body size of prey by applying the quantitative trait evolutionary theory. The results show that rapid evolution can increase the density of prey and avoid population extinction, and with the worsening of pollution, the evolutionary traits becomes smaller gradually. Next, by employing the adaptive dynamic theory, a long-term evolutionary model is formulated to evaluate the effects of long-term evolution on the population dynamics and the effects of pollution on the body size of prey. The invasion fitness function is given, which reflects whether the mutant can invade successfully or not. Considering the trade-off between the intrinsic growth rate and the evolutionary trait, the critical function analysis method is used to investigate the dynamics of such slow evolutionary system. The results of theoretical analysis and numerical simulations conclude that pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution leads to a smaller body size of prey due to natural selection, while the opposite is more likely to generate evolutionary branching. [ABSTRACT FROM AUTHOR]

Cooperative investments in social dilemmas can spontaneously diversify into stably coexisting high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation, we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual-based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be understood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavorable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong. [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.

The Coffee Berry Borer (CBB) is the main pest that affects coffee crops around the world, causing major economic losses and diminishing beverage quality. A mathematical model is formulated, from the perspective of the Adaptive Dynamics (AD) framework, to describe the evolution of coffee quality as a continuous differentiating attribute related to the mix of healthy and bored coffee. The study involves three stages: first, an agro-ecological model describes coffee production and growth of the CBB population prior to the processing of different qualities of coffee; second, a market model describes the competition between different blends of standard and special coffee; finally, the AD canonical equation is derived to describe the evolution of coffee quality resulting from innovations in the quality attribute filtered by market competition. Interestingly, AD allows to derive conditions for the emergence of diversity, i.e., the establishment of a second type of coffee that coexists with the former and, similarly, for subsequent branching in the quality attributes. The full model provides insights on the impact of CBB control strategies on the long-term market structure. Specifically, a strong control aimed at increasing coffee quality may impoverish the market diversity, independently of the consumers' budget limitations and corresponding preference for either high or low quality. [ABSTRACT FROM AUTHOR]

In this paper, we develop a single species evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment and discuss the effects of pollution on the individual size of the species. The invasion fitness function of a monomorphic species is given, which involves the long-term average exponential growth rate of the species. Then the critical function analysis method is used to obtain the evolutionary dynamics of the system, which is related to interspecific competition intensity between mutant species and resident species and the curvature of the trade-off between individual size and the intrinsic growth rate. We conclude that the pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution can lead to rapid stable evolution toward a smaller individual size, while the opposite is more likely to generate evolutionary branching and promote species diversity. The adaptive dynamics of coevolution of dimorphic species is further analyzed when evolutionary branching occurs. [ABSTRACT FROM AUTHOR]

• A new stochastic evolutionary adaptive dynamics model. • Conditions for continuously stable strategy and evolutionary branching. • Influence of the stochastic disturbance on the evolutionary dynamics. • Rigorous numerical simulations for dimorphic coexistence and coevolution. This paper proposes a stochastic model for the evolutionary adaptive dynamics of species subject to trait-dependent intrinsic growth rates and the influence of environmental noise. The aim of this paper is twofold: (a) mathematically we make an attempt to investigate the evolutionary adaptive dynamics for models with noises; (b) biologically we investigate how the noises in environment affect the evolutionary stability. We first investigate the extinction and permanence of the population in the presence of environmental noises. Combining evolutionary adaptive dynamics with stochastic dynamics, we then establish a fitness function with stochastic disturbance and obtain the evolutionary conditions for continuously stable strategy and evolutionary branching. Our study finds that under intense competition among species, increasing stochastic disturbance can lead to rapidly stable evolution towards smaller trait values, but there is an opposite effect under weak competition among species. This yields an interesting evolutionary threshold, beyond which any increasing stochastic disturbance can go against evolutionary branching and promote evolutionary stability. We then carry out the evolutionary analysis and numerical simulations to illustrate our theoretical results. Finally, for demonstrating the emergence of high-level polymorphism we perform long-term simulation of evolutionary dynamics. [ABSTRACT FROM AUTHOR]

This study explores the evolutionary dynamics of host resistance based on a susceptible-infected population model with density-dependent mortality. We assume that the resistant ability of susceptible host will adaptively evolve, a different type of host differs in its susceptibility to infection, but the resistance to a pathogen involves a cost such that a less susceptible host results in a lower birth rate. By using the methods of adaptive dynamics and critical function analysis, we find that the evolutionary outcome relies mainly on the trade-off relationship between host resistance and its fertility. Firstly, we show that if the trade-off curve is globally concave, then a continuously stable strategy is predicted. In contrast, if the trade-off curve is weakly convex in the vicinity of singular strategy, then evolutionary branching of host resistance is possible. Secondly, after evolutionary branching in the host resistance has occurred, we examine the coevolutionary dynamics of dimorphic susceptible hosts and find that for a type of concave-convex-concave trade-off curve, the finally evolutionary outcome may contain a relatively higher susceptible host and a relatively higher resistant host, which can continuously stably coexist on a long-term evolutionary timescale. If the convex region of trade-off curve is relatively wider, then the finally evolutionary outcome may contain a fully resistant host and a moderately resistant host. Thirdly, through numerical simulation, we find that for a type of sigmoidal trade-off curve, after branching due to the high cost in terms of the birth rate, always the branch with stronger resistance goes extinct, the eventually evolutionary outcome includes a monomorphic host with relatively weaker resistance. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Consumers regularly experience trade-offs in their ability to find, handle, and digest different resources. Evolutionary ecologists recognized the significance of this observation for the evolution and maintenance of biological diversity long ago and continue to elaborate on the conditions under which to expect one or several specialists, generalists, or combinations thereof. Existing theory based on a single evolving trait predicts that specialization requires strong trade-offs such that generalists perform relatively poorly, while weak trade-offs favor a single generalist. Here, we show that this simple dichotomy does not hold true under joint evolution of two or more foraging traits. In this case, the boundary between trade-offs resulting in resource specialists and resource generalists is shifted toward weaker trade-off curvatures. In particular, weak trade-offs can result in evolutionary branching, leading to the evolution of two coexisting resource specialists, while the evolution of a single resource generalist requires particularly weak trade-offs. These findings are explained by performance benefits due to epistatic trait interactions enjoyed by phenotypes that are specialized in more than one trait for the same resource. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Cooperative interactions between species, termed mutualisms, play a key role in shaping natural ecosystems, economically important agricultural systems, and in influencing human health. Across different mutualisms, there is significant variation in the benefit that hosts receive from their symbionts. Empirical data suggest that transmission mode can help explain this variation: vertical transmission, where symbionts infect their host's offspring, leads to symbionts that provide greater benefits to their hosts than horizontal transmission, where symbionts leave their host and infect other hosts in the population. However, two different theoretical explanations have been given for this pattern: firstly, vertical transmission aligns the fitness interests of hosts and their symbionts; secondly, vertical transmission leads to increased relatedness between symbionts sharing a host, favouring cooperation between symbionts. We used a combination of analytical models and dynamic simulations to tease these factors apart, in order to compare their separate influences and see how they interact. We found that relatedness between symbionts sharing a host, rather than transmission mode per se, was the most important factor driving symbiont cooperation. Transmission mode mattered mainly because it determined relatedness. We also found evolutionary branching throughout much of our simulation, suggesting that a combination of transmission mode and multiplicity of infections could lead to the stable coexistence of different symbiont strategies. [ABSTRACT FROM AUTHOR]

Darwinian evolution consists of the gradual transformation of heritable traits due to natural selection and the input of random variation by mutation. Here, we use a quantitative genetics approach to investigate the coevolution of multiple quantitative traits under selection, mutation, and limited dispersal. We track the dynamics of trait means and of variance–covariances between traits that experience frequency‐dependent selection. Assuming a multivariate‐normal trait distribution, we recover classical dynamics of quantitative genetics, as well as stability and evolutionary branching conditions of invasion analyses, except that due to limited dispersal, selection depends on indirect fitness effects and relatedness. In particular, correlational selection that associates different traits within‐individuals depends on the fitness effects of such associations between‐individuals. We find that these kin selection effects can be as relevant as pleiotropy for the evolution of correlation between traits. We illustrate this with an example of the coevolution of two social traits whose association within‐individuals is costly but synergistically beneficial between‐individuals. As dispersal becomes limited and relatedness increases, associations between‐traits between‐individuals become increasingly targeted by correlational selection. Consequently, the trait distribution goes from being bimodal with a negative correlation under panmixia to unimodal with a positive correlation under limited dispersal. [ABSTRACT FROM AUTHOR]

Coevolution can impose density‐dependent selection through reciprocal biotic interactions on the fitness of involved species, driving directional and disruptive trait evolution and rich evolutionary possibilities. Coevolution has since Darwin been considered a potential path leading to adaptive diversification that could explain the emergence of ecological networks of biotic interactions that harbour multiple interacting species (eg, pollination networks and food webs). Here, we present adaptive dynamics, a powerful tool of evolutionary invasion analysis that explores how quantitative traits undergo incremental evolution, to exploring the emergence of multi‐species networks through coevolution. Specifically, we exemplify the feasibility of using adaptive dynamics to investigate trait evolution in 4 ecological networks, driven, respectively, by resource competition, trophic interactions, as well as bipartite mutualistic and antagonistic interactions. We use a set of ordinary differential equations to describe, at different paces, the population dynamics and trait dynamics of involved species assemblages. Through computing ecological equilibrium, invasion fitness, selection gradient and evolutionary singularity, and testing for evolutionary stability and the coexistence criterion of mutual invasibility, we illustrate the typical evolutionary dynamics and the criteria of evolutionary stability and branching in these ecological networks. Results highlight the importance of the form of trait‐mediated interaction kernel (ie, interaction strength as a function of trait difference) to adaptive diversification in these coevolutionary systems. We conclude by advocating that biotic interactions between two species can indeed lead to diffuse and even escape‐and‐radiate coevolution, making the emerged ecological networks an ideal model for studying complex adaptive systems. [ABSTRACT FROM AUTHOR]

Theoretical studies over the past decades have revealed various factors that favor or disfavor the evolution of dispersal. Among these, environmental heterogeneity is one driving force that can impact dispersal traits, because dispersing individuals can obtain a fitness benefit through finding better environments. Despite this potential benefit, some previous works have shown that the existence of spatial heterogeneity hinders evolution of dispersal. On the other hand, temporal heterogeneity has been shown to promote dispersal through a bet-hedging mechanism. When they are combined in a patch-structured population in which the quality of each patch varies over time independently of the others, it has been shown that spatiotemporal heterogeneity can favor evolution of dispersal. When individuals can use patch quality information so that dispersal decision is conditional, the evolutionary outcome can be different since individuals have options to disperse more/less offspring from bad/good patches. In this paper, we generalize the model and results of previous studies. We find richer dynamics including bistable evolutionary dynamics when there is arrival bias towards high-productivity patches. Then we study the evolution of conditional dispersal strategy in this generalized model. We find a surprising result that no offspring will disperse from a patch whose productivity was low when these offspring were born. In addition to mathematical proofs, we also provide intuition behind this initially counter-intuitive result based on reproductive-value arguments. Dispersal from high-productivity patches can evolve, and its parameter dependence behaves similarly, but not identically, to the case of unconditional dispersal. Our results unveil an importance of whether or not individuals can use patch quality information in dispersal evolution. • We study the evolution of dispersal in a patch-structured population. • Dispersal can evolve when patch qualities are independently fluctuating. • For unconditional dispersal, arrival bias can induce bistability. • For conditional dispersal, dispersal from low-productivity patches evolves to zero. • Use of patch-quality information drastically changes the evolutionary dynamics. [ABSTRACT FROM AUTHOR]

It is widely recognized that spatial structure in a population has some, and occasionally great, impacts on ecological and evolutionary dynamics. However, it has been observed that in the homogeneous Wright’s island model with a certain standard demographic assumption, spatial structure does not affect the fitness gradient of a fecundity-affecting trait. The location and convergence stability of singular strategies thus remain unchanged. Furthermore, evolutionary branching is impossible for small dispersal rates, and for a wide class of fecundity functions, evolutionary branching is impossible for any dispersal rate if branching does not occur in the corresponding well-mixed model. Spatially homogeneous structure thus often inhibits evolutionary branching. Here we study the impact of spatial heterogeneity on evolutionary dynamics. We consider an infinite Wright’s island model, where different islands have different capacity and fecundity consequences, and therefore the population is spatially heterogeneous. Through the analysis of metapopulation fitness, we derive its first-order and second-order derivatives with respect to mutant’s trait, which are explicitly represented in terms of fecundity derivatives. The selection gradient turns out to be a biased average of local selection pressures in different patch types. We find that evolutionary branching is generally favored in the presence of spatial heterogeneity. We also find a simple condition under which evolutionary branching is particularly favored. Applications to public-goods cooperation and emergent evolutionary branching to cooperators and defectors are discussed. [ABSTRACT FROM AUTHOR]

Abstract: Indirect biotic interactions—such as intransitive competition—are increasingly recognized as being important in shaping ecological patterns in natural systems. Over long time‐scales, such indirect interactions may affect the evolution of species phenotypes, which in turn can modify these interactions, thereby begetting eco‐evolutionary feedbacks. If indirect intransitive interactions can emerge in situ during lineage diversification, they could profoundly affect species’ phenotypic diversity, temporal stability, and subsequent diversification rates. We address these questions by investigating the conditions under which indirect intransitive competition can emerge from a lineage diversifying in sympatry. We use an adaptive dynamics model to study the ecological and evolutionary properties of this lineage under different scenarios where competition for resources between phenotypes varies in strength and (a)symmetry. Results show that weak‐intransitive competition can emerge during the sympatric diversification of a single lineage. “Weak‐intransitivity” here refers to situations where species interactions are not perfectly transitive, that is, there is no strict hierarchy in species competitive abilities. The strength of such weak‐intransitivity increases when the competition between phenotypes increases in strength and asymmetry. The strength of intransitivity also correlates with other system properties. We notably found that the strength of intransitivity increases with the number of phenotypes, and that greater intransitivity correlates with the evolution of greater functional trait divergences between phenotypes, greater resistance to invasion by new phenotypes but lower resistance to disturbances as well as slower evolutionary rates. Synthesis. This theoretical exploration of the evolution of intransitive competition provides the first formal bridge between the ecological and evolutionary aspects of intransitive competition. We show that, when competitive interactions are strong enough, weak‐intransitive competition is more likely to emerge through adaptive diversification than from a random community assembly. Intransitive competition is, therefore, not only restricted to between‐species interactions but can also function as a regulator of diversification within species, thereby affecting lineage functional diversity, and ecological and evolutionary stability. [ABSTRACT FROM AUTHOR]

The search for mates is often accompanied with conspicuous behaviour or morphology that can be exploited by predators. Here we explore the evolutionary consequences of a trade-off that arises naturally between mate acquisition and risk of predation and study evolution of the rate at which male prey search for mates in a population subject to a mate-finding Allee effect and exposed to either generalist or specialist predators. Since we show that the mate search rate determines the strength of the mate-finding Allee effect, we can alternatively view this as evolution of the mate-finding Allee effect in prey. We contrast two different life histories and find that, predominantly, male prey either evolve towards the maximal mate search rate yielding the weakest possible mate-finding Allee effect (thus showing no adaptive response in mating behaviour to predation risk) or evolutionary bi-stability occurs. In the latter case, males evolve a relatively low mate search rate (hence a relatively strong mate-finding Allee effect, interpreted as an adaptive response of male prey to predation) when initially slow or the maximal mate search rate when initially fast. Disruptive selection does not occur in populations exposed to generalist predators but is possible when predators are specialists. The dimorphic phase, in which fast and conspicuous male prey coexist with slow and cryptic ones, is however but a transient in evolutionary dynamics as one branch goes extinct while the other evolves towards the maximal mate search rate. [ABSTRACT FROM AUTHOR]

Abstract Constructivism in International Relations (IR) is popular, but constructivists seem disappointed. Allegedly something has been lost. Such criticisms are misplaced. There was never a uniform Constructivism. Since constructivism is socially constructed, to argue that constructivism has evolved “wrongly” is odd. This paper explains the dissatisfaction with constructivism followed by a second reading of its evolution as a tale of two cognitions. These two cognitions distinguish genera in the constructivist “family”. A criticism against one genus based on the cognition of the other is unfair. A focus on cognitions and the use of genera helps in perceiving constructivism’s future evolution.

An essential aspect of the current theory of adaptive speciation is the maintenance of phenotypic variation and the evolution of stationary stable phenotypic diversity, a phenomenon known as evolutionary branching. Theoretical and empirical evidence suggest that phenotypic variation can be maintained by favoring rare phenotypes, for example, through frequency-dependent selection. However, even when phenotypic variation is provided, the conditions leading to evolutionary branching are not universal. In order to lead to stable diversification, current models of adaptive speciation, such as the Lotka-Volterra competition model, must resort to strong assumptions that range from using unrealistic shape parameters for the competition and carrying capacity functions, modeling separately the generation of discontinuities in niche space, to increasing the dimensionality of phenotypic traits. Here, we introduce a stochastic version of the Lotka-Volterra competition model. We demonstrate that environmental fluctuations suffice to lead consistently to phenotypic diversification and evolutionary branching. Our observations build upon previous findings identifying a role for stochastic fluctuations on the evolution of phenotypic diversity, emphasize the difference between strong vs. weak assumptions in the stability of the LVC model, and suggest that the conditions for evolutionary branching are more relaxed than anticipated.

The three phases of dispersal - emigration, transfer and immigration - are affecting each other and the former and latter decisions may depend on patch types. Despite the inevitable fact of the complexity of the dispersal process, patch-type dependencies of dispersal decisions modelled as emigration and immigration are usually missing in theoretical dispersal models. Here, I investigate the coevolution of patch-type dependent emigration and patch-type dependent immigration in an extended Hamilton–May model. The dispersing population inhabits a landscape structured into many patches of two types and disperses during a continuous-time season. The trait under consideration is a four dimensional vector consisting of two values for emigration probability from the patches and two values for immigration probability into the patches of each type. Using the adaptive dynamics approach I show that four qualitatively different dispersal strategies may evolve in different parameter regions, including a counterintuitive strategy, where patches of one type are fully dispersed from (emigration probability is one) but individuals nevertheless always immigrate into them during the dispersal season (immigration probability is one). I present examples of evolutionary branching in a wide parameter range, when the patches with high local death rate during the dispersal season guarantee a high expected disperser output. I find that two dispersal strategies can coexist after evolutionary branching: a strategy with full immigration only into the patches with high expected disperser output coexists with a strategy that immigrates into any patch. Stochastic simulations agree with the numerical predictions. Since evolutionary branching is also found when immigration evolves alone, the present study is adding coevolutionary constraints on the emigration traits and hence finds that the coevolution of a higher dimensional trait sometimes hinders evolutionary diversification. [ABSTRACT FROM AUTHOR]

Models of community assembly have been used to illustrate how the many functionally diverse species that compose plankton food webs can coexist. However, the evolutionary processes leading to the emergence of plankton food webs and their interplay with migratory processes and spatial heterogeneity are yet to be explored. We study the eco-evolutionary dynamics of a modeled plankton community structured in both size and space and physiologically constrained by empirical data. We demonstrate that a complex yet ecologically and evolutionarily stable size-structured food web can emerge from an initial set of two monomorphic phytoplankton and zooplankton populations. We also show that the coupling of spatial heterogeneity and migration results in the emergence of specific biogeographic patterns: (i) the emergence of a source-sink structure of the plankton metacommunities, (ii) changes in size diversity dependent on migratory intensity and on the scale at which diversity is considered (local vs. global), and (iii) the emergence of eco-evolutionary provinces (i.e., a spatial unit characterized by some level of abiotic heterogeneity but of homogenous size composition due to horizontal movements) at spatial scales that increase with the strength of the migratory processes. [ABSTRACT FROM AUTHOR]

The pattern of connectivity between local populations or between microsites supporting individuals within a population is a poorly understood factor affecting the evolution of dispersal. We modify the well-known Hamilton–May model of dispersal evolution to allow for variable connectivity between microsites. For simplicity, we assume that the microsites are either solitary, i.e., weakly connected through costly dispersal, or part of a well-connected cluster of sites with low-cost dispersal within the cluster. We use adaptive dynamics to investigate the evolution of dispersal, obtaining analytic results for monomorphic evolution and numerical results for the co-evolution of two dispersal strategies. A monomorphic population always evolves to a unique singular dispersal strategy, which may be an evolutionarily stable strategy or an evolutionary branching point. Evolutionary branching happens if the contrast between connectivities is sufficiently high and the solitary microsites are common. The dimorphic evolutionary singularity, when it exists, is always evolutionarily and convergence stable. The model exhibits both protected and unprotected dimorphisms of dispersal strategies, but the dimorphic singularity is always protected. Contrasting connectivities can thus maintain dispersal polymorphisms in temporally stable environments. [ABSTRACT FROM AUTHOR]

By investigating metapopulation fitness, we present analytical expressions for the selection gradient and conditions for convergence stability and evolutionary stability in Wright's island model in terms of fecundity function. Coefficients of each derivative of fecundity function appearing in these conditions have fixed signs. This illustrates which kind of interaction promotes or inhibits evolutionary branching in spatial models. We observe that Taylor's cancellation result holds for any fecundity function: Not only singular strategies but also their convergence stability is identical to that in the corresponding well-mixed model. We show that evolutionary branching never occurs when the dispersal rate is close to zero. Furthermore, for a wide class of fecundity functions (including those determined by any pairwise game), evolutionary branching is impossible for any dispersal rate if branching does not occur in the corresponding well-mixed model. Spatial structure thus often inhibits evolutionary branching, although we can construct a fecundity function for which evolutionary branching only occurs for intermediate dispersal rates. [ABSTRACT FROM AUTHOR]

Cooperative interactions among individuals are ubiquitous despite the possibility of exploitation by selfish free riders. One mechanism that may promote cooperation is 'negotiation': individuals altering their behaviour in response to the behaviour of others. Negotiating individuals decide their actions through a recursive process of reciprocal observation, thereby reducing the possibility of free riding. Evolutionary games with response rules have shown that infinitely many forms of the rule can be evolutionarily stable simultaneously, unless there is variation in individual quality. This potentially restricts the conditions under which negotiation could maintain cooperation. Organisms interact with one another in a noisy world in which cooperative effort and the assessment of effort may be subject to error. Here, we show that such noise can make the number of evolutionarily stable rules finite, even without quality variation, and so noise could help maintain cooperative behaviour. We show that the curvature of the benefit function is the key factor determining whether individuals invest more or less as their partner's investment increases, investing less when the benefit to investment has diminishing returns. If the benefits of low investment are very small then behavioural flexibility tends to promote cooperation, because negotiation enables cooperators to reach large benefits. Under some conditions, this leads to a repeating cycle in which cooperative behaviour rises and falls over time, which may explain between-population differences in cooperative behaviour. In other conditions, negotiation leads to extremely high levels of cooperative behaviour, suggesting that behavioural flexibility could facilitate the evolution of eusociality in the absence of high relatedness. [ABSTRACT FROM AUTHOR]

The relationship between environmental productivity and species richness often varies among empirical studies, and despite much research, simple explanations for this phenomenon remain elusive. We investigated how phytoplankton and zooplankton coevolution shapes productivity-richness relationships in both phytoplankton and zooplankton, using a simple nutrient-phytoplankton-zooplankton model that incorporates size-dependent metabolic rates summarized from empirical studies. The model allowed comparisons of evolved species richness across productivity levels and at different evolutionary times. Our results show that disruptive selection leads to evolutionary branching of phytoplankton and zooplankton. Both the time required for evolutionary branching and the number of evolved species in phytoplankton and zooplankton tend to increase with productivity, producing a transient unimodal or positive productivity-richness relationship but followed by a positive productivity-richness relationship for both groups over long enough evolutionary time. Our findings suggest that coevolution between phytoplankton and zooplankton can drive the two common forms (unimodal and positive) of productivity-richness relationships in nature. [ABSTRACT FROM AUTHOR]

Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and it can incorporate both frequency- and density-dependent selection. This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems. The theory is presented in detail for a single, monomorphic, asexually reproducing population. We explain the necessary terminology to understand the basic arguments in models based on adaptive dynamics, including invasion fitness, the selection gradient, pairwise invasibility plots (PIP), evolutionarily singular strategies, and the canonical equation. The presentation is supported with a worked-out example of evolution of arrival times in migratory birds. We show how the adaptive dynamics methodology can be extended to study evolution in polymorphic populations using trait evolution plots (TEPs). We give an overview of literature that generalises adaptive dynamics techniques to other scenarios, such as sexual, diploid populations, and spatially-structured populations. We conclude by discussing how adaptive dynamics relates to evolutionary game theory and how adaptive-dynamics techniques can be used in speciation research.

Contemporary niche theory is a powerful structuring framework in theoretical ecology. First developed in the context of resource competition, it has been extended to encompass other types of regulating factors such as shared predators, parasites or inhibitors. A central component of contemporary niche theory is a graphical approach popularized by Tilman that illustrates the different outcomes of competition along environmental gradients, like coexistence and competitive exclusion. These food web modules have been used to address species sorting in community ecology, as well as adaptation and coexistence on eco-evolutionary time scales in adaptive dynamics. Yet, the associated graphical approach has been underused so far in the evolutionary context. In this paper, we provide a rigorous approach to extend this graphical method to a continuum of interacting strategies, using the geometrical concept of the envelope. Not only does this approach provide community and eco-evolutionary bifurcation diagrams along environmental gradients, it also sheds light on the similarities and differences between those two perspectives. Adaptive dynamics naturally merges with this ecological framework, with a close correspondence between the classification of singular strategies and the geometrical properties of the envelope. Finally, this approach provides an integrative tool to study adaptation between levels of organization, from the individual to the ecosystem. [ABSTRACT FROM AUTHOR]