Emergence of asymmetry in evolution

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.     

The evolution of phenotypic traits in a predator-prey system subject to Allee effect

This paper considers the evolution of phenotypic traits in a community comprising the populations of predators and prey subject to Allee effect. The evolutionary model is constructed from a deterministic approximation of the stochastic process of mutation and selection. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy and evolutionary branching. We find that the strong Allee effect of prey facilitates the formation of continuously stable strategy in the case that prey population undergoes evolutionary branching if the Allee effect of prey is not strong enough. Secondly, we show that evolutionary suicide is impossible for prey population when the intraspecific competition of prey is symmetric about the origin. However, evolutionary suicide can occur deterministically on prey population if prey individuals undergo strong asymmetric competition and are subject to Allee effect. Thirdly, we show that the evolutionary model with symmetric interactions admits a stable limit cycle if the Allee effect of prey is weak. Evolutionary cycle is a likely outcome of the process, which depends on the strength of Allee effect and the mutation rates of predators and prey.     

Evolution of Dispersal in a Structured Metapopulation Model in Discrete Time

In this article, a structured metapopulation model in discrete time with catastrophes and density-dependent local growth is introduced. The fitness of a rare mutant in an environment set by the resident is defined, and an efficient method to calculate fitness is presented. With this fitness measure evolutionary analysis of this model becomes feasible. This article concentrates on the evolution of dispersal. The effect of catastrophes, dispersal cost, and local dynamics on the evolution of dispersal is investigated. It is proved that without catastrophes, if all population–dynamical attractors are fixed points, there will be selection for no dispersal. A new mechanism for evolutionary branching is also found: Even though local population sizes approach fixed points, catastrophes can cause enough temporal variability, so that evolutionary branching becomes possible.     

The effects of large and small-scale random events on the synchrony of metapopulation dynamics: a theoretical analysis

We present an analysis of the conditions under which migration and global random factors may determine large scale synchrony in the dynamics of spatially structured populations. We derive an analytic approximation which describes how the desynchronizing influence of local environmental stochasticity combines with the synchronizing influences of larger scale environmental stochastic variation and migration to determine population cross correlation coefficients. Despite the simplifications made by this analysis, computer simulations show that the behaviour of more complicated models is well described by our approximation over considerable regions of parameter space. We conclude that population synchrony is largely determined by the coefficients of variation (CVs) of the local and larger scale stochastic processes, and that migration alone is only likely to maintain population synchrony when the CV of the local stochastic process is very small.     

Adaptive evolution of foraging-related traits in a predator-prey community

In this paper, with the method of adaptive dynamics and geometric technique, we investigate the adaptive evolution of foraging-related phenotypic traits in a predator-prey community with trade-off structure. Specialization on one prey type is assumed to go at the expense of specialization on another. First, we identify the ecological and evolutionary conditions that allow for evolutionary branching in predator phenotype. Generally, if there is a small switching cost near the singular strategy, then this singular strategy is an evolutionary branching point, in which predator population will change from monomorphism to dimorphism. Second, we find that if the trade-off curve is globally convex, predator population eventually branches into two extreme specialists, each completely specializing on a particular prey species. However, if the trade-off curve is concave-convex-concave, after branching in predator phenotype, the two predator species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist. The analysis reveals that an attractive dimorphism will always be evolutionarily stable and that no further branching is possible under this model.     

On the evolution of specialization with a mechanistic underpinning in structured metapopulations

We analyze the evolution of specialization in resource utilization in a discrete-time metapopulation model using the adaptive dynamics approach. The local dynamics in the metapopulation are based on the Beverton-Holt model with mechanistic underpinnings. The consumer faces a trade-off in the abilities to consume two resources that are spatially heterogeneously distributed to patches that are prone to local catastrophes. We explore the factors favoring the spread of generalist or specialist strategies. Increasing fecundity or decreasing catastrophe probability favors the spread of the generalist strategy and increasing environmental heterogeneity enlarges the parameter domain where the evolutionary branching is possible. When there are no catastrophes, increasing emigration diminishes the parameter domain where the evolutionary branching may occur. Otherwise, the effect of emigration on evolutionary dynamics is non-monotonous: both small and large values of emigration probability favor the spread of the specialist strategies whereas the parameter domain where evolutionary branching may occur is largest when the emigration probability has intermediate values. We compare how different forms of spatial heterogeneity and different models of local growth affect the evolutionary dynamics. We show that even small changes in the resource dynamics may have outstanding evolutionary effects to the consumers.     

The adaptive dynamics of the evolution of host resistance to indirectly transmitted microparasites

We use adaptive dynamics and pairwise invadability plots to examine the evolutionary dynamics of host resistance to microparasitic infection transmitted indirectly via free stages. We investigate trade-offs between pathogen transmission rate and intrinsic growth rate. Adaptive dynamics distinguishes various evolutionary outcomes associated with repellors, attractors or branching points. We find criteria corresponding to these and demonstrate that a major factor deciding the evolutionary outcome is whether trade-offs are acceleratingly or deceleratingly costly. We compare and contrast two models and show how the differences between them lead to different evolutionary outcomes.     

Evolution of density-dependent dispersal in a structured metapopulation

We study the evolution of density-dependent dispersal in a structured metapopulation subject to local catastrophes that eradicate local populations. To this end we use the theory of structured metapopulation dynamics and the theory of adaptive dynamics.The set of evolutionarily possible dispersal functions (i.e., emigration rates as a function of the local population density) is derived mechanistically from an underlying resource-consumer model. The local resource dynamics is of a flow-culture type and consumers leave a local population with a constant probability per unit of time κ when searching for resources but not when handling resources (i.e., eating and digesting). The time an individual spends searching (as opposed to handling) depends on the local resource density, which in turn depends on the local consumer density, and so the average per capita emigration rate depends on the local consumer density as well.The derived emigration rates are sigmoid functions of local consumer population density. The parameters of the local resource-consumer dynamics are subject to evolution. In particular, we find that there exists a unique evolutionarily stable and attracting dispersal rate κ^∗ for searching consumers. The κ^∗ increases with local resource productivity and decreases with resource decay rate. The κ^∗ also increases with the survival probability during dispersal, but as a function of the catastrophe rate it reaches a maximum before dropping off to zero again.     

Adaptive dynamics of Lotka-Volterra systems with trade-offs: the role of interspecific parameter dependence in branching

We determine the adaptive dynamics of a general Lotka-Volterra system containing an intraspecific parameter dependency--in the form of an explicit functional trade-off between evolving parameters--and interspecific parameter dependencies--arising from modelling species interactions. We develop expressions for the fitness of a mutant strategy in a multi-species resident environment, the position of the singular strategy in such systems and the non-mixed second-order partial derivatives of the mutant fitness. These expressions can be used to determine the evolutionary behaviour of the system. The type of behaviour expected depends on the curvature of the trade-off function and can be interpreted in a biologically intuitive manner using the rate of acceleration/deceleration of the costs implicit in the trade-off function. We show that for evolutionary branching to occur we require that one (or both) of the traded-off parameters includes an interspecific parameter dependency and that the trade-off function has weakly accelerating costs. This could have important implications for understanding the type of mechanisms that cause speciation. The general theory is motivated by using adaptive dynamics to examine evolution in a predator-prey system. The applicability of the general theory as a tool for examining specific systems is highlighted by calculating the evolutionary behaviour in a three species (prey-predator-predator) system.     

Joint evolution of specialization and dispersal in structured metapopulations

We study the joint evolution of dispersal and specialization concerning resource usage in a mechanistically underpinned structured discrete-time metapopulation model. We show that dispersal significantly affects the evolution of specialization and that specialization is a key factor that determines the possibility of evolutionary branching in dispersal propensity. Allowing both dispersal propensity and specialization to evolve as a consequence of natural selection is necessary in order to understand the evolutionary dynamics. The joint evolution of dispersal and specialization forms a natural evolutionary path leading to the coexistence of generalists and specialists. We show that in this process, the number of different patch types and the resource distribution are essential.     

A game theoretical approach to the evolution of structured communication codes

Structured meaning-signal mappings, i.e., mappings that preserve neighborhood relationships by associating similar signals with similar meanings, are advantageous in an environment where signals are corrupted by noise and sub-optimal meaning inferences are rewarded as well. The evolution of these mappings, however, cannot be explained within a traditional language evolutionary game scenario in which individuals meet randomly because the evolutionary dynamics is trapped in local maxima that do not reflect the structure of the meaning and signal spaces. Here we use a simple game theoretical model to show analytically that when individuals adopting the same communication code meet more frequently than individuals using different codes—a result of the spatial organization of the population—then advantageous linguistic innovations can spread and take over the population. In addition, we report results of simulations in which an individual can communicate only with its K nearest neighbors and show that the probability that the lineage of a mutant that uses a more efficient communication code becomes fixed decreases exponentially with increasing K. These findings support the mother tongue hypothesis that human language evolved as a communication system used among kin, especially between mothers and offspring.     

Antibiotic resistance and the evolution of group-beneficial traits. II: a metapopulation model

Inspired by the evolution of antibiotic resistance in bacteria, we have developed a model that examines the evolution of "producers" (who secrete a substance that breaks down antibiotics) and non-producers. In a previous study, we found that frequency-dependent selection could favor an intermediate frequency of producers in a single, large population. Here we develop a metapopulation model that examines the evolution of producers and non-producers. Our results indicate that in a metapopulation with many groups, each of size N, the equilibrial frequency of producers decreases with group size. Even when N is high (e.g. 150 individuals/group), however, a significant frequency of producers is still predicted. We also found that the equilibrial frequency of producers increases as the minimum numbers of producers necessary to provide protection to non-producers increases. Lastly, increasing the benefit/cost ratio (b/c) for producers increases their equilibrial frequency.     

Adaptive evolution of anti-predator ability promotes the diversity of prey species: critical function analysis

In this paper, with the method of adaptive dynamics and critical function analysis, we investigate the evolutionary diversification of prey species. We assume that prey species can evolve safer strategies such that it can reduce the predation risk, but this has a cost in terms of its reproduction. First, by using the method of critical function analysis, we identify the general properties of trade-off functions that allow for continuously stable strategy and evolutionary branching in the prey strategy. It is found that if the trade-off curve is globally concave, then the evolutionarily singular strategy is continuously stable. However, if the trade-off curve is concave-convex-concave and the prey's sensitivity to crowding is not strong, then the evolutionarily singular strategy may be an evolutionary branching point, near which the resident and mutant prey can coexist and diverge in their strategies. Second, we find that after branching has occurred in the prey strategy, if the trade-off curve is concave-convex-concave, the prey population will eventually evolve into two different types, which can coexist on the long-term evolutionary timescale. The algebraical analysis reveals that an attractive dimorphism will always be evolutionarily stable and that no further branching is possible for the concave-convex-concave trade-off relationship.     

Dispersal delays, predator-prey stability, and the paradox of enrichment

It takes time for individuals to move from place to place. This travel time can be incorporated into metapopulation models via a delay in the interpatch migration term. Such a term has been shown to stabilize the positive equilibrium of the classical Lotka-Volterra predator-prey system with one species (either the predator or the prey) dispersing. We study a more realistic, Rosenzweig-MacArthur, model that includes a carrying capacity for the prey, and saturating functional response for the predator. We show that dispersal delays can stabilize the predator-prey equilibrium point despite the presence of a Type II functional response that is known to be destabilizing. We also show that dispersal delays reduce the amplitude of oscillations when the equilibrium is unstable, and therefore may help resolve the paradox of enrichment.     

The evolution of habitat specialisation in a group of marine triplefin fishes

There has been considerable interest in the directionality of resource specialisation during the diversification of lineages. We developed a quantitative method to investigate habitat specialisation in a radiation of New Zealand triplefin fishes, as habitat use appears to be an important axis of diversification in this marine group. The degree of specialisation in 15 species was calculated by comparing each individual to all other individuals of a species, thus allowing for quantitative distinction between species. Species differed in habitat specialisation, but Bayesian comparative methods found no directional trend in the evolution of resource use. Further analyses showed that specialisation had evolved gradually and was phylogenetically constrained, with most differences between species arising toward the tips of the tree. No correlation between the degree of specialisation and body size was detected in this group, suggesting that habitat specialisation evolved independently of body size. Habitat specialisation does not appear to have been an impediment to ecological diversification in this group. Rather, diversification in these fishes appears to have followed different evolutionary trajectories in habitat specialisation, one in which species have sub-partitioned available resources, and another in which species have expanded their use of resources. These findings support recent studies suggesting that diversification does not necessarily proceed from generalised ancestors to specialised descendants.     

Mutational collapse of fitness in marginal habitats and the evolution of ecological specialisation

In spatially heterogeneous environments, natural selection for maintenance of adaptation to habitats that contribute little to the population's reproduction is weak. In this paper we model a mechanism that can result in loss of fitness in such marginal habitats, and thus lead to specialisation on the main habitat. It involves accumulation of mutations that are deleterious in the marginal habitat but neutral or nearly so in the main habitat (mutations deleterious in the main habitat and neutral in the marginal habitat have a negligible influence). If the contribution of the marginal habitat to total reproduction in the absence of the mutations is less than a threshold value, selection is too weak to counter accumulation of such mutations. A positive feedback then results in loss of fitness in the marginal habitat. This mechanism does not require antagonistic pleiotropy in adaptation to different habitats, although antagonistic pleiotropy facilitates the mutational collapse of fitness in the marginal habitat. We suggest that deleterious mutations with habitat-specific expression may play a role in the evolution of ecological specialisation and promote evolutionary conservatism of ecological niches.     

The Evolution of Resource Adaptation: How Generalist and Specialist Consumers Evolve

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.     

The effect of migration on metapopulation stability is qualitatively unaffected by demographic and spatial heterogeneity

Coupled map lattices (CMLs), using two coupled logistic equations, have been extensively used to model the dynamics of two-patch ecological systems. Such studies have revealed that migration rate plays an important role in determining the dynamics of the system, particularly when the two maps differ in their intrinsic growth rate parameter, r. However, under more realistic assumptions, a metapopulation can be expected to consist of more than two subpopulations, each with its own demographic parameters, which will in part be a function of the environment of that patch. The role of the spatial arrangement of heterogeneous (i.e. with different r values) subpopulations in shaping the dynamics of such a metapopulation has rarely been investigated. Here, we study the effect of demographic and spatial heterogeneity on the stability of one- and two-dimensional systems of 64 coupled Ricker maps with different r values, under periodic and absorbing boundary conditions. We show that the effects of migration rate on metapopulation stability do not depend upon either the precise spatial arrangement of the subpopulations in the lattice, or on the presence of a moderate proportion of vacant (uninhabitable) patches in the lattice. The results, thus, suggest that metapopulation models are robust to variation in spatial arrangement of patch quality and, hence, of demographic parameters. We also show that for any given arrangement of the patches, maximum stability of the metapopulation occurs when the migration levels are intermediate, a result that agrees well with previous studies on two-map CML systems.     

Evolution of life-history traits collapses competitive coexistence

Trade-offs between competitive ability and the other life-history traits are considered to be a major mechanism of competitive coexistence. Many theoretical studies have demonstrated the robustness of such a coexistence mechanism ecologically; however, it is unknown whether the coexistence is robust evolutionarily. Here, we report that evolution of life-history traits not directly related to competition, such as longevity, and predator avoidance, easily collapses competitive coexistence in several competition systems: spatially structured, and predator-mediated two-species competition systems. In addition, we found that a superior competitor can be excluded by an inferior one by common mechanisms among the models. Our results suggest that ecological competitive coexistence due to a life-history trait trade-off balance may not be balanced on an evolutionary timescale, that is, it may be evolutionarily fragile.     

Experimental translocation of juvenile water voles in a Scottish lowland metapopulation

Population density affects dispersal success because residents can hinder or facilitate immigration into a new site, via a “social fence effect” or “social attraction” (or “conspecific attraction”), respectively. These mechanisms can affect the dynamics of fragmented populations and the success of translocations. However, information on the settlement behaviour of dispersers is rare. We conducted a manipulative field experiment using wild water voles, which exist in metapopulations along waterways in Scotland. We translocated 17 young of dispersal age into either an occupied site or a vacant site containing good habitat, which had recently become extinct due to a feral predator (American mink) moving through. We monitored the movements of translocated voles using radio telemetry. Translocated voles were less likely to settle in occupied sites with higher densities of residents, suggesting a possible social fence effect at high density. There was evidence of a social attraction mechanism, because voles never remained at new sites unless another individual arrived soon after translocation, and they were more likely to settle in occupied or colonised sites than vacant ones. Voles remained in the transient phase of dispersal for many days, and often followed a “stepping stone” trajectory, stopping for several days at successive sites. We suggest that trajectories followed by dispersing water voles, the time scale and long dispersal distances found in this species are conducive to locating conspecifics at low density and colonising vacant habitat. These results are encouraging for prospects of metapopulation persistence and future translocation success.