Adaptive Dynamics in Allele Space: Evolution of Genetic Polymorphism by Small Mutations in a Heterogeneous Environment

We investigate how a plymorphism of distinctly different alleles can evolve in an initially monomorphic population under frequency-dependent selection if mutations have only a small phenotypic effect. We consider the case of a single additive locus with a continuum of potential allele types in a diploid outbreeding population. As a specific example, we use a version of Levene's (1953) soft selection model, where stabilizing selection acts on a continuous trait within each of two habitats. If the optimal phenotypes within the habitats are sufficiently different, then two distinctly different alleles evolve gradually from a single ancestral allele. In a wide range of parameter values, the two locally optimal phenotypes will be realized by one of the homozygotes and the heterozygote, rather than the two homozygotes. Unlike the haploid analogue of the model, there can be multiple polymorphic evolutionary attractors with different probabilities of convergence

Red Queen Evolution by Cycles of Evolutionary Branching and Extinction

We use the theory of adaptive dynamics to construct and analyse a generic example of cycling evolution with alternating levels of polymorphism. A monomorphic population evolves towards larger trait values until it reaches a so-called evolutionary branching point. Disruptive selection at the branching point splits the population into two strategies. In the dimorphic population the strategies undergo parallel coevolution towards smaller trait values. Finally one of the two strategies goes extinct, and the remaining single strategy evolves upwards again to the branching point. The reversal of the direction of evolution is brought about by the changing level of polymorphism. Extinction is deterministic, i.e., it occurs inevitably and always at the same trait values; which of the two strategies goes extinct is, however, random. The present model is discussed in relation to other mechanisms for evolutionary cycles involving branching and extinction

The Dynamics of Adaptation and Evolutionary Branching

We present a formal framework for modeling evolutionary dynamics with special emphasis on the generation of diversity through branching of the evolutionary tree. Fitness is defined as the long term growth rate which is influenced by the biotic environment leading to frequency-dependent selection. Evolution can be described as a dynamics in space with variable number of dimensions corresponding to the number of different types present. The dynamics within a subspace is governed by the local fitness gradient. Entering a higher dimensional subspace is possible only at a particular type of attractors where the population undergoes evolutionary branching

Evolutionary Optimization Models and Matrix Games in the Unified Perspective of Adaptive Dynamics

Matrix game theory and optimization models offer two radically different perspectives on the outcome of evolution. Optimization models consider frequency-independent selection and envisage evolution as a hill-climbing process on a constant fitness landscape, with the optimal strategy corresponding to the fitness maximum. By contrast, in evolutionary matrix games selection is frequency-dependent and leads to fitness equality among alternative strategies once an evolutionarily stable strategy has been established. In this review we demonstrate that both optimization models and matrix games represent special cases within the general framework of adaptive dynamics. Adaptive dynamics theory considers arbitrary nonlinear frequency and density dependence and envisages evolution as proceeding on an adaptive landscape that changes its shape according to which strategies are present in the population. In adaptive dynamics, evolutionarily stable strategies correspond to conditional fitness maxima: the ESS is characterized by the fact that it has the highest fitness if it is the established strategy. In this framework it can also be shown that dynamical attainability, evolutionary stability, and invading potential of strategies are pairwise independent properties. In optimization models, on the other hand, these properties become linked such that the optimal strategy is always attracting, evolutionarily stable and can invade any other strategy. In matrix games fitness is a linear function of the potentially invading strategy and can thus never exhibit an interior maximum: Instead, the fitness landscape is a plane that becomes horizontal once the ESS is established. Due to this degeneracy, invading potential is part of the ESS definition for matrix games and dynamical attainability is a dependent property. We conclude that adaptive dynamics provides a unifying framework for overcoming the traditional divide between evolutionary optimization models and matrix games

Polymorphic evolution sequence and evolutionary branching

We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the population process is approximated in the long time scale of mutations by a Markov pure jump process describing the successive trait equilibria of the population. This process, which generalizes the so-called trait substitution sequence, is called polymorphic evolution sequence. Then we introduce a scaling of the size of mutations and we study the polymorphic evolution sequence in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. To this end we finely analyze the asymptotic behavior of 3-dimensional competitive Lotka-Volterra systems

Species Invasion History Influences Community Evolution in a Tri-Trophic Food Web Model

Background: Recent experimental studies have demonstrated the importance of invasion history for evolutionary formation of community. However, only few theoretical studies on community evolution have focused on such views. Methodology and Principal Findings: We used a tri-trophic food web model to analyze the coevolutionary effects of ecological invasions by a mutant and by a predator and/or resource species of a native consumer species community and found that ecological invasions can lead to various evolutionary histories. The invasion of a predator makes multiple evolutionary community histories possible, and the evolutionary history followed can determine both the invasion success of the predator into the native community and the fate of the community. A slight difference in the timing of an ecological invasion can lead to a greatly different fate. In addition, even greatly different community histories can converge as a result of environmental changes such as a predator trait shift or a productivity change. Furthermore, the changes to the evolutionary history may be irreversible. Conclusions and Significance: Our modeling results suggest that the timing of ecological invasion of a species into a focal community can largely change the evolutionary consequences of the community. Our approach based on adaptive dynamics will be a useful tool to understand the effect of invasion history on evolutionary formation of community

Speciation Along Environmental Gradients

Traditional discussions of speciation are based on geographical patterns of species ranges. In allopatric speciation, long-term geographical isolation generates reproductively isolated and spatially segregated descendant species. In the absence of geographical barriers, diversification is hindered by gene flow. Yet a growing body of phylogenetic and experimental data suggests that closely related species often occur in sympatry or have adjacent ranges in regions over which environmental changes are gradual and do not prevent gene flow. Theory has identified a variety of evolutionary processes that can result in speciation under sympatric conditions, with some recent advances concentrating on the phenomenon of evolutionary branching. Here we establish a link between geographical patterns and ecological processes of speciation by studying evolutionary branching in spatially structured populations. We show that along an environmental gradient, evolutionary branching can occur much more easily than in non-spatial models. This facilitation is most pronounced for gradients of intermediate slope. Moreover, spatial evolutionary branching readily generates patterns of spatial segregation and abutment between the emerging species. Our results highlight the importance of local processes of adaptive divergence for geographical patterns of speciation, and caution against pitfalls of inferring past speciation processes from present biogeographical patterns

Malthusian assumptions, Boserupian response in models of the transitions to agriculture

In the many transitions from foraging to agropastoralism it is debated whether the primary drivers are innovations in technology or increases of population. The driver discussion traditionally separates Malthusian (technology driven) from Boserupian (population driven) theories. I present a numerical model of the transitions to agriculture and discuss this model in the light of the population versus technology debate and in Boserup's analytical framework in development theory. Although my model is based on ecological -Neomalthusian- principles, the coevolutionary positive feedback relationship between technology and population results in a seemingly Boserupian response: innovation is greatest when population pressure is highest. This outcome is not only visible in the theory-driven reduced model, but is also present in a corresponding "real world" simulator which was tested against archaeological data, demonstrating the relevance and validity of the coevolutionary model. The lesson to be learned is that not all that acts Boserupian needs Boserup at its core.Comment: Chapter in: "Society, Nature and History: The Legacy of Ester Boserup", Springer, Vienna (in press