Multilocus Migration-Selection Models

Many natural populations are geographically structured and selection varies spatially due to environmental heterogeneity. Population subdivision is known to have numerous important evolutionary consequences. For instance, it has the capacity to maintain genetic variation, it may lead to ecological specialization and, eventually, to speciation. The effects of geographic structure, dispersal, and spatially varying selection are reasonably well understood only if a single locus is under selection. Most ecologically and evolutionary important traits, however, are quantitative and are determined by many gene loci. This project is devoted to the analysis of population-genetic models that describe evolution under the combined action of migration, recombination, and selection on multilocus genotypes. Such models are usually formulated in terms of systems of (nonlinear) difference or differential equations. There are two interrelated goals that shall be achieved. The first is the identification of conditions under which multilocus polymorphism can be maintained by a balance between migration and selection, especially when this is impossible in a panmictic population. The second is the identification of conditions that generate or enhance local adaptation and genetic diversification at multiple loci. Both goals require the determination of the pattern and amount of genetic variation at evolutionary equilibrium. This shall be achieved by concentrating research on three ecologically motivated scenarios: a spatially heterogeneous environment but no population structure (the Levene model), antagonistic directional selection in a population distributed over two demes connected by migration, and stabilizing selection on a quantitative trait, where the optimum may vary among demes. Methodologically, this shall be achieved by applying techniques from the theory of dynamical systems to explore the equilibrium, stability, and bifurcation structure of the underlying models. Comprehensive computational studies will complement the analytical work.

Natural populations are often geographically structured and experience a variety of environmental conditions. Selection caused by environmental heterogeneity may have important consequences for the evolution of spatially subdivided populations. On the one hand, genetic diversity may be enhanced in such populations if different genetic types are favoured in different environments. On the other hand, adaptation to local environments and reduced dispersal between subpopulations may lead to increasingly strong differentiation and, eventually, to speciation.In this project, population-genetic models were analyzed mathematically that describe evolution under the combined action of migration, recombination, and selection on traits determined by many gene loci. One line of research identified conditions under which either polymorphism at multiple loci or polymorphism of multiple alleles can be maintained by a balance between migration and environmentally heterogeneous selection when this is impossible in a uniform environment. For instance, even if dispersal among subpopulations is so high that they are genetically homogeneous, spatially heterogeneous selection can maintain polymorphism at many loci provided different alleles are favored in different environments and they are partially dominant where they are beneficial. Thus, dominance relations and genotype-environment interaction play an important role for the maintenance of genetic variation under such conditions.In a second line of research, the evolution of local adaptation and genetic differentiation between subpopulations was investigated. It could be shown that the most favorable genetic setting for increasing local adaptation and differentiation is one in which new, locally adaptive mutants occur in close physical proximity to loci that are already selectively contributing to differentiation. Thus, clusters of locally adaptive genes are expected to emerge. These findings have interesting consequences for the evolution of genetic architecture and of mechanisms that reduce recombination, such as chromosome inversions.