| Abstract: |
| We study a system of semilinear parabolic partial differential equations which describes the evolution of gamete frequencies in a geographically structured population of migrating individuals. Fitness of individuals is determined by two recombining, diallelic genetic loci that are subject to spatially varying selection. Migration is modeled by diffusion. Of most interest are spatially non-constant stationary solutions, so-called clines. In a two-locus cline, all four gametes are present in the population. The key problem is the study of existence, uniqueness, and stability of two-locus clines and how their existence and properties depend on the interaction of diffusion, selection, and recombination. We provide conditions for existence and linear stability of a two-locus cline if recombination is either sufficiently weak or sufficiently strong relative to selection and diffusion. For strong recombination, we also prove uniqueness and global asymptotic stability. For arbitrary recombination, we determine the stability properties of the monomorphic equilibria, which represent fixation of a single gamete. |
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