A two-locus model of spatially varying stabilizing or directional selection on a quantitative trait

The consequences of spatially varying, stabilizing or directional selection on a quantitative trait in a subdivided population are studied. A deterministic two-locus two-deme model is employed to explore the effects of migration, the degree of divergent selection, and the genetic architecture, i.e., the recombination rate and ratio of locus effects, on the maintenance of genetic variation. The possible equilibrium configurations are determined as functions of the migration rate. They depend crucially on the strength of divergent selection and the genetic architecture. The maximum migration rates are investigated below which a stable fully polymorphic equilibrium or a stable single-locus polymorphism can exist. Under stabilizing selection, but with different optima in the demes, strong recombination may facilitate the maintenance of polymorphism. However usually, and in particular with directional selection in opposite direction, the critical migration rates are maximized by a concentrated genetic architecture, i.e., by a major locus and a tightly linked minor one. Thus, complementing previous work on the evolution of genetic architectures in subdivided populations subject to diversifying selection, it is shown that concentrated architectures may aid the maintenance of polymorphism. Conditions are obtained when this is the case. Finally, the dependence of the phenotypic variance, linkage disequilibrium, and various measures of local adaptation and differentiation on the parameters is elaborated.