GENE INTERACTION AFFECTS THE ADDITIVE GENETIC VARIANCE IN SUBDIVIDED POPULATIONS WITH MIGRATION AND EXTINCTION

Abstract

We investigated the effect of nonadditive genetic variance on the amount of additive genetic variance within local populations in an infinite-allele, infinite-island model with migration, extinction, and recolonization, using two-locus descent measures. For an island model with extinction, one- and two-locus descent measures are expressed in a matrix form that allows equilibrium solutions to be calculated similar to previous work on Wright's F-statistics. In a subdivided population, the additive genetic variation within a local deme depends on the dominance and epistatic genetic variation in the species. Moreover, to a good approximation, the amount of additive variance within a deme is a simple function of F_st , which is twice the demic fraction of genic variance. At equilibrium, it is equal to (1 - F_st ) V_A plus 4 F_st (1 - F_st ) V_A×A , where V_A and V_A×A are the additive and additive × additive epistatic variances at the level of the species, respectively, plus a contribution from the dominance variance and other terms including dominance. Paradoxically, with nonadditive genetic effects, drift on average increases the amount of additive genetic variance within populations, whereas migration decreases the equilibrium amount. In the presence of nonadditive genetic effects, measurements of additive genetic variance in natural populations must be taken at the proper spatial scale with respect to natural selection, or they will provide an inaccurate description of evolutionary potential both within local populations and within the species as a whole.

Keywords: Descent measures; dominance; epistasis; extinction and recolonization; genetic variance; migration; population structure; random genetic drift.