ABSTRACT

Dobzhansky's model of epistatic selection assumes that viable genotypes form ``clusters'' in genotype space so that populations can evolve from one state to a reproductively isolated state following a ``ridge'' of well-fit genotypes without crossing any deep adaptive valleys. Recently, the importance of Dobzhansky-type models in evolutionary studies has been re-emphasized by Gavrilets (1997) and Gavrilets and Gravner (1997) who argue that the existence of ``ridges'' of well-fit genotypes connecting reproductively isolated genotypes, which was postulated by Dobzhansky, is actually a general property of multidimensional adaptive landscapes. Using rigorous techniques and numerical simulations I analyze clines in the frequencies of selected and neutral alleles maintained by a balance of migration and Dobzhansky-type epistatic selection acting on two diallelic loci. I show that Dobzhansky-type epistatic selection can build up a very strong barrier to neutral gene flow. I describe properties of clines that are indicative of Dobzhansky-type selection.