The role of epistasis in the increase in the additive genetic variance after population bottlenecks

Abstract

The effect of population bottlenecks on the additive variance generated by two neutral independent epistatic loci has been studied theoretically. Three kinds of epistasis were considered: (1) additive×additive, (2) multiple dominant genotype favoured, and (3) Dobzhansky–Muller type. The additive variance in an infinitely large panmictic population (ancestral variance) was compared with its expected value at equilibrium, after t consecutive bottlenecks of equal size N (derived variance). Formulae were derived in terms of allele frequencies and effects at each locus and the corresponding epistatic effects. An increase in the additive variance after bottlenecks will occur only if its ancestral value is minimal or very small. This has been detected only for: (1) intermediate ancestral allele frequencies at both loci ; (2) extreme ancestral allele frequencies at one or both loci. The magnitude of the excess was inversely related to N and t. With dominance gene action, enhanced additive variance after bottlenecks implies a rise in the genotypic frequency of homozygous deleterious recessives, resulting in inbreeding depression. Considering multiple loci, simultaneous segregation of unfavourable alleles at intermediate frequencies, or of favourable recessives at low frequencies, cannot easily be conceived of unless there is strong genotype–environment interaction. With this possible exception, it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived additive variance over its ancestral value.