The effect of population bottlenecks on the components of the genetic variance generated by two neutral independent epistatic loci has been studied theoretically (V_A, additive; V_D, dominant; V_AA, additive × additive; V_AD, additive × dominant; V_DD; dominant × dominant components of variance). Nonoverdominance and overdominance models were considered, covering all possible types of marginal gene action at the single locus level. The variance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of allele frequencies and effects at each locus and the corresponding epistatic value. An excess of V_A after bottlenecks can be assigned to two sources: (1) the spatiotemporal changes in the marginal average effects of gene substitution α_i, which are equal to zero only for additive gene action within and between loci; and (2) the covariance between α_i² and the heterozygosity at the loci involved, which is generated by dominance, with or without epistasis. Numerical examples were analyzed, indicating that an increase in V_A after bottlenecks will only occur if its ancestral value is minimal or very small. For the nonoverdominance model with weak reinforcing epistasis, that increase has been detected only for extreme frequencies of the negative allele at one or both loci. With strong epistasis, however, this result can be extended to a broad range of intermediate frequencies. With no epistasis, the same qualitative results were found, indicating that dominance can be considered as the primary cause of an increase in V_A following bottlenecks. In parallel, the derived total nonadditive variance exceeded its ancestral value (V_NA = V_D V_AA V_AD V_DD) for a range of combinations of allele frequencies covering those for an excess of V_A and for very large frequencies of the negative allele at both loci. For the overdominance model, an increase in V_A and V_NA was respectively observed for equilibrium (intermediate) frequencies at one or both loci or for extreme frequencies at both loci. For all models, the magnitude of the change of V_A and V_NA was inversely related to N and t. At low levels of inbreeding, the between-line variance was not affected by the type of gene action. For the models considered, the results indicate that it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived V_A over its ancestral value.

Corresponding Editor: S. Tonsor