The effect of genetic drift on the variance/covariance components generated by multilocus additive×additive epistatic systems

Abstract

The effect of population bottlenecks on the components of the genetic variance/covariance generated by n neutral independent additive×additive loci has been studied theoretically. In its simplest version, this situation can be modelled by specifying the allele frequencies and homozygous effects at each locus, and an additional factor measuring the strength of the n-th order epistatic interaction. The variance/covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t bottlenecks of size N (derived components). Formulae were obtained giving the derived components (and the between-line variance) as functions of the ancestral ones (alternatively, in terms of allele frequencies and effects) and the corresponding inbreeding coefficient F t . The n-th order derived component of the genetic variance/covariance is continuously eroded by inbreeding, but the remaining components may increase initially until a critical F t value is attained, which is inversely related to the order of the pertinent component, and subsequently decline to zero. These changes can be assigned to the between-line variances/covariances of gene substitution and epistatic effects induced by drift. Numerical examples indicate that: (1) the derived additive variance/covariance component will generally exceed its ancestral value unless epistasis is weak; (2) the derived epistatic variance/covariance components will generally exceed their ancestral values unless allele frequencies are extreme; (3) for systems showing equal ancestral additive and total non-additive variance/covariance components, those including a smaller number of epistatic loci may generate a larger excess in additive variance/covariance after bottlenecks than others involving a larger number of loci, provided that F t is low. Our results indicate that it is unlikely that the rate of evolution may be significantly accelerated after population bottlenecks, in spite of occasional increments of the derived additive variance over its ancestral value.