The effect of linkage disequilibrium and deviation from Hardy-Weinberg proportions on the changes in genetic variance with bottlenecking

A growing body of experimental work has shown that the additive genetic variance of fitness components can increase following a founder event or a bottleneck of population size. This is usually explained theoretically by the conversion of dominance variance and/or epistatic variance to additive variance following bottlenecks. The present analysis considers the effects of deviation from Hardy-Weinberg proportions (DHW) and linkage disequilibrium (LD) caused by bottlenecks. It is shown that DHW may also cause an increase in the additive variance for rare recessive genes, the largest increase arising with completely recessive genes of low initial frequency in intermediate-sized populations. LD among nonadditive loci results in a large increase in genotypic variance and also a small increase in additive variance. Even for the case of no linkage among the loci and linkage equilibrium in the ancestral population, severe bottlenecks result in a significant increase in genotypic variance as a result of LD among dominant loci. More restrictive conditions (many linked loci with large dominance coefficients and rare recessive genes), however, are required for LD to cause an evident increase in the additive variance. The effects of LD on genetic variances enhance with an increase in number of loci and dominance coefficients and with a decrease in recombination fractions, bottleneck sizes and initial recessive gene frequencies. Although the effects of LD on genetic variance decline gradually in the flush population, they may persist for some generations, especially when there is high linkage among the relevant loci.