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 geneti c variance of fitness components can increase following a founder even t or a bottleneck of population size. This is usually explained theore tically by the conversion of dominance variance and/or epistatic varia nce to additive variance following bottlenecks. The present analysis c onsiders the effects of deviation from Hardy-Weinberg proportions (DHW ) and linkage disequilibrium (LD) caused by bottlenecks. It is shown t hat DHW may also cause an increase in the additive variance for rare r ecessive 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 varian ce and also a small increase in additive variance. Even for the case o f no linkage among the loci and linkage equilibrium in the ancestral p opulation, severe bottlenecks result in a significant increase in geno typic variance as a result of LD among dominant loci. More restrictive conditions (many linked loci with large dominance coefficients and ra re recessive genes), however, are required for LD to cause an evident increase in the additive variance. The effects of LD on genetic varian ces enhance with an increase in number of loci and dominance coefficie nts and with a decrease in recombination fractions, bottleneck sizes a nd initial recessive gene frequencies. Although the effects of LD on g enetic variance decline gradually in the flush population, they may pe rsist for some generations, especially when there is high linkage amon g the relevant loci.