On the Effect of Founder Events on Epistatic Genetic Variance

Mayr (1963) proposed that small isolated propagules from a large panmictic population would occasionally undergo a genetic revolution due to loss of genetic variability. More recently Templeton (1980a) has suggested that founder events may be much more important in systems that have strong epistasis. Because of the work of these and other authors it becomes an interesting theoretical problem to study the distribution of epistatic variance in a population following a founder event. In the model presented here measures of coancestry (Cockerham, 1967, 1984; Cockerham and Weir, 1973; Weir and Cockerham, 1973, 1977; Tachida and Cockerham, unpubl.) are used to examine the effect of founder events on additive-by-additive epistasis. Using this approach, the coancestries, or intraclass correlations, within individuals and within demes, together with the genetic variance components in the ancestral population are used to obtain the variance within and among demes following a founder event. Examples are analyzed for single founder events of 1-25 individuals and multiple founder events of two individuals. Following a single founder event, the contribution of the additive variance to the variance within demes relative to the additive variance in the ancestral population is always less than one. However, the contribution of epistatic variance to the variance within demes relative to the epistatic variance in the ancestral population is always greater than one. Thus, while a founder event decreases the contribution of additive variance to the variance within demes, it increases the contribution of epistatic variance to the variance within demes. The contribution of epistatic variance to the variance among demes following a single founder event is not qualitatively different from the contribution of additive variance to the variance among demes. These results indicate that epistatic variance is less likely than additive variance to cause a genetic revolution following a single founder event. When populations undergo multiple founder events the situation changes considerably. Epistatic variance may contribute as much as four times its original value to the variance among demes, while additive variance can contribute maximally twice its original value to the variance among demes. Thus, epistasis, which is relatively unimportant following a single founder event, may have major evolutionary implications if drift is allowed to continue for several generations.