THE PROBABILITY OF PEAK SHIFTS IN A FOUNDER POPULATION. II. AN ADDITIVE POLYGENIC TRAIT

Stochastic shifts between two alternative stable equilibria in an additive polygenic system are modelled. The effect of selection on the character is represented by a double-peaked function relating individual fitness to phenotypic value. The mean of a large population will equilibrate near one of the two peaks, although with weak selection there may be a substantial displacement from the closest peak, due to the attraction exerted by the other peak. It is assumed that a small population is founded as a random sample from a large population at equilibrium under selection, and that genetic drift and selection interact to determine the evolution of the mean and variance of the polygenic character during the phase of exponential population growth that follows the foundation of the population. The effects on the frequencies of peak shifts of selectively induced linkage disequilibrium, randomly induced linkage disequilibrium, and random deviations from Hardy-Weinberg equilibrium are investigated by computer simulation. The results are compared with the probabilities of shifts calculated by an approximate analytic method. It is found that the approximations are reasonably accurate when the heights of the peaks in fitness are similar, but the approximations fail when one of the peaks is much higher than the other. The probability of a peak shift is shown to be a decreasing function of the strength of selection on the character. Although substantial changes in phenotypic mean can be induced by a founder event, the probability of a peak shift that induces a significant degree of reproductive isolation is low. The significance of these findings in relation to theories of speciation is discussed.