ON HETEROZYGOSITY AND THE EFFECTIVE SIZE OF POPULATIONS SUBJECT TO SIZE CHANGES.

Abstract

When a population is subject to fluctuations in size, the effective population number during any time interval is usually approximated by the harmonic mean of the successive generation sizes (Wright, 1938, 1939). If there are no mutations, the population will eventually reach complete homozygosity. The rate at which such a population approaches homozygosity was investigated by Karlin (1968), for stochastic, and also by Chia (1968), for cyclic, deterministic changes in population size. The analysis of homozygosity levels in populations subject to stochastic size changes was extended by Chia and Pollak (1974), who included the possible existence of mutations. For a population recovering from a great reduction in size, Nei et al. (1975) have concluded, using numerical computations and considering the existence of mutations, that the harmonic mean approximation to the effective population number is quite robust. It is our purpose in this note to extend the analyses of Nei et al. (1975) and of Chakraborty and Nei (1977) concerning the robustness of the harmonic mean approximation in situations which take into account the existence of mutations. We propose to do this by investigating cases where a population is subject to cyclic, deterministic changes in size. In such a situation, because the mutation rate is not zero, the expected level of heterozygosity, and hence the effective population number, will change in value throughout the cycle. The harmonic mean approximation, on the other hand, will have, in the steady state, a constant value. However, it will be shown that the harmonic mean is a good approximation in many such cases. Large discrepancies between the expected degree of heterozygosity and the value obtained using the harmonic mean approximation are found in those cases which combine a bottleneck of a very small population size together with a long cycle period. Also demonstrated here is the effect of repeated bottlenecks on greatly reducing the expected level of heterozygosity of the population.