The effective number of a population that varies cyclically in size. I. Discrete generations

We consider a dioecious population having numbers of males and females that vary over time in cycles of length k. It is shown that if k is small in co mparison with the numbers of males and females in any generation of the cyc le, the effective population number (or size), N-e, is approximately equal to the harmonic mean of the effective population sizes during any given cyc le. This result holds whether the locus under consideration is autosomal or sex-linked and whether inbreeding effective population numbers or variance effective population numbers are involved in the calculation of N-e,. If, however, only two successive gen erations in the cycle are considered and t he population changes in size between these generations, the inbreeding eff ective population number, N-el, differs from the variance effective populat ion number, N-eV. The mutation effective population number turns out to be the same as the number derived using calculations involving probabilities o f identity by descent. It is also shown that, at least in one special case, the eigenvalue effective population number is the same as N-eV. (C) 2000 P ublished by Elsevier Science Inc. All rights reserved.