Abstract
The amount of variability in a population that experiences repeated restrictions in population size has been calculated. The restrictions in size occur cyclically with a fixed cycle length. Analytical formulas for describing the gene identity at any specific time in the expanded and restricted phases of the cycle, and for the average and second moment of the gene identity, have been derived. It is shown that the level of genetic diversity depends critically on the two parameters that account for the population size, mutation rate and the time of duration for each of the two phases in the cycle. If one or both of these composite parameters are small, the gene diversity will be much reduced, and population gene diversity will then be predictable from knowledge of the harmonic mean population size over the entire cycle. If these parameters take on intermediate values, diversity changes constantly during the cycle, fluctuating steadily from a high to a low value and back again. If these parameters are large, gene diversity will fluctuate rapidly between extreme values and will stay at the extremes for long periods of time.