Effective Size of Age-Structured Populations with Cyclic Change in Size

Abstract

Assuming a random mating population of monoecious diploid, I derived an expression for the effective size of an age-structured population that varies the size over time in cycles of a given length. From the asymptotic contributions of age groups to the coancestry after many repetitions of cycles, an equation for the effective population size per cycle was derived, which showed a different expression from the previously published equation. Effect of the discrepancy was numerically evaluated with a hypothetical ladybird population with seasonal periodicity in size. The equation derived in this study gave a reasonably precise value, while the published one underestimated the effective size. The effect of estimation error of the census population size on the estimate of the effective size was also evaluated with the obtained formulae.