A Neutral Model With Fluctuating Population Size and Its Effective Size

We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.