Effects of cyclic changes in population size on neutral genetic diversity

Recurrent changes in population size are often observed in nature, influencing the efficiency of selection and consequently affecting organismal evolution. Thus, it is important to know whether such changes occurred in the past history of a focal population of evolutionary interests. Here, we focused on cyclic changes in population size and investigated the distributional properties of Tajima's D and its power to distinguish a cyclic change model compared with the standard neutral model, changing the frequency and magnitude of the cyclic change. With very low or very high frequencies of the cycle, the distribution of Tajima's D was similar to that in a constant size population, as demonstrated by previous theoretical works. Otherwise, its mean was negative or positive, and its variance was smaller or larger depending on the time of sampling. The detection rate of the cyclic change against the constancy in size by Tajima's D depended on the sample size, the number of loci, and the time of sampling in addition to the frequency and amplitude of the cycle. Using sequence data of several tens of loci, the detection rate was fairly high if the frequency was intermediate and the sampling was made when population size was large; otherwise, the detection rate was not high. We also found that cyclic change could be discriminated from simple expansion or shrinkage of a population by Tajima's D only if the frequency was in a limited range and the sampling was made when the population was large.