The Sampling Theory of Neutral Alleles in an Island Population of Fluctuating Size

The sampling distribution of neutral alleles under a stochastic birth, death, and immigration (BDI) process, proposed as a model of fluctuating island populations, is studied by analytical methods. A new result is presented for the distribution of allele types in a sample of N individuals from an island when the allele frequencies among immigrants are constant. The sampling distribution of allele types depends on the sample size N, the array of allele frequencies among immigrants p, and the parameter theta=phi/lambda, where phi is the immigration rate and lambda is the individual birth rate. The sampling distribution of alleles does not depend on time or population size, and no "genetic equilibrium" assumption is therefore needed to apply the model to natural populations. The moments of the sampling distribution of allele types are used to calculate the expectation and variance of a sample identity by descent estimate (fN 0) within islands under the BDI model.