[For the entire collection see Zbl 0553.00010.]
W. J. Ewens [Theor. Popul. Biol. 3, 87-112 (1972; Zbl 0245.92009)] has originated a sampling theory of selectively neutral alleles in order to test wether observed patterns of variability are due to selection or are merely the outcome from random sampling (i.e. if they are consistent with the neutrality hypothesis).
In this paper the author extends the theory to populations that vary in size. More precisely, he considers a monoecious population of varying size that reproduces in each generation according to the Wrigth-Fisher model and assumes that the population size follows a finite irreducible Markov chain. Within this framework, an expression for the effective population number \(N_ e\) is derived which replaces the constant population number in Ewens sampling theory.
Furthermore, equations are obtained that either confirm or generalize earlier results in the literature such as probabilities of homozygosity, between population variance of sample homozygosity, and probabilities of configurations in which alleles are identical by descent.