Coalescent theory for a completely random mating monoecious population

Consider a large random mating monoecious diploid population that has N individuals in each generation. Let us assume that at time 0 a random sample of n << N copies of a gene are taken from this population. It is also assumed that G(1),..., G(N), the numbers of successful gametes produced by parents 1,... N, are exchangeable random variables. It is shown that if time is measured backward in units of 8N/E[G(1)(G(1) - 1)] = 2N(e) generations, where N-e is the effective population size, the separate copies of a gene ancestral to those observed at time 0 are almost certain to come from separate individuals as N, -> infinity. It is then possible to obtain a generalization of coalescent theory for haploid populations if the distribution of G(1) has a finite second moment and E[G(1)(3)]/N -> 0 as N -> infinity. (c) 2006 Elsevier Inc. All rights reserved.