Abstract
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 8 N/ E[ G 1( G 1 − 1)] = 2 N 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 e → ∞. 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 → ∞.
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