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Abstract:
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Consider a random mating monoecious diploid population that has N individuals in each generation.I 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 G1,...,GN, 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[ G1( G1-1)] = 2Ne generations, where Ne is the effective population size, the separate copies of a gene ancestral to those at time 0 are almost certain to come from separate individuals as Ne tends to infinity. It is then possible to obtain a generalization of coalescent theory for haploid populations if the distribution of G1 has a finite second moment and its third moment divided by N approaches 0 as N tends to infinity.
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