Genealogical theory for random mating populations with two sexes.

Consider a random mating population that has N(m) males and N(f) females in each generation. Let us assume that at time 0 a random sample of n copies of a gene is taken from this population. Then, for models introduced by Wright [Evolution in Mendelian populations, Genetics 16 (1931) 97; Inbreeding and homozygosis, Proc. Nat. Acad. Wash. 19 (1933) 420; Evolution and the Genetics of Populations, The Theory of Gene Frequencies, vol. II, The University of Chicago, Chicago and London, 1969.], it is possible to obtain generalizations of the haploid theory of genealogical processes developed by Felsenstein . It is conjectured that these hold generally, regardless of the effective population size, if n<<min(N(m),N(f)). Generalizations are also proved to hold if n=2.