Rare Alleles and Selection

A subpopulation of rare alleles is considered. The subpopulation is part of a large population that evolves according to a Moran model with selection and growth. Conditional on the current frequency, q, of the rare allele, an approximation to the distribution of the genealogy of is derived. In particular, the density of the age, T1, of the rare allele is approximated. It is shown that time naturally is measured in units of qN(0) generations, where N(0) is the present day population size, and that the distribution of the genealogy of depends on the compound parameters ρ=rqN(0) and σ=sqN(0) only. Here, s is the fitness per generation of heterozygote carriers of the rare allele and r is the growth rate per generation of the population. Amongst more, it is shown that for constant population size (ρ=0) the distribution of depends on σ only through the absolute value σ, not the direction of selection.