infinite-site model

Kimura M 1969 The number of heterozygous nucleotide sites maintained in a finite population due to steady flux of mutations. Genetics 61:893-903.

• the probability of a particular site being heterozygous for a selectively neutral mutant is 4N_eu
• u is of the order 10^{− 9} whereas N_e is probably less than 10⁵
• u (i.e. u = v / total number of sites) is the mutation rate per site
• so 4N_eu is completely adequate
• a cistron of 1000 sites will be heterozygous at one or more sites with probability 1 − (1 − 4N_eu)¹⁰⁰⁰ ≈ 1 − e^{− 4000N_eu}
• Kimura and Crow (1964) and Kimura (1968b) showed that for a model in which each new mutant per cistron is not previously represented in the population—a model that should be almost equivalent to the present model—the heterozygosity is 4N_eU / (1 + 4N_eU)
• U is the mutation rate per cistron
• the lack of correspondence between 1 − e^{− 4N_eU} and 4N_eU / (1 + 4N_eU) is because the first permits each site to come to equilibrium independently whereas the second regards all sites as completely linked
• if the number of heterozygous sites per individual is of interest, the formula of the present paper is appropriate