Is the between-population variance negligible in the total variance of heterozygosity? Case of a finite number of loci subject to the infinite-allele model in finite monoecious populations

Abstract

The decomposition of the variance of the average heterozygosity into variances between and within populations is studied in the general case of a finite number of loci. These loci are assumed randomly distributed over chromosome pairs having a non-interference recombination scheme, and independently subject to mutation according to the infinite-allele model. The equilibrium behavior of that decomposition is discussed in the monoecious mating case with regard to each parameter of the model: mutation rate per gene per generation ( u), population size ( N), number of loci ( n), map length of chomosome pairs ( L). It is shown that the proportion Q of the between-population variability in the total variance of the average heterozygosity is decreasing as either the mean heterozygosity ( θ = 4 Nu/(1 + 4 Nu)) or the mean number of mutations per gamete per generation ( v = nu) is increasing. Moreover, even if Q is always smaller than 1 3 for this model, it is not negligible unless θ is close to one or v is much larger than one for L long enough.