Zygotic Associations and Multilocus Statistics in a Nonequilibrium Diploid Population

The usual approach to characterizing and estimating multilocus associations in a diploid population assumes that the population is in Hardy-Weinberg equilibrium. The purpose of this study is to develop a set of summary statistics that can be used to characterize and estimate the multilocus associations in a nonequilibrium population. The concept of “zygotic associations” is first expanded to facilitate the development. The summary statistics are calculated using the distribution of a random variable, the number of heterozygous loci (K) found in diploid individuals in the population. In particular, the variance of K consists of single-locus and multilocus components with the latter being the sum of zygotic associations between pairs of loci. Simulation results show that the multilocus associations in the variance of K are detectable in a sample of moderate size (≥30) when the sum of all pairwise zygotic associations is greater than zero and when gene frequency is intermediate. The method presented here is a generalization of the well-known development for the Hardy-Weinberg equilibrium population and thus may be of more general use in elucidating the multilocus organizations in nonequilibrium and equilibrium populations.