Detecting selection-induced departures from Hardy-Weinberg proportions

Natural selection modifies the probabilities that alleles are found in either homozygous or heterozygous form. Given that one allele is A, what is the probability that the homologous copy of this gene is also A? In Hardy-Weinberg populations this is simply equal to p, the allele frequency of the A allele. When the assumptions of the Hardy-Weinberg principle are violated, such as when viability selection is present, this result cannot be expected to hold. While this has been known for decades, many current studies assume Hardy-Weinberg proportions (p2 : 2pq : q2) without explicitly considering the impact of selection. When viability selection results in significant departures from Hardy Weinberg (DHW), the genetic footprint of natural selection can be observed in sequence data [1-3]. Tests of Hardy-Weinberg proportions have been used to detect genotyping errors [4-6]. However, it is an open question whether natural selection confounds such tests. Consequently, one can ask: When does natural selection result in significant departures from Hardy-Weinberg proportions?Population genetics theory indicates that when fitnesses are non-multiplicative (wAB2 ≠ wAAwBB), genotype frequencies differ from Hardy-Weinberg proportions [7]. For example, one expects to only find post-selection copies of a recessive lethal in heterozygotes. While equations describing genotypic frequencies in terms of allele frequencies are deducible for overdominance, mutation-selection balance, and other equilibria, existing theory is lacking when it comes to non-equilibrium populations [8]. There is a need to determine when viability selection leads to significant departures from Hardy-Weinberg proportions [9]. Classical population genetics contains recursion equations that describe post-selection genotype frequencies in terms of pre-selection allele frequencies. However, DHW calculations require allele and genotype frequencies to be from the same time point (i.e. post-selection). In this paper popula