Efficient test for deviation from Hardy Weinberg Equilibrium with known or ambiguous typing in highly polymorphic loci
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The Hardy-Weinberg Equilibrium (HWE) assumption is essential to many population genetics models. Multiple tests were developed to test its applicability in observed genotypes. Current methods are divided into exact tests applicable to small populations and a small number of alleles, and approximate goodness of fit tests. Existing tests cannot handle ambiguous typing in multi-allelic loci.
We here present a novel exact test (UMAT - Unambiguous Multi Allelic Test) practically not limited in the number of alleles and population size, based on a perturbative approach around the current observations. We show its accuracy in the detection of deviation from HWE.
We then propose an additional model to handle ambiguous typing using either sampling into UMAT or a goodness of fit test with a variance estimate taking ambiguity into account, named ASTA (Asymptotic Statistical Test with Ambiguity). We show the accuracy of ASTA and the possibility to detect of the source of deviation from HWE.
We apply these tests to the HLA loci to recover multiple previously reported deviations from HWE, and a large number of new ones.
Author summary
Random mating of individuals in a fixed population leads to a Hardy-Weinberg Equilibrium (HWE) of the genotype composition, where the probability of a pair of alleles is simply the product of their probabilities.
However, often populations deviate from HWE. Such a deviation can be the result of a structured population, where alleles are more frequent in one part of the population, from selection favoring combinations of alleles, or from homozygotes or heterozygote advantages.
Current methods to measure the deviation from HWE are limited to a small number of alleles. We here propose methods to measure this deviation in muli-allele loci and handle ambiguous typing. We use these methods to measure the alleles associated with deviation from HWE in the HLA loci in different populations.
