Efficient test for deviation from Hardy Weinberg Equilibrium with known or ambiguous typing in highly polymorphic loci

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.