A straightforward multiallelic significance test for the Hardy-Weinberg equilibrium law

Abstract

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes.

Genetic signature of a severe forest fire on the endangered Gran Canaria blue chaffinch (Fringilla teydea polatzeki)

“…Observed (H O ) and expected (H E ) heterozygosity, as well as deviations from Hardy-Weinberg equilibrium (HWE) and the presence of linkage disequilibrium (LD) between loci were assessed with ARLEQUIN 3.11 (Excoffier and Schneider 2005). Deviations were considered significant at P \ 0.01, because test statistics have been shown to underestimate the error rate for both multiallelic data and small sample sizes (Lauretto et al 2009). Sequential Bonferroni correction (Rice 1989) was applied to obtain critical confidence limits for multiple comparisons, with an initial a of 0.01.…”

Genetic diversity following demographic recovery in the insular endemic plant Galium catalinense subspecies acrispum

“…1 Rousset 1995). Deviations were considered significant at P \ 0.01, because the test statistics have been shown to underestimate the error rate for both multiallelic data and small sample sizes (Lauretto et al 2009). Selfing rates were estimated with RMES (David et al 2007).…”

A Fundamental Statistical Tools Application for Livestock Diversity Studies from Microsatellite Data—A Mini Review

“…The Hardy Weinberg law defines a direct relationship between allele and genotypic proportions in a population [26]. This law states that for all loci except for sex chromosomes in diploid organisms, HWE is attained from one to next generation with the underlying conditions that the population is not under any gene force (non-random mating, selection for genotypes, migration and mutations), infinite population size and equal fertility of parent genotypes [20].…”

“…Goodness of fit such as chi square ratio ( 2 χ ) is commonly used to test if the population is in HWE for its simplicity which is based mainly on sample sizes [26] [27] and allele numbers [26] [28].…”