Performing the Exact Test of Hardy-Weinberg Proportion for Multiple Alleles

TLDR

The Hardy‑Weinberg law underlies many genetic inference methods, yet large‑sample goodness‑of‑fit tests can yield spurious results when sample sizes or certain genotypic frequencies are small, and although a complete enumeration algorithm exists, it is impractical for loci with many alleles due to computational demands. We propose two algorithms to estimate the significance level for a test of Hardy‑Weinberg proportions. The algorithms are easily applicable to loci with multiple alleles, are remarkably simple and computationally fast, and the authors compare their relative efficiency and merits while providing usage guidelines. Numerical examples illustrate the practicality of the algorithms.

Abstract

The Hardy-Weinberg law plays an important role in the field of population genetics and often serves as a basis for genetic inference. Because of its importance, much attention has been devoted to tests of Hardy-Weinberg proportions (HWP) over the decades. It has long been recognized that large-sample goodness-of-fit tests can sometimes lead to spurious results when the sample size and/or some genotypic frequencies are small. Although a complete enumeration algorithm for the exact test has been proposed, it is not of practical use for loci with more than a few alleles due to the amount of computation required. We propose two algorithms to estimate the significance level for a test of HWP. The algorithms are easily applicable to loci with multiple alleles. Both are remarkably simple and computationally fast. Relative efficiency and merits of the two algorithms are compared. Guidelines regarding their usage are given. Numerical examples are given to illustrate the practicality of the algorithms.