Testing for Hardy-Weinberg equilibrium in samples with related individuals

Abstract

When the classical chi(2) goodness-of-fit test for Hardy-Weinberg (HW) equilibrium is used on samples with related individuals, the type I error can be greatly inflated. In particular the test is inappropriate in population isolates where the individuals are related through multiple lines of descent. In this article, we propose a new test for HW (the QL-HW test) suitable for any sample with related individuals, including large inbred pedigrees, provided that their genealogy is known. Performed conditional on the pedigree structure, the QL-HW test detects departures from HW that are not due to the genealogy. Because the computation of the QL-HW test becomes intractable for very polymorphic loci in large inbred pedigrees, a simpler alternative, the GCC-HW test, is also proposed. The statistical properties of the QL-HW and GCC-HW tests are studied through simulations considering a sample of independent nuclear families, a sample of extended outbred genealogies, and samples from the Hutterite population, a North American highly inbred isolate. Finally, the method is used to test a set of 143 biallelic markers spanning 82 genes in this latter population.

Figure 1.—

Fifteen possible identity states for individuals A and B, grouped according to their nine condensed states. Lines indicate alleles that are IBD (from Abney et al. 2000).

Figure 2.—

Power of the QL-HW test in 30 nuclear families (solid line) and power of the Gof-HW test in the corresponding parent sample (dashed line), as a function of s, for a 5% type I error.

Figure 3.—

Proportion of markers typed with the eight different genotyping methods for the set of 143 SNPs tested (solid bars) and for the 14 SNPs with an associated P-value ≤0.05 (open bars).