Sample sizes required to detect linkage disequilibrium between two or three loci

Abstract

Estimates of the degree of nonrandom association among genes (linkage disequilibrium) can provide evidence of the role of natural selection in maintaining allozyme polymorphisms in natural populations. This paper outlines the maximum likelihood procedures for such estimates based on gametic or zygotic frequencies at the level of two loci. The analysis is extended to estimating disequilibrium between three loci. In particular, the question of the sampling requirements to detect different intensities of disequilibrium is considered. It is found that relatively large samples are required to detect nonrandom association, unless gene frequencies are intermediate and disequilibrium is relatively intense. This might be one reason why cases of linkage disequilibrium have so far proved to be the exception, rather than the rule, in population studies.