The relationship between homozygosity and the frequency of the most frequent allele

Honiozygosity is a commonly used summary of allele-frequency distributions at polymorphic loci. Because high-frequency alleles contribute disproportionately to the homozygosity of a locus, it often occurs that most homozygotes are homozygous for the most frequent allele. To assess the relationship between homozygosity, and the highest allele frequency at a locus, for a given homozygosity value, we determine the lower and upper bounds on the frequency of the most frequent allele. These bounds suggest tight constraints on the frequency of the most frequent allele as a function of homozygosity, differing by at most 1/4 and having an average difference of 2/3 = pi(2)/18 approximate to 0.1184. The close connection between homozygosity and the frequency of the most frequent allele-which we illustrate using allele Frequencies from human poptilations-has the consequence that when one of these two quantities is known, considerable information is available about the Other quantity. This relationship also explains the similar performance ol'stafistical tests of population-genetic models that rely on homozygosity and those that rely on the fi-equency of the most. frequent allele, and it provides a basis for understanding the utility of extended homozygosity statistics in