Correlation between the individual heterozygosity of parents and their offspring

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Abstract
Specific formulations are derived for the correlation between the heterozygosity of a randomly mating parent and its offspring for a diallelic locus, and for the correlation when multiple loci are considered. The expected correlation is maximal, approaching r=0.50, when allelic frequencies are highly asymmetric, and it is zero when the allelic frequencies are equal to 0.50. Parent-offspring correlations, up to a maximum of 0.50 for diallelic loci, indicate that levels of heterozygosity can respond to selection. Multilocus allozyme data from limber pine, Pinus flexilis, and from horses of standardbred and thoroughbred breeds are used to demonstrate correlations between a parent and its offspring. The Spearman rank correlation between the heterozygosity of a limber pine and the mean heterozygosity of her offspring is r=0.45. Correlations in the horses range from r=0.16 to 0.32.