More on Nei and Roychoudhury's sampling variances of heterozygosity and genetic distance.

The inequality relationship between the expected values of (j(x)-g)2 and (ĝ-g)2, where j(x) is a biased and ĝ is an unbiased estimate of population homozygosity g, were examined earlier by Nei and Roychoudhury (1974) and later by Mitra (1975). The improvement in the inequality still left much to be desired. In this paper a lower boundary of g has been obtained which may be regarded as ultimate for ensuring a smaller expected value of (j(x)-g)2 than the corresponding value of (ĝ-g)2.