Selection of sires to reduce sampling variance in the estimates of heritability by half-sib correlation

Standard methods to estimate heritability by half-sib correlation are biased if selection has operated in the parental generation. In this paper a simple method to correct for selection of animals used as sires is described. By selection of both the top and the bottom ranking sires, the sampling variances of the corrected estimates of heritability are substantially reduced. Algebraic expressions to predict the sampling variance of the estimates of heritability using selected sires are derived. Theoretical predictions were checked by Monte-Carlo simulation. The results may have application in the design of experiments to estimate heritabilities.