Linearity of heritability of Holstein first-lactation milk production.

The regression of daughter on dam first-lactation milk deviations from herd-mate averages was found to be linear from an analysis of 47,400 Holstein pairs. The linear equation was y=-25 .6 + .210 (x -27.6) and the quadratic equation was y-----25.6 + .208 (x -27.6) + .0000222 (x~-44131.4) with correlation coefficients, .18258 and .18268, respectively. These results suggest that selection response can be predicted adequately even with very large selection differentials. Linearity of heritability implies that selection response will be linearly related to the selection differential over all possible phenotypic values. Recently, artificial insemination organizations have begun mating highly selected sires and dams to produce sons for sampling in artificial insemination. The agreement between the expected and actual genetic value of these sons will depend on whether response to selection is linearly related to the selection differential. This study provides further evidence that selection response can be predicted adequately, even with very large selection differentials. The evidence is based on daughter-dam regression over a large range of phenotypic values of the dams. The evidence supports the findings of a similar study by Bradford and Van Vleck (2), with about 10% ~s much data. Their results were discussed primarily in terms of the theory of canalization of phenotypic development (5).