A note on non-random mating in progeny tests

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Abstract
The regression of progeny on mid-parent value is often used in progeny tests to estimate the heritability of a quantitative character. The statistical precision of such an estimate can be considerably increased without increasing the size of the test, by using assortative mating or selection of parents (or both together) so as to increase the mid-parent variance; but the danger arises that this may introduce bias into the estimate through correlation between non-additive gene effects.It is shown by a mathematical argument that such bias will be negligible provided that all individual gene substitution effects are small compared with the phenotypic standard deviation of the character. Under this condition, deviations from additive effects either within or between loci will not appreciably affect the expected value of the regression on mid-parent, compared with its expected value in a test using random mating.Correlation between the non-additive gene effects is likely to cause more serious bias to the correlation between sibs, when non-random mating is used.

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