Prediction Equations in Quantitative Genetics

One of the fundamental concepts in the application of statistical methods to the analysis of the inheritance of characters showing continuous variation is the additive genetic variance ao, the variance in any character in a population that is due to the average effects of genes. If this is expressed as a fraction of the total variance, oa, we get the related parameter, h2, the heritability (in the narrowest sense) of the character. It can be shown without great labour that the heritability is also equal to the regression coefficient of breeding value on performance or phenotype. This short paper presents an alternative derivation from the point of view of the combination of information from different sources, an approach which may be useful in teaching. Several other important prediction equations in quantitative genetics can be fitted into the same pattern. If we have a measurement P of an individual in a population in which the character measured has a mean P, we may consider ourselves as having two independent pieces of information on the animal's breeding value. They are: (i) that the animal is a member of a population whose mean breeding value is P with variance ao2; (ii) that the animal's own performance is P and that this will have variance ao_ oa2 about the true breeding value. If we knew only (i), we should take P as the best estimate of the individual's breeding and it would have error variance <, ,. If we knew only (ii), we should take P as the best estimate with error variance 2 2 O7) U. In combination, the correct weight to give the two estimates is the reciprocal of their respective variances. We then have