Correction to Fisher's correlations between relatives and environmental effects

Abstract

FISHER¹ has given a now much used model of assortative mating, and using formulae obtained for it he analysed data² on human height, span and forearm. In his model, phenotypic variance is regarded as the sum of three variances, additive, dominance and environmental; and genetic variance is the sum of the additive and dominance components. This was Fisher's first important contribution to genetics and it would seem that he did not appreciate fully the implications of his model. His formulae for parent–child correlation and sib correlation, in the presence of assortative mating, are not correct for his model. Moreover, the correct formulae for these correlations for his model suggest a different interpretation when the value for (genetic/phenotypic variance) is greater than 1. I present here a summary of criticisms of Fisher's formulae; details of which, with derivation of correct formulae will be presented elsewhere.