Estimation of phenotypic selection differentials for predicting genetic responses to ratio-based selection

Ratios of the phenotypic values of two traits may be used as selection criteria in animal and plant breeding to improve the ratio traits themselves or to effect changes in their two component (numerator and denominator) traits. Prediction of genetic responses to ratio-based selection would facilitate quantitative analysis and evaluation of selection based on ratios. Methods for predicting such responses are derived and presented here. They employ expressions for the truncation value of a ratio and for the phenotypic selection differentials of the numerator and denominator traits. The derivation of these expressions is based upon the assumption that the phenotypic values of each of these traits are normally distributed. Worked examples relating to livestock and crop improvement are included to demonstrate how responses to selection for ratios may be predicted.