Merit of Utilizing the Heritability of a Ratio to Predict the Genetic Change of a Ratio

The nature of a heritability for a trait defined as the ratio of two bivariate normal component traits was investigated. The heritability was calculated by intraclass correlation among half-sibs and from the genetic response realized from selection. Monte Carlo simulation techniques were utilized to compare these two methods. In all of the parameter situations studied, the heritability calculated from the intraclass correlation differed substantially from that realized after selection. This discrepancy indicates that the intraclass correlation among half-sibs calculated for a trait defined as a ratio does not estimate a statistic that can be used to predict genetic change for that ratio. A model was proposed that suggests that selection applied directly to a ratio trait is analogous to an index that simultaneously selects both component traits of the ratio. The similarity between the predicted genetic change and the genetic change of the components realized from selection supports the proposed mechanism at which selection acts on a trait as the ratio of two component traits.