Short communication: Recursive model approach to traits defined as ratios: Genetic parameters and breeding values

A novel method for analysis of ratio traits (Y2/Y1) is proposed. Utilizing a recursive modeling approach, a proxy for Y2/Y1 can be postulated as Y2 - λ × Y1 (i.e., Y2 adjusted for the effect of Y1), where λ is a structural parameter describing an effect of change in phenotype of Y2 caused by the phenotype of Y1. Estimates of parameters (direct effect parameters) for the recursive model Y1 → Y2 can be derived from parameters of an equivalent 2-trait mixed effects model for Y1 and Y2, using linear (location) and quadratic (dispersion) transformations. The method is illustrated with an application for milk fat (protein) content, calculated as a ratio of fat (protein) and milk yields (kg), in the context of genetic parameters estimation and genetic evaluation via the Canadian test-day model for production traits. Results indicated the potential usefulness of the proposed approach for analysis of any Y2/Y1 (or Y2 adjusted for the effect of Y1) type of trait utilizing standard multiple-trait modeling techniques for Y1 and Y2.