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.