Incorporation of economic values into the component traits of a ratio: Feed efficiency

ABSTRACT Direct selection on a ratio (R) of 2 traits (x 1/x 2) does not have a mechanism to accommodate the relative economic values (a 1 and a 2) between x 1 and x 2 because selection criteria x 1/x 2 and a 1 x 1/a 2 x 2 rank animals in the same order. This study presented a procedure to incorporate the economic weights into ratio traits through linear transformation. The partial derivatives of a nonlinear profit function evaluated at the means were widely taken as economic weights in the literature. This study showed that the economic weights derived in this manner were erroneous because they actually contain a mixture of actual economic weights and transformation effects. The ratios 1/2 and 2/4 are considered equal by selection on R, but are treated differently by the linear index. In addition, this study presented a unified approach to compare 4 different selection strategies for genetic improvement of ratio traits: linear index (I), selection on the ratio (R), selection on difference between x 1 and x 2 (D), and selection on x 1 alone. This study considered 3 levels of heritability each for variables x 1 and x 2 and 2 levels of genetic correlations (γG ), 2 ratios of means (µ 1/µ 2), and 4 ratios of phenotypic variances giving a total of 96 scenarios. Linear index I was the most efficient of the 4 criteria compared in all 96 scenarios studied. The superiority of index I over R, D, and selection on x 1 alone are particularly remarkable when x 1 and x 2 have a large difference in heritability and are highly correlated. Selection on x 1 alone is an economically viable alternative to criterion I or R for the improvement of ratio traits particularly when x 1 is more heritable than x 2 and when x 2 is costly to measure. Selection on D is more efficient than direct selection on R or selection on x 1 alone when x 1 is less heritable than x 2 and the difference between µ 1 and µ 2 is small.