Multi-trait selection with desired gains and non-linear indexes

A linear selection index for multiple traits is not satisfactory in many practical cases, such as when selecting for traits that have an optimum phenotypic value with a nonlinear profit function. This paper will discuss various ways to select for a breeding objective that includes a trait with an optimum phenotype. The study shows that, contrary to general belief, a linear updated index does not always achieve a desirable result due to correlated responses in multiple trait selection. A simple derivation of weights for a restricted index is proposed to deal with the problem.