Linear Index Selection to Improve Traits Defined as Ratios

Theoretical selection response is considered for a trait defined as a ratio of two component traits. A method is presented that estimates the genetic change in the components of a ratio when selection is practiced directly on the ratio. Theoretical responses for direct selection on the ratio are compared with linear selection index responses. The proposed linear index maximizes the correlation between the index and the genotype for the ratio of interest. Use of the linear index increases selection responses as compared with direct selection on the ratio. Monte Carlo simulation results are presented for a single generation selection experiment which indicate that the use of a linear index is more efficient for changing traits defined as a ratio of two components traits than direct selection on the ratio. Direct selection on the ratio is complicated by the disproportionate fashion by which selection pressure is exerted on the component traits. Linear selection indices place a predetermined amount of selection pressure on the traits of interest and therefore a predictable amount of genetic change should result.