Incorporating Molecular Markers and Causal Structure among Traits Using a Smith-Hazel Index and Structural Equation Models

Abstract

The goal in breeding programs is to choose candidates that produce offspring with the best phenotypes. In conventional selection, the best candidate is selected with high genotypic values (unobserved), in the assumption that this is related to the observed phenotypic values for several traits. Multi-trait selection indices are used to identify superior genotypes when a number of traits are to be considered simultaneously. Often, the causal relationship among the traits is well known. Structural equation models (SEM) have been used to describe the causal relationships among variables in many biological systems. We present a method for multi-trait genomic selection that incorporates causal relationships among traits by coupling SEM with a Smith–Hazel index that incorporates markers. The method was applied to field data from a Nebraska winter wheat breeding program. We found that the correlation and the relative efficiency increased for the proposed Smith–Hazel indices when the total causal information among traits was accounted for by the vector of weights (b), which includes the causal path coefficients in the causal matrix (Λ). On the other hand, when selection was based on a primary trait, for example yield, the proposed SI increased the mean yield of the best 28 (Top 10%) genotypes to 7%.