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Abstract
Production gains achieved through conventional breeding methods are gradually declining. Producing more food requires the development and implementation of novel new and genetic technologies. The goal in breeding programs is to choose candidates that produce offspring with best phenotypes. In conventional selection the best candidate is selected with high genotypic values (unobserved) in the assumption that this is related to 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. For example, the causal structure among yield components is well known where traits that develop earlier will affect those that develop later ( Dofing and Knight, 1992). 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 is applied to field data from the Nebraska winter wheat breeding program. One of the selection indices proposed in this research has the attributes to account the variability of all the available molecular markers through the use of Principal Components Analysis (PCA) by using 250 PC's which explained approximately 99% of the total variability, and to incorporate causal relationships among yield and yield contributors. We found that the correlation and the relative efficiency increased for the proposed Smith-Hazel indices when the causal information among traits was accounted by the vector of weights (b) which includes the causal path coefficients into the causal matrix ( Λ). On the other hand, when selection is based on a primary trait, for example yield, the proposed SIs increased the mean yield of the best 28 (Top 10%) genotypes to 7 %. Keywords: Selection Index (SI), Structural Equation Modeling (SEM), yield components, multi-trait, genomic selection (GS), principal component analysis (PCA), principal components (PC's).
