Statistical Models for Phenotyping Cultivars Using Fixed and Mixed Linear and Linear-Bilinear Models.
Jose Crossa1, Paul Cornelius2, and Juan Burgueno1. (1) CIMMYT, CIMMYT, Apdo Postal 6-641, Mexico DF, CP06600, MEXICO, (2) Dept. of Plant & Soil Sc. Rm 323, Lexington, KY 40546-0312
In agricultural and plant breeding research, multi-environment evaluation trials are used to develop recommendations concerning cultivars for adoption by farmers. Linear-bilinear (multiplicative) statistical models are useful for studying genotype by environment interaction (GEI) and estimating realized genotypic responses in specific sites. These models can be used within the fixed effects or mixed effects framework. In this presentation we will (1) summarize results on shrinkage estimates of multiplicative models for better estimation of phenotypic performance, (2) use mixed linear models with coefficient of parentage for better prediction of breeding values. Often shrinkage estimation of linear-bilinear models produce better estimates than BLUPs of the cell means and appear to always yield better estimates than do truncated multiplicative linear-bilinear models fitted by least squares. In plant breeding, multi-environment trials may include sets of related genetic strains. In self-pollinated species the covariance matrix of the breeding values of these genetic strains is equal to the additive genetic covariance among them. This can be expressed as an additive relationship matrix A multiplied by the additive genetic variance. Using mixed model methodology, the genetic covariance matrix can be estimated and BLUPs of breeding values obtained. The effectiveness of exploiting relationships among strains tested in multi environments trials and the usefulness of the BLUPs of breeding values for simultaneously modeling the main effects of genotypes and GEI have been studied using a Kronecker (direct) product of a sites factor analytic covariance matrix and a matrix (A) of genetic relationships among genotypes. Results comparing this approach with traditional fixed effects and random effects models for studying GEI ignoring genetic relationships showed that factor analytic structures with inclusion of matrix A efficiently model the main effects of genotypes and GEI. These models showed the lowest standard errors of BLUPs of breeding values.