Abstract
Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.
Highlights
Selection of plants and animals in a breeding program deals with experimental data for which the underlying genetic model is best formulated as a mixed linear model
We have investigated efficient model formulation and residual maximum likelihood (REML) estimation of variance parameters for multiple environment/trait data using the standard approach in ASReml, with an extension for the factor analytic structure
The inclusion of pedigree information in the analysis of multi-environment trials (METs) data adds to the complexity of the mixed model and associated variance structure
Summary
Selection of plants and animals in a breeding program deals with experimental data for which the underlying genetic model is best formulated as a mixed linear model. The genetic model is improved by including pedigree information through an additive relationship matrix, A. This matrix can be quite large and complex for large populations involving many generations, and its inverse is required when solving the mixed model equations. Its application to multiple traits or environments in crop populations, where both additive and non-additive genetic variation can be measured, raises some issues to be resolved. While pedigree information has been used extensively in animal breeding, adoption on a routine basis in the plant breeding sphere has been much slower. Genotype performance is typically measured in a series of replicated field trials grown across multiple (page number not for citation purposes)
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