COMPARISON OF LINEAR MIXED MODELS FOR MULTIPLE ENVIRONMENT PLANT BREEDING TRIALS

Abstract

Evaluations of genotypes in varied environmental conditions are referred to as multiple environment trials (MET), and are used in advanced stages of plant breeding programs to identify genotypes with superior performance across environments and within specific environments or sets of environments. Yield data from MET often show genotype by environment interactions (G×E), and often are analyzed using a two-way analysis of variance (ANOVA) model where genotype, environment, and their interaction are treated as fixed effects. The estimates of G×E effects are the means across replicates of each genotype in each environment (i.e. cell means). The major disadvantage of this approach is that these estimates are usually based on very little data (dependent on the number of replicates) and so are less predictively accurate than some alternative estimators. Various estimators have been shown to be more accurate for MET than cell means. These include the Additive Main effects Multiplicative Interaction (AMMI) models (Gauch 1994), and the mixed linear model (Piepho 1994). If a mixed linear model is used, genotypes are selected based on empirical best linear unbiased predictors (BLUPs). The model used by Piepho (1994) assumes that genotypes are independent, but in most MET at least a portion of the genotypes are related and therefore would be expected to show some correlation in their effects. Pedigree information can be used through a Genetic Relationship Matrix (GRM) to take advantage of these relationships and improve predictive accuracy . Another method that may improve the predictive accuracy of mixed models is to increase the complexity of the variance-covariance matrix of the random G×E effect; which can be described as the product of two other matrices, such that Gge = Ge ⨂ Ig, where Ig is an identity matrix with dimensions equal to the number of genotypes. Structures of varying complexity can be used to model Ge. One such structure is the factor analytic model (FA) which increases in complexity with the number of factors used. Crossa et al. (2006) demonstrated that a factor analytic structure can be combined with pedigree information to improve accuracy. Additional research is necessary to determine which methods are most effective in various breeding programs. Objective