Hans-Peter Piepho 'Mixed models for incorporating environmental covariates'

Mixed models for incorporating environmental covariates Hans-Peter Piepho, Maksym Hrachov Biostatistics Unit, University of Hohenheim In plant breeding and variety testing, there is an increasing interest in making use of environmental information to enhance predictions for new environments. Here, we will review linear mixed models that have been proposed for this purpose. The emphasis will be on predictions and on methods to assess the uncertainty of predictions for new environments. The relevance of the design of multi-environment trials and the way in which environments are selected will be considered. Our point of departure is straight-line regression, which may be extended to multiple environmental covariates (characterizations) and genotype-specific responses. When observable environmental covariates are used, this is also known as factorial regression. Early work along these lines can be traced back to Yates and Cochran (1938), who proposed a method nowadays best known as Finlay-Wilkinson regression. This method, in turn, has close ties with regression on latent environmental covariates and factor-analytic variance-covariance structures for genotype-environment interaction. Extensions of these approaches when observable environmental covariates are available will be the focus of this talk (reduced rank regression, kernel-or kinship-based approaches, random coefficient regression, extended Finlay-Wilkinson regression). Our objective is to demonstrate how seemingly disparate methods are very closely linked and fall within a common model-based prediction framework. The framework considers environments as random throughout, with genotypes also modelled as random in most cases. We will discuss options for assessing uncertainty of predictions, including cross validation and model-based estimates of uncertainty.