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QTL mapping with statistical likelihood-based procedures or asymptotically equivalent regression methods is usually carried out in a univariate way, even if many traits were observed in the experiment. Some proposals for multivariate QTL mapping by an extension of the maximum likelihood method for mixture models or by an application of the canonical transformation have been given in the literature. This paper describes a method of analysis of multitrait data sets, aimed at localization of QTLs contributing to many traits simultaneously, which is based on the linear model of multivariate multiple regression. A special form of the canonical analysis is employed to decompose the test statistic for the general no-QTL hypothesis into components pertaining to individual traits and individual, putative QTLs. Extended linear hypotheses are used to formulate conjectures concerning pleiotropy. A practical mapping algorithm is described. The theory is illustrated with the analysis of data from a study of maize drought resistance.

Of interest is the analysis of results of a series of experiments repeated at several environments with the same set of plant varieties. Suppose that the experiments, multi-environment variety trials, are all conducted in resolvable incomplete block (IB) designs. Following the randomization approach adopted in Caliński and Kageyama (2000, Lecture Notes in Statistics, 150), two models for analyzing such trial data can be considered. One is derived under a complete additivity assumption, the other takes into account possible different responses of the varieties to variable environmental conditions. The analysis under the first, the standard model, does not provide answers to questions related to the performance of the individual varieties at different environments. These can be considered when using the more general second model. The purpose of this article is to devise interesting parameter estimation and hypothesis testing procedures under that more realistic model. Its application is illustrated by a thorough analysis of a set of data from a winter wheat series of trials.