Analysis Of Multi-environment Trials Research Articles

Some vocabulary and grammar for the analysis of multi-environment trials, as applied to the analysis of FPB and PPB trials

For the improvement of genetic material suitable for on farm use under low-input conditions, participatory and formal plant breeding strategies are frequently presented as competing options. A common frame of reference to phrase mechanisms and purposes related to breeding strategies will facilitate clearer descriptions of similarities and differences between participatory plant breeding and formal plant breeding. In this paper an attempt is made to develop such a common framework by means of a statistically inspired language that acknowledges the importance of both on farm trials and research centre trials as sources of information for on farm genetic improvement. Key concepts are the genetic correlation between environments, and the heterogeneity of phenotypic and genetic variance over environments. Classic selection response theory is taken as the starting point for the comparison of selection trials (on farm and research centre) with respect to the expected genetic improvement in a target environment (low-input farms). The variance-covariance parameters that form the input for selection response comparisons traditionally come from a mixed model fit to multi-environment trial data. In this paper we propose a recently developed class of mixed models, namely multiplicative mixed models, also called factor-analytic models, for modelling genetic variances and covariances (correlations). Mixed multiplicative models allow genetic variances and covariances to be dependent on quantitative descriptors of the environment, and confer a high flexibility in the choice of variance-covariance structure, without requiring the estimation of a prohibitively high number of parameters. As a result detailed considerations regarding selection response comparisons are facilitated. The statistical machinery involved is illustrated on an example data set consisting of barley trials from the International Center for Agricultural Research in the Dry Areas (ICARDA). Analysis of the example data showed that participatory plant breeding and formal plant breeding are better interpreted as providing complementary rather than competing information.

Linear and bilinear models for the analysis of multi-environment trials: I. An inventory of models

The multi-environment trial, in which a number of genotypes is evaluated over a range of environmental conditions, is a standard experiment in plant breeding in general, and variety testing in particular. Useful statistical models for the analysis of multi-environment trials, with emphasis on the analysis of genotype by environment interaction, can be found in the classes of linear and bilinear models. Statistical properties of the most important representatives of these model classes are shortly reviewed. Structural differences between the models stem from: (1) the inclusion of random model terms in addition to fixed model terms; (2) the representation of the interaction by additive or multiplicative parameters; (3) the incorporation of concomitant variables on the levels of the environmental factor. For models with bilinear multiplicative structure for the interaction it is described how the interaction can be visualized by biplots. An illustration of the application of the models and biplots is given in a companion paper.

Linear and bilinear models for the analysis of multi-environment trials: II. An application to data from the Dutch Maize Variety Trials

As the sequel to a paper that dealt with the theoretical aspects of linear and bilinear models for the analysis of genotype by environment interaction in multi-environment trials, this paper presents an illustration of the application of these models to real life data. The data come from maize trials that were conducted within the ongoing evaluation programme for the Dutch Descriptive Variety List of Field Crops. The variable that is analyzed is dry matter content. It is shown how linear and bilinear models can be used supplementary to each other within a general strategy for dealing with genotype by environment interaction.