Summary
Methods of analysing variation between and within genotypes and environments are discussed. Principal component analysis, or an equivalent technique proposed by Mandel (1971) for examining interactions in two-way tables, is suggested as an appropriate method in many circumstances, followed by analysis of variance on these principal components for replicated data. Various techniques are applied to yields of carrots from a trial in which eight varieties were grown in 34 environments representing a set of 17 site/year combinations at two densities. The largest source of variation within genotypes is found to be that between environments but not conversely. Two other sources of variation are identified within genotypes and environments, one representing the interaction of varieties with site/year effects and the other their interaction with densities. Analysis of variance indicates the varieties and environments contributing to these interactions. The general implications of the use of principal component analysis are discussed, particularly in situations such as that with the carrot data where the method of joint regression analysis fails because the genotype-environment interaction contains more than one independent component.
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Freeman, G., Dowker, B. The analysis of variation between and within genotypes and environments. Heredity 30, 97–109 (1973). https://doi.org/10.1038/hdy.1973.15
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DOI: https://doi.org/10.1038/hdy.1973.15
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