Among-environment heteroscedasticity and genetic autocorrelation: implications for the study of phenotypic plasticity

The impact of among-environment heteroscedasticity and genetic autocorrelation on the analysis of phenotypic plasticity is examined. Among-environment heteroscedasticity occurs when genotypic variances differ among environments. Genetic autocorrelation arises whenever the responses of a genotype to different environments are more or less similar than expected for observations randomly associated. In a multivariate analysis-of-variance model, three transformations of genotypic profiles (reaction norms), which apply to the residuals of the model while preserving the mean responses within environments, are derived. The transformations remove either among-environment heteroscedasticity, genetic autocorrelation or both. When both nuisances are not removed, statistical tests are corrected in a modified univariate approach using the sample covariance matrix of the genotypic profiles. Methods are illustrated on a Chlamydomonas reinhardtii data set. When heteroscedasticity was removed, the variance component associated with the genotype-by-environment interaction increased proportionally to the genotype variance component. As a result, the genetic correlation rg was altered. Genetic autocorrelation was responsible for statistical significance of the genotype-by-environment interaction and genotype main effects on raw data. When autocorrelation was removed, the ranking of genotypes according to their stability index dramatically changed. Evolutionary implications of our methods and results are discussed.