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The calculation and significance testing of genetic correlations across environments

Genetic correlations within a trait across environments (rg) are important in the analysis of phenotypic plasticity. Not all methods are, however, equally reliable. An overview of all different methods for estimation of rg with one generation data sets is given. Formulae for the relationship between causal variance components and family means are derived. When these formulae are used covariances derived from family means, thought to be incorrect, are exactly the same as those derived with the ANOVA method. The bias, precision and power of the different methods are compared with Monte Carlo simulations. For all methods bias is small and precision is high for the large balanced data sets analyzed here, except when the variance in one or both of the environments is close to 0. Significance testing causes more problems. Confidence intervals with or without z‐transformation are not suitable for testing, nor is testing for g*e interaction in an ANOVA suitable for testing whether the rg is different from 1. The F‐test in a mixed model ANOVA and a likelihood ratio test in a REML‐analysis can be used for testing a difference from 0 but not from 1 or other values. Jackknife and Bootstrap, however, are suitable tests both for differences with 0,1 and other values, though negative variances can make these tests difficult to apply.