AMONG-ENVIRONMENT HETEROSCEDASTICITY AND THE ESTIMATION AND TESTING OF GENETIC CORRELATION

The genetic correlation between a character in two environments is of considerable interest in the context of plant and animal breeding for the prediction of evolutionary trajectories and for the evaluation of the amount of genetic variance maintained at equilibrium in subdivided populations. The two-way analysis of variance with genotype and envir onment as crossed factors is the usual basis for estimating this genet ic correlation. In plasticity experiments, the genetic variance can di ffer widely between environments, for instance when the variance compo nent associated with the genotype-environment interaction is not const ant over environments. When this is the case, the assumption of homosc edasticity is violated, and the ANOVA method tends to underestimate th e absolute value of the genetic correlation. To solve this problem, a variance-stabilizing transformation previously applied in a multivaria te ANOVA context was developed. This development resulted in a new pro cedure (method 3), in which the genetic correlation is estimated from the transformed data (i.e. after among-environment heteroscedasticity is removed, while the within-environment means are maintained). In a s imulation study and an analysis of Chlamydomonas reinhardtii growth ra te data, we compared method 3 with two existing methods in which the g enetic correlation is estimated from the raw data. Method 1 uses one ' global' variance component associated with the genotype-environment in teraction, and method 2 uses two variance components associated with t he genotype and obtained from one-way ANOVAs conducted separately in t he two environments. Under increasing among-environment heteroscedasti city, method 1 produces increasingly biased genetic correlation estima tes, whereas method 3 almost consistently provides accurate estimates; the performance of method 2 is intermediate, with more estimates out of range or indeterminate. This is the first demonstration that a vari ance-stabilizing transformation of the data removes the bias in the es timation of genetic correlation caused by among-environment heterosced asticity, while allowing valid statistical testing in an ANOVA-based a pproach.