Statistical convenience vs biological insight: consequences of data transformation for the analysis of fitness variation in heterogeneous environments

In plants, more favourable environmental conditions can lead to dramatic increases in both mean fitness and variance in fitness. This results in data that violate the equality-of-variance assumption of anova, a problem that most empiricists would address by log-transforming fitness values. Using heuristic data sets and simple simulations, we show that anova on log-transformed fitness consistently fails to match the outcome of selection in a heterogeneous environment or its sensitivity to environmental frequency. Only anova based on relative fitness within environments accurately predicts the sensitivity of genotype selection to the frequency of alternative environments. Parallel analyses of variance based on absolute fitness and relative fitness can bracket the expected success of alternative genotypes under hard and soft selection, respectively. For example, for Sinapis arvensis growing in full sun and partial shade treatments, families achieving high fitness in the best environment are favoured under hard selection, whereas soft selection favours different families that achieve consistently good performance across environments. Based on these findings, we recommend that log-transformation of fitness should no longer be standard practice in ecological genetics studies. Weighted anova is a preferable method for dealing with unequal variances, and investigators should also make greater use of techniques such as quantile regression or resampling to describe and evaluate fitness variation across heterogeneous environments.