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

Abstract

Summary• 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 logtransformed 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.

Quantifying nonadditive selection caused by indirect ecological effects

“…Fitness estimates may often be nonnormally distributed or contain outliers, leading to heteroscedasticity. Although logtransformations can help in restoring normality, they also affect the biological interpretation of results (Lande andArnold 1983, Stanton andThiede 2005). In cases where assumptions are violated, resampling (e.g., bootstrapping) to generate P values or generalized linear mixed models that incorporate non-Gaussian distributions are viable alternatives (Morrissey and Sakrejda.…”

Invasive ecosystem engineer selects for different phenotypes of an associated native species

“…Preliminary inspection of variance inflation factors indicated that these gradients were not compromised by multicollinearity. The significance of gradients was tested using randomization tests (Stanton and Thiede 2005). Briefly, we re-estimated all gradients from models in which relative performance was randomized across trait values, and used Monte Carlo simulations (using the PopTools add-in for Excel ;Hood 2008) to compare real and randomized gradients over 10 000 permutations.…”

“…Generally in bivalves, body size is an important measure of performance that correlates with fecundity (Byers 2005) and biomass of pre-reproductive Anadara is likely to be a good predictor of adult biomass. Prior to analysis, we calculated relative performance as the mass of each individual divided by the mean mass in each habitat (Caulerpa and unvegetated sediment; see Lande and Arnold 1983 for details on processing data for selection analyses), and logtransformed all traits except performance (see Stanton and Thiede 2005) to improve normality before converting them to units of standard deviation (SD).…”

Sex differences in phenotypic plasticity of a mechanism that controls body size: implications for sexual size dimorphism

“…However, interactions produced by ANOVA can be misleading when the proportional or relative effects (i.e. ratios such as female/male size) are of interest because ANOVA tests for interactions by measuring linear differences between treatment means (Stanton & Thiede 2005;Stillwell et al 2007b;Fraker & Peacor 2008). In other words, when there is a large effect of one variable on the overall mean, linear differences do not translate into proportional changes.…”

“…We first examined main effects (temperature, diet and sex; panels a and b in figures 1 -5). We then tested for diet-by-sex and temperature-by-sex interactions for all traits using relative trait values (individual trait value/ mean within each temperature or diet treatment (averaged across sexes)) to remove the large scaling effects of the diet and temperature treatments (Stanton & Thiede 2005;Stillwell et al 2007b; panels c and d in figures 1 -5). These relative trait values were normally distributed and thus did not violate assumptions of ANOVA.…”