Raphaël Royauté, Ned A Dochtermann

Many key questions in evolutionary ecology require the use of variance ratios such as heritability, repeatability, and individual resource specialization. These ratios allow to understand how phenotypic variation is structured into genetic and non-genetic components, to identify how much organisms vary in the resources they use or how functional traits structure species communities. Understanding how evolutionary and ecological processes differs among populations and environments therefore often requires the comparison of these ratios across groups (i.e. populations, sexes, species). Inference based on comparisons of ratios can be limited, however. Variance ratios can remain the same across group despite very different values in the numerator and denominator variances. Moreover, evolutionary ecologists are most often interested in differences in specific variance component among groups rather than in differences in variance ratios per se. Recommendations for how to infer whether groups differ in variance are not clear in the literature. Using simulations, we show how questions regarding the estimation of variance components and their differences among groups can be answered with Hierarchical Linear Modeling approaches (HLMs). Frequentist and Bayesian frameworks have similar abilities to identify differences in variance components. However, variance differences at higher levels of organization (i.e. the among-unit variance) can be difficult to detect with low sample sizes. We provide tools to conduct power analyses to determine the appropriate sample sizes necessary to detect differences in variance of a given magnitude. We conclude by supplying guidelines for how to report and draw inferences based on the comparisons of variance components and variance ratios.