Comparing ecological and evolutionary variability within datasets

Abstract

Many key questions in evolutionary ecology require the use of variance ratios such as heritability, repeatability, and individual resource specialization. These ratios allow researchers 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 differ 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 components 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 linear mixed models (LMMs). Frequentist and Bayesian frameworks have similar abilities to identify differences in variance components. However, variance differences at higher levels of organization 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

Significance statement

Many critical questions in ecology and evolution use variance ratios, such as repeatability, heritability, or individual resource specialization, to make inferences about ecological and evolutionary processes. In many cases, these inferences rely on the comparison of variance ratios among datasets (populations, sexes, or environments). In this article, we show that current approaches of drawing inferences about group differences from comparisons of ratios are inappropriate because ratios can differ due to differences in the numerator, denominator, or both. We investigated how questions regarding differences in variance ratios and constituent variance components can be evaluated using linear mixed model (LMM) approaches and provide guidance for appropriate sampling schemes under different scenarios and discuss common pitfalls associated with estimation of differences in variance component among datasets.