Meta-analysis of variation: ecological and evolutionary applications and beyond

1. Meta-analysis has become a standard way of summarizing empirical studies in many fields, including ecology and evolution. In ecology and evolution, meta-analyses comparing two groups (usually experimental and control groups) have almost exclusively focused on comparing the means, using standardized metrics such as Cohen's / Hedges' d or the response ratio. 2. However, an experimental treatment may not only affect the mean but also the variance. Investigating differences in the variance between two groups may be informative, especially when a treatment influences the variance in addition to or instead of the mean. 3. In this paper, we propose the effect size statistic lnCVR (the natural logarithm of the ratio between the coefficients of variation, CV, from two groups), which enables us to meta-analytically compare differences between the variability of two groups. We illustrate the use of lnCVR with examples from ecology and evolution. 4. Further, as an alternative approach to the use of lnCVR, we propose the combined use of ln s (the log standard deviation) and ln x (the log mean) in a hierarchical (linear mixed) model. The use of ln s with ln x ="false" overcomes potential limitations of lnCVR and it provides a more flexible, albeit more complex, way to examine variation beyond two-group comparisons. Relevantly, we also refer to the potential use of ln s and lnCV (the log CV) in the context of comparative analysis. 5. Our approaches to compare variability could be applied to already published meta-analytic data sets that compare two-group means to uncover potentially overlooked effects on the variance. Additionally, our approaches should be applied to future meta-analyses, especially when one suspects a treatment has an effect not only on the mean, but also on the variance. Notably, the application of the proposed methods extends beyond the fields of ecology and evolution.