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

Abstract

Summary1. 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 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.

Autosomal and X-Linked Additive Genetic Variation for Lifespan and Aging: Comparisons Within and Between the Sexes in Drosophila melanogaster

“…From this, it follows that X-linked variance should typically be higher in males than females (and two times higher when all variation is additive) (Reinhold and Engqvist 2013; Figure S4). This hypothesis has received mixed support from empirical studies comparing total male and female genetic variation across a broad range of species (Reinhold and Engqvist 2013; Wyman and Rowe 2014; Nakagawa et al 2015). With respect to D. melanogaster , point estimates of a male bias in X-linked additive genetic variation have previously been found in 20 out of 22 morphological characters (Cowley et al 1986; Cowley and Atchley 1988), as well as for locomotory activity (Long and Rice 2007) and fitness (Gibson et al 2002).…”

Sex differences in life history, behavior, and physiology along a slow-fast continuum: a meta-analysis

“…We choose to use lnCVR for comparing differences in variance between males and females because it accounts for corresponding changes in the mean; any change in variance could be explained simply by differences in the mean because of the strong mean–variance relationship we observed (Fig. S5; Nakagawa et al 2015). In our case, our effect sizes were the ratios of the mean (lnRR) and coefficient of variation (CV) (lnCVR) between males and females.…”

“…In our case, our effect sizes were the ratios of the mean (lnRR) and coefficient of variation (CV) (lnCVR) between males and females. Sample sizes and standard deviations for male and female samples do not affect the calculation of effect sizes but are used to calculate each effect size sampling variance (Hedges et al 1999; Nakagawa et al 2015). Importantly, for lnRR, we categorized traits as falling along the fast–slow POL continuum in line with predictions from Réale et al (2010) (see Table S1).…”

Measuring and interpreting sexual selection metrics: evaluation and guidelines

“…For this we computed effect sizes for Δ I s as the natural logarithm of the ratio between the coefficients of variation in mating success (lnCVR) when using gMS and cMS following Nakagawa et al . (), with higher values indicating that larger estimates were obtained when using gMS. Similarly, the effect size for Δβ ss was defined as Hedges d of the slope difference between the Bateman gradient obtained from using gMS and cMS, with larger values indicating a steeper gradient when using gMS.…”