One dataset, four meta-analyses: synthesising mean effects, within-population variability, and between-population heterogeneity in ecology

Haley Lacza, Ayumi Mizuno , Coralie Williams , Malgorzata Lagisz , Shinichi Nakagawa 

Ecological syntheses (meta-analysis) usually ask "what is the average effect?", but many ecological questions also depend on whether outcomes become more or less variable and whether effects are predictable across contexts.

We show how the same dataset can support a coherent workflow that separates: (i) within-population variability (dispersion among individuals or sampling units inside studies) from (ii) between-population heterogeneity (dispersion among effect sizes across studies), and targets both for mean effects and variability effects.

Using the organic versus conventional crop-yield dataset as an illustration, along with an online tutorial, we analyse mean effects with the log response ratio (lnRR; Model 1) and within-population variability with the log variance ratio (lnVR) and the log coefficient of variation ratio (lnCVR; Model 2), noting that these three effect sizes can be computed from the same summary statistics (means, SDs and sample sizes).

We then extend standard meta-regression to location-scale (mean-variance) modelling, allowing moderators to explain not only how lnRR (Model 3) and lnVR/lnCVR (Model 4) shift on average ("location") but also how their within-study/residual heterogeneity changes with context ("scale"), thereby distinguishing settings where effects are generalisable and transferable from those where they are strongly context-dependent.

The core message is that many ecological datasets already contain sufficient information to synthesise performance (lnRR), reliability/stability (lnVR/lnCVR), and predictability (context-dependent heterogeneity; i.e., four models or meta-analyses) side by side. Doing so improves not only statistical inference but also our understanding of the changing world, making meta-analytic outputs and insights more directly decision-relevant.