Nonindependence and sensitivity analyses in ecological and evolutionary meta-analyses.

Meta-analysis is an important tool for synthesizing research on a variety of topics in ecology and evolution, including molecular ecology, but can be susceptible to nonindependence. Nonindependence can affect two major interrelated components of a meta-analysis: (i) the calculation of effect size statistics and (ii) the estimation of overall meta-analytic estimates and their uncertainty. While some solutions to nonindependence exist at the statistical analysis stages, there is little advice on what to do when complex analyses are not possible, or when studies with nonindependent experimental designs exist in the data. Here we argue that exploring the effects of procedural decisions in a meta-analysis (e.g. inclusion of different quality data, choice of effect size) and statistical assumptions (e.g. assuming no phylogenetic covariance) using sensitivity analyses are extremely important in assessing the impact of nonindependence. Sensitivity analyses can provide greater confidence in results and highlight important limitations of empirical work (e.g. impact of study design on overall effects). Despite their importance, sensitivity analyses are seldom applied to problems of nonindependence. To encourage better practice for dealing with nonindependence in meta-analytic studies, we present accessible examples demonstrating the impact that ignoring nonindependence can have on meta-analytic estimates. We also provide pragmatic solutions for dealing with nonindependent study designs, and for analysing dependent effect sizes. Additionally, we offer reporting guidelines that will facilitate disclosure of the sources of nonindependence in meta-analyses, leading to greater transparency and more robust conclusions.