Introducing Meta-Partition, a Useful Methodology to Explore Factors That Influence Ecological Effect Sizes.

The study of the heterogeneity of effect sizes is a key aspect of ecological meta-analyses. Here we propose a meta-analytic methodology to study the influence of moderators in effect sizes by splitting heterogeneity: meta-partition. To introduce this methodology, we performed a meta-partition of published data about the traits that influence species sensitivity to habitat loss, that have been previously analyzed through meta-regression. Thus, here we aim to introduce meta-partition and to make an initial comparison with meta-regression. Meta-partition algorithm consists of three steps. Step 1 is to study the heterogeneity of effect sizes under the assumption of fixed effect model. If heterogeneity is found, we perform step 2, that is, to partition the heterogeneity by the moderator that minimizes heterogeneity within a subset while maximizing heterogeneity between subsets. Then, if effect sizes of the subset are still heterogeneous, we repeat step 1 and 2 until we reach final subsets. Finally, step 3 is to integrate effect sizes of final subsets, with fixed effect model if there is homogeneity, and with random effects model if there is heterogeneity. Results show that meta-partition is valuable to assess the importance of moderators in explaining heterogeneity of effect sizes, as well as to assess the directions of these relations and to detect possible interactions between moderators. With meta-partition we have been able to evaluate the importance of moderators in a more objective way than with meta-regression, and to visualize the complex relations that may exist between them. As ecological issues are often influenced by several factors interacting in complex ways, ranking the importance of possible moderators and detecting possible interactions would make meta-partition a useful exploration tool for ecological meta-analyses.