Location-scale Meta-analysis and Meta-regression as a Tool to Capture Large-scale Changes in Biological and Methodological Heterogeneity: a Spotlight on Heteroscedasticity

Heterogeneity is a defining feature of ecological and evolutionary meta-analyses. While conventional metal-analysis and meta-regression methods acknowledge heterogeneity in effect sizes, they typically as-sume this heterogeneity is constant across studies and levels of moderators (i.e., homoscedasticity). This assumption could mask potentially informative patterns in the data. Here, we introduce and develop a location-scale meta-analysis and meta-regression framework that models both the mean (location) and variance (scale) of effect sizes. Such a framework explicitly accommodates heteroscedasticity (differences in variance), thereby revealing when and why heterogeneity itself changes. This capability, we argue, is crucial for understanding responses to global environmental change, where complex, context-dependent processes may shape both the average magnitude and the variability of biological responses. For example, differences in study design, measurement protocols, environmental factors, or even evolutionary history can lead to systematic shifts in variance. By incorporating hierarchical (multilevel) structures and phylogenetic relationships, location-scale models can disentangle the contributions from different levels to both location and scale parts. We further attempt to extend the concepts of relative heterogeneity and publication bias into the scale part of meta-regression. With these methodological advances, we can identify patterns and processes that remain obscured under the constant variance assumption, thereby enhancing the biological interpretability and practical relevance of meta-analytic results. Notably, al- most all published ecological and evolutionary meta-analytic data can be re-analysed using our proposed analytic framework to gain new insights. Altogether, location-scale meta-analysis and meta-regression provide a rich and holistic lens through which to view and interpret the intricate tapestry woven with ecological and evolutionary data. The proposed approach, thus, ultimately leads to more informed and context-specific conclusions about environmental changes and their impacts.