Nakagawa Shinichi, Mizuno Ayumi, Morrison Kyle, Ricolfi Lorenzo, Williams Coralie, Drobniak Szymon M, Lagisz Malgorzata, Yang Yefeng
Department of Biological Sciences, Faculty of Science, University of Alberta, Edmonton, Canada.
Evolution and Ecology Research Centre, School of Biological, Earth and Environmental Sciences, University of New South Wales, Sydney, New South Wales, Australia.
Glob Chang Biol. 2025 May;31(5):e70204. doi: 10.1111/gcb.70204.
Heterogeneity is a defining feature of ecological and evolutionary meta-analyses. While conventional meta-analysis and meta-regression methods acknowledge heterogeneity in effect sizes, they typically assume 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, almost 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.
异质性是生态与进化元分析的一个决定性特征。虽然传统的元分析和元回归方法承认效应大小存在异质性，但它们通常假定这种异质性在各项研究以及调节变量的不同水平上是恒定的（即同方差性）。这一假设可能会掩盖数据中潜在的有用模式。在此，我们引入并开发了一种位置 - 尺度元分析和元回归框架，该框架对效应大小的均值（位置）和方差（尺度）都进行建模。这样一个框架明确考虑了异方差性（方差差异），从而揭示异质性本身何时以及为何发生变化。我们认为，这种能力对于理解对全球环境变化的响应至关重要，因为复杂的、依赖于背景的过程可能会塑造生物响应的平均幅度和变异性。例如，研究设计、测量方案、环境因素甚至进化历史的差异都可能导致方差的系统性变化。通过纳入层次（多级）结构和系统发育关系，位置 - 尺度模型可以区分不同层次对位置和尺度部分的贡献。我们还进一步尝试将相对异质性和发表偏倚的概念扩展到元回归的尺度部分。有了这些方法上的进展，我们能够识别在恒定方差假设下仍被掩盖的模式和过程，从而增强元分析结果的生物学可解释性和实际相关性。值得注意的是，几乎所有已发表的生态与进化元分析数据都可以使用我们提出的分析框架重新进行分析，以获得新的见解。总之，位置 - 尺度元分析和元回归提供了一个丰富而全面的视角，通过它可以审视和解释由生态与进化数据交织而成的复杂图景。因此，所提出的方法最终能够得出关于环境变化及其影响的更明智、更具针对性的结论。
