Halliwell Ben, Holland Barbara R, Yates Luke A
School of Natural Sciences, Private Bag 55, University of Tasmania, Hobart, Tasmania, Australia.
ARC Centre of Excellence for Plant Success in Nature and Agriculture, Private Bag 55, University of Tasmania, Hobart, Tasmania, Australia.
Biol Rev Camb Philos Soc. 2025 Jun;100(3):1294-1316. doi: 10.1111/brv.70001. Epub 2025 Apr 7.
The scale and resolution of trait databases and molecular phylogenies is increasing rapidly. These resources permit many open questions in comparative biology to be addressed with the right statistical tools. Multi-response (MR) phylogenetic mixed models (PMMs) offer great potential for multivariate analyses of trait evolution. While flexible and powerful, these methods are not often employed by researchers in ecology and evolution, reflecting a specialised and technical literature that creates barriers to usage for many biologists. Here we present a practical and accessible guide to MR-PMMs. We begin with a review of single-response (SR) PMMs to introduce key concepts and outline the limitations of this approach for characterising patterns of trait coevolution. We emphasise MR-PMMs as a preferable approach for analyses involving multiple species traits, due to the explicit decomposition of trait covariances. We discuss multilevel models, multivariate models of evolution, and extensions to non-Gaussian response traits. We highlight techniques for causal inference using graphical models, as well as advanced topics including prior specification and latent factor models. Using simulated data and visual examples, we discuss interpretation, prediction, and model validation. We implement many of the techniques discussed in example analyses of plant functional traits to demonstrate the general utility of MR-PMMs in handling complex real-world data sets. Finally, we discuss the emerging synthesis of comparative techniques made possible by MR-PMMs, highlight strengths and weaknesses, and offer practical recommendations to analysts. To complement this material, we provide online tutorials including side-by-side model implementations in two popular R packages, MCMCglmm and brms.
性状数据库和分子系统发育的规模与分辨率正在迅速提升。这些资源使得比较生物学中的许多开放性问题能够借助恰当的统计工具得以解决。多响应（MR）系统发育混合模型（PMMs）为性状进化的多变量分析提供了巨大潜力。尽管这些方法灵活且强大，但生态与进化领域的研究人员却并不常使用，这反映出相关专业技术文献给许多生物学家的使用造成了障碍。在此，我们为MR - PMMs提供一份实用且易懂的指南。我们首先回顾单响应（SR）PMMs，以引入关键概念并概述该方法在刻画性状协同进化模式方面的局限性。由于性状协方差的明确分解，我们强调MR - PMMs是分析涉及多个物种性状时更优的方法。我们讨论了多层次模型、进化的多变量模型以及对非高斯响应性状的扩展。我们重点介绍了使用图形模型进行因果推断的技术，以及包括先验设定和潜在因子模型在内的高级主题。通过模拟数据和直观示例，我们讨论了解释、预测和模型验证。我们在植物功能性状的示例分析中实现了许多所讨论的技术，以展示MR - PMMs在处理复杂现实世界数据集方面的普遍效用。最后，我们讨论了由MR - PMMs促成的比较技术的新兴综合，突出了其优缺点，并为分析人员提供了实用建议。为补充这些内容，我们提供了在线教程，包括在两个流行的R包MCMCglmm和brms中并行的模型实现。
