Reliable phylogenetic regressions for multivariate comparative data: illustration with the MANOVA and application to the effect of diet on mandible morphology in Phyllostomid bats

Understanding what shapes species phenotypes over macroevolutionary timescales from comparative data often requires studying the relationship between phenotypes and putative explanatory factors or testing for differences in phenotypes across species groups. In phyllostomid bats for example, is mandible morphology associated to diet preferences? Performing such analyses depends upon reliable phylogenetic regression techniques and associated tests (e.g. phylogenetic Generalized Least Squares, pGLS and phylogenetic analyses of variance and covariance, pANOVA, pANCOVA). While these tools are well established for univariate data, their multivariate counterparts are lagging behind. This is particularly true for high dimensional phenotypic data, such as morphometric data. Here we implement much-needed likelihood-based multivariate pGLS, pMANOVA and pMANCOVA, and use a recently developed penalized likelihood framework to extend their application to the difficult case when the number of traits p approaches or exceeds the number of species n. We then focus on the pMANOVA and use intensive simulations to assess the performance of the approach as p increases, under various levels of phylogenetic signal and correlations between the traits, phylogenetic structure in the predictors, and under various types of phenotypic differences across species groups. We show that our approach outperforms available alternatives under all circumstances, with greater power to detect phenotypic differences across species group when they exist, and a lower risk of improperly detecting nonexistent differences. Finally, we provide an empirical illustration of our pMANOVA on a geometric-morphometric dataset describing mandible morphology in phyllostomid bats along with data on their diet preferences. Overall our results show significant differences between ecological groups. Our approach, implemented in the R package mvMORPH and illustrated in a tutorial for end-users, provides efficient multivariate phylogenetic regression tools for understanding what shapes phenotypic differences across species.

依托比较数据解析宏观进化时间尺度下塑造物种表型的驱动因素，通常需要开展两项核心工作：一是探究表型与潜在解释因子间的关联，二是检验不同物种类群间的表型差异。以叶口蝠科（Phyllostomidae）蝙蝠为例，其下颌形态是否与食性偏好存在关联？开展此类分析离不开可靠的系统发育回归技术及配套检验方法，例如系统发育广义最小二乘法（phylogenetic Generalized Least Squares, pGLS）、系统发育方差与协方差分析（phylogenetic analysis of variance and covariance, pANOVA、pANCOVA）。尽管上述工具在单变量数据场景下已十分成熟，但多变量版本的开发却相对滞后，在性状数量p接近甚至超过物种数n的高维表型数据（如形态测量数据）中，这一短板尤为凸显。本研究实现了学界亟需的基于似然的多变量系统发育广义最小二乘法（phylogenetic Generalized Least Squares, pGLS）、多变量系统发育方差分析（phylogenetic Multivariate Analysis of Variance, pMANOVA）与多变量系统发育协方差分析（phylogenetic Multivariate Analysis of Covariance, pMANCOVA），并借助新近提出的惩罚似然框架，将方法拓展应用至p接近或超出n的高维难题场景中。随后我们聚焦pMANOVA方法，通过大规模模拟实验评估其在p递增时的性能表现，涵盖不同水平的系统发育信号与性状间相关性、预测变量中的系统发育结构，以及多种类型的物种类群间表型差异场景。结果显示，我们的方法在所有测试场景下均优于现有替代方案：当类群间存在真实表型差异时，该方法具备更高的差异检出效力；而在无真实差异时，误报差异的风险更低。最后，我们通过实证案例展示了该pMANOVA方法的应用：基于一组描述叶口蝠科蝙蝠下颌形态的几何形态测量数据集，结合其食性偏好数据开展分析。整体结果表明不同生态类群间存在显著表型差异。本研究开发的方法已在R包mvMORPH中实现，并为终端用户提供了配套教程，可为解析跨物种类群表型差异的驱动机制提供高效的多变量系统发育回归工具。