Supplementary material: How should functional relationships be evaluated using phylogenetic comparative methods? A case study using metabolic rate and body temperature

AbstractPhylogenetic comparative methods are often used to test functional relationships between traits. However, million-year macroevolutionary observational datasets cannot definitively prove causal links between traits --- correlation does not equal causation and experimental manipulation over such timescales is impossible. While this caveat is widely understood, it is far less appreciated that different phylogenetic approaches make different causal assumptions about the functional relationships of traits. In order to make meaningful inferences, it is critical that our statistical methods make biologically reasonable assumptions. Here we illustrate the importance of causal reasoning in comparative biology by examining a recent study by Avaria-Llautureo et al. (2019) that tested for the evolutionary coupling of metabolic rate and body temperature across endotherms and made the notable discoveries that these traits were unlinked through evolutionary time and that body temperatures were, on average, higher in the early Cenozoic than they are today. We argue that the causal assumptions embedded into their models made it impossible for them to actually test the relevant functional and evolutionary hypothesis. We then re-analyze their data using more biologically appropriate models and find support for the exact opposite conclusions, corroborating previous evidence from physiology and paleontology. We highlight the vital need for causal thinking, even when experiments are impossible. , MethodsThis dataset includes scripts and data from the original cited literature, as well as simulated data with the generating code. Supplementary Text and supplementary Figure 1 are available in the SupplementaryMaterial.* files. Version history, including up to date code, is available at the git repository: https://github.com/uyedaj/Tb_ALEA. Supplementary Figure 1. Simulated values of contrast correlations from phylogenetically-distributed rate scalars demonstrates reasonable power to detect significant relationships between rates directly from contrasts in the presence of rate variation. Open circles indicate that the contrast Pearson-correlation coefficient was non-significant, whereas filled black circles indicate it is significantly correlated in X and Y. Red outlines indicate that the true correlation coefficient among branch rates are significant, whereas black outlines indicate even with perfect knowledge of the branch rates, the obesrved correlation was non-significant. Observed values from the empirical data are shown, while note that the data are simulated to match the Mammalian, not bird data., Usage notesUsage information and a description of the contents of the repository, and the data sources used, is provided in \"README.txt\".

**摘要**：系统发育比较方法（phylogenetic comparative methods）常被用于检验性状间的功能关联。然而，百万年级别的宏观进化观测数据集无法确凿证明性状间存在因果联系——相关不等于因果，且在如此长的时间尺度上无法开展实验操控。尽管这一限定条件已被广泛认知，但不同系统发育方法对性状功能关系所做出的因果假设存在差异这一点，却鲜为人知。若要得出有意义的推论，我们的统计方法采用生物学上合理的假设至关重要。本文以Avaria-Llautureo等人2019年的一项近期研究为例，阐释了因果推理在比较生物学中的重要性：该研究检验了恒温动物（endotherms）的代谢率与体温的进化耦合性，并得到了两项重要发现——这些性状在进化时间尺度上并无关联，且早新生代（Cenozoic）的平均体温高于现代。我们认为，其模型中嵌入的因果假设使得他们实际上无法检验相关的功能与进化假说。随后，我们采用更符合生物学原理的模型对其数据进行了重新分析，得到了完全相反的结论，印证了此前生理学与古生物学的相关证据。我们强调了即使在无法开展实验的情况下，因果思维的至关重要性。

**方法**：本数据集包含引用的原始文献中的脚本与数据，以及带有生成代码的模拟数据。补充文本与补充图1可在*SupplementaryMaterial*系列文件中获取。包括最新代码在内的版本历史可在Git仓库（git repository）https://github.com/uyedaj/Tb_ALEA 中获取。补充图1：基于系统发育分布的速率标量得到的对比相关模拟值表明，在存在速率变异的情况下，直接通过对比检测变量间的显著关联具有合理的检验效力。空心圆圈代表对比皮尔逊相关系数不显著，而实心黑圆圈代表X与Y间存在显著相关。红色边框代表分支速率间的真实相关系数显著，而黑色边框代表即便完全知晓分支速率，观测到的相关仍不显著。图中展示了实证数据的观测值，需注意数据是为匹配哺乳动物数据集而非鸟类数据集而模拟的。

**使用说明**：仓库的内容说明、所用数据来源等使用信息详见"README.txt"。