Data from: Characterizing and comparing phylogenetic trait data from their normalized Laplacian spectrum

Figure_Supplemental_1Measuring the effect of phylogenetic signal on splitter values.} (A) Boxplot of the splitter values for 100 randomized datasets (white) obtained for each of the ten datasets with two monophyletic clusters. Splitter values for the initial BM datasets with two clusters are shown in purple. Boxplot of 100 datasets simulated under a simple BM process with no clusters on a single tree (coral) is shown for comparison. (B) Boxplot of Blomberg’s $K$ for each randomized dataset (white); values for the initial BM datasets with two clusters are shown in purple. Boxplot of 100 datasets simulated under a simple BM process with no clusters on a single tree (coral) is shown for comparison.Figure_Supplemental_2Measuring the effect of erroneous trait data on spectral density profile summary statistics.} Spectral density profile summary statistics for data simulated under a BM process (coral) with introduced error for $10\%$ of tips with a sampling variance equal to one, two, and three times the standard error of the simulated BM data; and with a sampling variance equal to one times the standard error for $10, 20, 30, 100\%$ of tips. Spectral density profile summary statistics for data simulated on the same tree under an ACDC process ($\beta=1.5$) is also shown (cornflowerblue).Figure_Supplemental_3Clustering phylogenetic trait data using the spectral density profile of the nMGL on a non-ultrametric tree.} Hierarchical clustering of spectral density profiles and three-dimensional plotting of spectral density profile summary statistics for phylogenetic trait data simulated under AC (cornflower blue), BM (coral), and DC (sea green) models of trait evolution on a single (A) constant-rate, (C) increasing-rate, and (D) decreasing-rate birth-death tree without pruning extinct lineages. Tree is shown in inset. Asterisks denote bootstrap probabilities $>0.95$ at the split. (B) Silhouette widths for profiles comprising each trait model cluster simulated on the ultrametric or non-ultrametric tree (see Fig. 5A).Figure_Supplemental_4Effect of tree size on the nMGL. (A) Scatterplots and OLS regression slopes for spectral density profile summary statistics for trait data simulated under DC (sea green), BM (coral), and AC (cornflower blue) models on constant-rate birth-death trees with different numbers of tips. (B) Phylogenetic trait space for trait models simulated under AC, BM, and DC models on trees with different numbers of tips.

补充图1 量化系统发育信号对分裂值的影响
(A) 针对10个包含两个单系类群的初始布朗运动（Brownian Motion, BM）数据集，分别生成100份随机化数据集，绘制其分裂值箱线图（白色箱线图）；同时展示含两个类群的初始BM数据集的分裂值（紫色箱线图）。为便于对比，同时给出在单棵树上模拟的不含类群的简单BM过程数据集（珊瑚色箱线图，共100份）的分裂值箱线图。(B) 各随机化数据集的布隆姆K值（Blomberg’s K）箱线图（白色箱线图）；含两个类群的初始BM数据集的布隆姆K值以紫色展示。为便于对比，同时给出在单棵树上模拟的不含类群的简单BM过程数据集（珊瑚色箱线图，共100份）的布隆姆K值箱线图。

补充图2 量化错误性状数据对谱密度剖面汇总统计量的影响
针对10%的终端类群（tips），引入其抽样方差分别为模拟BM数据标准误1倍、2倍、3倍的误差，对基于BM过程模拟的数据集（珊瑚色）计算谱密度剖面汇总统计量；同时设置10%、20%、30%、100%的终端类群的抽样方差为模拟BM数据标准误1倍的实验组。此外还展示了在同一棵树上基于ACDC过程（β=1.5）模拟的数据集的谱密度剖面汇总统计量（矢车菊蓝色）。

补充图3 在非超度量树上使用nMGL的谱密度剖面对系统发育性状数据进行聚类
针对在单棵恒定速率(A)、递增速率(C)及递减速率(D)的出生-死亡树上（未修剪灭绝支系），基于AC、BM及DC三种性状进化模型（分别对应矢车菊蓝色、珊瑚色及海绿色）模拟的系统发育性状数据，对其谱密度剖面进行层级聚类，并对谱密度剖面汇总统计量进行三维可视化。对应系统发育树以插图形式展示。分裂节点处自展概率大于0.95的节点以星号标注。(B) 分别在超度量树与非超度量树上模拟的各性状模型聚类对应的轮廓系数（silhouette widths）箱线图（详见图5A）。

补充图4 树的规模对nMGL的影响
(A) 针对在不同终端类群数量的恒定速率出生-死亡树上，基于DC、BM及AC三种模型模拟的性状数据，绘制其谱密度剖面汇总统计量的散点图及普通最小二乘（Ordinary Least Squares, OLS）回归斜率。(B) 针对在不同终端类群数量的树上，基于AC、BM及DC三种模型模拟的性状数据，绘制其系统发育性状空间分布图。