Euclidean Nature of Phylogenetic Distance Matrices
Euclidean Nature of Phylogenetic Distance Matrices
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DOI：
10.1093/sysbio/syr066
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发表时间：
2011-12-01
影响因子：
6.5
通讯作者：
Ollier, Sebastien
中科院分区：
文献类型：
--
作者：
de Vienne, Damien M.;Aguileta, Gabriela;Ollier, Sebastien
系统发育是比较生物学的基础，因为它们有助于识别统计检验所依赖的独立事件。可以区分两组系统发育比较方法（PCM）：一类通过引入明确的进化模型来考虑系统发育，另一类仅将系统发育视为统计约束，旨在将性状值划分为系统发育成分（系统发育惯性）和一个或多个与适应性进化相关的特定成分。将系统发育信息纳入 PCM 的方式取决于所使用的方法。对于第一组方法，系统发育按照给定的进化模型（例如布朗运动（BM））转换为性状的方差-协方差矩阵。对于第二组方法，系统发育被转换为距离矩阵，随后将其转换为欧几里德距离以执行主坐标分析。在这里，我们证明，简单地取从系统发育树中提取的距离矩阵的元素平方根可以确保拥有欧几里德距离矩阵。对于物种之间的任何类型的距离（父系或节点）以及具有多分叉节点的树木来说都是如此。此外，我们还说明，这种使用平方根的简单变换比文献中经典使用的更复杂的变换（例如 Cailliez 方法）带来的几何失真更小。给定系统发育距离矩阵的元素平方根的欧几里德性质，可以建立遵循BM模型或性状进化的相关模型的性状的系统发育方差-协方差矩阵的正半定性。这样，我们在比较分析中广泛使用的两组统计方法之间架起了一座桥梁。这些结果应该引起生态学家和进化生物学家进行结合系统发育的统计分析的极大兴趣。
Phylogenies are fundamental to comparative biology as they help to identify independent events on which statistical tests rely. Two groups of phylogenetic comparative methods (PCMs) can be distinguished: those that take phylogenies into account by introducing explicit models of evolution and those that only consider phylogenies as a statistical constraint and aim at partitioning trait values into a phylogenetic component (phylogenetic inertia) and one or multiple specific components related to adaptive evolution. The way phylogenetic information is incorporated into the PCMs depends on the method used. For the first group of methods, phylogenies are converted into variance-covariance matrices of traits following a given model of evolution such as Brownian motion (BM). For the second group of methods, phylogenies are converted into distance matrices that are subsequently transformed into Euclidean distances to perform principal coordinate analyses. Here, we show that simply taking the elementwise square root of a distance matrix extracted from a phylogenetic tree ensures having a Euclidean distance matrix. This is true for any type of distances between species (patristic or nodal) and also for trees harboring multifurcating nodes. Moreover, we illustrate that this simple transformation using the square root imposes less geometric distortion than more complex transformations classically used in the literature such as the Cailliez method. Given the Euclidean nature of the elementwise square root of phylogenetic distance matrices, the positive semidefinitiveness of the phylogenetic variance-covariance matrix of a trait following a BM model, or related models of trait evolution, can be established. In that way, we build a bridge between the two groups of statistical methods widely used in comparative analysis. These results should be of great interest for ecologists and evolutionary biologists performing statistical analyses incorporating phylogenies.