Combining Distance Matrices on Identical Taxon Sets for Multi-Gene Analysis with Singular Value Decomposition

We present a simple and effective method for combining distance matrices from multiple genes on identical taxon sets to obtain a single representative distance matrix from which to derive a combined-gene phylogenetic tree. The method applies singular value decomposition (SVD) to extract the greatest common signal present in the distances obtained from each gene. The first right eigenvector of the SVD, which corresponds to a weighted average of the distance matrices of all genes, can thus be used to derive a representative tree from multiple genes. We apply our method to three well known data sets and estimate the uncertainty using bootstrap methods. Our results show that this method works well for these three data sets and that the uncertainty in these estimates is small. A simulation study is conducted to compare the performance of our method with several other distance based approaches (namely SDM, SDM* and ACS97), and we find the performances of all these approaches are comparable in the consensus setting. The computational complexity of our method is similar to that of SDM. Besides constructing a representative tree from multiple genes, we also demonstrate how the subsequent eigenvalues and eigenvectors may be used to identify if there are conflicting signals in the data and which genes might be influential or outliers for the estimated combined-gene tree.本研究提出一种简单高效的方法，可将同一分类群集合下多个基因的距离矩阵进行整合，得到单一代表性距离矩阵，进而构建联合基因系统发育树（phylogenetic tree）。该方法通过奇异值分解（Singular Value Decomposition, SVD）提取各基因距离矩阵中共同存在的最强信号。该奇异值分解得到的首个右特征向量等价于所有基因距离矩阵的加权平均，因此可用于从多基因数据中构建代表性系统发育树。本研究将该方法应用于三个经典数据集，并通过自举法（Bootstrap）估算结果的不确定性。实验结果表明，该方法在这三个数据集上均表现优异，且估算结果的不确定性较低。本研究还开展了仿真实验，将所提方法与其他几种基于距离的方法（即SDM、SDM*及ACS97）进行性能对比，结果显示在共识构建场景下，所有对比方法的性能均相当。本方法的计算复杂度与SDM相近。除了从多基因数据构建代表性系统发育树之外，本研究还展示了如何利用后续得到的特征值（eigenvalue）与特征向量，识别数据中是否存在信号冲突，以及哪些基因对联合基因系统发育树的构建具有显著影响或属于异常值。