使用k-means和Robinson and Foulds距离构建备选共识树和超级树
Building alternative consensus trees and supertrees using k-means and Robinson and Foulds distance
摘要：
每个基因都有自己的进化历史，与其他基因的进化历史有很大不同。例如，某些个别基因或操纵子可能受到特定水平基因转移和重组事件的影响。因此，每个基因的进化历史应该由它自己的系统发育树来表示，它可能显示出与物种树不同的进化模式，物种树解释了垂直下降的主要模式。传统的共识树或超树推理方法的输出是唯一的共识树或超树。我们描述了一种新的有效的方法来推断多个备选的共识树和超树，以最好地代表一组给定的基因遗传的最重要的进化模式。我们展示了如何适应版本的流行的k-均值聚类算法，基于一些有趣的属性的罗宾逊和Foulds距离，可以用来划分一组给定的树到一个（同质数据）或多个（异构数据）集群（S）的树。此外，我们适应流行的Calienski-Harabasz，剪影，球和霍尔，差距聚类有效性指标树聚类与k-均值。一个特别注意的相关，但非常具有挑战性的问题，推断替代超树。该方法利用了目标函数的欧几里德性质，比现有的树聚类技术更快，因此非常适合分析大型进化数据集。我们应用新的方法来发现替代超树特征的主要模式的演变的SARS-CoV-2和遗传相关的β冠状病毒。
英文摘要：
Each gene has its own evolutionary history which can substantially differ from the evolutionary histories of other genes. For example, some individual genes or operons can be affected by specific horizontal gene transfer and recombination events. Thus, the evolutionary history of each gene should be represented by its own phylogenetic tree which may display different evolutionary patterns from the species tree that accounts for the main patterns of vertical descent. The output of traditional consensus tree or supertree inference methods is a unique consensus tree or supertree. We describe a new efficient method for inferring multiple alternative consensus trees and supertrees to best represent the most important evolutionary patterns of a given set of gene phylogenies. We show how an adapted version of the popular k-means clustering algorithm, based on some interesting properties of the Robinson and Foulds distance, can be used to partition a given set of trees into one (for homogeneous data) or multiple (for heterogeneous data) cluster(s) of trees. Moreover, we adapt the popular Caliński-Harabasz, Silhouette, Ball and Hall, and Gap cluster validity indices to tree clustering with k-means. A special attention is given to the relevant but very challenging problem of inferring alternative supertrees. The use of the Euclidean property of the objective function of the method makes it faster than the existing tree clustering techniques, and thus perfectly suitable for analyzing large evolutionary datasets. We apply the new method to discover alternative supertrees characterizing the main patterns of evolution of SARS-CoV-2 and genetically related betacoronaviruses.
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