小树邻居连接算法的几何结构
The Geometry of the Neighbor-Joining Algorithm for Small Trees
摘要：
在2007年，Eickmeyer等人表明，用于系统发育重建的邻居连接（NJ）算法和平衡最小进化（BME）方法输出的树拓扑结构均由相异性图空间的多面体细分${\R}^{n \choose 2}$确定，其中$n$是分类群的数量。在本文中，我们将分析的行为的邻居加入算法上的五个和六个分类群和研究的几何和组合学的多面体细分空间的相异性映射为六个分类群以及超平面表示的每个多面体细分。我们还研究了Eickmeyer等人提出的问题之一的模拟，即，NJ算法对树度量的小扰动的鲁棒性，已知树模型难以经由NJ算法重建。
英文摘要：
In 2007, Eickmeyer et al. showed that the tree topologies outputted by the Neighbor-Joining (NJ) algorithm and the balanced minimum evolution (BME) method for phylogenetic reconstruction are each determined by a polyhedral subdivision of the space of dissimilarity maps ${\R}^{n \choose 2}$, where $n$ is the number of taxa. In this paper, we will analyze the behavior of the Neighbor-Joining algorithm on five and six taxa and study the geometry and combinatorics of the polyhedral subdivision of the space of dissimilarity maps for six taxa as well as hyperplane representations of each polyhedral subdivision. We also study simulations for one of the questions stated by Eickmeyer et al., that is, the robustness of the NJ algorithm to small perturbations of tree metrics, with tree models which are known to be hard to be reconstructed via the NJ algorithm.
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