论文标题
系统发育树形状的热带几何变化
Tropical Geometric Variation of Phylogenetic Tree Shapes
论文作者
论文摘要
我们研究了树空间的热带几何解释中系统发育形状的行为。树状正式称为树拓扑；树拓扑也可以被认为是树的组合类型，这是由树的分支配置和叶子标记给出的。我们使用热带线段作为框架来定义方差概念以及树木拓扑的不变性：我们提供了一个组合搜索定理，描述了沿热带线段沿沿热带线段的所有树拓扑以及树下的设置，在哪些树下不会沿着热带线段变化。我们的研究是通过与Billera，Holmes和Vogtmann提出的（称为BHV空间）提出的大地测量指标相比的动机。我们将热带几何环境视为一组系统发育树的BHV空间的替代框架。我们给出了一种计算热带线段的算法，该算法比当前可用于BHV Geodesics的最快方法低于计算复杂性，并表明其轨迹的行为更加微妙：而BHV地理位置则导致非常不同的树木拓扑的起源，而Tropical Line Line Line Line段却绕过它。
We study the behavior of phylogenetic tree shapes in the tropical geometric interpretation of tree space. Tree shapes are formally referred to as tree topologies; a tree topology can also be thought of as a tree combinatorial type, which is given by the tree's branching configuration and leaf labeling. We use the tropical line segment as a framework to define notions of variance as well as invariance of tree topologies: we provide a combinatorial search theorem that describes all tree topologies occurring along a tropical line segment, as well as a setting under which tree topologies do not change along a tropical line segment. Our study is motivated by comparison to the moduli space endowed with a geodesic metric proposed by Billera, Holmes, and Vogtmann (referred to as BHV space); we consider the tropical geometric setting as an alternative framework to BHV space for sets of phylogenetic trees. We give an algorithm to compute tropical line segments which is lower in computational complexity than the fastest method currently available for BHV geodesics and show that its trajectory behaves more subtly: while the BHV geodesic traverses the origin for vastly different tree topologies, the tropical line segment bypasses it.
