Department of Mathematics, The University of Akron, Akron, OH, 44325-4002, USA.
J Math Biol. 2020 Apr;80(5):1235-1263. doi: 10.1007/s00285-019-01458-w. Epub 2020 Feb 11.
Balanced minimum evolution is a distance-based criterion for the reconstruction of phylogenetic trees. Several algorithms exist to find the optimal tree with respect to this criterion. One approach is to minimize a certain linear functional over an appropriate polytope. Here we present polytopes that allow a similar linear programming approach to finding phylogenetic networks. We investigate a two-parameter family of polytopes that arise from phylogenetic networks, and which specialize to the Balanced Minimum Evolution polytopes as well as the Symmetric Travelling Salesman polytopes. We show that the vertices correspond to certain level-1 phylogenetic networks, and that there are facets or faces for every split. We also describe lower bound faces and a family of faces for every dimension.
平衡最小进化是一种基于距离的构建系统发育树的准则。有几种算法可以找到这个准则下的最优树。一种方法是在适当的多面体上最小化某个线性泛函。在这里，我们提出了允许类似线性规划方法来寻找系统发育网络的多面体。我们研究了来自系统发育网络的一对数多面体，它们专门用于平衡最小进化多面体和对称旅行商多面体。我们表明，顶点对应于某些一级系统发育网络，并且每个分裂都有面或面。我们还描述了每个维度的下限面和一族面。
