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.

中文翻译：

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1级系统发育网络及其平衡的最小进化多表位。

平衡的最小演化是系统树重建的基于距离的标准。存在几种算法来找到关于该准则的最优树。一种方法是在适当的多位上最小化某些线性官能团。在这里，我们介绍了允许类似的线性规划方法来查找系统进化网络的多表位。我们研究了由系统发育网络产生的两参数多面体家族，这些多面体专门研究平衡最小进化多面体以及对称旅行推销员多面体。我们表明，这些顶点对应于某些级别1的系统发育网络，并且每个分割都有面或面。我们还描述了每个维度的下界面孔和一系列面孔。