Cox Shelby, Gross Elizabeth, Martin Samuel
Max-Planck Institute for Mathematics in the Natural Sciences, Leipzig, Germany.
University of Hawai'i at Mānoa, Honolulu, HI, USA.
Bull Math Biol. 2025 Aug 18;87(9):132. doi: 10.1007/s11538-025-01506-1.
Phylogenetic networks describe the evolution of a set of taxa for which reticulate events have occurred at some point in their evolutionary history. Of particular interest is when the evolutionary history between a set of just three taxa has a reticulate event. In molecular phylogenetics, substitution models can model the process of evolution at the genetic level, and the case of three taxa with a reticulate event can be modeled using a substitution model on a semi-directed graph called a 3-sunlet. We investigate a class of substitution models called group-based phylogenetic models on 3-sunlet networks. In particular, we investigate the discrete geometry of the parameter space and how this relates to the dimension of the phylogenetic variety associated to the model. This enables us to give a dimension formula for this variety for general group-based models when the order of the group is odd.
系统发育网络描述了一组分类单元的进化过程，在其进化历史的某个时刻发生了网状事件。特别令人感兴趣的是，当一组仅三个分类单元之间的进化历史出现网状事件时。在分子系统发育学中，替换模型可以在基因水平上模拟进化过程，具有网状事件的三个分类单元的情况可以使用一种称为3-小太阳的半定向图上的替换模型来建模。我们研究了一类在3-小太阳网络上基于群的系统发育模型的替换模型。特别是，我们研究了参数空间的离散几何以及它与该模型相关的系统发育多样体维度之间的关系。这使我们能够在群的阶为奇数时，给出一般基于群的模型的这个多样体的维度公式。
