van Iersel Leo, Moulton Vincent
Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB , Amsterdam, The Netherlands,
J Math Biol. 2014 Jun;68(7):1707-29. doi: 10.1007/s00285-013-0683-5. Epub 2013 May 17.
Phylogenetic networks generalize evolutionary trees, and are commonly used to represent evolutionary histories of species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer. Recently, there has been great interest in trying to develop methods to construct rooted phylogenetic networks from triplets, that is rooted trees on three species. However, although triplets determine or encode rooted phylogenetic trees, they do not in general encode rooted phylogenetic networks, which is a potential issue for any such method. Motivated by this fact, Huber and Moulton recently introduced trinets as a natural extension of rooted triplets to networks. In particular, they showed that [Formula: see text] phylogenetic networks are encoded by their trinets, and also conjectured that all "recoverable" rooted phylogenetic networks are encoded by their trinets. Here we prove that recoverable binary level-2 networks and binary tree-child networks are also encoded by their trinets. To do this we prove two decomposition theorems based on trinets which hold for all recoverable binary rooted phylogenetic networks. Our results provide some additional evidence in support of the conjecture that trinets encode all recoverable rooted phylogenetic networks, and could also lead to new approaches to construct phylogenetic networks from trinets.
系统发生网络是进化树的推广，通常用于表示经历杂交、重组和横向基因转移等网状进化过程的物种的进化历史。最近，人们对尝试开发从三元组构建有根系统发生网络的方法产生了浓厚兴趣，三元组即三个物种的有根树。然而，尽管三元组能确定或编码有根系统发生树，但它们通常并不编码有根系统发生网络，这对任何此类方法来说都是一个潜在问题。受这一事实的启发，胡贝尔和莫尔顿最近引入了三网作为有根三元组到网络的自然扩展。特别地，他们表明[公式：见原文]个系统发生网络由其三网编码，并且还推测所有“可恢复的”有根系统发生网络都由其三网编码。在此我们证明可恢复的二级二叉网络和二叉树子网络也由其三网编码。为此，我们基于三网证明了两个分解定理，它们适用于所有可恢复的二叉有根系统发生网络。我们的结果为三网编码所有可恢复的有根系统发生网络这一推测提供了一些额外证据，并且还可能引出从三网构建系统发生网络的新方法。
