University of Canterbury, Department of Mathematics and Statistics, Private Bag 4800, Christchurch, New Zealand.
J Theor Biol. 2011 Jan 21;269(1):245-55. doi: 10.1016/j.jtbi.2010.10.032. Epub 2010 Oct 31.
Rooted phylogenetic networks are used to model non-treelike evolutionary histories. Such networks are often constructed by combining trees, clusters, triplets or characters into a single network that in some well-defined sense simultaneously represents them all. We review these four models and investigate how they are related. Motivated by the parsimony principle, one often aims to construct a network that contains as few reticulations (non-treelike evolutionary events) as possible. In general, the model chosen influences the minimum number of reticulation events required. However, when one obtains the input data from two binary (i.e. fully resolved) trees, we show that the minimum number of reticulations is independent of the model. The number of reticulations necessary to represent the trees, triplets, clusters (in the softwired sense) and characters (with unrestricted multiple crossover recombination) are all equal. Furthermore, we show that these results also hold when not the number of reticulations but the level of the constructed network is minimised. We use these unification results to settle several computational complexity questions that have been open in the field for some time. We also give explicit examples to show that already for data obtained from three binary trees the models begin to diverge.
有根进化网络被用于模拟非树状进化历史。这些网络通常通过将树、聚类、三元组或字符组合成一个单一的网络来构建，在某种明确定义的意义上同时代表它们。我们回顾了这四个模型，并研究了它们之间的关系。受简约原则的启发，人们通常旨在构建一个包含尽可能少的网状进化事件（非树状进化事件）的网络。一般来说，所选的模型会影响所需的最少网状进化事件数量。然而，当从两棵二叉树（即完全解析）中获得输入数据时，我们证明了所需的网状进化事件数量与模型无关。表示树、三元组、聚类（在软连线意义上）和字符（具有不受限制的多次交叉重组）所需的网状进化事件数量都是相等的。此外，我们还证明了这些结果在不是网状进化事件数量而是构建网络的级别最小化的情况下也成立。我们利用这些统一的结果解决了该领域一段时间以来悬而未决的几个计算复杂性问题。我们还给出了具体的例子，以表明即使是从三棵二叉树获得的数据，模型也开始出现分歧。
