三叉树上两状态马尔可夫模型的代数分析
An algebraic analysis of the two state Markov model on tripod trees
摘要：
系统发育推断方法使用越来越复杂的模型从数据生成树。然而，即使是简单的模型及其影响也没有得到充分的理解。在这里，我们调查的两个状态的马尔可夫模型的三叉树，推断条件下，一组给定的观察引起这样的模型。这种类型的调查已经由来自不同研究领域的几位科学家进行过。与其他工作相比，我们充分分析了模型，提出了条件下，人们可以推断出一个模型的观察或至少得到支持的树形相互依存的叶子考虑。我们还提出了所有的条件下，结果可以从三脚架树扩展到四重树，一个必要的步骤，至少重建一个拓扑结构。除了找到这样的扩展工程的条件下，我们讨论的例子，这样的扩展不工作的情况下。
英文摘要：
Methods of phylogenetic inference use more and more complex models to generate trees from data. However, even simple models and their implications are not fully understood. Here, we investigate the two-state Markov model on a tripod tree, inferring conditions under which a given set of observations gives rise to such a model. This type of investigation has been undertaken before by several scientists from different fields of research. In contrast to other work we fully analyse the model, presenting conditions under which one can infer a model from the observation or at least get support for the tree-shaped interdependence of the leaves considered. We also present all conditions under which the results can be extended from tripod trees to quartet trees, a step necessary to reconstruct at least a topology. Apart from finding conditions under which such an extension works we discuss example cases for which such an extension does not work.
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