论文摘要
系统发生学是进化生物学的一个重要研究领域，而系统发生分析早在达尔文时期就已经开始了。系统发生是指生物形成或进化的历史，系统发生学研究物种之间的进化关系，其基本思想是比较物种的特征，并认为特征相似的物种在遗传学上接近。系统发生研究的结果往往以系统发生树表示，用它描述物种之间的进化关系。通过对生物学数据的建模提取特征，进而比较这些特征，研究生物形成或进化的历史。近些年来，重建系统发生树的resolved quartet方法越来越手到分子生物界的关注。给定系统发生树T，{a，b，c，d}是其叶子节点子集，ab|cd表示树T中ab-路与cd-路不交，称为resolved quartet。对于系统发生树T，其resolved quartet集Q（T）是唯一确定的，这正式resolved quartet方法的基本依据，但是resolved quartet集的兼容性问题是NP-hard的，不存在多项式时间算法。本文提出了resolved triple方法，不仅可以在多项式时间内重建系统发生树，还可以检验resolved triple集的兼容性。给定系统发生树T，{a，b，c}是其叶子节点子集，符号ab|c表示T中存在内部节点u，v，使得a，b，c∈des（u），a，b∈des（v），c （?） des（v），称为有resolved triple。我们首先通过特定规则建立resolved triple集R相对应的有向图GR，对GR中点不交有向路{pk}两两进行一系列规的化简，最终得到R的基。在第4部分中，我们利用resolved quartet集对此方法做出证明，并给出resolved quartet集兼容的必要条件。本文由四部分组成：第一章：引言，叙述问题的由来。第二章：经典结论及基本定义，主要叙述前人的一些经典方法并定义本文所涉及的基本符号。第三章：resolved triple集的兼容性及多项式时间算法，这是本文最重要的一章，也是最核心的一章。在这一章中，通过对有向图GR的分析提出了（n-2）基算法。第四章：resolved quartet集的兼容性，在这一章中，首先证明了（n-2）基算法，最后提出了resolved quartet集兼容的必要条件。
论文目录
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