分支分类学中和谐性概念与和谐性分析方法  

THE COMPATIBILITY CONCEPT AND COMPATIBILITY ANALYSIS METHOD IN CLADISTICS

作　　者：徐克学[1] 

机构地区：[1]中国科学院植物研究所系统与进化植物学开放研究实验室,北京100093

出　　处：《植物分类学报》1994年第4期380-388,共9页Acta Phytotaxonomica Sinica

基　　金：国家自然科学基金 38970070

摘　　要：和谐性是分支分类学中的一个基本概念。本文给出一个和谐性的数学定义,称为Kexue和谐性。并在Kexue和谐性的基础上开发出一个新的和谐性分析方法。 首先在集合论的意义下讨论和谐性概念。两个集合A与B若非相交,即A∩B=φ(空集),或者存在包含关系,即AB或BA,则称A与B是和谐的。两个集合类G和H若G与H中的任何一对集合都是和谐的,即对于任何A∈G和B∈H,A与B是和谐的,则称集合类G与H是和谐的。 令X=[x_(ij)]_(t×n)是一个tOTU_s×n性状的原始数据矩阵。对于固定的性状j,我们给出下面的符号表示其对应集和对应集类:对应集 D(i,j)={k|x_(kj)≥i,1≤k≤t} (i=0,1,……,m_j)对应集类: G(A_j)={D(1,j),D(2,j),…,D(m_j,j)}其中: m_j=max{x_(kj)} 1≤k≤t 于是,我们引导出分支性状的Kexue和谐性定义:两分支性状的对应集合类是和谐的,则称该分支性状相互是和谐的。取特征函数K(i,j)表示性状i与j的和谐性,即: K(i,j)=1 当性状i与j和谐, 0 否则。令i与j跑遍从1到n性状,得到和谐性矩阵。借助和谐性矩阵和各种与和谐性有关的数量指标,设计和谐性定量分析方法。来自动物演化的一个实际例子为此方法提供验证。 最后,对该方法在分支分类研究中的应用进行讨论。Compatibility is a fundamental concept for cladistics. In this paper a mathematical definition of compatibility , called Kexue compatibility , is proposed , and then a new compatibility analysis method for cladistics based on the Kexue compatibility is developed. At first we discuss the concept of compatibility in terms of set theory. Two sets A and B are of compatibility if A and B are disjoint, i. e. if (empty set) , or if there exist inclusion relation, i. e. or . Two classes G and H are of compatibility if any pair of sets from G and H are of compatibility, i. e. if sets A and B are of compatibility for any Let is original data matrix with t OTUs X n characters. For a fixed character j we give following notations to denote its corresponding sets and corresponding class; The corresponding sets D (i, j) = The corresponding class G (Aj) = where Then, we introduce the definition of Kexue compatibility for cladistic character; Two cladistic characters are compatible if its corresponding classes are compatible. Let K {i, j) be a characteristic function which denotes the compatibility of characters I and j , i. e. as characters i and j are compatible, otherwise. Let i and j run from 1 to n characters we obtain the compatibility matrix. A quantitative method for compatibility analysis is designed by means of the compatibility matrix and various numerical indexes related to the compatibility. A practical example from the evolution of animals is provided as evidence for this method. Finally, its application to the research of cladistics is discussed.

关 键 词：分支分类学 和谐性 植物分类学 

分 类 号：Q949[生物学—植物学]