分支分类学中和谐性概念与和谐性分析方法

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。并对该方法在分支分类研究中的应用进行讨论。

THE COMPATIBILITY CONCEPT AND COMPATIBILITY ANALYSIS METHOD IN CLADISTICS

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.