J Syst Evol ›› 1993, Vol. 31 ›› Issue (6): 578-586.

• Research Articles •

### An Algorithm for Cladistics—Method of Minimal Parallel Evolution

Xu Ke-xue

• Published:1993-11-18

Abstract: The paper presented here is Concerned with the numerical cladisties. In consideration of the fact that the parallel evolution has close relation to the length of evolution graph, a new method of reconstructing evolutionary tree has been developed for the application and practice of cladistics. The procedure of the algorithm of the new method presented in Table I is similar to the method described in paper "An algorithm for cladistics method of maximal same step length". An essential step of the algorithm is how to decide the coefficient between two cladistic units (CTUs). A coefficient called parallel evolutionary coefficient between CTUp and CTUq is defined as follows: where the j is code of CTU and the i is code of character; E(p, q, i, j) is a function given by following expression: min (Xij, Xpj)+(Xij, Xqj)-2min(Xpj, Xqj) as Xij>min (Xpj, Xqj) E(p,q, i,j ) = 0 otherwise. where the Xij is the ith row (CTU) jth colunm (Character) element of the data matrix. Because the method of minimal parallel evolution is closely related to the length of evolutionary graph, it is superior to the method of maximal same step length. A simple datum as an example for comparison shows that the method of minimal parallel evolution can arrive at a better result. But in some cases, we may combine one method with another and thus the coefficient should take following form: S(Sij)=M·S (C) ij-N·S(P) ij in which S (C) ij and S (P) ij are the same step coefficients and the parallel evolution coefficient respectively, and the M and N are positive integers as a weightnumber being given in advance.