Effects of Change of Characters and of Number of Characters in Numerical Taxonomy

Information on 214 morphological characters for 30 taxospecies of the genus Salix, willows, was obtained. Ten analyses were made using different subsets of these characters. The purpose of these analyses was to determine whether different analyses yield different results. Each analysis used the same coefficient of distance in Eu,clidean space to obtain similarities among the taxospecies. The unweighted pair group method (averages) was, used for cluster analysis. Results reveal different clusters of taxospecies with each analysis, although certain groups remained invariant in most of the analyses. In the absence of other information, those analyses using all available data are judged to estimate best the phenetic relationships among taxospecies in the context of all possible characters. The potential value of numerical taxonomy in biosystematics is indicated by its ability to, serve as an efficient context for the generation of hypotheses of biosystematic value. INTRODUCTION Crovello, (1968a) investigated the effect of change of number of OTU's (operational taxonomic units; see Sokal and Sneath, 1963) on the results of clustering in numerical taxonomy. I found a significant effect, which motivated the present study. The purpose of the present paper is to investigate the effect of change of characters and of number of characters in numerical taxonomy. Katz and Torres (1965) carried out an analogous study but they varied the statistical index. In zoology Boyce (1964), Minkoff (1965), Michener and Sokal (1966), and Ehrlich and Ehrlich (1967) have made somewhat similar analyses. The present investigation will also, serve as a test of the hypotheses of nonspecificity and of the matches asymptotes (Sokal and Sneath, 1963). The primary concern of the present study is analysis of part of the methodology of numerical taxonomy to, ascertain its value for plant systematics. The particular species used in the present study serve as a context in which results of the different taximetric analyses can be observed. Although increased knowledge about these species is a natural by-product, the evaluation of the present results in terms of formal taxonomy for the group, is the subject of another paper. MATERIAL AND METHODS Crovello (1966) obtained data on the willows of California as a by-product of a study of the taxonomy of section Sitchenses of the genus Salix. Measurements were made on 372 plants representing the 30 taxospecies of the genus Salix in California. The total number of morphological characters measured was 214. Details of sampling and of the methods of character state coding can be found in Crovello (1966, 1968b). Table 1 lists the 30 taxospecies of California recog-