Taxometric Maps

Abstract

Carmichael, J. W. (Mold Herbarium and Culture Collection, U. Alberta, Edmonton) and P. H. A. Sneath (M.R.C. Microbial Systematics Research Unit, U. Leicester, Leicester, England). 1969. Taxometric maps. Syst. Zool., 18:402–415. [Numerical taxonomy; taxometric maps].—An n × t table, recording the results of n different tests or observations on each of t items, contains information which may be used to classify the items (OTU's) according to their similarities and differences. We equate similarity with relative closeness, and difference with relative distance. Relative closeness and relative distance may be thought of as complementary measures of proximity. The process of converting an n × t table of test results into a t × t table of proximities between the pairs of items is called proximity analysis. The process of finding any isolated subsets of similar items is called cluster analysis. Taxometric methods are viewed as approaches to compressing the information in an n × t table into a graphic, best-fit model for the display of proximity and cluster relations among OTU's. Three general approaches are followed: 1) compression before proximity analysis, 2) compression as an intermediate step between proximity and cluster analysis, and 3) compression after cluster analysis. The utility of these approaches is compared. Taxometric maps are introduced as a means to display proximity and cluster relations. A procedure is given for preparing taxometric maps from cluster analysis results, and two examples are presented for illustration. An appendix on similarity and proximity equates three independently derived similarity coefficients, which are shown to be derivable from a city-block metric proximity measure.