A Study of Faunal Resemblance Using Numerical Taxonomy and Factor Analysis

This paper is an analysis of patterns of animal distribution by means of ( 1 ) calculation and clustering of a distance matrix, (2) factor analysis and trend surface maps of scores of five centroid factors, and (3) a stereogram of the counties projected on the principal axes. The data, which are the incidences of amphibians, reptiles, and mammals in the 105 counties of Kansas, were used principally for illustrative purposes, and comprise 185 OTU's consisting of 137 species (37 of which were subdivided into 85 subspecies). Five factors were extracted from a matrix of correlations among OTU's and mapped by trend surface analysis. These were shown to be of interest even though they yielded overlapping faunal zones. The predictive powers of the method, by the inclusion of environmental variables, is discussed. The present study is an application of certain multivariate analytical techniques in the description and analysis of faunal distribution patterns. Quantitative estimates of faunal resemblances have been largely limited to coefficients of resemblance, which authors often derive anew for a particular use. Simpson (1960) and Long (1963) have reviewed the various coefficients in the literature. Hagmeier and Stults (1964) and Hagmeier (1966) used a coefficient which measured the relative number of species distributions ending in areas of 50-miles-square. They grouped areas with low values into faunal zones, using areas of high values as borders. Coefficients were calculated between faunal zones and the resulting matrix was clustered by numerical taxonomic methods. R-type factor analyses of species distributions have been used extensively by some ecologists to describe vegetation (see Goodall, 1954). The uses of factor analysis in systematics have been reviewed by Sokal (1965). The major purpose of this analysis is to test the applicability of the methods of numerical taxonomy and trend surface analysis to biogeographic distribution patterns. The analysis is best viewed primarily as an illustrative example and not as a definitive study of the distribution of vertebrates in Kansas. THE DATA The data were taken from distribution maps for Kansas by Hall (1955), for mammals, and Smith (1956), for amphibians and reptiles. Because the data were used only as an example, the maps were assumed to depict accurately the distributions of these animals without further corroboration. The study included 61 species of mammals (17 of which were divided into 2 subspecies each, 6 into 3 subspecies, 1 into 4 subspecies, and 1 into 5 subspecies), 52 species of reptiles (7 of which were divided into 2 subspecies each), and 24 species of amphibians (5 of which were divided into 2 subspecies each), yielding a total of 185 OTU's. The raw data can be obtained by writing to the author. They comprise a data matrix consisting of ones and zeroes, representing presence and absence, respectively, of each species or subspecies within each of the 105 counties. The computations were carried out at the Computation Center of The University of Kansas using the NT-SYS system of multivariate routines developed by F. J. Rohlf, R. L. Bartcher and J. R. L. Kishpaugh for the IBM 7040 and the GE 625 computers. RESULTS USING A PHENOGRAM