EVOLUTIONARY PATTERNS IN PELYCOSAURIAN REPTILES: A FACTOR-ANALYTIC STUDY.

FACTOR ANALYSIS IN EVOLUTIONARY STUDIES The construction of a phylogeny from fossil data involves an inference based upon patterns of morphologic change. A description of these patterns as they affect the total organism provides the most desirable basis for approaching the fundamental problem of evolutionary paleontology-the explanation of form in terms of adaptation. Until recently, quantitative morphologists could proceed little beyond the presentation of morphologic data in pairs, using the statistical techniques of bivariate analysis. That this treatment of pairs abstracted from total form might obscure important patterns was never doubted, but prior to the advent of electronic computers, prohibitive computational labor precluded the application of many multivariate methods long known in theory. Extensive data tabulations are available in the monographic literature of several fossil vertebrate groups. A prerequisite for the fruitful use of these thousands of individual facts is their synthesis into a coherent scheme which can provide causal insights. The multivariate technique of factor analysis is one such scheme; a somewhat different approach with similar objectives was developed by Olson and Miller (1958). Many previous applications of factor analysis to biological problems have treated data as a tool to illustrate the multivariate technique. Since the technique is meant to be the tool, I shall concentrate on pelycosaurian evolution. Nonetheless, a few comments designed to make this work fully accessible to readers unfamiliar with factor analysis are in order. Thurstone (1947), Cattell (1952), and Harman (1960) are general texts on factor analysis. The specific form followed here was developed by Imbrie (1963) and Manson and Imbrie (1964), the latter containing a description of the program used hereCOVAP (Columbia Vector Analysis Program). COVAP was applied to geologic data by Imbrie and Van Andel (1964). The voluminous data of large tabular compilations cannot be handled conveniently in raw form. Methods which abstract simpler patterns from raw data are to be judged as models. The schemes themselves are descriptive and provide 'no a priori explanation of anything; they are simply ways of exposing information already implicit in the original data. The scheme of a useful model will suggest causal explanations of correlations observed in raw data; that of a useless model, while just as "true," provides no such insight. The computer can do no more than conveniently rearrange the data it is given; only human ingenuity can transcend the purely descriptive. Factor analysis is an abstracting scheme which resolves a set of samples (pelycosaur species here) or variables (measurements of homologous bones in all pelycosaurs considered) into a group of reference axes considerably fewer than the total sample or variable size. Each sample or variable is depicted as a single vector in m-space. Using a triaxial model which can be grasped geometrically, all vectors radiate from a single point in three dimensional space. When vectors have been normalized to unit length, the correlation of any two is given by the cosine of the angle separating