The descriptive use of discriminant functions in physical anthropology

Abstract The evolutionary status of the fossil Australopithecinae and of the fossil apes belonging to the genus Proconsul has stimulated considerable discussion. Particular attention has been paid to the teeth of the fossils, and many statements appear in the literature comparing their overall dimensions with those of human beings and of the extant great apes. By way of placing such statements on a sound basis, measurements designed to describe the main features of the teeth have been taken on series of skulls of three types of modern man (British, West African native, Australian aboriginal) and of the three living great apes (gorilla, orang-outang and chimpanzee). The statistical treatment of multivariate data of this type is considered. If p measurements are taken on a tooth, the results may be considered as points in a p-dimensional space. If we replace the original measurements by k p linear functions, we can represent the values of the functions in a space of k dimensions. We choose the linear functions so as to maintain the greatest possible separation between the populations which are being compared. These functions are the solutions of the equation (B - λW) x = 0, when B and W are the dispersion matrices between and within populations; the latent roots λ are proportional to the between-population variances of the corresponding linear functions. The measurements were transformed to logarithms before analysis, as this rendered the within-population dispersion matrices roughly equal. It proved that all but two of the λ’s were small for the nine teeth considered, so that the measurements could be plotted without loss of information on plane diagrams. The positions of the fossils were plotted on the same diagrams, and by computing the values of the remaining linear functions it could be tested whether the points representing the fossils in fact lay close to the planes of the diagrams. It was found that in the measurements examined, Pithecanthropus pekinensis resembled the Australian aboriginal more closely than any ape. Proconsul africanus and P. nyanzae resembled the chimpanzee more closely than any type of man. The Australopithecinae, on the other hand, differed from both men and apes. Their incisors, canines and lower first premolars resembled those of man more closely than those of any ape, whereas their molars and remaining premolars were in these features more ape-like than human. The arithmetical labour of the method of analysis adopted is very considerable and would not be practicable without the use of electronic computing equipment. The results, however, are more trustworthy and also more easily appreciated than those obtained from the alternative technique of examining the measurements one at a time.