Abstract
When comparing populations or classifying unknown specimens on the basis of their morphology, one can either rely on visual comparison or follow an approach which involves the use of the mathematical techniques of discriminant analysis.
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This has led to a rather negative opinion of many an anthropologist on the usefulness of mathematical multivariate techniques for hominid investigation. As a significant example we may mention a paragraph from a letter that was sent to us by Professor Tobias some years ago: “Of course the computer has changed all that and further studies, both using D2 and using Penrose and other approaches, are now commonplace. But the more recent studies on small groups of early hominid fossils have yielded fantastically diverse results”.
G.N. van Vark, Some aspects of the reconstruction of human phylogeny with the aid of multivariate statistical methods. Proceedings of the Indian Statistical Institute Golden Jubilee Conference on Human Genetics and Adaptation, Calcutta, 1–5 February 1982. (1983).
G.N. van Vark, On the phylogenetic position of the Petralona skull. Aνθρωπoζ, 9 (1983).
As early as 1974 an extensive survey of the literature concerned was published by Kanal (I. Kanal, Patterns in pattern recognition. IEEE Transac. Inform. Theory., IT. 20/6, 697 (1974).
W. Schaafsma & T. Steerneman, Classification and discrimination procedures when the number of features is unbounded. IEEE Transac. SMC 11/2, l44 (1981). These investigators showed that the diminishing performance is intrinsically caused by sampling phenomena: the vector of weights of the discriminant function is unreliable if the dimensionality is too large.
G.N. van Vark, A critical evaluation of the application of multivariate statistical methods to the study of human populations from their skeletal remains. Homo, 27/2, 94 (1976). In this paper also the problem of the ordering of variables is dealt with. This problem is of no less practical importance than is variable selection. Before applying a variable selection procedure, one shall wish to order the variables according to their independent contribution to discrimination. As may be taken from the above, it is most important to incorporate as much diagnostic capacity in as few a number of variables as is practically possible, since the role of adverse sampling effects is then minimized.
P.A. Lachenbruch, An almost unbiased method of obtaining confidence intervals for the probabilities of misclassification in discriminant analysis. Biometrics, 23, 639 (1967).
Further argumentation is to be found in:F. N. van Vark & P.G. Van der Sman, New discrimination and classification techniques in anthropological practice. Zeitschr. Morph. Anthrop., 73/1, 21 (1982).
According to M. Abercombie et al., A Dictionary of biology, Penguin Books (1961), by a subspecies is meant a “subdivision of a species forming a group whose members resemble each other in certain characteristics, and differ from other members of the species, though there may be no sharp dividing line”. The total present human world population may be regarded as the present representation of the subspecies Homo sapiens sapiens which may be somewhere around 100,000 years old. See also Section 8.
These measurements were taken from the series described in: W.W. Howells, Cranial variation in man. (Pap. Peabody Mus., 67, Harvard Univ., Cambridge, Mass., 1973), as well as from other series which were measured later by this author.
G.N. van Vark, The investigation of human cremated skeletal material, Part 1. OSSA, 1, 63 (1974).
During the “1er Congrès International de Paléontologie Humaine”, held in Nice, on October 1982, Dr. Alfred Czarnetzki (University of Tubingen, West Germany) told the author that the skull was being restored.
T.W. Anderson, An introduction to multivariate analysis, Wiley (1958).
N.A. Campbell, Cranial variate analysis: some practical aspects. Thesis, Univ. of London (1979).
W.W. Howells, Current theories on the origin of Homo sapiens. In: D. Ferembach, ed. Les processus de l’hominisation. Colloques internationaux du C.N.R.S., 599, 73 (1980).
G.J. Hennig, et al., ESR-dating of the fossil hominid cranium of Petralona Cave, Greece. Nature, 292, 533 (1981).
The last one known to us is his brief note in Nature, 299, of l6 September 1982: A.N. Poulianos, Petralona Cave dating controversy. In this opinion, Poulianos is supported by B. Kurten.
Well-known candidates for a side branche are, for example, the Neanderthals. Populations of anatomically modern man may have arisen from a strictly Neanderthal population or a non-Neanderthal one. (See e.g. E. Trinkaus & W.W. Howells, The Neanderthals. Scient. American, 241/6, 118 (1979). Our figures rather seem to favour the latter viewpoint.
R. Mukerjee, C.R. Rao & J.C. Trevor, The ancient inhabitants of Jebel Moya Sudan. Cambridge Univ. Press, Cambridge (1955).
J.M. Chrichton, A multiple discriminant analysis of Egyptian and African Negro crania. Pap. Peabody Mus., 57, Harvard Univ., Cambridge, Mass. (1966).
G.P. Rightmire, Cranial measurements and discrete traits compared in distance studies of African Negro skulls. Hum. Biology, 44/2, 263 (1972).
E.g. recently (July 1983), Professor Rao told the author that he had some ideas for the further testing of our hypotheses.
It may be difficult to imagine two isolated human evolutionary lines which have developed in an analogous way. Professor Oxnard (personal communication) suggested the following possible explanation: “We usually think of human cultures and societies as allowing social intercourse, communication, trading and therefore considerable intermarriage between populations. This means that parallel and separately evolving populations are harder to envisage for humans than for non-human forms. However, though this may well be the case in the somewhat late stages of cultural and social evolution, the very earliest stages may result in an opposite phenomenon. In the earliest stages part of the adaptive value of social and cultural evolution may be in the protection of small populations from various environmental dangers; this protection could well include, of course, those from neighbouring human groups; these earliest stages therefore could sometimes result in Isolation”.
S.M. Stanley, Macroevolution, Pattern and Process. Freeman, San Francisco (1979).
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van Vark, G.N. (1984). On the Determination of Hominid Affinities. In: Van Vark, G.N., Howells, W.W. (eds) Multivariate Statistical Methods in Physical Anthropology. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6357-3_19
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