Bushman Hottentot and South African Negro crania studied by distance and discrimination.код для вставкиСкачать
Bushman, Hottentot and South African Negro Crania Studied by Distance and Discrimination G . P. RIGHTMIRE Department of Anthropology, State University of New York, Binghamton, N e w York 13901 ABSTRACT Anthropometric, serological and previous skeletal studies bearing on the question of Bushman-Hottentot similarities and the relationships of these populations to South African Negroes are summarized briefly. Measurements of well documented crania representative of these three groups are then examined using the multivariate statistical techniques of generalized distance and discriminant function analysis, and the following points emerge: ( 1) The Bushman-Hottentot generalized distance as computed on Mahalanobis’ DZ for six characters, and again on DZ and Penrose’s CZH using 12 measurements, appears small (and non-significant) relative to the Bushman-Negro and Hottentot-Negro separations, which achieve statistical significance a t the 5% level; in general the analysis suggests Bushmen and Hottentots to be fully as similar in cranial form as i n blood group and serum protein distributions. That these peoples should be “lumped” in a Negro category appears doubtful on the evidence available. (2) Simple two-group discriminant functions, computed o n subsets of variables selected from the 35 original measurements, correctly assign “race” in 89% of cases when Bushman and Hottentot males are compared, and in 98-100% of cases when Bushman skulls are paired with those of Zulus. The latter discriminants also perform well when confronted with “new” (Sotho) skulls of both sexes. By showing which measurements or aspects of morphology are important to group separation, discriminant analysis provides a n interpretation of differences between these series, and the functions themselves should prove efficient aids for classifying material of unknown or questionable origin, assuming that such skulls in fact belong in one of the parent groups included i n the analysis. ( 3 ) A multiple discriminant approach, whereby seven groups of Bushman, Hottentot and Negro crania are located in a multidimensional space or statistical framework defined by six 29-variable functions as axes, permits simultaneous discrimination by both sex and race and allows correct assignments to be made for nearly 80% of all (179) individuals tested. Examination of the scaled vector versions of the functions suggests that measurements of over-all vault size are generally important in distinguishing between the sexes, while various aspects of skull form are the more efficient race discriminators. It seems likely that other shape-directed measurements, more sensitive to racial variation in cranial morphology than many currently employed, could and should be devised in order to exploit fully the capabilities of discriminants as tools not only for assigning individual specimens to a population but also for classifying the populations themselves in objective terms. The Khoisan peoples alive today, comprising both the Bushmen dwelling in semiisolated regions in or adjacent to the Kalahari desert and an undetermined number of increasingly hybridized individuals of Hottentot ancestry, constitute the scattered remnants of populations which once ranged over much of southern Africa. The surviving Bushmen, estimated by Tobias (’57) to number over 50,000, have been the subject of assorted research projects. Various tribes have been measured and photographed, and diverse anatomical peculiarities have been duly recorded; in other instances, determinations of skin reAM. J. Pwus. ANTHROP.,33: 169-196. flectance, metabolic response to desert temperature extremes and nutritional status have been of primary concern. Studies of blood groups and hemoglobins, serum proteins and enzymes, are proceeding apace, and members of several groups have been tested for color blindness, cholesterols, and estrogens. Many useful data have emerged from such work, and more is certain to follow. However, despite this trend, there is yet scant agreement as to the range and importance of morphological variation among Bushmen and Hottentots, and little information concerning the origins of these peoples has come to light. We should like 169 170 G. P. RIGHTMIRE to know more, not only about the interrelationships of Bushmen and Hottentots and thc ties of each to other modern populations (e.g., the Bantu-speaking peoples), but also about the wealth of ancient skeletal material from southern Africa, which must hold the key to our understanding of human evolution as it has occurred in this area since the Late Pleistocene. The present study is biometric in approach and comparative in nature, the material to be compared consisting of Bushman, Hottentot and South African Negro crania. As such, it is neither novel in concept, measurements having been used by Linnaeus and Blumenbach to separate races in the eighteenth century, nor especially broad in scope, but differs from previous work carried out on the same or similar material in the mode of analysis employed. Emphasis is here placed on the application of multivariate statistical techniques which, unlike more traditional univariate approaches, allow comparisons of several groups or populations to be based on many variables - all treated simultaneously and with due regard for the effects of intercorrelation. General aims and objectives of this work may be set out briefly as follows. ( 1 ) Determination of generalized distances, based on measurements of skulls, between Bushman, Hottentot and South African Negro populations, and comparison of results yielded by different distance techniques (e.g., Mahalanobis’ D2and Penrose’s CZn). (2) Calculation of simple, two-group discriminant functions useful for distinguishing members of these populations, and also computation of multiple discriminants which, as axes, together define a multidimensional space within which the groups may severally be located by both race and sex; such functions serve a purely practical purpose, as aids in the classification of individuals, on the one hand, but also provide indications as to which measurements or skeletal features are important to the differentiation of particular groups. The topics to be dealt with are thus rather specialized, both within the broad confines of human biology and, to a degree, in the statistical concepts necessarily intro- duced and utilized. This does not of cousse detract from their general importance. Despite an unfortunate tendency on the part of some more genetically-minded anthropologists to downgrade craniometry as old fashioned, there is certainly no sound basis for assuming, because development in such systems is complex and not under simple genetic control, that skulls or other skeletal components are not a potential source of valid taxonomic information. However, the findings of craniometry do in fact encompass only a small part of measureable human variation and are perhaps best viewed in the light of anthropometric, anthroposcopic and serological investigations of the living peoples. The essential results of such investigations, as well as a review of previous skeletal studies carried out on the South African populations, are presented below. Treatment here is in part historical, but selective, and is not meant to be a fullscale history of all work done to date. Mophology of living Bush,men and Hottentots. The numerous reports left us by European travelers who had reached South Africa in the seventeenth and eighteenth centuries contain many references to indigenous populations encountered. Much of this early material is illustrated, and a woodcut apparently depicting Hottentots (Ottentoo, Hottentoo, etc. : the origin of the term is uncertain) was published as early as 1508 (Singer and Jopp, ’67); in some instances these sources provide valuable ethnographic data and physical descriptions of native South Africans. Impressions as usually recorded indicate the pastoral Hottentots to be culturally and physically distinct from the Bushman hunter-gatherers. Cultural differences have been confirmed by subsequent work, though the question of morphology remains a tender one. Anthropometric surveys of the living shed some light on this and related problems, though studies in this field have yielded some rather remarkable and largely unacceptable conclusions. Dart’s (’37) much cited paper on the /?Auni-ZKhomani people of the southern Kalahari is a case in point. After much careful observation and measurement of some 77 Bushmen, Dart affirms that in this group he can detect evidence of segregation into BUSHMAN, HOTTENTOT A N D AFRICAN NEGRO CRANIA two separate “types” and that these types are “sex-linked.” The first, prevalent among females, is labeled “Bush’ and the second, to which a majority of males is allocated, is termed the “Boskop.” These stocks, isolated primarily on the basis of head form but later characterized as to hair and eye color and even the nature of the external genitalia, are thought to represent pure races which in the past had hybridized to form present day Bushmen and Hottentots. In addition, varying amounts of “alien admixture” with the “Brown race,” the “Armenoid” and the “Mongolian” races can be recognized. This sort of approach, while not out of place 30 years ago, is somewhat less palatable today. Strong typological seasoning also flavors much of the work done since, though this has not impeded a modest flow of useful anthropometric data. The Kalahari group studied by Dart has subsequently been found to resemble most closely a sample of 20 Bushmen from the Lake Chrissie area of the eastern Transvaal, although the latter are “smaller in stature, length of head, minimum frontal width, bizygomatic width, . . . cranial width . . . and arm length” (Toerien, ’58). These findings render the /?Auni-#Khomani and Lake Chrissie peoples generally shorter than central Kalahari (Naron) and Northern Bushmen (Kung, Auen, Heikum), but Wells (’52, ’60) doubts that these differences are “significant.” Dart’s Bushmen appear to have wider (and shorter?) faces and broader noses than do the Kung, though possible differences in measurement technique make comparison awkward at best. Perhaps the most complete single summary of Bushman and Hottentot measurements is that of Tobias (’55-’56). In this comparative study of some 49 Auen and Naron Bushmen (spread from Gobabis in South West Africa to Ghanzi in Botswana), the author finds both groups to be of relatively large stature (male means of about 158 cm) and thus concurs with previous opinions concerning a north-south stature gradient. Still, the tallest Northern Bushmen apparently fall slightly short of the Nama Hottentot male mean of 163 cm recorded by Schultze (’28) and that for Kor- 171 ana (Hottentot) males given as 160 cm by Grobbelaar (’56). Thus, beyond the fact that Hottentots seem to be generally taller than Bushmen, and that some Bushmen differ from some Hottentots in a few other miscellaneous features, not much can be concluded from the anthropomctric treatment so far accorded the living peoples. Perhaps a more significant contribution of this type of research lies in the elucidation of that complex of anatomical characters common to many Bushmen and Hottentots but distinguishing them from other African populations. Certain peculiarly Khoisan traits have received considerable attention over the years and are now mentioned in any elementary text on race. The most striking of these is of course steatopygia, referring to a localized accumulation of fatty tissue on the buttocks and thighs of the individual affected. This condition is largely restricted to females, though the associated lumbar lordosis is present in both sexes. The popular suggestion that it is analogous to the camel’s hump (or tail of the fattailed sheep) and hence acts as a reserve supply of fat useful in times of food shortage seems to be unsubstantiated, though a similar function of nutriment for mother and fetus during pregnancy bears looking into (Tobias, ’57; Coon, ’65). In an analysis of subcutaneous adipose tissue taken from the Hottentot buttocks, Krut and Singer (’63) find a significant sex difference in fatty acid composition, but this difference is paralleled in other white and Bantu populations examined. Comparability in the composition of adipose tissue between groups leads the authors to stress the role of fibrous (non-adipose) tissue in the steatopygeous protrusion; it is hoped that this new emphasis may yield more concrete results concerning causal relationships involved. Other morphological distinctions include the well-known “pepper-corn” or tufted type of scalp hair, short stature and small faces, presence of eye-folds, macronympha (protrusion of the large labia minora) among females, a horizontal or semi-erect placement of the penis in males, and a light yellow-brown skin coloration. African variation in the last feature has recently been investigated with the aid of sophisti- 172 G. P. RIGHTMIRE cated spectrophotometric equipment, and this technique provides clear separation of Khoisan from Bantu peoples (Weiner, Harrison, Singer, Harris and Jop, ’64). Naron Bushmen and Richtersveld Hottentot males give percent reflectance figures of 40 to 45 at 685 mp, whereas Okavango Bantu register in the low ’20’s. Although results vary somewhat with the wavelength used, Bushmen and Hottentots are thus appreciably ‘lighter” than the Negroes studied. That these small light (“yellow”) skinned peoples have been deemed similar in many respects to Mongoloids is perhaps not surprising; however, despite claims to the contrary (see Dart, ’52, ’54), it is difficult to envision any substantial flow of Asiatic genes into southern Africa, a conclusion strengthened by the absence of the Diego blood type in African populations (next section). The cause of these resemblances must therefore be sought elsewhere. Tobias (’55-’56, ’ 5 7 ) , while not rejecting Dart’s’ theories out of hand, opines that both groups have been subject to “infantilizing tendencies” over long periods and have thus come to resemble one another largely via mutual retardation of developmental processes underlying differentiation of bodily structures. So-called “pedomorphic” features have long been recognized in supposed early “Bush crania and are coilsidered quite prominent in extant groups, though just why this tendency, accompanied by short stature, has prevailed remains a mystery. Part of the answer may lie in adaptation to a dry desert environment, but Tobias (‘64) argues convincingly that this cannot be a factor, desert conditions having been forced upon the Bushmen only in recent, historic times. Also, a hormonal basis cannot be discounted; preliminary studies with South West African Bushmen show these individuals to have surprisingly high levels of total urinary estrogens, levels differentiating them from Bantu and European subjects tested (Tobias, ’66). Whatever the reasons, the fact that the South African Bushmen share with Hottentots a rather distinctive set of morphological traits is certain and well documented; however, whether these findings should be viewed as conclusive evidence for separation of the Khoisan peoples from other, Negro Africans is questionable. Blood group investigations allow of no such simple dismissal of the problem and instead underline its complexity. Serological considerations. Peoples of Africa south of the Sahara, including Bushmen and Hottentots, were by no means exempted from the attentions of early investigators eager to apply the then relatively new techniques of blood typing to as many of the worlds populations as possible. The various tentative and often conflicting conclusions arising out of this work (ABO system only) have been summarized by Dart (’50) and need not be considered further. Suffice to say that, with the recognition of new alleles and loci (including some confined almost exclusively to persons of African origin) and continuing perfection of methodology, a rather more reliable serological picture of affinities among these groups is becoming available. Studies of more than 400 northern Bushmen from South West Africa carried out by Zoutendyk, Kopec and Mourant ( ’ 5 3 ) not only suggest ABO similarity with other (Heikum) people from the same area (Pijper, ’ 3 2 ) but also provide evidence for essential continuity of pattern (MNSs, Henshaw, Duffy) with African Negroes. Other Bushman groups, resident in the central Kalahari near Ghanzi, have been subjected to extensive testing by Weiner and Zoutendyk (’59 ) , and the results do much to confirm previous conclusions. Thus, in their high frequency of cDe (one of the highest yet recorded for the continent), the ratio of A, to A1, and most notably in the occurrence of V and Js, the Bushman closely resemble their African neighbors. That some differences do exist however is apparent in the Bushman Combination of high A and low B frequency coupled with a virtually complete absence of Rh-negative individuals. Information relating to Hottentot blood groups is also available for a variety of tribes and localities across southern Africa, though exact identification of individuals tested has not always been reported. ABO frequencies appear to be similar for “South West African Hottentots” sampled by Pijper (’35), two groups of Korana centered near Upington, Cape and from Kimberly eastward into the Orange Free State (Grob- BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA belaar, ’55), and for more than 200 individuals living on reserves in South West Africa (Zoutendyk, Kopec and Mourant, ’55). More recent findings also demonstrate marked parallels among the Nama Hottentots and the Eondelswarts (Singer, Weiner and Zoutendyk, ’61; Singer and Weiner, ’63). To a large extent these Hottentots reflect that series of serological traits peculiar to African Negroes and Bushmen; V and Js are both present, A1 is more frequent than A, and cDe and Henshaw occur in relatively high proportions (the cDe figure is not extreme as in the Bushmen, but the Henshaw frequency is one of the highest known). The total lack of Diego antigen apparent in the Nama and the Bondelswarts agrees with the Bushman result and may hold for (most) other African populations as well. Nevertheless the Hottentots, while Bushman-like in the absence of Rh-negatives, are somewhat distinctive in possessing a B frequency high by South African standards. Published data on the distribution in Africa of abnormal haemoglobins, haptoglobins, transferrins, enzymes and their deficiencies, etc., are still rather scarce (see Tobias, ’66, for a review), but several relevant population differences have been noted. The sickle-cell trait, present in varying amounts among Bantu-speaking Negroes, has yet to be identified in the Bushmen and Hottentots studied, this despite the fact that Bushmen sampled at the Etosha Pan and along the Okavango River are regularly infected with malaria parasites during the annual rainy period (Singer, ’60). The Bushmen are also set apart from other African peoples in their incidence of the Hp’ (haptoglobin) allele: these Kalahari people geld a frequency of 29%, whereas the figures for the rest of the continent rarely drop below the 51% recorded for Nama Hottentots (Barnicot, Garlick, Singer and Weiner, ’59; Singer, ’61). That this should be the case is rendered (even more) remarkable upon recalling the opposite Bushman extreme in frequency for “typically African” cDe. Still, while no adequate explanation in terms of selective agents or migrations can be advanced to account for the observed patterns in gene frequencies, one may rea- 173 sonably conclude that both Bushmen and Hottentots are generally African and Negroid serologically. This concordance has led Singer and Weiner (’63) to suggest altering the definition of “Negro” to include both groups, though obvious differences prompt reservations to the effect that each has undergone extensive local differentiation in the southern part of Africa. One point is definite : blood group evidence militates against any appreciable contribution by Mongoloids or Caucasoids to these gene pools. “Europoid or Hamitic influence, “Australoid brow ridges, and Mongoloid eye-folds notwithstanding, the Bushman, Hottentot and Bantu Negro skeletal material at hand must be analyzed with strictly African evolution, perhaps from a common stock, in mind. Previous skeletal studies. Probably the major portion of all anthropological and anatomical investigation of the Bushman and Hottentot peoples has been centered on their skeletal remains. The volume of literature dealing with this subject is considerable, and, not surprisingly, a number of different points of view have been put forward. However, in all this three main classes or schools of interpretation seem apparent, the central themes of which may be set out as follows. (1) Bushmen and Hottentots, thought to be indistinguishable morphologically, are considered as representatives of a single homogeneous “ B u s h or Khoisan race (Shrubsall, ’1 1; Schapera, ’30; Galloway, ’33, ’37; Dart, ’37). (2) A second view, adumbrated in Dart’s (’37) work on living Bushmen, holds that present day Bushmen and Hottentots are physically diverse, hybrid populations. Differences both within and between these groups are postulated and attributed to the unequal contribution of some five or six (pure) strains or physical types (e.g., Bush, Boskop, Kakamas, Gerontomorph or Australoid, Europoid or Europide, etc.) to the make-up of the various regionally distinct modern peoples (Wells, ’49, ’51; Tobias, ’55, ’57; see also the discussion of morphology of the living.) (3) Inherent in other studies is the assumption that, although most living Khoisan peoples are heavily hybridized, 174 G . P. RIGHTMIRE “true” Bushman and Hottentot physical types may be discerned in certain of the skeletal remains exhumed from old burials, middens, and the like; there is disagreement as to just which material best exemplifies either type. This view difIers from both ( 1 ) and ( 2 ) above in that by and large the traditional Bush-Hottentot dichotomy is retained as physically significant (Shrubsall, ’07, ’22; Slome, 29; Broom, ’23, ’41; Drennan, ’38; Dreyer and Meiring, ’37, ’52; Keen, ’47, ’52). The evident confusion surrounding the question of Bushman-Hottentot similarities or differences is not traceable to any one simple cause, but must stem in part from the nature of the skeletal material available. That forming the subject of most studies has been obtained through excavation or chance finds and is often of entirely unknown provenience; reliably documented specimens, skeletons secured from individuals known as Bushman or Hottentot during life, for example, are at a high premium indeed, and though the value of such remains has been pointed out by Wells (’51) there has been little attempt to build up a collection of this sort for systematic study. Further, heavy reliance on a typological approach (wherein some individuals are recognized as “typical” or “pure” on the basis of preconceived ideas as to what a Bushman or Hottentot skull should look like while others are diagnosed as hybrids on similar morphological grounds) has tended to obscure results even in cases where the material itself is reasonably adequate. Shrubsall’s final ( ’ 2 2 ) assertion that “the Hottentot skull is longer, narrower and higher and more prognathous than that of the Bushman” seems to be fairly soundly based, at least some of his material being assignable to “known native tribes,” but Slome’s (’29) descriptions of skulls of “relatively pure Bushman type” and Keen’s more recent (’47, ’52) comparisons of “typical Bushman” “typical Hottentot” and “Bush-Hottentot hybrid’ crania (not separated by sex) are of little value, the “sampling” procedures employed taking no account of the range of variation to be expected in any natural populations. A rather more significant contribution to the craniology of these peoples has been made in a preliminary report by Stern and Singer (‘67), who have in fact heeded Well’s (’51) suggestion in the selection of their specimens. Using only authenticated material (eight skulls identified as Bushman male, six as Bushman female and four as Hottentot), these authors are able to demonstrate via a series of univariate (t-test) comparisons that, while Bushman males are significantly larger than females, “racial‘‘ differences are slight and confined mainly to general size; overlap in the ranges of most metrical features between the two categories is quite extensive. However, as Stern and Singer are quick to emphasize, the sizes of the samples employed are dangerously small, and the conclusions reached are subject to revision. Clearly then, there is yet room for, even need for, some added clarification of Bushman and Hottentot origins and interrelationships. Modern multivariate statistical methods have been little used in such studies and would seem to constitute valuable tools with which to get at the question of what, if any, morphological significance can be attributed to the terms “Bushman” and “Hottentot” and further to obtain estimates of biological distance separating these groups from South African Negroes. MATERIALS Of utmost importance here is the selection of samples of crania which are reliably documented as Bushmen, Hottentot and South African Negro. Although a number of “Bushman” and “Hottentot” skeletal remains can be found in South African museum and medical school collections, inspection of the (often very limited) catalogue entries associated with this material reveals that in many instances identification has been based on morphological criteria alone. In the present study, such specimens of obviously dubious origin have been excluded from consideration, and instead, an attempt has been made to utilize only those skulls for which racial diagnosis is supported by some evidence (records giving some particulars, such as tribal affiliation, indicating that the individual was known in life, for example) other than that of skeletal anatomy. As already noted, Bushman and Hottentot BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA material meeting this requirement is h a d to come by, so that sample sizes are not as large as might be hoped; well documented South African Negro skulls are fortunately more plentiful, and adequate numbers of these could be obtained in the Raymond A. Dart collections of the University of the Witwatersrand, Johannesburg. The material finally selected for use has been described in greater detail in another paper (Rightmire, ’70) and is here listed only in brief: Bushmen. Twenty males and 16 females, examined at the University of the Witwatersrand Medical School, Johannesburg; the McGregor Museum, Kimberley; the South African Museum and the University of Cape Town Medical School, Cape Town. Hottentots. Sixteen males and three females, from the institutions cited above. South African Negroes. Sixty-two Zulu (30 males and 32 females), 65 Sotho ( 3 5 males and 30 females), and 24 Xosa males, all from the University of the Witwatersrand Medical School. Sex as listed in institution records was usually accepted, though wherever possible these designations were checked by inspection of diagnostic postcranial remains; in seven instances (all Bushmen), sex was necessarily assigned on the basis of cranial appearance alone. All specimens included in the samples were clearly adult. 175 complete at the time of actual card punching. GENERALIZED DISTANCE The concept of intergroup distance, measured in terms of gene frequencies or miles, biometric or (as possible for man) linguistic criteria, is basic to the assessment of affinity, whether between closely related populations within a species or between such diverse organisms as rattlesnakes and tuna fish.’ Recent advances made possible through the availability of modern computing equipment have been concerned mainly with the estimation of divergence at the molecular level, or at the level of gene frequencies, and several measures of so-called genetic distance (based mainly on blood traits) now seem promising for the study of man. However, the trend in anthropology has been toward development of generalized distance statistics designed for use with morphological (e.g., anthropometric) characters. The history of Pearson’s “Coefficient of Racial Likeness” is well known, and while no longer in use in its original form, the C.R.L. has given rise, directly or indirectly, to the family of distance techniques employed today. Mahalanobis’ D2 One such technique, which has perhaps acquired an undue reputation for difficulty of computation, is the Dz statistical apMEASUREMENTS proach suggested by Mahalanobis as early A complete listing and description of as 1925 and later elaborated by the same the 35 cranial measurements employed, author (’30, ’36) and by Rao (’48, ’ 5 2 ) .D’ together with a discussion of the criteria has been applied fairly frequently to probunderlying this selection, may be found lems involving morphological divergence in human populations (Trevor, ’47; Maelsewhere (Rightmire, ’70). Data collected “in the field were re- halanobis, Majumdar and Rao, ’49; Mukcorded on mimeographed blanks prepared herjee, Rao and Trevor, ’55; Hiernaux, ’56; so as to permit easy transfer to standard Talbot and Mulhall, ’62) and seems to be 80-column computer punch cards. In those rather widely accepted as the best method few cases where localized damage to a allowing mutual comparison of three or skull had resulted in missing observations more groups (Campbell, ’63; Marshall and (not tolerated by the several computer Giles, unpublished). Although there is programs used), preliminary means were some doubt as to whether the conditions calculated for the variables and groups in (normal distributions, homogeneous variquestion, and these sample means were ances and correlations) underlying the use then inserted into individual data records 1 See Fitch and Margoliash (’67)for an example of comparisons (via “mntation distance”) on so as to make all specimens (excepting intergroup a grand scale. Howells (’66a) has reviewed the question of correlation between various distance estimates Hottentot females, numbering three, for (biological, geographical, linguistic) in a specifically which no corrections were introduced) anthropological context. 176 G. P. RIGHTMIRE of this statistic are met by most anthropological data (Penrose, '54), the extensive testing undertaken in several studies has yielded encouraging results (see especially Talbot and Mulhall, '62) ; likewise the close agreement between D2 and other simpIer distance techniques obtained in some limited comparisons (Huizinga, '62; Hiernaux, '64) does not in any way detract from the status of D2 as that method most soundly based in theory. The advantages apparent in treatment of intragroup correlations and insensitivity to variations in sample size should easily compensate for any "extra" time spent in applying this slightly more complex statistic. The actual determination of Dz has been considered extensively by Rao ('52), and his method of transforming ("decorrelating") the original measurements, summarized in Rightmire ('69), is followed here. Since the computation of distance becomes laborious if more than 10 to 12 variables are included, the usual procedure is to effect a choice of measurements to be used in the analysis. A general rule of thumb is that highly correlated characters should be avoided, and that those selected should have means which vary appreciably between groups; a better method of selection exists, as will be demonstrated later on, but traditional approaches are here followed throughout. Pooled coefficients of correlation for 12 measurements (basibregmatic height, maximum frontal breadth, biauricular breadth, prosthion subtense, maximum malar length, occipital sagittal chord, total sagittal arc, orbit height, inter-orbital breadth, nasal breadth, palate breadth and mastoid length) meeting these criteria are given in table 1. Raw (uncorrected) D2 values for the Bushman, Hottentot and Negro male groups (lack of Hottentot and Xosa specimens precluded similar treatment for females), computed for only the first six variables and again using the entire subset, are presented in tables 2 and 3 respectively. These raw distances may be tested for significance quite simply, as the quantity (nml / ni -k n,) Da, is distributed as chi-square with p degrees of freedom (ni = sample size of group i; nj = sample size of group j; Deil = square of the gen- m I6 ii i M m 0 IT 0 oi N cd N % E d N Y Y c 3o.i s 0 0 0 0 BUSHMAN, HOTTENTOT A N D AFRICAN NEGRO CRANIA 177 Interpretation of results. Firstly it eralized distance between groups i and j ; and p = number of characters employed). should be pointed out that the set of disThe magnitude of this quantity is com- tances computed using only six characpared with the value of chi-square for ters provides essentially the same picture the desired probability level in order to of group interrelationships as that obassess significance of any given I)” (Talbot tained after application of the entire 12 and Mulhall, ’62). measurement battery. All individual D2 Since the samples are small and differ estimates, and especially those for Hottensomewhat in size, a correction should be tot-Negro pairings, increase to a limited applied to all raw D2 found to be signifi- extent as more variables are included in cant. The amount p (ni nj / ninj) is the analysis, but there is no change in subtracted from DZijso as to insure that the distribution of values found to be sigthis value is an unbiased estimate of the actual population distance. If ni and nj nificant at the 5% level. Here one might were large, then this correction would be logically assume that the analysis has trivial and need not be carried out. Table been carried far enough and that succes4 contains corrected values of (signifi- sive distance determinations based on even cant) Dz calculated for 12 measurements. greater numbers of measurements (all at least moderately correlated with those entered previously) would not yield “new” TABLE 2 information in a quantity sufficient to Uncorrected values of DZ f o r male groups based justify the additional effort expended. That on six characters, and chi-square figures f o r significance this should be the case has been suggested on theoretical grounds, though empirical Bush. Hott. Zulu Sotho Xosa proof is so far lacking (Talbot and MulBush. 1.011 4.217’ 3.124’ 3.4801 hall, ’62). Hott. 8.895 1.847 1.814 1.7031 Granting then that the 12-character Dz Zulu 50.604 19.271 0.577 0.325 Sotho 39.759 19.917 9.320 0.174 values adequately reflect the actual interXosa 37.963 16.348 4.333 2.477 group distances, there remains the quesDistances are i n upper portion of the table, chition of attaching some biological interpresquares are below. tation to the results. Of the ten distances 1 Significant ( p < 0.05). listed in table 3, those separating the TABLE 3 several Negro samples from each other are the lowest recorded and are statistiUncorrected values of D 2 for male groups based on 12 characters, and chi-square figures cally non-significant; i.e., the null hypothef o r significance sis that there is no difference between these group means is not rejected at the Bush. Hott. Zulu Sotho Xosa 5% level arbitrarily selected. This would Bush. 1.506 4.561 3.416’ 4.0601 Hott. 13.385 3.132 2.700 2.961 1 seem not unreasonable in view of de Villiers’ (’68) conclusion, based on examiZulu 54.732 32.679 1.255 1.203 Sotho 43.475 29.646 20.272 0.490 nation of some hundreds of crania, that Xosa 44.290 28.425 16.039 6.976 the four tribal series (Cape Nguni, Natal Distances are in upper portion of the table, chiNguni, Sotho and Shangana-Tonga) studsquares are helow. ied by her “may be considered as samples 1 Significant ( p < 0.05). of a single South African Negro population.” However, the simple fact of staTABLE 4 tistical significance, or lack thereof, is not Corrected values of D2 f o r male groups based on 12 characters to be overemphasized, especially when sample sizes are of the order dealt with Bush. Hott. Zulu Sotho Xosa here; non-significance of a D2 value does Bush. n.s. 3.562 2.474 2.960 not in itself prove that two samples are Hott. 1.982 1.608 1.711 drawn from the same population but does Zulu - n.s. n.s. 1 Sotho - n.s. 1 indicate that differences in the characters Xosa used are too small for detection in groups of the size available. no correction introduced. 1 n.s , not significant; + 178 G. P. RIGHTMIRE With these reservations in mind, it is clearly rather premature to suggest that Bushmen and Hottentots, whose Dz estimate of 1.506 quite definitely fails to attain significance on chi-square, differ no more than would be expected of local breeding isolates; still it is evident that those two groups are closely associated, more so than either is with any Bantu tribe. In other words, the Bushman-Hottentot generalized distance is “small” within the framework of the present study, but it would be informative to have a somewhat less restricted scale against which to assess the degree of afinity implied by a distance of this magnitude. One would like, for example, to know just how “large” a DZ (preferably based on cranial measurements) might be obtained in an analysis involving widely divergent human populations. Unfortunately a comparison of the D2 results given here with those published by previous investigators is complicated both by variations in the number and type of measurements employed-most prior studies are based on anthropometric, not craniometric, data-and by minor differences in actual computation of the generalized distance. In an attempt to clarify further these limited conclusions arrived at using Mahalanobis’ D’, an additional generalized (i.e., multivariate) distance technique has been applied to the Khoisan and Bantu Negro data. Values of Penrose’s mean square distance ’ calculated for each group pair on the same subset of 12 variables utilized for D2 are given in table 5, and much the same set of relationships is apparent; in fact, CZHand D2are here highly correlated, with r = 0.959. Bushmen and Hottentots are again closely allied while both, but Bushmen especially, are somewhat removed from the Bantu cluster. However, coincidence of the two sets of distances is by no means exact, and the simpler Penrose estimates appear to overemphasize the basic Khoisan-Bantu dichotomy; on D2 Bushmen are roughly three times as distant from Zulus as from Hottentots, while CZHyields a figure of over 6 : 1 for the same distance ratio. Other discrepancies exist, and in fact one must be wary of attaching any quantitative sig- TABLE 5 Values of Penrose’s mean square distance (C%) partitioned into size and shape components. Distances apply to males only, and are computed on the same subset of 12 measurements used for D’ -~ - Bush. Bush. Hott. Zulu Sotho Xosa- 0.180 1.159 1.010 1.250 0.109 Hctt. Zulu Sotho Xosa 0.579 0.504 0.071 1.028 0.642 0.467 0.056 0.059 0.131 0.112 0.926 0.399 0.002 0.064 1.179 0.105 0.570 0.054 0.005 0.046 0.015 0.070 0.072 0.054 0.031 Values of .mean square distance are in the upper part of the table; size and shape components are given as thc upper and lower figures, respectively, in each cell in the lower part of the table. nificance to relations between the mean square distances computed for different pairs of groups (see Cain and Harrison, ’58, for a pertinent discussion); in this respect, D2is far preferable, as betweengroup separations may be visualized as “real” distances in Euclidean space (Kendall, ’57). Despite these shortcomings, Penrose’s method is informative in that the total distance (CZH)may be broken down into “size” (the square of the mean of all character differences) and “shape” (the variance of the character differences) components, which appear to be independent or uncorrelated with each other. If this is done, the Bushman-Hottentot distance is seen to be heavily size dependent, in the sense that the dispersion of group mean differences is relatively slight. The size component again outweighs the contribution of shape in the several Bushman-Bantu and HottentotBantu distances listed in table 5, but shape seems to become important in distinguishing between the closely related Zulu, Sotho and Xosa tribes. However, a cautionary note : the terms “size” and “shape” as used here refer to statistical approximations and are only very loosely related to biological reality; the suggestion that an over-all difference expressed in the form of C2,, is based predominately on zThe mean square distance, C%, is computed bj summing the squares of differences between (stan dardized) mean values in any two populations and dividing the result by the number of characters used This statistic incorporates n o correction for measure ment intercorrelations. See Penrose (’54). BUSHMAN, HOTTENTOT A N D AFRICAN NEGRO CRANIA size (or shape) differences in actual morphology may therefore be quite misleading (Huizinga, ’65). Further evidence bearing on this point, available from discriminant analysis, will be presented later on. DISCRIMINANT ANALYSIS That human skeletal morphology provides many indications of racial affinity (as well as sex) is well known, and it is generally agreed that the skull, more than any other portion of the skeleton, is of value in studies of this nature. However, accurate appraisal of “race” from osseous remains is an exacting task usually reserved for the trained anatomist or physical anthropologist, and even those most skilled in these fields make no claim to 100% success in all trials. A discriminant function approach to the problem has the advantage of simplicity (one need be familiar only with common cranial landmarks in order to apply a function) while yielding good results, judging from the limited number of reports so far available (see Giles and Eliott, ’62; Howells, ’66b). Also, inquiry as to the way in which discrimination is actually accomplished in specific cases may provide substantial insight into which aspects of cranial morphology are important in distinguishing between groups or populations; information of this sort is generally not obtainable from a D’ analysis, though Penrose’s partitioning of mean square distance into size and shape components is a step in this direction. In the discussion following, cranial measurements have been utilized to compute a series of simple two-way discriminant functions serving to distinguish between Bushmen, Hottentots and South African Negroes when sex is held constant; i.e., the sexes are treated separately throughout. Various Limitations, both of machine time and in the material itself, dictate that the number of comparisons be kept to three: (1) Bushman males vs. Hottentot males. ( 2 ) Bushman males vs. Zulu males. ( 3 ) Bushman females vs. Zulu females. Dz results and the work of de Villiers (’68) suggest that the several groups of 179 Bantu Negroes are much the same in their morphology, so use of Zulus only in computing the discriminants should cause little loss of generality; this can be checked, employing Sotho males and females as test series where appropriate. The several discriminant analyses were carried out at the University of Wisconsin Computer Center using a slightly modified version of program EIDISC, written by D. Morrison and C. Art and distributed by the Vogelback Computing Center, Northwestern University, Evanston, Illinois. Selection of variables. Before a discriminant function can be computed, one must first make a decision as to which, if not all, of the available measurements are to be included in the analysis. A total of 35 cranial dimensions could be used here (the computer will accept 5 or 55 with equal grace), but application of the resulting discriminant would be quite laborious if more than a handful1 of skulls are to be tested. Also, a shorter function computed on a subset of variables might be nearly as effective in terms of the level of discrimination achieved. Selection of such a subset has previously been discussed with reference to D2,though the method employed is f a r from soundly based; variables were chosen by virtue of their low interdependence as determined by simple inspection of correlation coefficients. The 12 measurements selected then had to be transformed before being utilized in distance determinations. ClearIy a better procedure, as pointed out by Howells (’66b), is to remove correlation before, rather than after, inclusion of a measurement in a subset, as the “best” variables for discrimination should be those which contribute most to group separation after having been adjusted for correlation with others already selected. That is, after a first character has been specified, and its correlation partialed out for all those remaining, the second entered should be that which now provides the best discrimination between groups; a third may be chosen after the effects of these two have been partialed out, and so on until all the variables have been ranked in an order reflecting their efficiency, when taken together, in distinguishing the particular groups under scru- 180 G. P. RIGHTMIRE tiny. The discriminant function may then be constructed using some number ( a subset) of the characters which are ranked most highly. The decision as to just how many variables are to be used is still fairly arbitrary, as there is no way to predict beforehand how effective a given function will be; however, any set of characters selected in this fashion should in all likelihood perform better than one composed of the same number of variables chosen without regard for the effects of intercorrelation. Thus, as a preliminary to computation of discriminants for the South African material, 33 measurements ( 2 were omitted for technical reasons) were first run on a program (BMD07M, distributed by the Health Sciences Computing Facility, U.C.L.A.) capable of ranking them by a procedure similar to that briefly outlined above. This program computes pooled within-groups and total sample crossproduct matrices using all the data and selects the character giving the highest F-ratio as the first and “best” measurement; other characters are then added in stepwise fashion. At each step the variables are divided into two disjoint sets (“included and “remaining”), and the two cross-product matrices are partioned to permit independent analysis of the dispersion of those remaining. The variable entered is that which gives the highest F-value computed after removal of the effects of those already selected. The results of this serial ordering procedure were then used as a guide in selecting the measurements to be employed in each of the three discriminant trials carried out. Bushmen ‘us. Hottentots. Sequencing of all measurements, when the groups considered are male Bushmen and Hottentots, indicates that 19 characters are best combined to form a discriminant, as shown in table 6. Group differences in most of these characters are quite small (see table 7), and only two of the univariate F-ratios, given to illustrate the discriminatory power of each measurement when considered alone, are significant ( p < .05 for palate length; p < .001 for basibregmatic height). The immediate expectation, that discrimination achieved with these variables will be poor, is not entirely fulfilled, however, as is evident from figure 1; this plot shows the distributions of scores in both groups. The mean discriminant score for 20 Bushman males is - 60.18 with a variance of 11.12 and a standard deviation of 3.33; that for 16 Hottentot males is - 68.29 with a variance of 8.93 and a standard deviation of 2.98. Graphed results indicate three Bushmen and one Hottentot to be incorrectly as- TABLE 6 The 19 characters best combined to form a discriminant function between male Bushmen and male Hottentots Variables Y= 1. Cranial length Alveolare-basion Basibregmatic height Maximum frontal breadth Bizygomatic breadth Bimaxillary breadth Prosthion subtense Subspinal subtense Maximum malar length Malar subtense Malar height Frontal sag. chord Frontal angle Occipital subtense Orbit breadth Orbit height Nasal breadth 30. Nasal height 33. Palate length 4. 5. 9. 10. 12. 13. 14. 15. 16. 17. 18. 20. 22. 26. 27. 29. Scaled vector Weights 0.214 -0.556 -0.933 - 0.823 0.657 0.664 0.506 -0.705 - 0.655 0.800 0.764 0.169 0.793 0.727 0.331 - 0.802 - 0.451 0.500 0.509 - Univ ariate f-ratio - 23.404 -20.296 15.992 19.546 7.116 - 12.221 - 10.127 2.06 0.61 17.00 0.66 0.00 0.36 2.73 3.72 0.58 4.550 0.12 8.293 4.002 14.799 12.734 3.980 - 9.236 - 5.680 7.486 8.421 0.67 0.68 1.44 0.78 0.75 0.54 0.01 2.45 4.71 6.059 - 16.873 - - BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA SECT. PT. 20 BUSHMAN I -52 I -54 I -56 I -58 I -60 HOTTENTOT 16 181 d d I -62 I -64 I -66 I -68 I -70 1 -72 I -74 I -76 Fig. 1 Djstribution of individual scores on the Bushman-Hottentot (male) discriminant. Relative to the sectianing point (-64.24), three Bushmen and one Hottentot are misassigned by the function. signed by the function when a sectioning point (here - 64.24, the average of the group mean scores) is used as the basis for decision on group membership; correct assignments then total 32 or roughly 88%. The erring Hottentot and one Bushman are also misclassifwd (i.e., excluded from their own group) relative to the 5% limits of their respective distributions, the direction of deviation being in each case toward the mean of the inappropriate group; these individuals are thus rather emphatically rejected as belonging in the populations to which they were originally a l l ~ c a t e d , ~ Applying a one-sided test for exclusion yields the limits and results listed below: ( 1 ) At a 99% probability, 13 Bushmen with scores of - 61.35 or higher (less negative) are excluded from being Hottentot; eight Hottentot skulls, falling at - 67.93 or below (Le., with more negative scores), are excluded from the Bushman distribution. (2) At a 95% probability, 15 Bushmen scored at - 63.38 or above are excluded as Hottentots; 13 Hottentot skulls, with scores of -- 65.67 or lower, are excluded from being Bushman. On the second, less stringent, test, over 77% of all crania are excluded from the “wrong” group, or to the correct one, and the function is performing about as well as could be hoped for, considering the obvious similarities (and low Dz) between the two populations. This close agreement in cranial morphology is underlined by the fact that, despite the larger number of characters (19) included in the function, the level of discrimination observed is noticeably lower than that for any of the other discriminant trials reported. Careful reading of the Bushman-Hottentot scaled vector (the vector of weights re-scaled to correct for differences in measurement size and dimensionality) suggests that the group differences upon which discrimination depends can be summarized approximately as follows. The Hottentot skull is higher (basion to bregma) with greater breadth across the frontal bone as measured at the coronal suture; these characteristics, both quite heavily weighted on the function, seem of prime importance to group separation. Also, the subnasal portion of the face is generally more projecting, a condition implied by the moderate negative scaling for alveolare-basion length and subspinale subtense (and confirmed by a review of the means for both measurements given in table 7). Greater height of the Hottentot orbit plays a somewhat smaller role. The Bushman cranium is lower, both absolutely and as measured by a height/ length index, but is “fuller” in the frontal region; i.e., the bone is expanded in an antero-superior direction rather than postero-laterally as in Hottentots. The forehead is thus more nearly vertical in appearance. Greater breadth across the middle face and orbits seems a prominent Bushman feature (bimaxillary breadth is 3 Nevertheless, the Hottentot is reliably documented as such in the records of the South African Museum, Cape Town; the Bushman’s credentials are less satisfactory, as identification is based mainly on the locality (Pearston, S.E. Cape) in which the skeleton was found. G . P. RIGHTMIRE 182 TABLE 7 Male and female arouz)means for 86 cranial measurements Measurement 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. Cranial In. Glabella prot. Nasion-basion Alveolare-basion Basibreg. ht. Upper face ht. Cranial br. Least front. br. Max. front. br. Bizygomatic br. Biauricular br. Bimaxillary br. Prosthion subt. Subspinale subt. Max. malar In. Malar subt. Malar ht. Front. sag. chord Front. subt. Front. angle Occ. sag. chord Occ. subt. Occ. angle Tot. sag. arc Horiz. circ. Orbit br. Orbit ht. Inter-orhital Nasal br. Nasal ht. Nasion subt. Nasion angle Palate In. Palate br. Mastoid In. Bush. Male 180.60 4.80 94.20 92.95 123.30 62.05 134.80 94.40 110.35 124.40 111.80 90.45 30.60 19.95 51.20 11.30 19.43 111.00 29.50 31.10 88.45 28.45 33.65 360.20 502.05 39-60 31.20 21.95 25.80 44.15 16.40 18.20 43.25 36.95 24.55 Bush. Female Zulu Male Female Zulu Sotho Male Sotho Female Xosa 186.33 5.10 102.00 101.oo 134.43 68.56 135.20 9S.13 115.80 129.80 113.13 95.23 35.23 23.93 55.73 180.44 4.50 96.81 96.18 129.72 65.62 133.34 95.31 114.37 123.50 109.97 90.81 33.93 21.43 51.68 187.17 5.11 101.34 101.77 131.91 68.42 133.82 98.14 115.85 130.28 114.73 93.88 35.37 23.54 55.22 179.56 4.13 96.76 98.00 126.33 66.40 188.08 5.08 100.87 11.86 12.12 11.88 11.46 11.66 Hott. Male 170.68 182.94 3.50 5.37 90.37 96.93 88.43 94.31 119.25 129.25 59.43 62.87 130.25 135.81 9o.m 92.43 106.12 111.50 117.25 124.43 105.00 112.00 86.43 89.44 29.87 31.94 20.00 21.87 46.31 51.87 10.87 11.43 17.00 18.94 105.00 112.12 29.25 28.31 29.81 33.18 87.00 92.31 26.56 27.56 31.68 32.25 345.75 368.37 478.06 505.37 39.00 37.62 31.50 31.68 22.81 22.18 25.87 24.62 45.50 42.62 15.62 15.50 17.37 18.18 45.31 41.12 35.81 38.25 20.12 24.50 Male 101.24 132.04 67.37 130.03 135.70 98.45 9zao 110.30 116.12 121.03 130.50 108.50 113.70 90.53 93.54 36.03 35.16 23.13 24.08 51.37 55.08 20.23 18.56 20.51 19.10 18.83 112.63 110.56 113.25 109.30 113.04 27.77 28.34 28.63 28.23 27.79 30.20 30.87 30.28 31.43 29.50 95.80 96.91 94.91 93.03 96.45 26.76 26.56 27.05 26.83 28.50 30.66 28.46 29.74 30.30 31.50 368.30 365.56 371.65 359.73 375.83 513.96 503.93 514.85 496.76 518.66 38.86 39.03 39.34 38.13 39.50 33.46 33.53 33.51 33.16 33.66 24.47 23.15 22.91 22.03 24.00 27.66 27.65 27.60 26.73 28.33 49.57 46.81 50.00 46.03 49.45 17.86 15.68 16.71 15.77 17.37 19.17 17.53 18.08 ia.13 18.58 48.63 46.21 49.02 47.60 46.91 39.40 38.71 39.45 37.73 40.33 28.53 24.53 28.28 23.73 28.66 Values are given in mm or, where appropriate, dezrees. weighted positively), as does strong development of the cheek bones; bizygomatic breadth, absolutely about the same in both groups, is relatively greater in these skulls. The malar itself is longer in Hottentots but more robust, deeper in a vertical dimension, in the Bushmen. Differences in other characters, of skull length and nose form for example, are de-emphasized on the scaled vector and are of lesser significance to discrimination. Discriminant analysis thus suggests that, while Bushman crania are generally a little smaller than those of Hottentots, gross size is only one of several factors permitting (limited) success in separation of these groups; predominance of the “size” component in CgH, the interpopulation distance calculated by Penrose’s method, is somewhat misleading. Aspects of form in the frontal region, of facial projection, and of malar development are also important, though to repeat, “important” does not here imply statistical significance of mean measurement differences. The relative inefficiency of the computed function complements the distance results in showing considerable homogeneity among the Khoisan peoples. Bushman males vs. Zulu males. Preliminary checking of Bushman and Zulu measurements with program BMD07M suggests that the discriminant function for males be composed of 15 variables, given in table 8. Quite a few of these measurements, now showing generally high F-ratios, appear in the preceding Bushman-Hottentot comparison; but the weighting is here rather different, and the function evidently does not operate 183 BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA TABLE 8 The 1 5 characters best combined to t o m a discriminant functw?ebetweea male Bushmen and male Zulus Variables Y = 1. 2. 3. 4. 5. 6. 7. 10. 12. 13. 20. 21. 22. 23. 30. _____ Cranial length Glabella protrusion Nasion-hasion length Alveolare-basion Basibregmatic height Upper face height Maximum cranial breadth Bizygomatic breadth Bimaxillary breadth Prosthion subtense Frontal angle Occipital sag. chord Occipital subtense Occipital angle Nasal height SECT. PT. Weights 0.242 0.212 - 0.421 0.391 0.444 -0.399 - 0.368 0.420 -0.452 0.482 0.484 0.574 - 0.348 0.336 0.517 Scaled Univariate f-ratio vector 7.236 1.822 - 14.715 12.058 16.368 - 10.249 '- 12.526 13.161 - 15.457 7.895 10.683 20.670 - 7,981 9.957 9.882 - 65 21.19 0.70 28.70 39.17 52.44 37.16 0.08 17.11 11.26 46.11 0.96 24.01 3.10 5.84 46.19 NEGRO^ SOTHO 20 B U S H M A N d I 135 I I40 I 145 BZULU 1 I50 I 155 1 I60 a I 165 Fig. 2 Distribution of individual scores on the Bushman-Negro (male) discriminant. Relative to the sectioning point (143.93), one Zulu and four Sotho test crania are misassigned as Bushman by the function. in the same way. Discussion of the scaled vector is better left until the corresponding female function can be considered at the same time. The mean discriminant score for 20 Bushman males is 137.92 with a variance of 4.69 and a standard deviation of 2.16; that for 30 Zulu males is 149.93 with a variance of 9.74 and a standard deviation of 3.12. Not surprisingly, segregation of Bushmen and Zulus is better than that obtained for Bushmen and Hottentots; with respect to the midpoint (143.93), all of the Bushman crania and 29 of 30 Zulu skulls are assigned correctly, for a total of 98%. Assignment becomes perfect, all individuals are properly allocated, if the sectioning point is shifted by 1.5 units to 142.43. (That the function really serves to distinguish Bushmen from Bantu Negroes generally is demonstrated by the following: of 35 Sotho male skulls run as a test series, only four are incorrectly assigned as Bushmen when the original sectioning point is used, bringing the total number of correct assignments to 80,/85 or 94% (see fig. 2). (Only two Sothos are misassigned if the lower point is substituted.) Misclassifications at 95% are about as expected; one Bushman and two Zulus deviate beyond the limits of their distributions, calculated as 133.67 - 142.16 and 143.81 - 156.04 respectively. None of the three individuals is similarly misclassified at a 99% probability. As for exclusion, results are perfect (all Bushmen are excluded as Zulus and vice 184 G . P. RIGHTMIRE versa) if a 5% probability of error is accepted, i.e., using a limit of 5% for each appropriate tail. Thirty-four of the 35 Sotho skulls, with scores of 141.48 or higher, are also excluded as Bushmen by the same test. Bushman females vs. Zulu females. When the samples compared are Bushman and Bantu females, rather than males, the 14-variable discriminant shown in table 9 applies. This choice of measurements shows some agreement with that used for male discrimination, but correspondence of the two functions is hardly exact. Discrepancies may be traced, at least in part, to the role of basibregmatic height in the two comparisons. For males, this variable has the highest univariate F-ratio and is therefore the first entered by the selection program: for females, however, skull height falls second to palate length in F-value, thereby just missing a prominent position in the subset. At subsequent steps the measurement is again rejected and does not appear in the function at all. Since the order of variables obtained is in fact heavily dependent on the first character selected, differences in this female subset, "based on palate length, are not surprising. The mean discriminant score for 16 Bushman females is 91.25 with a variance of 3.08 and a standard deviation of 1.75; that for 32 Zulu females is 104.23 with a variance of 9.54 and a standard deviation of 3.08. Relative to the midpoint (97.74), assignment is correct for all cases, so that the function does a perfect job when tested on the same data from which it was computed. When confronted with new material in the form of 30 Sotho female crania, the discriminant performs less well, misassigning eight of these individuals as Bushmen (fig. 3). Note, however, that if the sectioning point is lowered by 1.5 units to 96.24, only five Sotho skulls are so misplaced, while 100% of Bushmen and Zulus are still assigned correctly; cases of mistaken identity then number 5/78 or 6.4% of the total sample tested. If the actual group distributions are considered, individuals are seen to be misclassified, or excluded from their own groups, as follows: Two Bushmen at 95% probability, 1 at 9 9 % ; three Zulus at 9 5 % , none at 99%. Absolutely correct classifications as assessed on a one-sided hypothesis, using a probability of 99%, are made for: All (16) Bushman skulls, which are excluded as Zulus; all (32) Zulu skulls, excluded from the Bushman distribution; 25 Sotho test crania, also excluded as Bushmen . The efficiency of discrimination obtained for these female skull series is thus about the same as that observed for males and is generally quite high, indicating a definite divergence in morphology between Bushmen and Bantu Negroes. Population differences, as read from the scaled versions of the functions, seem especially apparent in the occiput, which is strongly TABLE 9 The 14 characters best combined to form a discriminant function between female Bushmen and female Zulus Variables Y = 1. Cranial length 2. 3. 9. 12. is. 16. 17. 20. 21. 22. 28. 29. 33. Glabella protrusion Nasion-basion length Maximum frontal breadth BimaxiUary breadth Maximum malar length Malar subtense Malar height Frontal angle Occipital sag. chord Occipital subtense Inter-orbital breadth Nasal breadth Palate length Scaled vector F-ratio 9.645 2.666 -11.824 16.362 - 3.585 5.954 - 2.309 4.940 9.692 9.771 11.389 - 1.842 6.555 7.785 32.13 6.63 22.73 33.55 8.35 19.35 8.59 7.99 8.05 41.84 Weights 0.253 -0.310 -0,395 0.519 -0.107 0.220 -0.244 0.404 0.537 0.288 - 0.490 -0.106 0.406 0.554 - - - 0.00 1.53 17.27 64.55 185 BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA 62 NEGRO$! PT. SECT. I SOTHO n 16 B U S H M A N 1 1 1 I 1 I 88 90 92 94 96 98 I 100 I I02 QZULU I 104 I 106 $! I I I 108 110 il2 Fig. 3 Distribution of individual scores on the Bushman-Negro (female) discriminant. Relative to the sectioning point (97.74), eight Sotho test crania are misassigned as Bushman by the function. curved in Bushmen, flatter in the Negroes men must be determined separately; only ( a point verified by Tobias, ’59). Breadth two groups or populations may be conacross the maxilla is again a Bushman sidered in any single trial. However, this feature in combination, while a high simple one-dimensional approach can be cranial vault is more characteristic o i generalized without much difficulty to a Bantu, at least for males; basibregmatic situation in which there are more than height does not figure in the female com- two groups of objects, and discrimination parison. Facial projection, bizygomatic is accomplished in several dimensions, or breadth (males), and width of the frontal along several functions, simultaneously. (females) all contribute moderately to dis- In other words, it is possible to construct crimination, though it is of interest that a “test” space in which an individual, or aspects of malar form and forehead full- sets of individuals distributed as natural ness, important to the Bushman-Hottentot populations, can be located by means of distinction, here play lesser roles. scores obtained on some number of axes In conclusion, then, these two-way dis- or multiple discriminant functions; fossils criminants perform sufficiently well to be or other material to be classified can then of practical use in distinguishing between be plotted in this space and a decision crania of several South African popula- made as to probable group membership. tions; they should prove efficient tools for Such an analysis has been carried out classifying material of unknown or ques- for seven groups of Bushman, Hottentot tionable origin, providcd of course that and Negro crania, comprising 179 specisuch material can legitimately be con- mens in all. In order to insure the greatest tained in one or another of the groups possible efficiency of discrimination, there being tested. The technique supplies a has been no systematic attempt to select decision between two specific alternatives, a subset or otherwise cut down on the and no more; that is, judgment will not number of variables used, though six of usually be withheld, even if neither is the 35 available measurements, missing biologically “correct.” This limitation, un- for certain likely test specimens (Hottentot avoidable in simple discriminant analysis, females, for example), have been omitted. becomes less troublesome as more popula- Computation yields six functions, listed in tions (and functions) are introduced. table 10 with the percentage each contributes to total discrimination. Multiple discriminants The first discriminant is the most imThe discriminant functions presented in portant, others making successively less the preceding sections have the advantage contribution, and it may be questioned of being easy to apply, but their use is whether all six are indeed statistically restricted in that sex and race of a speci- significant, i.e., whether there is “real” 186 G. P. RIGHTMIRE TABLE 10 Multiple discriminant functions for differentiating Bushman, Hottentot, and South African Negro crania, w i t h the percentage each contributes to total discrimination Variables Roofs, per cent of trace: 1. Cranial In. 2. Glabella prot. 3. Nasion-basion 5. Basibreg. ht. 8. Least front. br. 9. Max. front. br. 10. Bizgyomatic br. 11. Biauricular br. 12. Bimaxillary br. 13. Prosthion subt. 14. Subspinale subt. 15. Max. malar In. 16. Malar subt. 17. Malar ht. 18. Front. sag. chd. 19. Front. subt. 20. Front. angle 21. Occ. sag. chd. 22. Occ. subt. 23. Occ. angle 24. Tot. sag. arc 26. Orbit br. 27. Orbit ht. 28. Inter-orbital 29. Nasal br. 30. Nasal ht. 31. Nasion subt. 32. Nasion angle 35. Mastoid In. Weights I 11 54.11 24.13 0.244 0.098 0.277 -0.101 0.025 0.099 -0.157 0.268 0.019 0.004 -0,147 0.214 0.038 0.125 0.166 - 0.137 0.089 0.179 -0.011 0.166 -0.077 -0.106 - 0.020 -0.148 0.166 0.016 -0.125 0.067 -0.084 -0.254 -0.039 -0.233 0.151 -0.061 -0.142 - 0.055 -0.113 -0.191 0.073 - 0.077 0.376 -0.279 -0.291 0.200 -0.042 -0.058 0.107 -0.394 -0.208 -0.157’ 0.080 0.184 -0.185 0.077 0.155 0.058 -0.050 0.377 I11 8.40 -0.106 -0.018 0.372 -0.427 0.219 -0.210 -0.060 0.197 -0.a~ 0.519 - 0.069 -0.018 -0.152 0.216 0.126 -0.012 -0.071 -0.313 0.158 -0.174 0.335 -0.051 0.113 -0.266 0.100 -0.174 -0.129 0.037 -0.190 VI V 3.91 IV 6.29 0.090 0.147 0.111 0.172 - 0.247 -0.198 -0.070 -0.201 0.127 0.185 -0.059 -0.144 0.069 0.079 0.090 -0.480 -0.199 0.281 -0.179 0.069 0.037 -0.137 0.107 -0.246 0.111 -0.112 -a.i30 0.373 0.336 -0.043 0.178 0.055 -0.012 -0.016 -0.061 -0.1% 0.120 - o.oa0 - 0.034 0.329 - 0.018 0.006 - 0.096 -0.190 -0.150 0.209 -0.185 -0.171 0.268 0.185 -0.135 -0.0991 0.246 - 0.235 0.094 0.062 -0.124 - 0.132 3.15 - 0.253 - 0.009 0.243 -0.283 0.143 -0.174 0.535 - 0.208 -0.328 - 01.155 0.252 - 0.410 0.088 0.027 - 0.231 0.110 0.023 0.045 - 0.013 - 8.337 0.389 -0.191 -0.183 -0.052 -0.089 0.439 -0.090 0.122 -0.088 - TABLE 11 The distribution of group mean scores for Bushman, Hottentot, and South African Negro crania ~~~ Discriminant functions Variables I Bushman males Bushman females Hottentot males Zulu males Zulu females Sotho males Sotho females 70.22 65.64 71.45 77.92 72.70 77.01 71.79 separation of the group means in all six dimensions specified. This can be tested with the aid of Bartlett’s chi-square approximation for the latent roots associated with each function (see Rao, ’52, pp. 371373). Using this approximation, residual variation (distributed as chi-square) left over after removal of the first (1, 2, 3, . . . etc.) roots can be tested for significance; if this residual chi-square is attributable to chance, there is then no evidence for variation in other dimensions, and the remaining roots (and functions) can be 11 - 37.51 -39.64 -40.21 -42.42 -43.97 -41.24 -43.16 111 IV 71.68 67.57 71.36 69.49 69.75 72.93 71.95 64.53 63.24 69.08 65.29 67.92 67.18 64.95 discarded. Test results indicate only the f i s t four roots (together accounting for about 93% of the total variance) to be significant, and the corresponding functions thus essentially exhaust the discriminatory power of the battery. Only these four functions need be considered further. Group mean scores on each of the significant discriminants are presented in table 11. As coordinates, these figures specify the mean vectors or “centroids” (analogous to distribution means in the univariate case) 187 BUSHMAN, HOTTENTOT A N D AFRICAN NEGRO CRANIA of each group in the discriminant space. Individual skulls, also located by their scores on the four functions, are distributed as swarms of points surrounding the centroids, these distributions (simple ellipses in 2 dimensions) here taking the form of hyperellipsoids oriented differently for each group. Graphic portrayal of the mean vectors, some shown with expected distribution limits (90% contours, or ellipses drawn so as to contain 90% of individuals belong to the populations indicated), is attempted in figures 4, 5 and 6. Each plot utilizes only two functions, so that the figures really represent slices or planes taken through the test space of four (actually 6 ) dimensions. This is a convenient way of visualizing the relative proximity of one group to another and also the placement of individuals with respect to their own and other group centroids; however, it is not especially accurate and can give false impressions concerning inter- and intragroup relation- ships, which are better interpreted by reference to classification data computed by the program. The problem of inferring an individual's group membership from his several discriminant scores is rather complex, as the sectioning point and standard deviation approach, familiar from the two-way analyses, is no longer applicable. Instead, chi-square is used to provide an index of the extent to which a skull resembles a particular group, or one centroid resembles another; these classification chi-squares are computed by pre- and postmultiplying the inverse of a group's dispersion (variance-covariance) matrix by a vector of the individual's deviation scores (Cooley and Lohnes, '62, chapter 7). The seven figures resulting for each skull are used as the basis for assignment (e.g., to that group with which the specimen has the lowest chi-square and hence the greatest similarity) and also classification. For example: since for six degrees -50r I +ZULU A I- 60 MALE SKULLS HOTTENTOT F E M A L E SKULLS I I I 1 I 65 70 75 80 85 Fig. 4 Bushman, Hottentot and Negro group centroids on multiple discriminants I and 11; 90% contours are shown for Bushman and Zulu groups. Zulu male and Hottentot female crania are plotted individually. 188 G. P. RIGHTMIRE Hottentot males (26). Correctly assigned in 14 cases; two misassigned as Sotho female. No misclassifications at 95%. Zulu males (30). Five skulls misassigned, four as Sotho male, one as Sotho female. Two misclassified at 95%, none at a 99% probability. (Of the Zulu males plotted in fig. 4, 3 are shown lying outside of the 90% probability ellipse; computed chi-squares indicate that in fact 4 individ75 80 85 uals are misclassified at this level.) Fig. 5 Group centroids on multiple discrimiZulu females (32). Seven cases misnants I and 111. assigned, two as Sotho male, five as Sotho female. Only one skull is misclassified at a 95% probability. Sotho mazes ( 3 5 ) . 12 individuals misI Hd assigned, two as Hottentot, the rest as Zulu male or Sotho female. Two misclassified Ozp .sd at 95%, none at a 99% probability. Sotho females ( 3 0 ) . Nine skulls misassigned, three as Bushman or Hottentot, five as Zulu, and one as Sotho male. Again, two are misclassified at 9 5 % , none at a 99% probability. Correct assignments, using multiple tH I L25 discriminants, are thus made for 141 70 75 80 05 Fig. 6 Group centroids on multiple discrimi- cases totaling approximately 79% of the nants I and IV. entire series tested. Although lower than that obtained on the several separate twoof freedom the probability of obtaining way functions (which are not directly chi-square larger than 12.6 is 0.05, an in- comparable), this level of efficiency seems dividual would be excluded at 95% prob- quite satisfactory, considering the numability from any group for which his ber of groups involved. It is worth pointcomputed value is 12.6 or higher but ing out that ( a ) fewer than 10% of Bushwould be correctly classified at the same man and Hottentots are misassigned, and probability if chi-square for his own group (b) Bantu individuals are misassigned were below this level. Thus the distances mainly by sex or tribe (or both), but not of a particular skull from each of the pop- as members of some Khoisan population. ulation centroids may be tested for sig- Considerable blurring of the Zulu-Sotho nificance and an appropriate assignment distinction, rather than sharp discriminamade, or, if the skull is sufficiently dis- tion, is only to be expected. Absolute classification at a 95% probsimilar to all populations included in the analysis, it may be excluded from mem- ability, meaning exclusion at this level of a n individual from all groups other than bership in any group. Assignments and classifications as read his own, is made for only 23% of cases, directly from the program output are as the figures ranging from a high of 69% (11/16 Bushman females) to 6% ( 2 / 3 2 follows : Bushman males ( 2 0 ) . Correctly as- Zulu females). Things are somewhat betsigned in 18 cases; one misassigned as ter if only two categories, Khoisan and Hottentot, another as Sotho female. No Bantu, are employed, in which case 50% (26/52) Bushmen and Hottentots) and misclassifications at a 95% probability. Bushman females (16). 15 skulls as- 57% (72/127) Zulu and Sotho) of skulls, signed correctly, one incorrectly as Sotho respectively, are excluded from membership in the inappropriate group constellafemale. No misclassifications at 95%. . I I J 189 BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA tion. Three additional Negro specimens, correctly excluded from being Bushman or Hottentot, also deviate beyond the expected 5% limits of all Bantu distributions. When the functions are tested against new material of known Bantu origin (24 Xosa male skulls), results are again encouraging. In all, 19 of the test crania, or nearly 80% of the series, are excluded by chi-square from the several Khoisan distributions, and the five remaining specimens are at least outside the Bushman 5% limits (though just within the corresponding Hottentot distribution). None of the Xosa skulls are assigned (‘%best fit”) as Bushman or Hottentot. Three Hottentot female crania, useless as a sample, have also been treated as test material and are plotted in figure 4. Their positions in the discriminant space are about as expected, and no further comment seems required. Interpretation of the functions. The several discriminants, together demon- strated to be reasonably efficient in assigning both sex and race of South African crania, may now be examined on an individual basis; each is contributing rather differently to over-all group separation, and from one function to another, corresponding measurements do not everywhere have equal roles. Scaled vectors and univariate F-ratios, again useful as interpretory aids, are listed in table 12. Function I, which accounts for 54.1% of total discrimination, appears to separate the groups by sex primarily; the listing of mean scores and figure 4 show a segregation of males from females within both Bantu and Bushman categories (along axis I in the figure). Also, if function I is considered for the moment as an independent sexing formula and applied in separate trials within populations, results are reasonably good; using appropriate sectioning points (again the average of mean scores for the two groups, males and females, tested in a given trial), totals of 89% of Bushman. 85% of Zulu and TABLE 12 Scaled vectors and iinivariate F-ratios for differentiating Bushman, Hottentot, and South African Negro crania ~ ~~~~ 1. 2. 3. 5. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 26. 27. 28. 29. 30. 31. 32. 35. Cranial In. Glabella prot. Nasion-basion Basibreg. ht. Least front. br. Max. front. br. Bizygomatic br. Biauricular br. Bimaxillary br. Prosthion subt. Subspinale subt. Max. malar In. Malar subt. Malar ht. Front. sag. cha. Front. subt. Front angle Occ. sag. chd. Occ. subt. Occ. angle Tot. sag. arc Orbit br. Orbit ht. Inter-orbital Nasal br. Nasal ht. Nasion subt. Nasion angle Mastoid In. ~ Scaled vectors Variables I 17.726 0.063 - 8.771 14.879 2.433 7.654 9.668 - 7.491 5.503 6.691 0.402 7.720 - 1.453 - 2.801 - 1.256 - 5.235 6.019 1.115 - 5.390 3.550 - 14.302 - 6.051 - 1.060 - 8.145 4.779 6.673 1.913 - 1.574 12.843 - I1 7.134 4.717 - 6.036 1.762 6.265 - 9.661 15.629 1.037 3.792 - 5.295 - 2.054 - 5.259 - 3.580 1.942 4.932 13.280 - 10.091 - 20.658 8.628 - 2.245 - 9.835 2.549 - 10.651 - 7.278 - 4.960 3.447 6.055 - 5.m 2.609 - - I11 - 7.681 - 0.300 22.202 -29.692 13.833 - 12.856 - 3.484 10.752 - 5.124 19.368 - 2.549 - 0.842 - 2.847 5.710 8.017 0.412 2.566 -22.195 6.829 9.193 57.144 - 1.208 3.054 9.315 3.166 - 7.485 4.237 1.157 6.475 - - IV - 14.613 -~ ~ 2.158 11.009 - 4.117 - 9.095 4.255 4.616 4.896 - 29.652 - 7.417 10.443 - 8.287 1.302 0.972 - 8.739 3.777 - 8.923 7.838 - 4.831 - 6.868 63.534 8.001 - 1.173 6.214 1.744 - 0.531 - 0.531 - 1.925 - 6.253 F-ratio 20.88 5.15 17.61 21.10 9.31 13.12 26.91 13.96 8.72 16.54 7.80 17.12 1.98 7.51 6.69 1.13 3.06 10.35 0.90 4.34 9.04 3.07 5.90 6.91 5.07 16.17 3.12 1.52 28.84 190 G . P. RIGHTMIRE 89% of Sotho skulls are correctly assigned by sex. Distinctions by race are not as clear on this discriminant, despite, for example, the extreme divergence of Bushman females from Zulu and Sotho males. Further examination of the scaled vector indicates that the variables contributing most to separation of the sexes are mainly gross measurements of the skull vault: maximum length, height taken from basion to bregma, total sagittal arc, and various breadths, that taken across the zygomatic arches outweighing the biauricular dimension in relative importance. Maximum frontal breadth fares well, though the closely correlated minimum breadth (perhaps not properly a vault dimension at all) does not seem particularly useful. Further generalization is difficult, though evidently mastoid length, height of the nasal aperture and maximum malar length provide additional independent information while other measures of malar development and angularity do not. Breadth taken between the orbits achieves at least a moderate loading on all sexing functions and surpasses both orbit breadth and height in this respect; this is unexpected as the inter-orbital distance has the lowest F-ratio of the three. Function I1 contributes roughly half as much (24.1% ) to overall discrimination and furnishes limited segregation of groups in a new dimension, this time mainly by race or population rather than by sex. The Bushmen receive the highest (least negative) scores and are removed from Bantu of either sex; Hottentots, with a lower mean score, make a closer approach to the Negro groups and so occupy a more intermediate position. Sex differences within each population are consistent (males have higher scores than females) but slight, and discrimination on a sex basis seems of only minor concern. That this function is indeed doing something different from discriminant I is obvious from its scaled vector; while bizygomatic breadth is again ranked highly (and apparently is operating once more as a sex indicator), many other measurements seen to be of major importance in sexing (e.g., cranial length and height, biauricular breadth, and mas- toid length) here receive little emphasis and have some of the lowest scaled weights listed. Sagittal arc (registering size?) and nasal height are also reduced, though the contrast is not so striking. Far more significant to discrimination along axis I1 are various measurements already demonstrated to be of use in distinguishing Bushman crania from those of Hottentots and Negroes. As expected, the occipital chord and subtense are reversed in sign, the result being a positive bias for (Bushman and Hottentot) skulls with curved occipitals; a flatter occiput, characteristic of Negro crania, makes for a lower, more negative, score. Dimensions registering maximum width and, more important, curvature or fullness of the frontal contribute heavily to discrimination and in much the same way; the bone is broader in Hottentots and Bantu, less sloping in Bushman skulls. Orbit height, greater in Negroes, also plays a role of some note, and the two measurements registering protrusion of the nasal root (nasion subtense and angle) are relatively more important here than on the f h t discriminant. All in all then, it seems quite clear that the dimensions stressed on function I1 relate primarily to shape or form of the face and braincase, not to general size of the vault. These measurements, which include several rather unorthodox subtenses and angles taken with a coordinate caliper, are evidently the crucial ones for discrimination between populations, though not for separation of the sexes. The obvious inference here, that racial differences among the South African cranial series are a matter of shape while sexual dimorphism is reflected in size, must be made with reservation, however; the distinction implied is one of degree and of course not absolute. Neither sex nor race differences in these skulls are wholly “shape” or “size”’ dependent, though one or the other of these two aspects of morphology may predominate. Functions I11 and IV together absorb only about 14% of the total generalized variance and so contribute little to discrimination as afforded by the entire six-function battery. However, both are significant on Bartlett’s chi-square approxi- BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA mation and merit at least passing mention here. Discriminant I11 serves to set off Sotho males and females from Zulu individuals of both sexes and hence seem to be picking up differences confined within a broad Bantu Negro framework; segregation by sex is not obvious (except perhaps “accidentally” among the Bushmen), and this function adds nothing to the separation of Khoisan from Bantu groups accomplished on axis 11. Measures of skull height, facial prognatbism, the occiput and total sagittal arc seem most useful in discrimination, though ZuluSotho mean differences in most of these characters are small. Function IV is of consequence only in so far as it is the first discriminant to separate Hottentots from both Bushman series; male representatives of these groups are closely associated on the three axes previously described. Prominence of bimaxillary breadth in the scaled vector is not surprising, as this middle facial measurement is among those weighted heavily on the separate Bushman-Hottcntot race discriminant. TO sum up; these four functions, each a compound of 29 cranial measurements, make separate (and unequal) contributions to discrimination in the sense that each is measuring some different aspect of total variation within and between the populations studied; to some extent at least, differences of sex and race, and finer distinctions within the Khoisan and Bantu categories, are treated in statistically independent fashion, but are scaled always in proportion to the biology involved; the technique, no matter how sophisticated mathematically, cannot inflate or conjure into being a distance between groups which does not exist in nature. The end result, when the several functions are viewed together as axes in a discriminant space, is a biologically accurate (given the limitations of the original measurements) and statistically satisfying rendering of relationships among the seven groups included in the analysis. DISCUSSION Generalized distance estimates calculated with Dz and CzH already have been treated at some length and need not be 191 reexamined in detail. The independent sets of distances are mutually consistent in suggesting Bushman and Hottentot males to be quite similar cranially (in fact not significantly different) from samples of Zulu, Sotho and Xosa tribal populations. Two points are of particular interest here. Firstly, the Bushman and Hottentot series are judged to be composed of individuals documented more reliably than has generally been the case in previous comparative surveys, excepting that of Stern and Singer (’67) in which multivariate statistics have not been used. These samples are not as large as could be hoped but must include nearly all of the authenticated specimens to be found in South African museum and medical school depositories. Secondly, the distance analysis, based on cranial characters, implies a degree of Bushman-Hottentot affinity at least as great as that which has been inferred from the study of morphological and biochemical variation in the living peoples. However, whether the Bushman-Bantu and Hottentot-Bantu distances should also be interpreted as “small” (and therefore indicative of a close Khoisan-Negro tie as is suggested by the serological evidence) is a question not easly decided. Comparison of the present Dz values with those published elsewhere is hampered by differences in both computational methodology and number and type of measurements used, and there is little information as to how sensitive to such differences the statistic may be. Thus, while these distances appear only moderate in magnitude relative to others calculated, say, for Nigerian tribes (Talbot and Mulhall, ’62) or Indian caste groups (Mahalanobis, Majumdar and Rao, ’49), there is no certainty that the latter D* values are actually being measured on the same scale as are the former. Because, of this, inclusion of Bushmen and Hottentots in a Xegro category does not seem justified on the evidence available. (An additional finding, that 98% of male and 100% of female Bushman and Zulu crania can be differentiated in discriminant analysis, connotes a marked degree of morphological divergence and argues against any lumping of these groups. ) 192 G. P. RIGHTMIRE Much the same set of relationships as by virtue of their performance when conindicated by D2is also evident when the sidered alone, without appreciation of groups are run in a multiple discriminant their intercorrelations; i.e., a high unianalysis, though here more variables are variate I?-ratio is not necessarily a reliable utilized, and treatment has been expanded guide and, where choice of a subset of to include samples of female crania as variables must be made, selection is better well as males. (Distances between cen- based on some step-wise ordering procetroids in the discriminant space, while not dure such as that available in program computed as such by the program used, BMD07M. may be thought of as D” determinations Bushman-Hottentot mean differences in based on 29 measurements; the two ap- cranial characters are small in an absolute proaches, distance and discrimination, are sense, though Hottentots seem to be a conceptually quite similar and would be little larger, especially in height of the expected to yield about the same result.) skull vault. Cranial length, found by Stern Addition of the several female series is and Singer (’67) to differ significantly seen to be a necessary adjunct to the male between these two groups, plays only a only analysis carried out with D2,as the minor role in the computed discriminant, female centroids are well removed from whereas certain other measures, of frontal the corresponding male means in the expansion, facial breadth and projection, space provided. Sexual variation is ob- malar length and height, account for the viously important in these South African greater apart of the “racial” separation populations - recall that the first and observed. Other “shape” differences, no“best” function of the six computed sepa- tably degree of occipital curvature as rates the groups largely on a sex basis - registered by the occipital subtense and and to ignore it would quite severely lessen angle, contribute to the discrimination afthe value of the (discriminant) approach forded by the Bushman-Zulu functions as a tool for the classification of unknown and by function I1 of the multiple disor unsexed material. criminant set, so that shape-directed All in all, in showing the importance measurements appear to be most useful in of specific variables to group separation, in distinguishing between these populations treating populations as distributions of while measures of general skull size tend, individuals and providing estimates of dis- on the whole, to be the better sex indipersion, and not least, in yielding results cators. Whether this holds for other than in a form amenable to graphic represen- IUloisan and South African Negro series tation in a limited number of dimensions, remains to be tested, though a somewhat multiple discriminant analysis provides a similar conclusion, that dimensions of the good deal more information than does DZ, face and primarily of the nasal region are even when this is combined with canonical more efficient in race discrimination than variates as in Mahalanobis, Majumdar those taken on the cranial vault, has been and Rao (’49). Probably, in biometric reached by Crichton (’66) in a study of studies of this nature, generalized dis- Egyptian and Teita Negro skulls. tance as a separate technique could be In any case, certain sets of characters replaced entirely by discriminants, though which when combined in multivariate D2 values are fairly easily obtained with analyses separate the South African crania Rao’s transformations and their use should by sex and race have been identified, and be retained in cases where the facilities these should serve as a convenient guide necessary for the computation of discrimi- €or workers planning further craniometric nant functions are not available. research on similar material. There is of Simple two-group discriminants also course no guarantee that the measureprove useful for separating Bushman ments cited are the best or only ones that skulls from those of Hottentots and South could be found, and if this work were to African Negroes, and it is of interest that be done over, some changes in original measurements found to be quite useful dis- choice of variables and in measurement criminators in a multivariate context are technique would be introduced. Since in not always those which would be selected a multivariate analysis of this sort it is BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA possible to treat a skull as a unit, rather than as a series of single traits, and to compare these units in population terms, inter-related measurements likely to bring out aspects of shape characterizing populations should be the goal in mind. Some such characters, which do not all correspond with those traditionally employed in univariate comparisons, have been included here, but there is much need for continued experimentation. ACKNOWLEDGMENTS Professors J. T. Robinson, L. Freedman, G . Wahba, R. Singer and R. H. Osborne provided advice and assistance during various stages of the planning and execution of this work, and Miss C. Hughes is responsible for final drafting of the figures. Access to collection of skeletal material was kindly given by the following: Professor P.V. Tobias and Dr. H. de Villiers, Johannesburg; Professor L. H. Wells, Dr. T. Barry and Mr. Q. B. Hendey, Cape Town; and Mr. A. J. B. Humphreys, Kimberley. I am indebted to the National Institute of Dental Research for support on a Training grant (144-8742) and to the National Science Foundation for the award of a Doctoral Dissertation Completion Grant (GS-1960). Use of the University of Wisconsin Computing Center was made possible through support, in part, from the National Science Foundation, other United States Government agencies and the b7isconsin Alumni Research Foundation (WARF) through the University of Wisconsin Research Committee. LITERATURE CITED Barnicot, N. A., J. P. Garlick, R. Singer and J. S. TVeiner 1959 Haptoglobin and transfenin variants in Bushmen and some other South African peoples. Nature, 184. 2042-2044. Broom, R. 1923 A contribution to the craniology of the yellow skinned races o f South Africa. J. Roy. Anthropol. Inst., 53: 132-149. 1941 Bushmen, Koranas and Hottentots, Ann. Transvaal Mus., 20: 217-251. Cain, A. J., and G. A. Harrison 1958 A n analysis of the taxonomist’s judgment of affinity. Proc. Zool. SOC.London, 131: 85-98. Campbell, B. 1963 Quantitative taxonomy and human evolution. In: Classification and Human Evolution. S. L. Washburn, ed. Aldine, Chicago. pp. 5LL74. 193 Cooley, W. W., and P. R. Lohnes 1962 Multivariate Procedures for the Behavioral Sciences. John Wiley and Sons, Inc., New York. Coon, C. S. 1965 The Living Races of Man. Alfred A. Knopf, New York. Crichton, J. M. 1966 A multiple discriminant analysis of Egyptian and African Negro crania. Pap. Peabody Mus., 57: 47-67. Dart, R. A. 1937 The physical characters of the /?Auni-#Khomani Bushmen. Bantu Stud., 11: 176-295. 1950 African serological patterns and human migrations. Presidential Address given to The South African Archaeological Society, Claremont, Cape Town. 1952 A Hottentot from Hong-Kong: pre-Bantu population exchanges between Africa and Asia. S. Afr. J. Med. Sci., 17: 117-154. 1954 The Oriental Horizons of Africa. Text of a series of talks broadcast by the S.A.B.C., Johannesburg. De Villiers, H. 1968 The Skull of the South African Negro. Witwatersrand University Press, Johannesburg. Drennan, M. R. 1938 Archaeology of the Oakhurst Shelter, George. Part 111. The cavedwellers. Trans. Roy. SOC.s. Afr., 25: 259-293. Dreyer, T. F., and A. J. D. Meiring 1937 A preliminary report on a n expedition to collect old Hottentot skulls. Soijl. Navors. Nas. Mus., Bloemfontein, I: 81-88. 1952 The Hottentot. Navors. Nas. Mus., Bloemfontein, 1: 19-22. Fitch, W. M., and E. Margoliash 1967 Construction of phylogenetic trees. Science, 155: 279-284. Galloway, A. 1933 The Nebarara skull. S. Afr. J. Sci., 30. 585-596. -1937 Man in Africa i n the light of recent discoveries, S. Afr. J. Sci., 34: 89-120. Giles, E., and 0. Elliot 1962 Race identification from cranial measurements, J. Foren. Sci., 7: 147-157. Grobbelaar, C. S. 1955 The distribution of the blood groups of the Koranas. S. Afr. J. Sci., TO^. 52: 323-326. 1956 The physical characters of the Korana. S . Afr. J. Sci., 53: 99-143. Hiernaux, J. 1956 Analyse de la variation des caractkres physiques humains e n une d g i o n de 1’Afrique centrale: Ruanda-Urundi et Kivu. Ann. mus. Roy. Congo Belge, 3: 131-143. 1964 The measuring o f morphological differences between populations for a set of variables. Yearbook of Physical Anthropology, 12: 127-135. Howells, W. W. 1966a Population distances: biological, liguistic, geographical and environmental. Curr. Anthropol., 7: 531-540. -196613 The Jomon population o f Japan: a study by discriminant analysis of Japanese and Ainu crania, Pap. Peabody Mus., 57: 1-43. Huizinga, J. 1962 From DD to D2 and back. The quantitative expression of resemblance. Proc. Konink. Nederl. Akad. Wetensch., 65: 1-12. -1965 Some more remarks on the quantitative expression of resemblance (distance co- 194 G. P. RI(ZHTMIRE - 1922 A note o n Bushman craniology. efficients). Proc. Konink. Nederl. Akad. WeMan, 22: 185-187. tensch., 68: 69-80. Keen, J. A. 1947 A statistical study of the dif- Singer, R. 1960 Some biological aspects of the ferences between Bantu, Hottentot and BushBushmen. Z. Morphol. Anthropol., 51: 1-6. man skulls. Saiil Navors. Nas. Mus., Bloem1961 Serum haptoglobins in Africa. S. fontein, 1: 191-199. Afr. Med. J., 35: 520-523. 1952 Craniometric survey of the South Singer, R., and W. Jop 1967 The earliest ilAfrican Museum collection of Bushman, Hotlustration of Hottentots: 1508. S. Afr. Archaeol. tentot and Bush-Hottentot hybrid skulls. Ann. Bull., 22: 15-19. S. Afr. Mus., 37: 211-226. R., and J. S. Wejner 1963 Biological Kendall, M. G. 1957 A Course in Multivariate Singer, aspects of some indigenous African populaAnalysis. Charles Griffin and Co., London. tions. Southwest. J. Anthropol., 19: 168-176. Krut, L. H., and R. Singer 1963 Steatopygia; the fatty acid composition of subcutaneous Singer, R., J. S. Weiner and A. Zoutendyk 1961 The blood groups of the Hottentots. Proceedadipose tissue in the Hottentot. Am. J. Phys. ings of the Second International Congress of Anthrop., 21: 181-188. Human Genetics, Rome, pp. 884-887. Mahalanobis, P. C. 1925 Analysis of race mixture in Bengal. J. Asiatic SOC.Bengal, 23: 301- Slome, D. 1929 The osteology of a Bushman tribe. Ann S. Afr. Mus., 24: 33-60. 333. 1930 On tests and measures of group Stern, J. T., and R. Singer 1967 Quantitative morphological distinctions between Bushman divergence. J. Asiatic SOC.Bengal, 26: 541-588. and Hottentot skulls: A preliminary report. S. 1936 On the generalized distance in Afr. Archaeol. Bull., 22: 103-111. statistics. Proc. Nat. Inst. Sci. India, 2: 49-55. Mahalanobis, P. C., D. N. Majumdar and C. R. Talbot, P. A., and H. Mulhall 1962 The Physical Anthropology of Southern Nigeria. CamRao 1949 Anthropometric survey of the bridge University Press. United Provinces, 1941: A statistical study. Tobias, P. V. 1955 Physical anthropology and Sankhya, 9: 90-324. somatic origins of the Hottentots. Afr. Stud., Marshal, D., and E. Giles (unpublished) Poly14: 1-15. nesian relationships: New cranial and linguistic 1955-56 Les Bochimans Auen et indicators, Naron de Ghanzi. Contribution B L’etude des Mukherjee, R,. C. R. Rao and J. C. Trevor 1955 “anciens jaunes” Sud-Africains. L’AnthroThe Ancient Inhabitants of Jebel Moya. Campologie, 59: 235-252, 429-461; 60: 22-52, 268bridge University Press. 289. Penrose, L. S. 1954 Distance, size and shape. 1957 Bushmen of the Kalahari. Man, Ann. Eugen., 18: 337-343. 57: 33-40. Pijper, A. 1932 Blood groups of Bushmen. S. 1959 Studies on the occipital bone in Afr. Med. J., 6: 35-37. Africa. 11. Resemblances and differences of occipital patterns among modem Africans. Z. - 1935 Blood groups in Hottentots. S. Morphol. Anthropol., 50: 9-19. Afr. Med. J., 9: 192-194. 1964 Bushman hunter-gatherers: A Rao, C. R. 1948 The utilization of multiple study in human ecology. In: Ecological Studies measurements in problems of biological classii n Southern Africa. D. H. S. Davis, ed. Junk, fication, J. Roy. Statist. SOC., 10: 159-194. The Hague, pp. 67-86. 1952 Advanced Statistical Methods in 1966 The peoples of Africa south of Biometric Research, John Wiley and Sons, the Sahara. In: The Biology of Human AdaptNew York. abiIity. P. T. Baker and J. S. Weiner, eds. Rightmire, G. P. 1969 On the computation of Clarendon Press, Oxford, pp. 111-200. Am. Toerien, M. J. 1958 The physical characters Mahalanobis’ generalized distance (P). J. Phys. Anthrop., 30: 157-160. of the Lake Chrissie Bushmen. S. Afr. J. Med. 1970 Iron Age skulls from southern Sci., 23: 121-124. Africa re-assessed by multiple discriminant Trevor, J. C. 1947 (published 1950) The analysis. Am. J. Phys. Anthrop., 33: 147-168. physical characteristics of the Sandawe. J. Roy. Anthropol. Inst., 77: 61-78. Schapera, I. 1930 The Khoisan Peoples of South Africa: Bushmen and Hottentots. Rout- Weiner, J. S., G. A. Harrison, R. Singer, R. ledge, London. Harris and W. Jop 1964 Skin colour in southern Africa. Hum. Biol., 36: 294-307. Schultze, L. 1928 Zur Kenntnis des Korpers der Hottentoten und Buschmanner. Jenaische Weiner, J. S., and A. Zoutendyk 1959 Blood group investigations on central Kalahari BushDenkschr., 17: 147-228. men. Nature, 183: 843-844. Shrubsall, F. C. 1907 Notes on some Bushman crania and bones from the South African Wells, L. H. 1949 A note on some human skulls from Louisvale, near Upington. S. Afr. museum, Cape Town. Ann. S. Afr. Mus., 5: J. Sci., 45: 106. 227-270. 1951 The Broom collection af Nama -1911 A note o n craniology of South Hottentot skulls in the Edinburgh University , : 202African Bushmen. Ann. S. Afr. M U ~ . 8 Anatomical Museum. S. Afr. J. Sci., 48: 97-103. 208. - - - - - BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA 1952 Physical measurements of Northern Bushmen. Man, 52: 53-56. 1960 Bushman and Hottentot statures: A review of the evidence. S. Afr. J. Sci., 56: 277-28 1. - 195 Zoutendyk, A., A. C. Kope6 and A. E. Mourant 1953 The blood groups of the Bushmen. Am. J. Phys. Anthrop., 11: 361-368. - 1955 The blood groups of the Hottentots. Am. J. Phys. Anthrop., 13: 691-697.