# An alternative method of estimating the cranial capacity of Olduvai Hominid 7.

код для вставкиСкачатьAMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 65:71-81(1984) An Alternative Method of Estimating the Cranial Capacity of Olduvai Hominid 7 J. RIMAS VAISNYS, DAN LIEBERMAN, AND DAVID PILBEAM Departments of Electrical Engineering and Geology and Geophysics, Yale Uniuersity, New Haven, Connecticut 06520 (J.R. V) and Department of Anthropology, Haruard Uniuersity, Cambridge, Massachusetts 02138 (0.L., D. P ) KEY WORDS Cranial capacity, Homo habilis, Partial endocasts, OH7, Regression analyses, Early hominids ABSTRACT The cranial capacity of Olduvai Hominid 7 is estimated to be 690 cc, with a standard uncertainty range of 538 to 868 cc. The estimate is derived from a systematic consideration of the relationships between BregmaAsterion chords and cranial capacities obtained from a large sample of Homo sapiens and Pan troglodytes and from available fossil hominids. The estimation technique is applicable to other characters and specimens. The parietal fragments of Olduvai Hominid 7 (OH7),discovered in 1961(Tobias, 1964, 1971; Leakey et al., 19641, have been the source of considerable debate, in particular concerning the cranial capacity of the fossil. Tobias (1964, 1968,1971) estimated the brain volume to be 657 cc by measuring the volume of the reconstructed parietal endocast and multiplying by the ratio of the total cranial capacity to parietal partial endocast volume of other relevant specimens. More recently, multiple regression techniques have been employed by both Holloway and Wolpoff to reach conclusions that are, however, strikingly different. Holloway (1980, 1983))using a combined sample of pongids and hominids, estimates the cranial capacity of OH7 to be between 700 and 750 cc. Wolpoff (19811, on the other hand, using a sample of Australopithicus africanus and Homo habilis fossils, estimates a brain volume between 580 and 600 cc. The controversy over the OH7 parietals illustrates two general problems encountered in paleontological work: how one should reconstruct a fossil to minimize the effects of postmortem events, and how one should estimate characters not available directly from the specimen. Answers to the first problem tend to be different for each specimen and depend on a variety of factors, including the specific details of the damage, the preservational environment, and the nature of the fossil itself. Intuition, based on experience, 0 1984 ALAN R. LISS, INC. will undoubtedly remain the basis of any approach to this problem. An answer to the second problem, however, rather than being solely based on the fossil itself, usually requires some generalization and involves data from related individuals or related classes of organisms. This paper will examine the second problem of how to estimate individual characteristics not directly available from a fossil. Although the approach is primarily concerned with arriving a t a n endocranial volume for OH7, the same method could be applied to other problems. The next section outlines a systematic approach to the estimation of one character from data concerning other characters for a given specimen. The section after that details the calculations needed to estimate the cranial capacity of the OH7 specimen, with a discussion of the uncertainties associated with the estimate being presented in a following section. We then conclude with a discussion of earlier estimates and point out some of the implications of the approach. We have chosen not to enter the argument about parietal reconstruction for two reasons. First, we are not in a position to examine the originals and believe that alternative reconstructions can only be seriously evaluated by those familiar with the fossil mateReceived August 26, 1983; revised and accepted March 14, 1984. J.R. VAISNYS, D. LIEBERMAN, AND D. PILBEAM 72 rial. Second, our primary aim is approach: how should one go about tackling a problem of this kind? APPROACH We begin with the observation that the population making up a species may be described by a probability density function f(c1,c2,...,c,,sl ,...,sm), where the variables cl,...,c, are character variables used in the description of the individuals of that species and the variables sl, ...,s, are variables used to characterize the species itself. If the sets of variable are chosen to incorporate allometric and dimensional considerations, the function f( ) usually acquires a simpler form and often can be approximated by a multidimensional normal expression with regard to the variables cl, ...,c,,. In such a case some of the species characterizing variables may be identified with the parameters characterizing the distribution. The method of estimation to be presented below can be used with a distribution function of any form (including a purely empirically derived function), although the calculations are much simpler for the normal distribution. If we have a specimen for which we know the values of the variables ~ 2 , ~..., 3c,, and desire to estimate the value of c1, then, under the preceding assumptions, it is appropriate to seek a relationship of the following form among the various quantities: c1 = a&) + a2(5) . c2 + a3b) c3 + ... + v1(s), * (1) where s stands for all the pertinent species characterizing variables. This equation describes the relationship among the measurements characterizingdifferent individuals of the same species. We draw attention to several aspects of the above expression. First, note that while the coefficients appearing in the equation are derivable from f( ), in practice they are usually determined by doing a regression using a population sample for which all the characters have been measured. Second, note that the coefficients are species specific: populations drawn from different species will be described by different regression equations, as expected from the observation that different species are described by different probability density functions. Third, note the presence of the term vl, which is a random variable (and under our assumptions normally distributed). The term v1 describes the inherent biological variability of the charac ter c1 from individual to individual, even ij the individuals are of the same species and even if they have the same values for all the other character variables. It should be noted that the statistics describing this term are derivable from the original species probability density function, that the term is species specific, and also depends upon the choice of independent variables in the regression. The importance of this term in this problem arises from the fact that it sets a lower limit to the uncertainty with which the value of the character c1 can be estimated for a given specimen from a knowledge of other character values for that specimen. (The term v1 should not be confused with any error terms due to measurements or sampling. If these latter sources of uncertainty are present they will increase the uncertainty of any prediction still further.) The above equation is useful in estimating the value of c1 for a n individual for which only fragments determining values of c2,...,c, have been preserved, provided we have enough other complete specimens to determine the regression equation for the species. However, this estimation procedure is useless in estimating values of a character from finds (incomplete for that character) of a new species, in which the regression coefficients will be unknown. A solution to this latter problem is provided once one recalls the important point that the regression coefficients are functions of the species characterizing variables; if these functions can be determined then the pertinent regression relationship can be calculated. To determine these functions it is necessary to examine populations for which complete characterizations are available and which are closely related to the population from which the specimens of interest come. Any regularities in the pattern of species characterizations, if present, can be used to make inferences about the properties of the unknown related species. Within the framework introduced above, where a species is described by a distribution function and different species are specified by different values of the species characterizing variables s1,...,sm,such regularities take the form of functional relationships among the species characterizing variables. This means that some of the species characterizing variables depend (either deterministically or stochastically) on the other species characterizing variables; in the sequel we refer to the depen- ESTIMATING CRANIAL CAPACITY dent variables as parameters, and use the term species variables as a n abbreviation for the independent species characterizing variables. Basically the approach involves five steps: 1)estimation of both the values of the species variables and the parameters for the known populations, 2) determination of the functional relationship between the parameters and the species variables, 3) estimation of the value of the species variables for the specimen in question and the computation of the corresponding distribution parameters, 4)calculation of the regression equation appropriate to the specimen from the distribution parameters, and 5) prediction of the value of the unknown specimen character from the measured values of the other characters by means of the regression equation. CALCULATION OF OH7 CRANIAL CAPACITY A specific application of this approach to the determination of the cranial capacity of OH7 is given in this section. Before presenting the details we wish to summarize the notation and make several general remarks about the choice of variables. Choice of variables and populations As we are primarily concerned with the problem of estimating the cranial capacity of OH7 from its parietal measurements, we will use the following character variables: the cranial capacity, c; the cube root of the cranial capacity, y; the Bregma-Asterion chord, x or B-Ac (depending on context); BregmaLambda chord, B-Lc; Bregma-Asterion chord, B-Ac; Bregma-Pterion chord, B-Pc; LambdaAsterion chord, L-Ac; Lambda-Pterion chord, L-Pc; Asterion-Pterion chord, A-Pc; Biasterionic breadth, A-A'; Bregma-Lambda arc, BLa; Bregma-Asterion arc, B-Aa; BregmaPterion arc, B-Pa; Lambda-Asterion arc, LAa; Lambda-Pterion arc, L-Pa; and AsterionPterion arc, A-Pa. We will use the population mean of the Bregma-Asterion chord, X, as the species characterizing variable. (In passing it should be mentioned that it is important to distinguish between the specimen characterizing variables (such as x) and the species characterizing variables (such as X) despite the fact that in certain cases the two may have numerically identical values.) As related populations for the determination of the species dependence of the various parameters we use chimpanzees and humans. When it is necessary to refer to different populations, we add a n appropriate superscript to 73 the variable: for chimpanzee, for Homo sapiens, O for OH7. A few comments are in order about the choices of the variables and populations. In the ideal problem, the character variables would be chosen to completely and conveniently characterize the individual specimens, the parameters and species variables to conveniently and unambiguously specify the species, and the fact that these choices were appropriate would be well established. In practical paleoanthropological research, one is forced to use variables that are provided by imperfectly preserved specimens, by the need to have common characterization of different specimens, and by the availability of needed measurements from other sources. The verification that some set of choices is appropriate often must be done with the same data set that is being used for the calculation, thus raising the danger of circularity. As will be detailed below, the available sets of data were examined, some additional data collected, some preliminary analyses were done, and decisions about the final choices were made in light of these preliminary results. The comparison populations of Homo s a p iens and of Pan troglodytes were chosen not only on the basis of intuitive phylogenetic considerations but also on the basis of the numerical values of the population means for a number of the characters of interest. The two species constitute large existing populations that are quite close phylogenetically to each other and to fossil hominids such as OH7. A more preferable alternative to chimpanzees might be a large sample of complete australopithecines, which, unfortunately, does not yet exist. Even so there is reason to hope that the species are sufficiently closely related so that the distribution function parameters will be nearly linear in the species characterizing variables; in any event the appropriateness of this assumption can be verified empirically. The set of variables and populations mentioned above then reflects those that were found useful in this problem, satisfied the various practical constraints, and led to useful (we hope) and simple results. Unlike Wolpoff we have used as comparative material the living hominoids Pan troglodytes and Homo sapiens because we wish to have biologically and numerically realistic samples for estimating predictors. Unlike Holloway we have kept these samples separate because we do wish to draw biologically 74 J.R. VAISNYS, D. LIEBERMAN, AND D. PILBEAM TABLE 1. Parietal arc and chord measurements on reconstructed Olduvai Hominid 7 sDecimen Measurement B-Lc B-Ac B-Pc L-Ac L-Pc A-Pc A-A'c B-La B-Aa B-Pa L-Aa L-Pa A-Pa This work (mm) Holloway' (mm) Wolpo@ (mm) 97.5 105.1 67 67 k .2 109 69 k .2 94 .2 105 124 78 70 .3 126 70 5 .2 94 101.5 87 107.8(1) 70.7 61.0 * + Tobias3 (mm) - 88 98 117.5 71.6 85.6 95 121 80 67 69 105 - 'Holloway (1980, 1983). 'Personal communication :'Tobias (1971). realistic inferences, and for these we need to work a t the species level. As noted, we could improve the accuracy of prediction by adding more samples, although ideally we would like samples with mean volumes between Pan and Homo sapiens and regrettably there are no such living hominoids. Museum collections. The parietal measurements were made with sliding calipers and a tape measure and are accurate to 1mm. The cranial capacities were measured with plastic beads and are accurate to about 10 cc. The human and chimpanzee data are presented in Appendix 1. A number of regressions of the cube root of Data and calculations the cranial capacity (y) against the parietal A set of 13 chord and arc measurements variables as independent variables were were measured on a cast of the Tobias recon- computed using SPSS. The cube root of the struction of the OH7 parietals, using sliding cranial capacities was used to preserve dicalipers and a tape measure. The reader is mensional compatibility with the parietal referred to Tobias (1971) for details concern- variables. The five most important indepening the particulars of the reconstruction. The dent variables, common to both the chimpanmeasurements and results are summarized zee and human populations, were selected on in Table 1 (the measurement abbreviations the basis of their beta coefficients (Norusis, were given in the preceding subsection), 1982). These were found to be Bregma-Asteralong with comparable measurements taken ion chord, Lambda-Pterion chord, Bregmaby Holloway, Wolpoff, and Tobias for compar- Pterion chord, Lambda-Pterion arc, and ison and future reference. Bregma-Pterion arc. The results of the two A s shown by Table 1, there are certain regressions are presented in Table 2. differences in the various reconstructions. These five parietal measurements can be For further discussion of the reconstructions used as reasonable predictors of cranial cathe reader is referred to Holloway (1980, pacities within a sample: the average error 1983),Wolpoff (1981),and Tobias (1968, 1971). of prediction is about 5%. Note, as expected, Although our method of estimation for the that the two regression formulas are differcranial capacity of OH7 is not dependent on ent. In other words, the relationship between the parietal reconstruction used, the outcome the parietal dimensions and cranial capaciof the estimation is affected by the values of ties is different for chimpanzees and humans. the measurements. In a n effort not only to simplify the relaThe same set of 13 chord and arc parietal tionship among the variables but also to find measurements, along with brain volumes, a set of variables common to all the fossil was measured on a sample of 60 human samples we planned to use, we also regressed crania from Europe, Africa, and America and the cube root of the volume against a number 60 chimpanzee crania (30 male, 30 female) of single parietal variables. The regression from Liberia, all in the Harvard Peabody equations using Bregma-Asterion chord (x) 75 ESTIMATING CRANIAL CAPACITY as the independent variable were found to give the best results, giving the following relationships for members of the two populations: yc=4.4448 + .03212 yh=5.6376 + .03925 . x', * xh. (2) (3) These equations can be used to predict the cranial capacity of a specimen within the appropriate sample with a n average predictive error of less than 8%. Further work and calculations required to estimate the cranial capacity of the OH7 specimen, following the steps given in the Approach, were based on these last results. The development of the calculation is presented in a step-wise manner in Table 3, along with the numerical values of all needed parameters and variables. On the basis of these relationships we estimate the cranial capacity of OH7 to be 690 cc. UNCERTAINTY OF THE ESTIMATE Any interpretations of the cranial capacity estimate must take into account the uncertainties associated with the result. A first order calculation of the uncertainty in the estimate of the cranial capacity of OH7 follows. As mentioned above, there is a n unavoidable prediction uncertainty associated with any regression equation. For our regression relationshi this uncertainty is given by sg * (l-(ro) 2 %) , where the parameters are defined and given in Table 3. Thus, the standard uncertainty in the prediction of y for OH7 is 0.23. The corresponding range in the cranial capacity of OH7 is then 638 to 746 cc, about the best estimate of 690 cc obtained above. The above uncertainty is calculated on the assumption that all the necessary parameters and variables are precisely known; however, any uncertainty associated with these values will increase the uncertainty in the value of the cranial capacity. The largest such contribution to the uncertainty arises from the availability of only a single specimen for the estimation of Xo, the population mean of B-Ac for OH7. The standard error associated with a n estimate of this parameter (equal to sg in Table 3) gives rise to a corresponding uncertainty in yo of(yh - Y") * s:/(xh that, using the values given in Table 3, evaluates to 0.33. (The range in cranial capacity corresponding to this uncertainty in y is 616 to 771 cc.) A further source of uncertainty in the estimation of yo comes from the use of the interpolating relationship between the parameters of the population distribution functions and the species characterizing variable X, as given in the interpolating equations of Table 3. The linearity of the relationship between the distribution characterizing parameter Y (mean cube root of the cranial capacity for the population) and the species (and also distribution) characterizing variable X (mean B-Ac of the population) can be tested using existing samples of Homo erectus, Austral@ pithecus africanus, Australopithecus boisei, and KNM-ER 1470 (which, because so few Homo habilis specimens exist, will be considered a n "average" Homo habilis). The data from these samples and their predicted cube root cranial capacities are presented in Table 4. (Ypred for each population was calculated by using the first interpolation equation of Table 3 with Xo being replaced by the appropriate population X value. Because the sample sizes are so small there is little point in doing a similar verification for the other population parameters.) x") TABLE 2. Regression of the cube root of the cranial capacity on the indicated parietal variables for populations chimDanzees and humans (N = 60 in each) Chimpanzee Variable B-A arc L-P arc B-P chord B-A chord L-P chord Constant Multiple-r Standard error of Human B Sie T B Sie T -.0003138 0.0486 0.3727 0.0000 0.0001 0.0164 0.0002 ,00784 -.01966 ,01516 ,01929 .03499 4.12004 0.1457 0.0391 0.0814 0.0165 0.0002 0.0000 - ,00468 ,02621 ,02470 ,01943 2.31119 0.79131 0.13598 0.79809 0.23254 76 J.R. VAISNYS, D. LIEBERMAN, AND D. PILBEAM TABLE 3. Relations and equations used in estimating the cranial capacity of the Olduvai Hominid 7 specimen Specimen characterizing variables x = specimen B-Ac (Bregma-Asterion chord) y = specimen cube root cranial capacity c = specimen cranial capacity Species identifying variables X = population mean of B-Ac Y = population mean of cube root cranial capacity Other symbols N = sample size, sx = standard deviation x, sy = standard deviation y, r = correlation coefficient y and x Ao, Al = regression coefficients Statistics for chimpanzee sample (using data of Appendix 1) NC= 60,Xc= 81.72,Yc= 7.154,s: = 3.08,s; =0.212,rC= 0.481 Statistics for human sample (using data of Appendix 1) Nh =60,Xh= 132.85, Yh = 10.852,s~=6.23,s,h=0.369,rh =0.662 Interpolation for OH7 parameters Yo = Yc - (Y" - Yh) . ((Xc - Xo)/(Xc - Xh)),Yo = 8.838 c o c h o o c c h s,=s,-(s,-s ).((X -X )/(X - X )),sy=O.283 o c c h c s,=s,-(s,-s,)~(OX o c h o -X )/(X - X )),sX=4.514 ro = rc - (rC- rh) . ((X" - Xo)/(Xc- Xh)),r" = 0.563 Calculation of OH7 cranial capacity 0 AO--sy;r0/s~,A~=0.00354 0 0 D O A,=Y -Al.X ,A,=5.123 0 y 0 0 0 c" = " = A O + A I . X,y =8.838 Co = 690 cc TABLE 4. Population means of the cube root of the cranial capacity and of the Bregma-Asterion chord for several groups Yobs Ypred Ypred - Yobs N X (mm) Vobs Sample (cc) (cm) (cm) (cm) Vpred (cc) Human Chimp H. erectus' A. africanus2 A. boisei3 KNM-ER14704 60 60 8 2 2 1 132.85 81.72 123.77 91.75 92.5 106 1278.0 366.1 1045.7 479.7 519.9 751.6 10.852 7.154 10.150 7.828 8.041 9.092 10.195 7.879 7.934 8.910 Used as input data Used a s input data 0.045 0.051 -0.107 -0.182 1059.7 489.1 499.4 707.4 'From a sample of Sinanthropus pekinensis and Homo soloensis found in Weidenreich (1943). *Measurements of MLD 37/38 and STS 5 (Tobias, 1971). 'Measurements of 0.H.5 and KNM-ER 406 (Tobias, 1971; Holloway, 1973). 4Holloway (1978). As shown in Table 4,the B-Ac relationship is able to predict the cube root of the sample population's brain volumes quite well, with a n average error of 1.4%.It should be noted that this test is not a stringent one because the sample sizes for the test populations (as shown in Table 4) are so small, but it does indicate that it is reasonable to begin with simple relations. The test also shows that the contribution of this step to the uncertainty in any estimate of Yo is very probably greater than 0.02. Even if one assumes that the appropriateness of this linear relationship need not be tested, its use nevertheless injects an uncertainty for the estimation of yo because the parameters of the relationship must be calculated from observations characterizing the comparison populations (statistics entries of Table 3). With sample sizes of 60 the parameters of these populations are known 77 ESTIMATING CRANIAL CAPACITY TABLE 5. Humans B-LC (mm) 114 107 121 108 095 116 115 119 112 112 109 114 112 108 102 112 098 102 098 104 116 112 109 104 103 116 103 100 118 089 B-AC (mm) 134 123 138 130 122 131 131 146 128 128 137 128 131 129 122 143 128 132 129 131 141 133 141 128 139 133 124 133 135 125 B-PC (mm) 099 091 097 087 093 091 099 100 095 095 091 086 095 084 087 095 087 090 094 098 094 091 088 085 095 097 086 091 094 083 L-AC (mm) L-PC (mm) 088 078 089 089 08 1 075 081 095 088 087 090 079 082 079 086 086 084 080 078 079 098 085 091 088 093 088 091 085 088 082 147 132 145 148 127 142 137 145 148 143 134 135 135 137 137 137 134 131 122 130 150 128 131 133 143 149 124 130 143 132 A-PC (mm) A-A’ (mm) 106 102 109 109 100 106 106 120 100 117 109 103 111 103 111 114 112 110 097 110 109 106 107 113 109 105 107 091 115 099 097 090 096 09 1 085 099 093 099 099 091 094 097 088 102 094 101 102 091 083 095 101 089 095 094 106 097 086 103 092 092 B-La (mm) 126 120 131 135 105 126 125 131 125 121 121 128 122 117 115 126 105 110 106 115 126 125 120 113 120 119 116 113 138 120 ~ B-Aa (mm) 164 168 176 169 158 166 164 183 171 160 169 172 155 156 163 175 152 159 167 163 166 160 185 161 177 169 163 161 173 160 B-Pa L-Aa L-Pa (mm) (mm) - (mm) 117 104 106 106 110 112 113 116 116 110 103 099 105 096 098 113 099 104 111 118 114 102 107 103 118 114 106 113 116 101 177 097 085 092 099 091 085 090 097 095 093 098 084 088 086 095 099 094 087 086 083 110 095 098 095 096 096 098 089 097 089 161 173 175 164 176 173 177 182 172 163 172 159 165 168 172 164 164 156 161 178 156 166 168 181 178 163 164 174 166 A-Pa (mm) Vol 1’3 (cm) 102 095 102 196 089 106 098 105 105 094 103 100 091 105 103 105 107 098 094 094 104 092 102 098 110 100 092 103 099 097 10.997 10.520 11.382 10.714 10.132 10.829 10.627 11.573 11.292 11.473 11.085 10.775 11.052 10.928 10.543 11.011 10.723 10.844 10.582 10.522 11.421 11.187 10.801 10.071 11.200 11.052 10.416 10.758 10.829 10.507 TABLE 6. Humans B-Lc (mm) B-ac (mm) B-Pc (mm) 107 117 117 120 122 109 108 112 110 108 106 116 108 103 120 104 131 133 140 144 127 129 131 139 135 141 146 133 132 138 142 129 131 129 131 137 144 125 125 130 139 135 133 136 120 132 089 089 094 099 096 090 089 095 091 100 107 093 096 09 1 101 089 089 096 089 096 099 084 087 089 097 099 095 095 086 093 111 108 115 109 107 103 100 105 119 113 098 104 096 107 L-Ac L-Pc (mm) (mm) 078 077 089 090 089 076 088 091 082 092 084 082 086 093 086 079 080 083 084 084 092 084 083 080 082 084 083 094 082 085 128 136 137 143 145 133 129 144 131 151 141 142 133 135 136 131 134 146 144 137 139 127 131 132 146 143 134 140 130 143 B-Aa (mm) B-Pa (mm) L-Aa (mm) L-Pa (mm) A-Pa (mm) 166 171 183 193 180 169 182 170 168 173 178 175 171 175 167 159 162 155 168 170 179 152 152 156 167 134 _ . 171 _ 160 106 165 112 105 148 164 116 102 113 116 127 115 106 114 113 107 118 125 115 115 110 113 101 105 110 100 089 089 094 097 103 082 099 101 087 106 103 088 095 097 095 085 087 089 093 090 097 089 085 085 086 092 089 100 093 090 159 173 174 187 178 168 170 182 166 191 176 178 172 173 166 161 167 173 168 170 175 157 166 163 178 175 168 175 158 176 098 105 104 113 099 100 094 110 103 116 101 111 097 107 096 098 100 110 106 105 106 094 102 105 114 104 110 109 096 106 A-Pc A-A’ (mm) (mmf B-La (mm) 104 105 106 108 093 101 106 110 102 110 107 110 109 113 105 097 105 106 100 105 113 108 108 111 109 103 109 104 107 116 116 126 129 130 130 122 116 124 123 116 114 127 120 110 139 116 123 115 127 123 120 113 113 114 136 092 095 094 103 090 096 088 102 093 108 095 103 095 100 089 093 094 105 102 100 102 088 096 096 107 099 102 099 089 101 ~~ 111 115 095 102 101 108 113 107 114 102 104 VO~”~ (cm) 10.431 10.354 10.597 11.313 11.319 10.627 10.900 10.318 10.712 10.995 11.583 11.131 10.911 10.967 11.237 10.474 10.683 10.878 10.981 10.712 11.184 10.474 10.226 10.505 11.495 10.813 10.798 10.967 10.162 10.535 J.R. VAISNYS, D. LIEBERMAN,AND D. PILBEAM 78 TABLE Z Male chimpanzees B-Lc B-Ac (mm) (mm) 061 069 068 066 063 069 068 073 067 068 068 063 067 061 059 063 070 062 067 062 069 069 072 066 073 070 066 065 B-Pc (mm) L-Ac (mm) 074 082 086 079 081 082 077 083 075 081 079 082 078 085 081 082 082 083 083 076 083 078 086 087 080 089 080 080 083 082 083 048 062 043 058 051 071 043 061 042 061 041 061 048 062 043 054 047 058 044 067 043 059 037 064 048 058 047 063 047 059 046 06 1 045 062 048 066 061 044 062 050 049 063 048 066 051 064 046 062 051 068 044 062 055 048 063 048 063 050 065 __ 044 B-Lc (mm) B-Ac (mm) B-Pc (mm) L-Ac (mm) 068 062 065 066 064 064 059 066 058 066 068 064 062 066 059 066 065 064 068 062 07 1 066 064 068 067 067 06 1 064 065 066 081 082 083 082 083 08 1 079 085 076 083 083 077 080 083 081 083 078 085 083 084 086 079 076 080 082 084 086 077 087 086 057 064 048 060 063 071 06 1 063 059 064 066 062 063 068 064 063 059 063 056 061 063 064 064 053 062 069 064 062 063 064 041 045 043 045 046 048 046 044 046 04 1 046 044 050 052 049 049 04 1 045 047 052 046 044 048 046 047 049 055 049 051 053 066 . ~ . L-Pc (mm) A-Pc (mm) A-A' (mm) 087 089 090 089 085 094 084 086 089 094 087 086 087 089 086 094 094 087 086 086 099 094 094 086 098 092 084 092 091 093 069 07 1 066 068 068 074 059 059 067 075 064 067 069 068 070 078 075 087 063 065 076 075 073 064 074 073 062 076 068 070 076 078 086 082 08 1 075 082 081 086 078 076 074 089 080 096 082 081 093 082 090 086 076 083 078 083 083 085 078 079 077 - B-La (mm) B-Aa (mm) B-Pa (mm) L-Aa (mm) L-Pa (mm) (mm) (cm) 065 074 073 07 1 068 072 073 077 071 074 074 066 070 062 062 065 072 065 068 066 071 070 080 069 075 072 068 066 067 _.. 095 092 092 088 087 081 088 078 084 091 088 084 090 088 086 091 093 094 087 091 082 093 097 090 097 090 084 078 066 089 069 065 07 1 07 1 061 065 078 067 075 066 076 067 070 072 073 066 068 068 076 070 066 077 070 058 068 070 072 055 045 052 045 044 042 050 047 050 045 045 042 051 051 048 050 053 052 047 052 052 048 051 048 054 047 049 048 053 045 104 103 111 104 101 112 092 098 108 114 103 104 102 107 094 106 111 105 098 101 118 113 112 100 117 110 096 110 109 112 074 077 074 072 076 082 059 060 071 080 072 074 073 072 077 082 077 071 073 068 081 082 080 068 077 045 064 081 073 044 6.966 7.166 7.337 7.356 7.275 6.804 7.127 6.619 7.000 7.243 7.114 7.179 7.114 7.034 7.047 7.114 7.337 7.221 7.114 7.243 7.305 7.517 7.558 6.944 7.604 7.273 6.978 7.336 7.178 7.633 1176 ~~ 090 ... 092 090 A-Pa TABLE 8. Female chimpanzees L-Pc A-Pc (mm) (mm) __ A-A' (mm) B-La (mm) B-Aa (mm) B-Pa (mm) L-Aa (mm) L-Pa (mm) A-Pa (mm) (cm) 063 068 068 068 063 081 071 069 066 069 07 1 068 058 078 073 062 069 066 062 066 069 069 069 066 069 064 069 068 075 075 077 08 1 078 079 076 081 078 073 076 079 083 084 084 097 084 086 072 076 078 078 077 083 08 1 084 077 078 084 081 082 079 073 078 069 070 077 068 060 070 062 073 071 067 064 071 061 069 067 078 072 065 072 069 068 071 070 070 064 066 077 068 091 094 093 090 095 090 090 093 080 093 091 083 086 088 092 092 084 088 091 092 097 087 082 092 092 099 094 086 096 100 067 072 056 072 070 082 068 072 069 076 074 075 070 080 083 072 065 072 060 073 068 071 074 058 069 080 070 070 070 070 044 046 045 047 049 087 054 048 055 042 047 046 052 053 052 051 043 047 050 053 046 045 050 046 047 051 055 050 053 058 100 106 094 104 100 121 109 107 105 110 106 071 070 074 071 072 085 074 080 074 078 076 072 061 084 078 066 073 069 065 073 073 071 073 070 073 066 072 070 079 082 6.903 7.014 6.694 7.101 7.192 7.275 6.910 7.014 6.980 6.980 7.380 7.101 7.014 7.368 7.047 7.147 6.854 6.980 6.945 7.081 7.317 7.046 7.126 7.112 7.046 7.397 7.379 7.273 7.112 7.644 085 087 083 089 084 085 088 087 087 09 1 092 088 083 098 093 085 086 088 084 087 087 087 088 084 086 090 086 089 091 095 111 096 120 118 098 103 103 098 103 104 101 106 099 103 106 100 105 111 116 ESTIMATING CRANIAL CAPACITY to be about 3%, so that the contribution to the uncertainty of Yo is only 0.03. The preceding analysis shows that the estimation of y (the cube root of the cranial capacity) for OH7 has a minimum total uncertainty of about 0.7, when all the various sources of uncertainty are considered. Thus, the corresponding estimate of the cranial capacity should be described as 690 1781- 151 cc, or as 690 cc, with a standard uncertainty range from 539 to 868 cc. (The reader who prefers to think in terms of 95% confidence intervals may construct a rough approximation of them by doubling the above ranges.) + COMPARISON WITH PREVIOUS ESTIMATES AND DISCUSSION In the original cranial capacity estimates of Tobias (19681, where a value of 657 cc was obtained, it is implicitly assumed that the specimens of A. afiicanus, A. boisei, Homo erectus, and OH7 form a homogenous population with respect to the ratio of cranial capacity and parietal endocast volume. Tobias’ technique of using the average ratio, obtained from several specimens from four species (the Homo erectus sample, in fact, constitutes two species) for which both quantities are known, is equivalent to a regression between the two quantities subject to the constraint that the intercept coefficient be zero. While the approach is intuitively appealing, the absence of any explicit specifications for recognizing members of such a population, or for testing the validity of the approach, makes it difficult to generalize or extend the results. In addition, the small size of the sample suggests that the uncertainty of the estimate would be quite high. Holloway (1980) proposed a range of 700 to 750 cc for the cranial capacity of OH7. In regressing a sample of pongids with a sample of hominids, he assumes that the members of certain modern and fossil groups constitute a single statistical population. This assumption has a number of practical disadvantages. Enough is known about the nature of the distributions describing modern groups to be certain that such composite distributions will be nonstandard (e.g., multimodal), possibly difficult to analyze, and will have properties that require changes in the interpretation of the usual statistical parameters (e.g., r as a n indicator of predictive value becomes meaningless when one regresses two different populations together). In addition, by neglecting the distinction between varia- 79 bles describing individuals and groups, the approach needlessly increases the uncertainty of any estimate. The method is also limited because there is no specification for generating the regression sample, such as criteria for including species or for choosing the sample size of each. Moreover, Holloway does not test the accuracy of his equations in predicting the cranial capacities of any known samples, including the populations that he used to generate the equation, on fossils such a s KNM-ER 1470, which he claims to be similar to OH7. It should be noted that while we may have reservations about the method of analysis, we have little doubt about the relevance of the data sets considered. Wolpoff (1981), who estimated the cranial capacity to range between 580 and 600 cc, attempts to obtain a homogeneous population for the regression by limiting his sample to certain fossil specimens. In addition to the problem of small sample size, the approach has to assume that the specimens are indeed sufficiently related to make up a meaningful population. The utility of the method is greatly limited because no independent criteria are offered to recognize when a specimen belongs to such a population. To derive his regression formula Wolpoff also uses fossils (e.g., Omo 338y-6) that have distortions and cranial capacity estimates as much in question as OH7; thus Omo 338y-6 consists only of parietal and occipital fragments. It should further be noted that the use of repeated regressions with subsets of the same small sample will lead to a n artificially low estimate of the uncertainty associated with predictions made from the regression equation. The cranial capacity estimation procedure introduced in this paper is more formal than those used in prior works, particularly with regard to the calculation of the uncertainty to be associated with the character estimate. It will be noted that the uncertainty calculated in this approach is higher than that of earlier estimation procedures; this is not because this procedure is less accurate, but because these uncertainty estimates are more realistic. If the uncertainty estimates of this work are accepted, then it is seen that the numerical values calculated in all of the cranial capacity estimations discussed above overlap: they differ from each other by amounts less than the uncertainty associated with the estimates. (It should be noted that 80 J.R. VAISNYS, D. LIEBERMAN. AND D. PILBEAM this statement does not amount to a n asser- zation of different populations with sufficient tion that all of the estimation procedures are accuracy so that differences between populacompatible: the preceding discussion shows tions may also be defined accurately. In some that they are not.) cases this characterization may best be done One advantage of formal estimation proce- by reporting the various distribution paramdures is that they invite examination for eters, but the realities of observational reways in which they can be improved; in this search being as they are, we recognize that case we can search for ways to decrease the samples in a given study may not be large sources of uncertainty. Clearly the quality of enough to provide such estimates with the the estimate would be improved if we could desired precision. In such cases it is desirable decrease the prediction uncertainty associ- that data about individual specimens be reated with the regression equation. This would ported, rather than simply summary statisrequire a new regression relationship using tics, so that subsequent studies may add to a new independent variable, or more likely a the sample size and thus eventually lead to combination of such variables, and having a results of the needed precision. As a small lower prediction uncertainty for the depen- step in this direction, we have included a dent variable. The generation and testing of complete listing of our own data so that othany such improved relationship would re- ers may extend the data set or use it in ways quire a larger set of sample populations, all not anticipated by us. Overall, the first major characterized with regard to a common set of source of uncertainty defined in the precedvariables. In addition, the size of these popu- ing section can probably be reduced substanlations would have to be increased with a n tially if better and systematic characteriincrease in the number of variables being zations of morphological relationships beconsidered so that statistical significance can tween species, a s well as within species, are be maintained. In many cases the required obtained. increases in the amount of data will be posAs will be recalled, the second major source sible only if extant biological populations are of uncertainty in the specimen character esused. timation process is associated with the naIn this application we need to keep the ture of the data characterizing the fossil find total uncertainty arising from errors in the and its population properties; clearly it will estimation of the regression coefficients be- be much harder to affect the availability of low some fixed value, consistent with the data bearing on this source of uncertainty. prediction uncertainty for the variable of in- Thus, it is unlikely that more than about terest. If all the coefficients are about the twofold improvement in the precision of our same size, then a n increase in the number of knowledge about the cranial capacity of OH7 independent variables will require that the can be obtained without further finds of coefficients be determined with a proportion- closely related fossil specimens. ately greater precision. In turn this may reACKNOWLEDGMENTS quire that the sample size be increased in proportion to the square of the number of We would like to thank Professor Ralph variables. An estimate of the number of ref- Holloway and Professor Milford Wolpoff for erence populations that will be needed is their cooperation. Last, but not least, thanks much harder to make because too little sys- to MaryAnne Larson for helping to measure tematic information about species interrela- the many skulls. tionships is available. If the relationships were to be deterministic, then the number of LITERATURE CITED reference populations needed would about RL (1973) New endocranial values for East equal the number of interpolation parame- Holloway, African hominids. Nature 243t97-99. ters; if the relations were to be stochastic a Holloway, RL (1978) Problems of brain cast interpretamuch larger number might be required. tion and African hominid evolution. In CJ Jolly (ed): Early Hominids of Africa. London: Duckworth, pp. 379If the required data are to become avail402. able (at present they are not) greater attenRL (19801 The 0.H.7 (Olduvai Gorge, Tanzation will have to be given to the systematic Holloway, nia) Hominid parietal brain endocast revisited. Am. J. collection and reporting of population dePhys. Anthropol. 53t267-274. scriptions. What is wanted is the characteri- Holloway, RL (1983)The 0.H.7 (Olduvai Gorge, Tanza- 81 ESTIMATING CRANIAL CAPACITY nia) parietal fragments and their reconstruction: A reply to Wolpoff. Am. J. Phys. Anthropol. 60505-516. Leakey, LSB, Tobias, PV, and Napier, JFt (1964) A new species of the genus Homo from Olduvai Gorge. Nature 202:7-9. Norusis, MJ (1982) SPSS Introductory Guide. New York: McGraw Hill. Tobias, PV (1964) The Olduvai Bed I hominine with special reference to its cranial capacity. Nature 202:34. Tobias, PV (1968) Cranial capacity in anthropoid apes, Austrulopithecus and Homo habilis, with comments on skewed samples. S. Afr. J. Sci. 64(2):81-91. Tobias, PV (1971) The Brain in Hominid Evolution. New York: Columbia University Press. Weidenreich, F (1943)The skull of Sinunthropos pekznensis;A comparative study on a primitive hominid skull. Palaeontologica Sinica D. No. 10. Wolpoff, MH (1981)Cranial capacity estimates for Olduvai Hominid 7. Am. J. Phys. Anthropol. 56:297-304. APPENDIX 1 Parietal and cube root cranial capacity measurements for specimens of Homo sap iens and Pan troglodytes. See text for details.

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