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

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AMERICAN 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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