AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 8711-13 (1992)
Cranial Capacity Evolution in Homo erectus and Early Homo sapiens STEVEN R. LEIGH Departments of Anthropology and Cellular, Molecular, and Structural Biology, Northwestern University, Evanston, Illinois 60208
KEY WORDS
Hominid evolution, Brain size, Trend analysis
ABSTRACT This paper investigates patterns of cranial capacity evolution in Homo erectus, early Homo sapiens, and in regional subsamples ofH. erectus. Specifically, models explaining evolution of cranial capacity in these taxa are evaluated with statistical techniques developed for the analysis of time series data. Regression estimates of rates of evolution in cranial capacity are also obtained. A non-parametric test for trend suggests that cranial capacity in both H. erectus and early H . sapiens may increase significantly through time. Cranial capacity in an Asian subsample of H. erectus (comprised of Chinese and Indonesian specimens) increases significantly through time. Other subsamples of H. erectus (African, Chinese, and Indonesian) do not appear to increase significantly through time. Regression results generally corroborate results of the test for trend. Spatial and temporal variation may characterize evolution of cranial capacity in H. erectus. Different patterns of cranial capacity evolution may distinguish H. erectus from early H. sapiens. The study of the evolution of cranial capacity in fossil hominids has long occupied the attention of evolutionists (Darwin, 1871; Tobias, 1971; Weidenreich, 1941). An unmistakable tendency toward increasing cranial capacity (which reflects the size of the brain and associated soft tissue) characterizes the course of hominid evolution in general (Blumenberg, 1983; Godfrey and Jacobs, 1981; Henneberg, 1987, 1989; Lestrel, 1976; Lestrel and Read, 1973; Wolpoff, 19801, but debate surrounds many phylogenetic issues related t o this increase. Disagreement about changes in hominid cranial capacity is especially pronounced when limited numbers of taxa are investigated. In these cases, the familiar paucity of specimens and the relative lack of time depth may obscure evolutionary patterns, severely restricting our ability to understand factors involved in the evolution of taxa under investigation. Analyses of cranial capacity evolution in Homo erectus and early Homo sapiens typify the problems entailed in understanding the finer details of cranial evolution in hominids; these analyses have engendered substantive discord among scholars about the
@ 1992 WILEY-LISS.INC.
patterns of later hominid evolution (Eldredge, 1985; Holt, 1988; Levinton, 1982; Rightmire, 1981, 1982,1985,1986; Wolpoff, 1984, 1986). The present analysis attempts to clarify this issue through an investigation of changes in H. erectus and early H. sapiens cranial capacity through time. Previous authors have discussed the significance of various evolutionary models to the problem of later hominid evolution. Models that specify either a punctuated equilibrium process or a gradualist process have been advocated by various researchers (Eldredge, 1985; Rightmire, 1981, 1982, 1985, 1986; Wolpoff, 1984, 1986). These contrasting models make very different predictions about the ways in which evolution occurs. Briefly, as proposed by Eldredge and Gould (1972), the punctuated equilibrium model addresses the tempo and mode of evolution. Evolutionary change is the result of two basic processes: stasis of an ancestral species followed by rapid allopatric evolution of new species. Traditionally, the punctuated equilibrium model has been contrasted with a Received March 8,1990 revision accepted J u n e 24,1991
2
S.R. LEIGH
gradualist model that portrays evolutionary change as a relatively slow, steady, and sympatric process. The nature of cranial capacity evolution in Homo has figured prominently in debates over the adequacy of these contrasting views as general models of evolutionary change. Within the Homo lineage, attention has centered upon comparisons of rates of change between the taxa H. erectus and early H. sapiens (e.g., Rightmire, 1985). Stasis followed by rapid evolution in H. erectus would tend to support a punctuated equilibrium model of evolutionary change. On the other hand, significant and sustained increases in H. erectus cranial capacity through time followed by significant increases in cranial capacity in those samples classified as early H. sapiens would approximate a “gradualist” model of evolutionary change. Previous literature relevant to this problem is plainly divided between these two positions. Rightmire (1981, 1982, 1985, 1986) and Eldredge (1985) have strongly suggested that the evolution of early H. sapiens from H. erectus populations can be best understood as a process predicted by the punctuated equilibrium model. On the other hand, several authors (Cronin et al., 1981; Wolpoff, 1984, 1986) have argued that later hominid evolution fails to follow a pattern predicted by the punctuated equilibrium model. The hypotheses investigated in this paper attempt to distinguish between alternatives posed by Rightmire (1981, 1985, 1986) and Wolpoff (1984, 1986) but also address some more basic issues. Specifically, the hypothesis that H. erectus cranial capacity is randomly variable through time is tested. A similar hypothesis is also investigated in early H. sapiens. This possibility is relevant because a trend in the change of cranial capacity through time may characterize these data. A trend is defined as “any systematic change in the level of a time series’‘ (McCleary and Hay, 1980:31). The presence of a significant trend in H. erectus cranial capacity would provide evidence t o reject a punctuated equilibrium model of later hominid evolution. A study of the evolutionary history of a variable is clearly a time series problem, and such problems should be addressed with appropriate statistical techniques. As stressed by McCleary and Hay (19801, regression analyses of time series data may present the
impression that changes in the level of a variable through time are non-random, even thoilgh stochastic processes may actually account for the observed trend. In addition to investigating the possibility that change in cranial capacity is random during later hominid evolution, hypotheses about differences in rates of change among and within taxa are addressed. Specifically, the null hypothesis that rates of change in H. erectus and early H. sapiens are equal is tested. The hypothesis that rates of change among geographically defined subsamples of H. erectus are equal is also tested. Evaluation of these hypotheses may provide insight into processes affecting patterns of evolution in H . erectus and in early H . sapiens. Investigation of regional patterns of change in H. erectus may be especially important given the emphasis of punctuated equilibrium models on allopatric speciation (Eldredge and Gould, 1972; Gould andEldredge, 1977). In order to test these hypotheses, this study utilizes a variety of statistical approaches to measuring rates of cranial capacity evolution. These include a nonparametric test for trend in a time series,-nonparametric and parametric regression analysis, and analysis of covariance. The test for trend utilized in this study is of critical importance because it circumvents some of the problems inherent in previous statistical investigations of the nature of cranial capacity changes during later hominid evolution. MATERIALS AND METHODS
Materials Materials for this analysis include cranial capacities estimated for 20 specimens classified as H. erectus (Table 1). The H. erectus cranial capacities used are published by Rightmire (1985). A supplemental sample (Table 2) that includes several poorly dated and taxonomically debatable specimens (the Sambungmachan and Ngandong crania) is also analyzed (see Pope, 1988; Santa Luca, 1980). These crania are not investigated by Rightmire (1985). Separate analysis of this sample permits comparisons with previous investigations without the confounding effects of alternative sample composition. The Sambungmachan individual is classified here as H . erectus, roughly contemporaneous with Zhoukoudien (following Wolpoff, 1984:Table 1). The Ngandong crania are treated as H. erectus in some analyses and as H. sapiens in others. Measurements of early H. sapiens cranial
3
H. ERECTUS AND EARLY H. SAPIENS CRANIAL CAPACITY TABLE I. Specimens, estimated geologic age, and cranial capacity for the Homo erectus sample (N = 20)' Locality and specimen African subsample SaleOlduvai Hominid 12 Olduvai Hominid 9 East Turkana 3883 East Turkana 3733 Chinese subsample Hexian Zhoukoudian V Zhoukoudian I1 Zhoukoudian I11 Zhoukoudian VI Zhoukoudian X Zhoukoudian XI Zhoukoudian XI1 Gongwangling Indonesian subsample Sangiran 10 Sangiran 12 Sangiran 17 Trinil Sangiran 2 Sangiran 4
Estimated geologic age (myr)
Cranial capacity
.25 .70 1.23 1.52 1.60
880 727 1,067 804 848
.25 .42 .42 .42 .42 .42 .42 .42 30
1,025 1,140 1,030 915 850 1,225 1,015 1,030 780
.62 .62 .62 .62 .76 .93
855 1,059 1,004 940 813 808
(4 Specimen
'These data are published hy Rightmire (1985).
TABLE 2. Specimens included in supplemental analyses'
Specimen1 Ngandong I Ngandong V Ngandong VI Ngandong IX Ngandong X Ngandong XI Sambungmachan
TABLE 3. Specimens, estimated geologic age, and cranial capacity for the Homo sapiens sample (N = 10)'
Estimated geologic age (mw)
Cranial capacity kc)
.25 .25 .25 .25 .25 .25 .42
1,172 1,251 1,013 1,135 1,231 1,090 1,035
'These specimens werenot analyzed by Rightmire(l985).Analyses of these crania are presented separately. The Ngandong sample is analyzed both as H. erectus and early H. sapiens (seetext). Cranial capacities for Ngandong are published by Holloway(l980) (and by Weidenreich (1943) for Ngandong IX). The cranial capacity estimate for Sambungmachan is presented by Pope (1988).
capacities (Table 3) are those published by Rightmire (1985) and by other researchers (Table 2). An alternative ordering of early H . sapiens specimens is also provided and analyzed (Table 4). This alternative ordering is investigated because several of the early H . sapiens specimens are insecurely dated. Correction for body size was not attempted (see ''Discussion''). Regional subdivisions of the H . erectus sample are not intended to reflect morphologically based taxonomic differences be-
Laetoli Hominid 18 Omo 2 Broken Hill Petralona Steinheim Swanscombe Hopefield Dali Arago 21 Ndutu
Estimated geologic age (myd
Cranial capacity kc)
,125 .13 .15 .20 .25 .25 .30 .30 .40 .40
1,367 1,430 1,285 1,200 1,100 1,250 1,225 1,120 1,166 1,100
'Data are from Adam (1985), Brauer (19841, Rightmire(1985), and Wolpoff (1980).
TABLE 4 . Alternative ordering of early Homo sapiens specimens1
Specimen Laetoli Hominid 18 Omo 2 Broken Hill Ndutu Dali Swanscombe Hopefield Steinheim Arago 21 Petralona
Estimated geologic age (myr)
Cranial capacity
,125 .13 .15 .20 .25 .25 .30 .30 .40 .40
1,367 1,430 1,285 1,100 1,120 1,250 1,225 1,100 1,166 1,200
(4
'This ordering is made to account for the uncertain geologic age of several specimens. Ties are not assumed in tests of trend in this particular sequence. Dates from Table 2 are retained in the same order.
tween these specimens. Taxonomic discussions of the H . erectus sample have been provided by numerous aathors (Bilsborough and Wood, 1986; Rightmire, 1985, 1986; Stringer, 1984,1987; Turner and Chamberlain, 1989). It should be noted that the Sale specimen exhibits unusual (possibly pathological) occipital morphology (Hublin, 1985), which may have affected cranial capacity, Accordingly, analyses that both include and exclude this specimen were undertaken.
Methods Regression analysis has typically been used to investigate change in hominid cranial capacity through time (Godfrey and Jacobs, 1981; Lestrel and Read, 1973; Lestrel, 1975;Rightmire, 1981,1985).Ordinaryleast squares regression has frequently been employed to measure these rates, despite the
4
S.R. LEIGH
possibility that this technique may not be suitable for modeling change in a variable through time. The inadequacy of ordinary least squares regression may be the result of several factors. First, in a time series, the assumption of independence between dependent variables is often violated. Correlation among residuals, or serial correlation, may result if values of Y in one time period are affected by values of Y at other time periods (Younger, 1979). Second, ordinary least squares regression lines tend to be best-fitted to the first and last observations in the series. Third, ordinary least squares regressions are heavily influenced by outliers. These problems lead to difficulty in obtaining accurate estimates of both slope and intercept in regressions of time series. Thus, if a trend toward increasing cranial capacity is present, ordinary least squares estimation may not detect the presence of such a trend. Conversely, ordinary least squares regression may indicate the presence of a trend when stochastic behavior (drift) actually accounts for changes in a variable through time (McCleary and Hay, 1980:35-36). In addition to the general problems of modeling time series with ordinary least squares regression, there may be substantial error in measurement of the independent variable (geologic age) in this particular sample. This very serious general problem is discussed by Sokal and Rohlf (1981).Wolpoff (1984)considers this problem with respect to measuring evolutionary rates in H. erectus. Regression techniques that account for measurement error in both X and Y variables (such as reduced major axis, major axis, and related techniques) are not well suited to the present problem. These methods are subject to the same limitations in time series applications as ordinary least squares regression. Moreover, the low correlation between geologic age and cranial capacity in the H. erectus sample (see Rightmire, 1985;) produces extremely narrow reduced major axis confidence intervals (Jolicoeur, 1975; see also Jolicoeur, 1973, for discussion of similar problems with major axis regression). Analyses with Model I1 regressions would likely minimize the differences in rates of evolution between taxa. Specifically, the H. erectus rate of cranial capacity increase would be inflated as a result of low correlation. The general complications of time series
analysis and the presence of error in measurement of geologic age place a premium on methods that are capable of accurately describing patterns of hominid cranial capacity evolution. Unfortunately, the unequal time intervals between observations and the presence of more than one cranial capacity for a given date lead to difficulties in using standard methods for the analysis of time series (Vandaele, 1983). Although these obstacles are often encountered in paleobiological context s, little theoretical statistical research has been undertaken to solve these problems. However, Kitchell et al. (1987)discuss the problem of unequal intervals in paleobiological contexts, while Quenouille (1957), and Cleveland and Devlin (1980, 1982) address this problem in econometric applications. A simple nonparametric test for trend that minimizes the deficiencies of these data is provided by Hubert et al. (1985; see also Konigsberg, 1990). Specifically,this test is a distribution-free permutational test for randomness in ordered data. The test makes no assumptions about the length of intervals between observations. In addition, multiple observations sharing the same geologic age (ties) can be accommodated by this technique. It is essential t o note that measurement error in geologic age is minimized because observations are merely ordered from earliest to latest. Hubert et al.’s test allows detection of a trend in cases where regression may not prokide an accurate measure of trend. The procedure is based on a test statistic (r) derived from the cross-product (or dot product) of two 1 x N matrices or vectors where:
r =a’b The first vector (a)is, in this case, a vector of cranial capacities ordered by time. The second vector (b) consists of an ordered series (e.g., 1,2,3,4,5)with equal intervals between each observation. The b vector reflects the chronological order of the variables in the a vector. In the case of ties (cranial capacities from the same date) the cells of the b vector are “stuttered (e.g., 1,2,2,2,3,4,5). Hubert et al. (1985) recommend that the dot product of these vectors serve as a test statistic for measuring the presence of randomness in ordered data. The significance of the initial summed cross-product statistic (r)can be estimated by obtaining a distribu-
H . ERECTUS AND EARLY H . SAPIENS CRANIAL CAPACITY
tion of summed cross-products calculated from random permutations of the values in one of the original vectors. In other words, one vector is randomly re-arranged, and a cross-product is calculated for each new permutation. The significance level of the test statistic is defined by (M + l)/(N + 11, where M is the number of values as large or larger than r and N is the number of permutations (Hubert et al., 1985). Thus, the significance of the association between vectors can be estimated. A significant positive trend is implied when only a small percentage of randomly obtained dot product values exceeds the value of gamma derived from the original vectors. Conversely, randomness in the order of observations is suggested if the value of the original gamma lies near the center of the distribution of permutational gammas. Up to N! permutations are possible. In the present study, tests for trend are undertaken for the H. erectus, early H . sapiens, supplemental samples, and in subdivisions of the H. erectus sample. The subdivisions of the H. erectus sample include African, Chinese, Indonesian, and “Asian” (represented by the combined Chinese and Indonesian samples). All analyses were undertaken with 1,000 random permutations with the exception of the African (120 exact permutations) and Indonesian (720 exact permutations) samples. Exact permutations utilize every unique cross-product value and are feasible because the African and Indonesian samples are very small. The test for trend offers information about the presence and significance of directional change in the variable of interest. Unfortunately, it does not provide information about rates of change. Nonparametric and ordinary least squares regressions are used for this purpose, but only with the assumption that estimates of regression parameters are unbiased. If regressions detect a trend after the presence of trend has been established with Hubert et al.’s method, then the regression results may be interpreted more confidently. Nonparametric spline regression described by Schluter (1988; see also Eubank, 1988; Seber and Wild, 1989) is used for visual assessment of changes in cranial capacity. This method is not constrained by choice of model (e.g., linear, nonlinear), allowing flexibility in the modeling of complex distributions. Most importantly, confidence inter-
5
vals with these regressions are calculated through bootstrap techniques, which are based upon iterative random selection (with replacement) of data points from the original sample. The main assumption of this technique is that the sample analyzed bears a relatively close relationship to the probability distribution from which the sample was drawn (Efron, 1982). With iterative sampling, relatively accurate confidence intervals should be obtained. In all cases, 300 iterations are undertaken in construction of confidence intervals, Finally, ordinary least squares regression and analysis of covariance are employed to estimate the significance of differences between rates of change in H. erectus and early H. sapiens. These techniques are used only after tests for trend and modeling of bivariate distributions with nonparametric regression. Thus, their roles can be viewed as corroborative. Only linear models were used, facilitating tests of significance between regressions. It should be noted that nonlinear models may suffer the same limitations as ordinary least squares linear models in time series analysis (Seber and Wild, 1989). Analysis of covariance permits tests of significance of differences in regression lines. This analysis is comprised of two parts. The first is a test for difference in slope, while the second is a test for difference in intercepts (see Edwards, 1985). Together, these tests provide a basis for distinguishing between several hypotheses that specify the relation between regression lines. Specifically, analysis of covariance permits identification of 1)identical regression lines (equal slopes and intercepts), 2) parallel regression lines (equal slopes, unequal intercepts), or 3) unequal slopes. Throughout this study, significance for all statistical tests is measured at the .05 level. Regression significance values are evaluated as two-tailed tests because previous analyses (Rightmire, 1981, 1985) suggest that slopes near zero will be obtained in the H. erectus analyses. Tests for trend are treated as one-tailed tests. RESULTS
Trend The test for trend indicates that cranial capacity in H. erectus may not vary randomly with respect to geologic age (Table 5). Of 1,000 random permutations, only 58 (5.8%) of the randomly obtained values of gamma equaled or exceeded the value of gamma
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S.R. LEIGH
TABLE 5. Results of tests for trend by taxon, by region, and withing the Homo erectus sample*
Sample or subsample
Probability*
Number of permutations
.058
1,000' 1,000' 1,000'
Homo erectus Homo erectus, excluding SaleEarly Homo sapiens Early Homo sapiens, re-ordered African Homo erectus Asian Homo erectus Chinese Homo erectus Indonesian Homo erectus
.041 ,001 ,020
.500
1,000' 1202
,014 ,079 ,200
1,000' 1,0001 7202
*Probability values are based on the No. of randomly permuted gammas equal to or larger than observed gammas. 'Random permutations. 'Exact permutations.
based upon the original ordering of data. When the Sale specimen is removed from the sample, the trend in H . erectus is more significant. In this analysis, 41 of 1,000permutations (4.1%) exceeded the observed gamma. Thus, a significant positive trend toward increasing cranial capacity appears present in the H . erectus sample, although this result is not quite significant when the Sale specimen is included. The early H . sapiens sample also appears to exhibit a trend toward increasing cranial capacity. In this analysis, only 1 of 1,000 randomly calculated gamma values (. 1%) equaled or exceeded the original observed gamma. A positive trend is also present when some of the less securely dated early H . sapiens specimens are re-ordered (see Table 4). Trend in this re-ordered sample is less obvious than in the analysis with the original ordering, with 20 of 1,000 (2.0%) randomly calculated gammas exceeding the initial reordered gamma. The patterns among subsamples of H . erectus are not as clear. The Chinese subsample may show a significant trend toward increased cranial capacity, with 79 of 1,000 randomly obtained gammas (7,9%)equal to or exceeding the observed gamma. Obviously, this is not quite significant at the .05 level. Trend is apparent neither in the Indonesian subsample (143 of 720 exact gammas equal to or exceeding the observed gamma) nor in the African subsample (59 of 120 exact gammas equal t o or exceeding the observed gamma). Combination of the Chinese and Indonesian subsamples to form the Asian subsample produces significant results. Only 14 of 1,000 random gammas equal or exceed the observed test statistic for the combined Asian sample.
TABLE 6. Results of tests for trend in the supplemental sample* __ Samiole or subsamole Probabilitv* Homo erectus, Ngandong a s Homo erectus Early Homo sapiens, Ngandong as Homo sapiens Asian Homo erectus, with Ngandong Indonesian Homo erectus, with Ngandong -
,003
,003 ,001
,001
*Probability values are based on the No. of randomly permuted gammas equal to or larger than observed gammas, and there are 1,000 permutations in each analysis.
Analyses of the supplemental sample mirror analyses based on Rightmire's (1985) sample (Table 6). Trend in the H . erectus sample appears more significant. Inclusion of the Ngandong crania either with the early H . sapiens sample or with the Asian H . erectus sample produces significant trend. Significant trend seems present in the supplemental Indonesian sample, in contrast to results based on the original sample. Regression analysis Spline regressions of H . erectus cranial capacity against geologic age suggest little change, with some possible variation in rates through time (Fig. 1). The rate of cranial capacity evolution may fluctuate through time in H . erectus, although the rate increase between 1.2 and 1.6 myr is based upon only three specimens. In contrast, early H . supiens cranial capacity appears to increase markedly during a short time span. Visual assessment of predicted lines and confidence intervals indicates that the rate of change in early H . sapiens probably exceeds the rate of change in H. erectus. Unfortunately, regional subsamples are too small to allow
H . ERECTUS AND EARLY H . SAPIENS CRANIAL CAPACYW
7
0.9
0.7 0.5 0
0.2
0.4
0.6
0.8 1 Geologlc Age (Miillons)
-Homo erectus
1.2
1.4
1.6
+Early Homo sapiens
Fig. 1. Predicted regression lines and 95% confidence intervals obtained from spline regression. Confidence intervals are based upon bootstrap procedures with 300 iterations for each sample. Only predicted values are shown.
TABLE 7. Ordinary least-squares regresion results by taxon, and by region within the Homo erectus sample Sample or subsample
RZ
Slope
Intercept
P-value for slope
Homo erectus Homo erectus, excluding Sale Early Homo sapiens Early Homo sapiens, re-ordered African Homo erectus Asian Homo erectus Chinese Homo erectus Indonesian Homo erectus
.14 .18
-124.87 -145.13
1,029.79 1,050.00
Cranial Capacity Evolution in Homo erectus and Early Homo sapiens STEVEN R. LEIGH Departments of Anthropology and Cellular, Molecular, and Structural Biology, Northwestern University, Evanston, Illinois 60208
KEY WORDS
Hominid evolution, Brain size, Trend analysis
ABSTRACT This paper investigates patterns of cranial capacity evolution in Homo erectus, early Homo sapiens, and in regional subsamples ofH. erectus. Specifically, models explaining evolution of cranial capacity in these taxa are evaluated with statistical techniques developed for the analysis of time series data. Regression estimates of rates of evolution in cranial capacity are also obtained. A non-parametric test for trend suggests that cranial capacity in both H. erectus and early H . sapiens may increase significantly through time. Cranial capacity in an Asian subsample of H. erectus (comprised of Chinese and Indonesian specimens) increases significantly through time. Other subsamples of H. erectus (African, Chinese, and Indonesian) do not appear to increase significantly through time. Regression results generally corroborate results of the test for trend. Spatial and temporal variation may characterize evolution of cranial capacity in H. erectus. Different patterns of cranial capacity evolution may distinguish H. erectus from early H. sapiens. The study of the evolution of cranial capacity in fossil hominids has long occupied the attention of evolutionists (Darwin, 1871; Tobias, 1971; Weidenreich, 1941). An unmistakable tendency toward increasing cranial capacity (which reflects the size of the brain and associated soft tissue) characterizes the course of hominid evolution in general (Blumenberg, 1983; Godfrey and Jacobs, 1981; Henneberg, 1987, 1989; Lestrel, 1976; Lestrel and Read, 1973; Wolpoff, 19801, but debate surrounds many phylogenetic issues related t o this increase. Disagreement about changes in hominid cranial capacity is especially pronounced when limited numbers of taxa are investigated. In these cases, the familiar paucity of specimens and the relative lack of time depth may obscure evolutionary patterns, severely restricting our ability to understand factors involved in the evolution of taxa under investigation. Analyses of cranial capacity evolution in Homo erectus and early Homo sapiens typify the problems entailed in understanding the finer details of cranial evolution in hominids; these analyses have engendered substantive discord among scholars about the
@ 1992 WILEY-LISS.INC.
patterns of later hominid evolution (Eldredge, 1985; Holt, 1988; Levinton, 1982; Rightmire, 1981, 1982,1985,1986; Wolpoff, 1984, 1986). The present analysis attempts to clarify this issue through an investigation of changes in H. erectus and early H. sapiens cranial capacity through time. Previous authors have discussed the significance of various evolutionary models to the problem of later hominid evolution. Models that specify either a punctuated equilibrium process or a gradualist process have been advocated by various researchers (Eldredge, 1985; Rightmire, 1981, 1982, 1985, 1986; Wolpoff, 1984, 1986). These contrasting models make very different predictions about the ways in which evolution occurs. Briefly, as proposed by Eldredge and Gould (1972), the punctuated equilibrium model addresses the tempo and mode of evolution. Evolutionary change is the result of two basic processes: stasis of an ancestral species followed by rapid allopatric evolution of new species. Traditionally, the punctuated equilibrium model has been contrasted with a Received March 8,1990 revision accepted J u n e 24,1991
2
S.R. LEIGH
gradualist model that portrays evolutionary change as a relatively slow, steady, and sympatric process. The nature of cranial capacity evolution in Homo has figured prominently in debates over the adequacy of these contrasting views as general models of evolutionary change. Within the Homo lineage, attention has centered upon comparisons of rates of change between the taxa H. erectus and early H. sapiens (e.g., Rightmire, 1985). Stasis followed by rapid evolution in H. erectus would tend to support a punctuated equilibrium model of evolutionary change. On the other hand, significant and sustained increases in H. erectus cranial capacity through time followed by significant increases in cranial capacity in those samples classified as early H. sapiens would approximate a “gradualist” model of evolutionary change. Previous literature relevant to this problem is plainly divided between these two positions. Rightmire (1981, 1982, 1985, 1986) and Eldredge (1985) have strongly suggested that the evolution of early H. sapiens from H. erectus populations can be best understood as a process predicted by the punctuated equilibrium model. On the other hand, several authors (Cronin et al., 1981; Wolpoff, 1984, 1986) have argued that later hominid evolution fails to follow a pattern predicted by the punctuated equilibrium model. The hypotheses investigated in this paper attempt to distinguish between alternatives posed by Rightmire (1981, 1985, 1986) and Wolpoff (1984, 1986) but also address some more basic issues. Specifically, the hypothesis that H. erectus cranial capacity is randomly variable through time is tested. A similar hypothesis is also investigated in early H. sapiens. This possibility is relevant because a trend in the change of cranial capacity through time may characterize these data. A trend is defined as “any systematic change in the level of a time series’‘ (McCleary and Hay, 1980:31). The presence of a significant trend in H. erectus cranial capacity would provide evidence t o reject a punctuated equilibrium model of later hominid evolution. A study of the evolutionary history of a variable is clearly a time series problem, and such problems should be addressed with appropriate statistical techniques. As stressed by McCleary and Hay (19801, regression analyses of time series data may present the
impression that changes in the level of a variable through time are non-random, even thoilgh stochastic processes may actually account for the observed trend. In addition to investigating the possibility that change in cranial capacity is random during later hominid evolution, hypotheses about differences in rates of change among and within taxa are addressed. Specifically, the null hypothesis that rates of change in H. erectus and early H. sapiens are equal is tested. The hypothesis that rates of change among geographically defined subsamples of H. erectus are equal is also tested. Evaluation of these hypotheses may provide insight into processes affecting patterns of evolution in H . erectus and in early H . sapiens. Investigation of regional patterns of change in H. erectus may be especially important given the emphasis of punctuated equilibrium models on allopatric speciation (Eldredge and Gould, 1972; Gould andEldredge, 1977). In order to test these hypotheses, this study utilizes a variety of statistical approaches to measuring rates of cranial capacity evolution. These include a nonparametric test for trend in a time series,-nonparametric and parametric regression analysis, and analysis of covariance. The test for trend utilized in this study is of critical importance because it circumvents some of the problems inherent in previous statistical investigations of the nature of cranial capacity changes during later hominid evolution. MATERIALS AND METHODS
Materials Materials for this analysis include cranial capacities estimated for 20 specimens classified as H. erectus (Table 1). The H. erectus cranial capacities used are published by Rightmire (1985). A supplemental sample (Table 2) that includes several poorly dated and taxonomically debatable specimens (the Sambungmachan and Ngandong crania) is also analyzed (see Pope, 1988; Santa Luca, 1980). These crania are not investigated by Rightmire (1985). Separate analysis of this sample permits comparisons with previous investigations without the confounding effects of alternative sample composition. The Sambungmachan individual is classified here as H . erectus, roughly contemporaneous with Zhoukoudien (following Wolpoff, 1984:Table 1). The Ngandong crania are treated as H. erectus in some analyses and as H. sapiens in others. Measurements of early H. sapiens cranial
3
H. ERECTUS AND EARLY H. SAPIENS CRANIAL CAPACITY TABLE I. Specimens, estimated geologic age, and cranial capacity for the Homo erectus sample (N = 20)' Locality and specimen African subsample SaleOlduvai Hominid 12 Olduvai Hominid 9 East Turkana 3883 East Turkana 3733 Chinese subsample Hexian Zhoukoudian V Zhoukoudian I1 Zhoukoudian I11 Zhoukoudian VI Zhoukoudian X Zhoukoudian XI Zhoukoudian XI1 Gongwangling Indonesian subsample Sangiran 10 Sangiran 12 Sangiran 17 Trinil Sangiran 2 Sangiran 4
Estimated geologic age (myr)
Cranial capacity
.25 .70 1.23 1.52 1.60
880 727 1,067 804 848
.25 .42 .42 .42 .42 .42 .42 .42 30
1,025 1,140 1,030 915 850 1,225 1,015 1,030 780
.62 .62 .62 .62 .76 .93
855 1,059 1,004 940 813 808
(4 Specimen
'These data are published hy Rightmire (1985).
TABLE 2. Specimens included in supplemental analyses'
Specimen1 Ngandong I Ngandong V Ngandong VI Ngandong IX Ngandong X Ngandong XI Sambungmachan
TABLE 3. Specimens, estimated geologic age, and cranial capacity for the Homo sapiens sample (N = 10)'
Estimated geologic age (mw)
Cranial capacity kc)
.25 .25 .25 .25 .25 .25 .42
1,172 1,251 1,013 1,135 1,231 1,090 1,035
'These specimens werenot analyzed by Rightmire(l985).Analyses of these crania are presented separately. The Ngandong sample is analyzed both as H. erectus and early H. sapiens (seetext). Cranial capacities for Ngandong are published by Holloway(l980) (and by Weidenreich (1943) for Ngandong IX). The cranial capacity estimate for Sambungmachan is presented by Pope (1988).
capacities (Table 3) are those published by Rightmire (1985) and by other researchers (Table 2). An alternative ordering of early H . sapiens specimens is also provided and analyzed (Table 4). This alternative ordering is investigated because several of the early H . sapiens specimens are insecurely dated. Correction for body size was not attempted (see ''Discussion''). Regional subdivisions of the H . erectus sample are not intended to reflect morphologically based taxonomic differences be-
Laetoli Hominid 18 Omo 2 Broken Hill Petralona Steinheim Swanscombe Hopefield Dali Arago 21 Ndutu
Estimated geologic age (myd
Cranial capacity kc)
,125 .13 .15 .20 .25 .25 .30 .30 .40 .40
1,367 1,430 1,285 1,200 1,100 1,250 1,225 1,120 1,166 1,100
'Data are from Adam (1985), Brauer (19841, Rightmire(1985), and Wolpoff (1980).
TABLE 4 . Alternative ordering of early Homo sapiens specimens1
Specimen Laetoli Hominid 18 Omo 2 Broken Hill Ndutu Dali Swanscombe Hopefield Steinheim Arago 21 Petralona
Estimated geologic age (myr)
Cranial capacity
,125 .13 .15 .20 .25 .25 .30 .30 .40 .40
1,367 1,430 1,285 1,100 1,120 1,250 1,225 1,100 1,166 1,200
(4
'This ordering is made to account for the uncertain geologic age of several specimens. Ties are not assumed in tests of trend in this particular sequence. Dates from Table 2 are retained in the same order.
tween these specimens. Taxonomic discussions of the H . erectus sample have been provided by numerous aathors (Bilsborough and Wood, 1986; Rightmire, 1985, 1986; Stringer, 1984,1987; Turner and Chamberlain, 1989). It should be noted that the Sale specimen exhibits unusual (possibly pathological) occipital morphology (Hublin, 1985), which may have affected cranial capacity, Accordingly, analyses that both include and exclude this specimen were undertaken.
Methods Regression analysis has typically been used to investigate change in hominid cranial capacity through time (Godfrey and Jacobs, 1981; Lestrel and Read, 1973; Lestrel, 1975;Rightmire, 1981,1985).Ordinaryleast squares regression has frequently been employed to measure these rates, despite the
4
S.R. LEIGH
possibility that this technique may not be suitable for modeling change in a variable through time. The inadequacy of ordinary least squares regression may be the result of several factors. First, in a time series, the assumption of independence between dependent variables is often violated. Correlation among residuals, or serial correlation, may result if values of Y in one time period are affected by values of Y at other time periods (Younger, 1979). Second, ordinary least squares regression lines tend to be best-fitted to the first and last observations in the series. Third, ordinary least squares regressions are heavily influenced by outliers. These problems lead to difficulty in obtaining accurate estimates of both slope and intercept in regressions of time series. Thus, if a trend toward increasing cranial capacity is present, ordinary least squares estimation may not detect the presence of such a trend. Conversely, ordinary least squares regression may indicate the presence of a trend when stochastic behavior (drift) actually accounts for changes in a variable through time (McCleary and Hay, 1980:35-36). In addition to the general problems of modeling time series with ordinary least squares regression, there may be substantial error in measurement of the independent variable (geologic age) in this particular sample. This very serious general problem is discussed by Sokal and Rohlf (1981).Wolpoff (1984)considers this problem with respect to measuring evolutionary rates in H. erectus. Regression techniques that account for measurement error in both X and Y variables (such as reduced major axis, major axis, and related techniques) are not well suited to the present problem. These methods are subject to the same limitations in time series applications as ordinary least squares regression. Moreover, the low correlation between geologic age and cranial capacity in the H. erectus sample (see Rightmire, 1985;) produces extremely narrow reduced major axis confidence intervals (Jolicoeur, 1975; see also Jolicoeur, 1973, for discussion of similar problems with major axis regression). Analyses with Model I1 regressions would likely minimize the differences in rates of evolution between taxa. Specifically, the H. erectus rate of cranial capacity increase would be inflated as a result of low correlation. The general complications of time series
analysis and the presence of error in measurement of geologic age place a premium on methods that are capable of accurately describing patterns of hominid cranial capacity evolution. Unfortunately, the unequal time intervals between observations and the presence of more than one cranial capacity for a given date lead to difficulties in using standard methods for the analysis of time series (Vandaele, 1983). Although these obstacles are often encountered in paleobiological context s, little theoretical statistical research has been undertaken to solve these problems. However, Kitchell et al. (1987)discuss the problem of unequal intervals in paleobiological contexts, while Quenouille (1957), and Cleveland and Devlin (1980, 1982) address this problem in econometric applications. A simple nonparametric test for trend that minimizes the deficiencies of these data is provided by Hubert et al. (1985; see also Konigsberg, 1990). Specifically,this test is a distribution-free permutational test for randomness in ordered data. The test makes no assumptions about the length of intervals between observations. In addition, multiple observations sharing the same geologic age (ties) can be accommodated by this technique. It is essential t o note that measurement error in geologic age is minimized because observations are merely ordered from earliest to latest. Hubert et al.’s test allows detection of a trend in cases where regression may not prokide an accurate measure of trend. The procedure is based on a test statistic (r) derived from the cross-product (or dot product) of two 1 x N matrices or vectors where:
r =a’b The first vector (a)is, in this case, a vector of cranial capacities ordered by time. The second vector (b) consists of an ordered series (e.g., 1,2,3,4,5)with equal intervals between each observation. The b vector reflects the chronological order of the variables in the a vector. In the case of ties (cranial capacities from the same date) the cells of the b vector are “stuttered (e.g., 1,2,2,2,3,4,5). Hubert et al. (1985) recommend that the dot product of these vectors serve as a test statistic for measuring the presence of randomness in ordered data. The significance of the initial summed cross-product statistic (r)can be estimated by obtaining a distribu-
H . ERECTUS AND EARLY H . SAPIENS CRANIAL CAPACITY
tion of summed cross-products calculated from random permutations of the values in one of the original vectors. In other words, one vector is randomly re-arranged, and a cross-product is calculated for each new permutation. The significance level of the test statistic is defined by (M + l)/(N + 11, where M is the number of values as large or larger than r and N is the number of permutations (Hubert et al., 1985). Thus, the significance of the association between vectors can be estimated. A significant positive trend is implied when only a small percentage of randomly obtained dot product values exceeds the value of gamma derived from the original vectors. Conversely, randomness in the order of observations is suggested if the value of the original gamma lies near the center of the distribution of permutational gammas. Up to N! permutations are possible. In the present study, tests for trend are undertaken for the H. erectus, early H . sapiens, supplemental samples, and in subdivisions of the H. erectus sample. The subdivisions of the H. erectus sample include African, Chinese, Indonesian, and “Asian” (represented by the combined Chinese and Indonesian samples). All analyses were undertaken with 1,000 random permutations with the exception of the African (120 exact permutations) and Indonesian (720 exact permutations) samples. Exact permutations utilize every unique cross-product value and are feasible because the African and Indonesian samples are very small. The test for trend offers information about the presence and significance of directional change in the variable of interest. Unfortunately, it does not provide information about rates of change. Nonparametric and ordinary least squares regressions are used for this purpose, but only with the assumption that estimates of regression parameters are unbiased. If regressions detect a trend after the presence of trend has been established with Hubert et al.’s method, then the regression results may be interpreted more confidently. Nonparametric spline regression described by Schluter (1988; see also Eubank, 1988; Seber and Wild, 1989) is used for visual assessment of changes in cranial capacity. This method is not constrained by choice of model (e.g., linear, nonlinear), allowing flexibility in the modeling of complex distributions. Most importantly, confidence inter-
5
vals with these regressions are calculated through bootstrap techniques, which are based upon iterative random selection (with replacement) of data points from the original sample. The main assumption of this technique is that the sample analyzed bears a relatively close relationship to the probability distribution from which the sample was drawn (Efron, 1982). With iterative sampling, relatively accurate confidence intervals should be obtained. In all cases, 300 iterations are undertaken in construction of confidence intervals, Finally, ordinary least squares regression and analysis of covariance are employed to estimate the significance of differences between rates of change in H. erectus and early H. sapiens. These techniques are used only after tests for trend and modeling of bivariate distributions with nonparametric regression. Thus, their roles can be viewed as corroborative. Only linear models were used, facilitating tests of significance between regressions. It should be noted that nonlinear models may suffer the same limitations as ordinary least squares linear models in time series analysis (Seber and Wild, 1989). Analysis of covariance permits tests of significance of differences in regression lines. This analysis is comprised of two parts. The first is a test for difference in slope, while the second is a test for difference in intercepts (see Edwards, 1985). Together, these tests provide a basis for distinguishing between several hypotheses that specify the relation between regression lines. Specifically, analysis of covariance permits identification of 1)identical regression lines (equal slopes and intercepts), 2) parallel regression lines (equal slopes, unequal intercepts), or 3) unequal slopes. Throughout this study, significance for all statistical tests is measured at the .05 level. Regression significance values are evaluated as two-tailed tests because previous analyses (Rightmire, 1981, 1985) suggest that slopes near zero will be obtained in the H. erectus analyses. Tests for trend are treated as one-tailed tests. RESULTS
Trend The test for trend indicates that cranial capacity in H. erectus may not vary randomly with respect to geologic age (Table 5). Of 1,000 random permutations, only 58 (5.8%) of the randomly obtained values of gamma equaled or exceeded the value of gamma
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S.R. LEIGH
TABLE 5. Results of tests for trend by taxon, by region, and withing the Homo erectus sample*
Sample or subsample
Probability*
Number of permutations
.058
1,000' 1,000' 1,000'
Homo erectus Homo erectus, excluding SaleEarly Homo sapiens Early Homo sapiens, re-ordered African Homo erectus Asian Homo erectus Chinese Homo erectus Indonesian Homo erectus
.041 ,001 ,020
.500
1,000' 1202
,014 ,079 ,200
1,000' 1,0001 7202
*Probability values are based on the No. of randomly permuted gammas equal to or larger than observed gammas. 'Random permutations. 'Exact permutations.
based upon the original ordering of data. When the Sale specimen is removed from the sample, the trend in H . erectus is more significant. In this analysis, 41 of 1,000permutations (4.1%) exceeded the observed gamma. Thus, a significant positive trend toward increasing cranial capacity appears present in the H . erectus sample, although this result is not quite significant when the Sale specimen is included. The early H . sapiens sample also appears to exhibit a trend toward increasing cranial capacity. In this analysis, only 1 of 1,000 randomly calculated gamma values (. 1%) equaled or exceeded the original observed gamma. A positive trend is also present when some of the less securely dated early H . sapiens specimens are re-ordered (see Table 4). Trend in this re-ordered sample is less obvious than in the analysis with the original ordering, with 20 of 1,000 (2.0%) randomly calculated gammas exceeding the initial reordered gamma. The patterns among subsamples of H . erectus are not as clear. The Chinese subsample may show a significant trend toward increased cranial capacity, with 79 of 1,000 randomly obtained gammas (7,9%)equal to or exceeding the observed gamma. Obviously, this is not quite significant at the .05 level. Trend is apparent neither in the Indonesian subsample (143 of 720 exact gammas equal to or exceeding the observed gamma) nor in the African subsample (59 of 120 exact gammas equal t o or exceeding the observed gamma). Combination of the Chinese and Indonesian subsamples to form the Asian subsample produces significant results. Only 14 of 1,000 random gammas equal or exceed the observed test statistic for the combined Asian sample.
TABLE 6. Results of tests for trend in the supplemental sample* __ Samiole or subsamole Probabilitv* Homo erectus, Ngandong a s Homo erectus Early Homo sapiens, Ngandong as Homo sapiens Asian Homo erectus, with Ngandong Indonesian Homo erectus, with Ngandong -
,003
,003 ,001
,001
*Probability values are based on the No. of randomly permuted gammas equal to or larger than observed gammas, and there are 1,000 permutations in each analysis.
Analyses of the supplemental sample mirror analyses based on Rightmire's (1985) sample (Table 6). Trend in the H . erectus sample appears more significant. Inclusion of the Ngandong crania either with the early H . sapiens sample or with the Asian H . erectus sample produces significant trend. Significant trend seems present in the supplemental Indonesian sample, in contrast to results based on the original sample. Regression analysis Spline regressions of H . erectus cranial capacity against geologic age suggest little change, with some possible variation in rates through time (Fig. 1). The rate of cranial capacity evolution may fluctuate through time in H . erectus, although the rate increase between 1.2 and 1.6 myr is based upon only three specimens. In contrast, early H . supiens cranial capacity appears to increase markedly during a short time span. Visual assessment of predicted lines and confidence intervals indicates that the rate of change in early H . sapiens probably exceeds the rate of change in H. erectus. Unfortunately, regional subsamples are too small to allow
H . ERECTUS AND EARLY H . SAPIENS CRANIAL CAPACYW
7
0.9
0.7 0.5 0
0.2
0.4
0.6
0.8 1 Geologlc Age (Miillons)
-Homo erectus
1.2
1.4
1.6
+Early Homo sapiens
Fig. 1. Predicted regression lines and 95% confidence intervals obtained from spline regression. Confidence intervals are based upon bootstrap procedures with 300 iterations for each sample. Only predicted values are shown.
TABLE 7. Ordinary least-squares regresion results by taxon, and by region within the Homo erectus sample Sample or subsample
RZ
Slope
Intercept
P-value for slope
Homo erectus Homo erectus, excluding Sale Early Homo sapiens Early Homo sapiens, re-ordered African Homo erectus Asian Homo erectus Chinese Homo erectus Indonesian Homo erectus
.14 .18
-124.87 -145.13
1,029.79 1,050.00
