AMERICAN JOURNAL. OF PHYSICAL ANTHROPOLOGY 88:37-57 11992)

Allometry and Prediction in Hominoids: A Solution to the Problem of Intervening Variables SIGRID HARTWIG-SCHERER AND ROBERT D. MARTIN Anthropologisches Institut und Museum, Uniuersitat Zurich, CH-8057 Zurich, Switzerland

Ontogenetic allometry, Static allometry, Size estiKEY WORDS mators, Body weight, Long bone dimensions, Line fitting

ABSTRACT To avoid misinterpretation of allometric exponents determined from interspecific allometric comparisons, specific conditions must be met with respect to the common reference variable. Body weight is considered to be the best general indication of overall size and is hence widely acknowledged to be the most suitable reference variable. However, because of the paucity of recorded body weights for museum specimens, various comparative studies have used other size indicators as intervening variables, although the allometric relationships to body sizelweight were often unknown and possibly differed between species. Because of differences in the scaling properties of alternative intervening variables across the species investigated, conflicting conclusions may be drawn if different variables are chosen as substitutes for overall size. This is illustrated with two examples. In this study, series of skeletons with associated body weights of Gorilla, Pan, Pongo, and Homo were investigated. Both ontogenetic and static adult allometric relationships between several widely used reference variables and body weight were determined. Neither these variables nor additional estimators investigated in this study displayed allometric exponents and coefficients similar enough across species to justify direct interspecific comparison. To generate a n alternative size estimator for both ontogenetic and static interspecific investigations, equations for combined sexes were derived to predict body weight from various long bone dimensions for individual hominoid species. From a total of 25 predictors, 12 prediction equations per species (six €or nonadults and six for adults) were selected according to their relative suitability for reliable prediction of body weight. It is shown that the derived reference variable “predicted body weight” avoids problems of intervening variables, is valid for any interspecific ontogenetic and static allometric comparison, and displays less fluctuation in comparison to actual body weight. o 1992 Wiley-Liss, Inc. Comparative quantitative investigations (see Giles, 1956, and Shea, 1981, 1983a, of great apes and humans provide an impor- 1985, for great apes), based either on detertant tool €or investigating questions in hu- mination of absolute growth rates or on inman evolution. They are essential for inter- vestigation of relative growth employing alpreting fossil hominids and for inferring lometric techniques. Although absolute possible interrelationships among extant growth rate, the change of a given parameandlor extinct forms. Ontogenetic compari- ter in relation to developmental time, can be sons, in particular, provide a powerful tool analyzed and compared interspecifically for determination of phylogenetic relation- (Cochard, 1985; Jungers and Fleagle, 1980), ships (Gould, 1977; Dean and Wood, 1984). One aspect of comparative ontogenetic studies is the quantitative analysis of growth Received November 12,1990; accepted November 4,1991. 0 1992 WILEY-LISS, INC.

38

S. HARTWIG-SCHERER AND R.D. MARTIN

the choice of the time abscissa-either chronological time or craniodental age categories (Schultz, 1935; Dean and Wood, 1981bmay be practically restricted when using museum specimens. It may also be theoretically questionable when comparing species with different life histories. Furthermore, an unequivocal statistical evaluation of growth curves is difficult to achieve. In the alternative approach, the relative growth of a given feature is commonly analyzed in relation to some other body dimension serving as a reference variable. The concept of relative growth, also known as allometric growth (Huxley, 1932; see Gould, 1966, for a detailed discussion), renders it possible to investigate growth processes while eliminating the time variable. The relative growth of one variable (Y) in relation to the reference variable (X) is described by the allometric power equation Y = kXa, with a being the ratio of the growth rates under investigation. The power equation can be logarithmically transformed to permit easier analysis (log Y = a log X + b, with intercept b = log k). If the plot of logarithmically transformed data yields a straight line, then relative growth rate (a) is constant. If not, differential growth occurs, with rates changing during development (Lumer, 1937). Examination of relative growth permits comparison of proportional changes in different species during their ontogeny. This concept of allometry-originally intimately linked with the investigation of growth processes-was subsequently applied to static adult intra- and interspecific studies to investigate the effect of body size on any given dimension. Here, the focus of interest is on change relative to overall size, often with the aim of “removing”the effect of size. In either case, regardless of whether patterns of relative growth or scaling effects within a given set of species are compared, it is important to remember that the resulting allometric exponent depends on the choice of the reference variable (Martin, 1982; Smith, 1981b). Reliable comparisons between species using a reference variable instead of a direct measure of overall size of course require carefully standardized conditions. To meet this requirement, it is necessary not only to use the same reference variable in

allometric studies (Jungers, 1984) but also to ensure that the variable scales to overall size with the same allometric exponent for all species investigated (Smith, 1981b). If not, differences in relative growth rates or scaling properties of the reference variable across species can obscure allometric interpretation of the specific feature under investigation (Jungers, 1984; Aiello, 1981b; Mosimann and James, 1979). Furthermore, it should be noted that in many interspecific comparisons it is also important for the same allometric coefficient to apply, for instance, when the deviation of individual species from the overall trend is investigated. If there is a significant parallel transposition (i.e., grade shift) in the double logarithmic plot of the reference variable against body weight in the species investigated, conclusions based on the reference variable alone may be misleading. An example of this is provided by the use of skeletal trunk length as a reference variable for body size by Biegert and Maurer (1972). A plot of hind limb length against skeletal trunk length seems to indicate that in the great apes the relative length of the hind limbs matches the general trend for simian primates. Examination of a plot of skeletal trunk length against body weight indicates, however, that the length of the trunk has undergone reduction in great apes. Relative to actual body weight, it is found that the hind limbs are shorter in great apes than in other simians (Aiello, 1981b, 1984). Body weight has been used as an indicator of overall size for a wide variety of interspecific allometric comparisons dealing with questions in ecology (Peters, 1983; CluttonBrock et al., 1977), physiology (Kayser and Heusner, 1964), adaptive strategies and life history (Martin, 1981; Martin and McLarnon, 1985; Calder, 19841, systematics and taxonomy (Rohrs, 1958; Shea, 1983a),development (Jungers and German, 1981; Jungers and Fleagle, 1980), and evolutionary biology (Jerison, 1970; Martin and Harvey, 1985; McHenry, 1988; Pilbeam and Gould, 1974). Body weight is relatively easy to determine (as long as the specimen does not exceed a certain size). It is also commonly regarded as the least biased reference variable (Jungers, 1984; Jungers and Sus-

PREDICTION OF BODY WEIGHT FOR HOMINOIDS

mann, 1984; Lande, 1979) because it best reflects overall size. Body weight is “the primary determinant of ecological opportunities, a s well a s of the physical and morphological requirements of an animal” (Lindstedt and Calder, 19811, because it is little confounded with special adaptations and does not depend on shape. It has even been described a s “the single most appropriate and biological meaningful size variable” and it is doubted that “measures other than weight or mass would permit meaningful comparisons among different species” (Jungers, 1984). A more cautious note is, however, sounded by Grand (19771, who rightly cites certain drawbacks of using body weight uncritically when dealing with physiological processes and when comparing species with body masses of very different composition (such as marine and terrestrial mammals). For ontogenetic investigations, specially designed longitudinal studies, in which body weight can be readily determined, are to be preferred over cross-sectional studies for many reasons (Sholl, 1950; Tanner, 1962; Cock, 1966). However, longitudinal studies are not always feasible, and it is commonly necessary to resort to study of specimens already available in collections. Unfortunately, museum specimens often do not have associated records of body weights. Furthermore, for investigations of fossil material, with which body weight would also be a useful reference variable, some kind of estimation is always necessary. Because of these practical limitations, skeletal features rather than body weight have commonly been used a s reference variables for various purposes such a s ontogenetic, static interspecific, or phylogenetic comparisons. As was noted above, the choice of a substitute for body weight in allometric studies is a crucial issue for any interspecific interpretation. High correlation with body weight alone does not justify the use of a reference variable for interspecific comparison a s long a s the pattern of allometric growth or scaling relative to body weight remains unknown. Jungers and German (1981) recommended the identification of “some other variable, preferably one that is both highly correlated and isometric with body mass.” However, there is in fact no

39

need for the variable to be isometric with body weight other than the convenience of directly interpreting allometric exponents relative to body weight (cf. Martin, 1982). Provided that the variable displays both identical allometric exponents and identical allometric coefficients relative to body weight across all species investigated, it would meet the requirements for interspecific comparisons, either ontogenetic or static. Skeletal features so far proposed as substitutes for body weight in (mainly static) allometric studies include: 1)long bone dimensions, such as humerus or femur length and midshaft circumferences/diameters (Aiello, 1981a,b; Aello and Day 1982; Lovejoy, 1975; Wood, 1976, 1979a,b); 2) cross-sectional dimensions of long bones (Ruff, 1987; see also Ruff et al., 1989); 3) partial skeletal weight (Steudel, 1980,1981);4) cranial dimensions (skull length: Blaney, 1986; Pirie, 1978; Wood, 1979a,b; basicranial length for ontogenetic investigations: Shea, 1982, 1983a,b, 1985; other skull dimensions: Radinsky, 1967; Wood and Stack, 1980); 5 ) trunk length (Biegert and Maurer, 1972; Jungers, 1979; Lumer and Schultz, 1947); and 6) internally generated overall size variables (Corruccini and Ciochon, 1976; Creel, 1986; Healy and Tanner, 1981; Hursh, 1974; Jolicoeur, 1963; Sneath, 1967). Variables belonging to the last category were initially assumed to be isometric relative to body weight, a supposition subsequently shown to be unfounded (Jungers and German, 1981). Additional methods of size adjustment are critically reviewed by Reist (1985). Most of the size variables listed above have been tested in the present study for their suitability a s reference variables in both ontogenetic and static allometric investigations for the species Pan troglodytes, Pan paniscus, Gorilla gorilla, Pongo pygmaeus, and Homo sapiens. The results indicate that the allometric exponents determined are not similar enough across these species to permit use of any one of them a s a common reference variable for interspecific comparisons. An alternative approach is therefore needed. Because body weight itself is widely believed to be the best indicator of overall

40

S. HARTWIG-SCHERER AND R.D. MARTIN

TABLE 1. Distribution by age and sex of skeletons size, this paper reports a n attempt to predict with recorded body weights body weight, thus recruiting a size reference Numbers of specimens for interspecific allometric studies (HartwigMale Female Total Scherer, 1990) without the problems of intervening variables. The samples of skele- Pan troglodytes 13 26 13 Nonadult 9 18 9 tons with associated body weight available 4 Adult 4 8 for five hominoid species permitted deriva- Pan paniscus 11 10 21 tion of equations to predict body weight from 3 8 Nonadul t 5 7 Adult 6 13 a variety of skeletal dimensions. Body 8 gorilla 8 16 weight has been predicted in previous stud- Gorilla 6 Nonadult 2 8 ies for individual adult specimens of various Adult 6 2 8 11 8 19 species, but this procedure has been applied Pongo pygmaeus Nonadult 4 5 9 primarily to fossils. Predicted body weight 6 Adult 4 10 19 48 29 has never previously been applied as a com- Homo sapiens Nonadult 11 18 29 mon reference variable for interspecific alloAdult 8 11 19 metric comparisons of extant hominoids. Most body weight predictions published in the literature are not designed to be applicable to individual specimens of a given spe- (Cleveland Museum of Natural History, cies, because prediction equations are often Cleveland, OH); the Collection of the Debased on a number of species covering a partment of Mammalogy and the Terry Colmore or less broad taxonomic range and on lection of the Department of Anthropology species means rather than individually re- (U.S. National Museum of Natural History, corded body weights. Moreover, body weight Smithsonian Institution, DC); American predictions derived from static adult series Museum of Natural History, New York, NY; should not be extrapolated to nonadult spec- the Powell-Cotton Collection (Birchington, imens, because ontogenetic allometric expo- Kent, England); and the Musee de 1’Afrique nents may differ significantly from static Centrale (Tervuren, Belgium). The 295 skelconditions (Gould, 1975; Martin, 1986; Cock, etons studied, covering both adults and non1966; Jungers and Susman, 1984; Shea, adults, included 26 Pan troglodytes, 21 Pan paniscus, 16 Gorilla gorilla, 19 Pongo pyg1982). This study is the first to generate age- and maeus, and 48 Homo sapiens with recorded species-specific equations for the prediction body weights (see Table 1for distribution of of body weight for adult and nonadult speci- sex and age categories). With one exception mens of Pan, Gorilla, Pongo, and Homo, us- in each case, all specimens of Gorilla and ing a variety of long bone variables from Pongo were wild caught. For the much both ontogenetic and static skeletal series larger Pan sample, consisting predomiwith individually recorded body weights. nantly of wild-caught animals, five individThe derived variable “predicted body uals with associated body weights were reweight”-separately determined for each corded as captive, while for eight specimens age group and species-permits valid inter- there were no records concerning their orispecific comparison without incurring the gin. problems associated with intervening variMETHODS ables.

Measurements

MATERIALS Skeletal material of Pan troglodytes, Pan paniscus, Gorilla gorilla, Pongo pygmaeus, and Homo sapiens from eight collections was

investigated: the Adolf H. Schultz-Collection and the Institute Collection (Anthropologisches Institut und Museum, Zurich, Switzerland); the Hamann-Todd Collection

All measurements were conducted by S.H.-S. Limb bones Lengths of individual limb bones (humerus, radius, femur, tibia) are defined as the distances between the most proximal and distal ends, measured with a n osteo-

PREDICTION OF BODY WEIGHT FOR HOMINOIDS

metric board. Because species with different locomotor patterns were measured, the long bone shaft was placed parallel to the side wall of the osteometric board to achieve comparable lengths. Midshaft circumferences were taken midway between the articular surfaces of proximal and distal joints, using transparent film (0.07 mm thick x 3 mm broad) with millimeter display, giving more reliable recordings of the actual shaft size than the mean of anteroposterior and transverse diameters. The weight of each individual long bone was determined to an accuracy of 1g. Long bones of both right and left sides were measured wherever possible and means were taken whenever both sides were available. Cranial dimensions Cranial dimensions were determined either by measuring the skull with electronic calipers (for cranial breadths and sagittal dimensions) or by measuring x-ray films (sagittal dimensions). Measurements derived from x-ray images have been cross checked with and calibrated against measurements taken directly on the skull. The length of the cranial base is defined as the distance between basion and nasion, following Shea (1982, 1985), and skull length as the distance between prosthion and opisthocranion. Biorbital breadth (Shea, 1981) was measured between the right and left frontomalare orbitale, where the zygomaticofrontal suture intersects the inner lateral orbital ridge. Bitubercular breadth is defined a s the distance between the two lateral tubercules of the articular fossae. Derived variables In addition to long bone weight, length, and circumference, composite variables derived from the latter two dimensions were tested, as a combination of variables might generally be expected to reflect the overall size of each individual specimen more precisely than a single measurement (Martin, 1986). Two- and three-dimensional variables designated, respectively, “surface estimator” (SURF; the product of longbone length and circumference) and “shaft volume estimator” (VOL; the product of cross-

41

sectional area and long bone length), were tested for each long bone separately as well as for combinations of all long bones together, Body weight records To test the reliability of body weight records, data sets were cross checked with those of other studies wherever possible. However, comparisons are severely restricted because of the limited availability of comparable longitudinal and cross-sectional studies (Jungers and Fleagle, 1980). Data for North American blacks (Fig. 1B; data from Verghese e t al., 1969, given in Eveleth and Tanner, 1976, Tables 40-43) served a s a good comparison for the human material investigated here, because the samples are reasonably similar (70% of the skeletons measured in our sample were from U.S. blacks, 30% from U S . whites). This comparison permitted the exclusion of some aberrant body weights (exclusively from the Hamann-Todd material) before conducting the analysis. Some of the immature human skeletons of the Hamann-Todd Collection are known to be associated with body weights lower than those for other comparable human data sets, due to postmortem changes in the cadavers and, in some cases, to chronic debilitating diseases. Clearly aberrant individuals were excluded from the sample. By contrast, the exclusively adult specimens from the much larger human material of the Terry Collection could be preselected a s nonpathological according to accompanying medical records and postmortem photographs. Gavan’s outstanding longitudinal studies (1953, 1971) permit a comparison for Pan, although unfortunately slightly different skeletal dimensions were used. The body weights of Pan used in this investigation correspond satisfactorily to those determined in the longitudinal studies and data points scatter without bias around the longitudinal curve derived from Gavan (1971) (Fig. 1A). In both human and Pun samples, the double logarithmic plot yields slopes and intercepts that are slightly different from those determined for previously published data.

S. HARTWIG-SCHERER AND R.D. MARTIN

42

E

-E 5m

W c

6ool

&

500

A

.. .. . - . m.

.o

00

m

m

W 1

GWM 1971 v this study &

0

10

20

30

40

M

60

Body weight (kg)

2000 I

Fig. 1. Comparison of body weight records of this study with those derived from longitudinal studies performed by Gavan (1971) for Pan troglodytes (A) and Verghese et al. (1969; in Eveleth and Tanner, 1976)for Homo sapiens (B).

However, the differences are due mainly to differences in the type of study (cross-sectional with limited sample size vs longitudinal and true cross-sectional). Even longitudinal studies may yield substantial differences, possibly because of differing sample sizes, individual variation, differing nutritional conditions, and different distribution of the sexes in the analysis. As an example, in Gavan (1971), female chimpanzees display ontogenetic allometric exponents 1.02 times higher than those for males, whereas corresponding data derived from Schultz (1940) indicate a multiplication factor of 1.17. Cock (1966) notes that variation in individual growth among specimens of one species can easily bring about the intersection or convergence of ontogenetic allometric lines. Undulations occur during ontogeny (Sholl, 1954; Lande, 1985) and contribute to the noise of the data.

Therefore, no attempt was made here to correct equations in any direction, as differences cannot be regarded as significant. Because no corresponding studies are known for ontogenetic series of Gorilla and Pongo, no cross check could be conducted. However, the two data sets for these genera are fortunately characterized by relatively limited scatter of points around best fit lines.

Line fitting Because the course of relative growth of any given body dimension changes during ontogeny, i.e., the ratio of the specific growth rates does not remain constant (Laird et al., 19681, two age ranges were selected for the determination of equations for each species (for definition of age ranges, see below). Major changes in the general growth

PREDICTION OF BODY WEIGHT FOR HOMINOIDS

trajectory occur at the very beginning of postnatal development and at its conclusion, as sexual maturity approaches (Lumer, 1937; Cock, 1966), whereas there are relatively constant rates in the central age ranges (but see also Sholl, 1954). Restriction to the “linear” region of the relative growth curve is necessary when calculating a prediction equation, i.e., when fitting a straight line. Because no other nonlinear equation is known to fit differential growth curves satisfactorily (Lumer, 1937; Ricklefs, 1969),the fitting of a straight line to the double logarithmic plot is a justifiable approximation for the age range selected. Three different line-fitting methods (least squares regression, LS; major axis analysis, MA; reduced major axis, RMA) may in principle be applied to determine linear biological relationships (see Hofman, 1988, for a review). As long as correlation coefficients exceed 0.98, there is no appreciable difference in the results yielded by these methods. However, as the scatter of points increases, the empirical values determined for both slopes and intercepts diverge significantly. For the determination of relationships between two biological variables in allometric studies, various authors indicate that a symmetrical line-fitting method such as MA or RMA is to be preferred over the asymmetric LS (Olivier, 1976; Martin, 1980; Martin and Harvey, 1985; Hofman, 1988; Martin and Barbour, 1989).As far a s prediction of Y from X is concerned, discussion concerning the appropriate line-fitting model continues. Various authors argue in favor of the use of LS for prediction, not only for data sets in which Y is clearly dependent on X and X can be measured without error (where LS is indeed the only appropriate model) but also for data sets with variance in both Y and X variables (see, e.g., Smith, 1980; Jungers, 1984). Recently, more authors have come to favor use of MA for predictive purposes (see, e.g., Gingerich et al., 1982; Jungers, 1988). For biological data sets in which both variables are subject to variance, LS is not expected to give appropriate results because it involves a n asymmetrical assumption that the residual variance of X is zero. By contrast, symmetrical line-fitting models (MA,

43

RMA) assume that both variables are subject to variance. For MA, the residual variances are assumed to be equal for both variables (C[Y, - Y12 = C[X,- XI’), while for RMA the squared residuals for both Y and X variables are assumed to be proportional (Z[Yi - Y12 = h * C[Xi - XI’). The residual variances cannot be determined or estimated in most biological cases. However, it can be argued as a general rule 1)that both variables are subject to variance and 2) that these variances are not expected to be identical for both variables. For this reason, RMA might seem to be the most appropriate statistical model (Hofman, 1988). Because of the difficulties involved in estimating the residual variances, a n empirical test was developed (Hartwig-Scherer and Lehner, in preparation) to determine the appropriate line-fitting model for any given data set individually. In the majority of cases, RMA yields the most satisfactory results, closely followed by MA, so allometric formulae have been determined from the RMA in this study. Because the literature contains arguments in favor of all three line-fitting methods for purposes of prediction, however, prediction equations have been calculated with all three as a precautionary measure. Nevertheless, it should be noted that there is now compelling evidence that LS is generally unsuitable. Prediction equations

Prediction equations for body weight using lengths and circumferences of four long bones are derived for two different age ranges: nonadult (specimens with complete deciduous dentition to those with the third molar not yet erupted) and adult (specimens with complete permanent dentition). The application of prediction equations must naturally be restricted to the age range from which they are derived. Pan paniscus and Pan troglodytes have been combined for variables showing the same scaling pattern. All other variables that did not display the same relationship to body weight in these two species have been excluded from this report (indicated with asterisks in Table 3). Both raw and logarithmically transformed data were investigated, to avoid un-

44

S. HARTWIG-SCHERE:RAND R.D. MARTIN

Table 2, allometric growth of the cranial base is negative, not only in the chimpanzees and gorilla but also in the orang-utan and man. Because of different patterns of ontogenetic scaling, this variable is inappropriate for interspecific comparisons across all hominoids. In most cases, long bone dimensions scale positively in ontogeny and either positively or negatively under static conditions. Most variables show scaling to body weight that departs from isometry (i.e., a = 0.33 for linear bone dimensions, a = 0.67 €or two-diError estimation mensional variables and a = 1.00 for threeIn addition to correlation coefficients, pre- dimensional variables). More importantly, diction error (PE) was calculated for a more for all variables allometric exponents and general comparison of the predictive power coefficients differ significantly across the of equations (Smith, 1980; Jungers, 1982). four species investigated. Therefore, these Following Smith, PE was calculated in per- variables are probably not suitable for use as general reference dimensions. cent as follows: In the search for another, more reliable reference variable, additional dimensions (obs. BW - pred. BW) P E (ind.) = 100 X based on long bones were tested for their pred. BW scaling properties. However, among the toPE (mean) = l l n C -\/(PE [ i n d i v i d ~ a l l ) ~ . tal of 25 skeletal variables tested in this study, none-not even the derived variables SURF or VOL-met the requirement of simRESULTS AND DISCUSSION ilar scaling across species. Scaling of widely used intervening variables The problem of intervening variables: Two examples Patterns of static and ontogenetic allometry of widely used reference variables relaThe following examples demonstrate that tive to body weight were investigated in Pan the use of different skeletal dimensions a s troglodytes, Gorilla gorilla, Pongo pyg- size reference variables in allometric studies maeus, and Homo sapiens. Allometric expo- can yield markedly different results. The nents and coefficients for seven of these first example concerns relative skull growth variables yielded by reduced major axis in hominoids (Shea, 1982, 1983a,b, 1984; Giles, 1956) and involves the scaling of bioranalysis are given in Table 2. Skull length does not scale isometrically bital breadth of Pan paniscus in comparison with body weight in hominoids, a s was sug- to that of Pan troglodytes. A double logarithgested for Gorilla by Blaney (1986), but typ- mic plot of biorbital breadth against individically displays a strongly negative allomet- ually recorded body weight (Fig. 2A) reveals ric relationship with body weight in both that this dimension does not scale in a simistatic and ontogenetic contexts. (In Blaney’s lar fashion in these two species but displays allometric study, skull length was used and diverging ontogenetic patterns. As a result, discussed interchangeably with body weight, for any given body weight, adult P. paniscus although i t does not in fact scale isometri- are more gracile in this facial dimension cally with the latter.) than P. troglodytes. In one of his allometric studies of African However, if basicranial length is used as apes, Shea (1983b) writes a s follows: “It is the size reference, a s was the case in Shea’s not known whether it [basicranial length] investigation, no distinction between the scales isometrically with weight during two species emerges (Shea, 1982:235, 259): growth in the three species.” As is shown in Biorbital breadth scales with a common onwarranted use of logarithmic transformation (Cock, 1966; Smith, 1980; Jungers, 1988). For those cases in which isometry could not be excluded at the 95% level, a prediction equation was derived from untransformed data and mean prediction error was compared with that obtained with the log-transformed equation. As logarithmic transformation-performed to the base 10consistently yielded better or at least equally good predictions, only transformed data have been presented here.

Static2 Ontogen. Static Ontogen. Static Ontogen. Static Ontogen. Static Ontogen. Static Ontogen. Static Ontogen.

0.35 0.39 0.35 0.41 0.57 0.39 0.53 0.43 0.98 1.10 0.27 0.22 0.32 0.20

a3

0.84 0.69 0.84 0.60 -0.79 0.08 -0.59 -0.12 -1.87 -2.34 0.73 0.99 0.81 1.37

0.78 0.92 0.74 0.92 0.82 0.85 0.82 0.86 0.95 0.94 0.92 0.90 0.81 0.85

Pan troglodytes b r4

0.03 0.02 0.08 0.03

-

0.96 0.97 0.66 0.96

1.22 1.17 1.17 1.27

-

0.18 0.18 0.25 0.23

-

0.04 0.03 0.05 0.04 0.07 0.03 0.06 0.04 0.07

0.89 0.99 0.90 0.98 0.91 0.97 0.91 0.97 0.98

1.59 0.63 1.39 0.52 -0.06 0.46 0.38 0.26 -0.77

0.20 0.41 0.23 0.42 0.40 0.29 0.32 0.35 0.7:

0.09 0.04 0.10 0.04 0.13 0.05 0.13 0.06 0.14 0.13 0.05 0.03 0.11 0.03

SE

a

SE5

Gorilla gorilla b r

0.21 0.41 0.21 0.40 0.31 0.33 0.28 0.32 0.74 1.21 0.17 0.14 0.25 0.19

a

1.57 0.65 1.44 0.59 0.41 0.27 0.50 0.28 -0.78 -2.94 1.21 1.31 1.15 1.43 0.98 0.88 0.98

0.90

0.85 0.99 0.90 0.99 0.85 0.99 0.87 0.98 0.91 0.99

Pongo pygmaeus b r

~~

0.51 0.53 0.48 0.62 0.67 0.32 0.54 0.4,4

0.04 0.02 0.03 0.03 0.06 0.02 0.05 0.03 0.11 0.07 0.03 . 0.01 0.05 0.02 I

0.716

1.5,3

-

a

SE

TABLE 2. Static and ontogenetic allometry of intervening size indicators (reduced major axis analysis)

+

'Variables are plotted against individual body weight. 'For ontogenetic investigations only nonadult, for static only adult specimens have been used (for definition of age groups, see Methods). Sexes combined. "Form of equation is log (variable, in mm or g) = a log (body weight, in g) b. Isometry if a = 0.33 (lengths) and a = 1.0 (weight),respectively. 'Correlation coefficient (r). "Standard error (SE) of allometric exponent a. "Data unreliable (see Discussion). 'LOWcorrelation.

Humerus length Femur length Humerus circumf. Femur circumf. Long bone weight Basicranial length Skull length

Size indicator'

1.24

-

-

-4.35

0.09 0.03 0.39 -0.22 -1.35 0.20 -0.62 -0.17

0.93

-

-

0.98

0.77 0.94 0.87 0.93 0.81 0.94 0.84 0.97

Homo sapiens b r

-

0.01

0.09

-

SE 0.08 0.04 0.05 0.06 0.10 0.03 0.07 0.03

S. HARTWIG-SCHERER AND R.D. MARTIN

46

3.9

37

log,,

41 4.3 4.5 (observed body weight, gm)

4.7

2 .oo

g 1.95 -

B

@

A

f 1.90 .

ef

-* g

PAA

:

1.85 .

,/"*,

1.80 I -g*1.80.

A

A

EU tMledYh

A

1.75'

75

1.85 1.95 1.9 log,, (basicmniol length mm)

2.0

Log,, (observed body weight, gm) Fig. 2. Relative to body weight (A), biorbital breadth displays different patterns of ontogenetic scaling in Pan troglodytes and Pan panzscus. In pygmy chimpanzees beyond the infant stage, biorbital breadth is smaller for any given body weight in comparison to the common chimpanzee. However, if basicranial length

is used as size reference (B), no difference is seen between the two species. These conflicting patterns of scaling of biorbital breadth result from differential scaling of basicranial length relative to body weight in the two species (0.

togenetic pattern (Fig. 2B), suggesting that there will be no difference between adult forms a t any given size. These apparently conflicting results are a consequence of differential allometric growth of basicranial length relative to body weight (Fig. 2C). For several other facial widths, comparable to

those examined by Shea (1982, 1983b, 19841, a similar conflict is observed (data not shown). In contrast to Shea's assumption, therefore, it can be concluded that facial breadth does not scale with a common ontogenetic pattern in relation to overall body size in P. troglodytes and P. paniscus.

PREDICTION OF BODY WEIGHT FOR HOMINOIDS

Thus, while it may be correct to conclude that P. troglodytes and P. paniscus possess a common ontogenetic pattern for skull growth relative to basicranial length it would be incorrect to conclude that the two species follow the same ontogenetic pattern with respect to the growth of the body generally. [The fact that P. panzscus has a more gracile skull than P. troglodytes for any given body weight provides a n explanation for the enigma that the former species bears the label “pygmy chimpanzee” despite the fact that there is only a minor difference in average body weights for adults (Shea, 1984).] The second example concerns interspecific static allometry. Smith (1981b) addressed the problem of why teeth seem to show different scaling patterns in different studies. Exponents calculated by Wood (1976, 1979a,b) indicate positive allometry, while Smith (1981a) determined negative exponents for the same tooth dimension. Wood used femur length and cranial length as size references, whereas Smith used body weight. The conflicting results reflect the properties of the reference variables used (Smith, 1981b). As will be shown, certain intervening variables not only distort but may totally conceal any existing relationship between the dimension of interest and overall size. The scaling property of bitubercular breadth is investigated here (Fig. 3A,B). Femur length and body weight, respectively, were used a s size references. If femur length is used a s the reference variable, three different patterns can be detected among the hominoids (Fig. 3A). In contrast, when bitubercular breadth is related to body weight (Fig. 3B), a similar pattern emerges for African apes and humans, while there is a grade shift for Pongo. I n Figure 3A, both African apes and Pongo display positive allometry for the scaling of bitubercular breadth [allometric exponents a = 1.19 and 1.27, respectively], in contrast to the strongly negative allometric relationship in Homo [a = 0.521. If body weight is used as the reference variable (Fig. 3B), however, all species investigated display weakly negative allometry [allometric exponent a = 0.27 for Homo, a = 0.28 for African apes, and a = 0.29 for Pongo]. Thus Figure

47

3A actually provides information about the different scaling properties of the femur relative to body weight (cf. Fig. 3C) rather than about the size relationship of the cranial dimension of interest (for scaling of femur length in primates, see Jungers, 1985, and Ruff, 1987). Quite generally, therefore, conclusions regarding allometric properties might be strongly biased by different scaling a n d o r growth of the reference variable relative to overall body size. To avoid the major problems associated with the use of intervening variables, it was decided to predict body weight from various long bone dimensions. This procedure yields a derived variable, referred to here as “predicted body weight,” that is free from the problems discussed, is easily accessible to any investigator, and may be applied to hominoid skeletons of all ages. Prediction equations Twenty-five sets of raw and derived long bone variables have been tested with respect to correlation coefficients and prediction error (PE) (Table 3). Six have been selected as predictors for each age and species group (Table 4A-D). (P. troglodytes and P. paniscus have been combined for those variables that showed the same pattern of scaling for both species.) Selection of the best predictors

The best prediction equations were carefully selected to ensure maximum reliability, despite the inevitably small sample sizes. Prediction errors were used a s the initial basis for selecting the six best predictors for each intraspecific age group, as they give a good indication of overall predictive power (Table 3). Ideally, prediction errors should be calculated using several specimens from each array that have not been included in the derivation of the original equation. Unfortunately, this was not possible in this study because so few specimens were available with recorded body weights. Bone weight frequently ranked among the best predictors, a s did several combined variables, which commonly displayed higher correlation coefficients and lower prediction errors than the raw variables from which

S. HARTWIG-SCHERER AND R.D. MARTIN

48 I

I

A .20 . .lo .

1.27 ISE=0.161

V

*-

-

8

.oo 1-

I

2.1

2.5 2.6 log,, (femur length, mm)

2.I

s

i

3

220

n 2! L

0

z

n kj

2.10

3

c s g2.00

0

log,

2.5 2.6 (femur Length, mm)

2 .I

Fig. 3. Example of the distorting influence of intervening variables: If femur length is used a s the size reference to investigate interspecific scaling of bitubercular breadth, no common pattern can be observed across extant hominoids (A). By contrast, a clear common scaling trend is revealed for African apes and humans (with Pongo transposed towards a larger bitubercular breadth relative to body weight) when body weight is taken as the overall size reference (B). Differential scaling properties of femur length relative to body

weight in the different hominoid species (C) disguise the relationship between the cranial dimension and overall body size. [In addition to the 58 adult specimens with individually recorded body weight (see Table I),another 56 adult specimens (11-14 per species, none available for P. panzscus) with predicted body weight were included to obtain sample sizes comparable with A (for prediction of body weight see text)l. (Note: for easier comparison with A, body weight has been plotted on the Y axis in C).

they were derived. (The former do not necessarily indicate a better fit; they may simply reflect a change in the range of X values and in the slope.) Although the reduction of prediction error is a desirable aim, combinations derived from more than one long bone

are not given, because this would have restricted the applicability of the prediction equations to specimens with a relatively complete set of limb bones. In certain cases, correlation coefficients and prediction errors may lead to erroneous

2

2

0.97 0.96 0.97 0:.7

L

13.2 14.2 12.1 13.7

13.1 14.4

0.97 0.96

2

14.3 17.3

14.3 13.1 11.9 14.2 14.3 14.5 13.9 15.8

0.96 0.;4

2

0.96 0.96 0.98 0.96 0.96 0.96 0.96 0.95

PE 12.0 13.0 12.3 2.1 10.3 10.5 12.3 7.3 15.1 21.8 15.4 10.5 10.1 13.5 11.4 8.8 10.4 15.8 11.0 9.6 4.9 7.9 13.1

8.9 9.7

0.98 0.98 0.98 0.99 0.99 0.99 0.98 0.99 0.97 0.95 0.97 0.98 0.98 0.98 0.99 0.99 0.98 0.97 0.98 0.99 0.95 0.99 0.98

0.99

0.99

0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.98 0.98 0.97 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.98 0.99 0.99

9.7 11.5 10.3 7.9 8.0 9.9 10.1 8.9 11.1 17.3 17.4 17.6 7.3 8.8 9.3 11.3 8.1 9.8 11.1 12.8 9.3 8.8 14.5 8.2 9.2

Nonadults Gorilla Pongo r PE r PE

' P . troglodytes and P.paniscus were combined for given predictors. "or some variables, they do not display the same allometric pattern

Weight humerus Weight radius Weight femur Weight tibia Length humerus Length radius Length femur Length tibia Circ. humerus Circ. radius Circ. femur Circ. tibia SURF humerus SURF radius SURF femur SURF tibia VOL humerus VOL radius VOL femur VOL tibia Total bone weight Total bone length Total circ. Total SURF Total VOL

r

Pan' 0.97 0.97 0.96 0.98 0.94 0.93 0.93 0.95 0.94 0.94 0.97 0.98 0.95 0.95 0.96 0.98 0.95 0.95 0.96 0.98 0.98 0.94 0.97 0.97 0.97

13.8 13.3 13.3 10.2 18.2 21.1 19.8 17.6 19.1 19.7 11.4 10.1 16.3 17.3 15.0 10.9 16.0 16.8 13.6 9.9 10.1 18.8 11.6 12.9 12.0

Homo r PE

10.4 10.1 14.9 13.4 10.5 11.5 14.0 8.9 9.5 11.3 10.7 7.8 10.5 11.2 8.9

0.75 0.78 0.69 0.67 0.283 0.78 0.72 0.76

7.3 6.3 9.5 8.8

PE

0.76 0.79 0.69 0.68 0.72 0.75 0.p

2 2 2

0.86 0.87 0.78 0.81

r

Pan'

n 97

0.96

0.97 0.99 0.97 0.97 0.89 0.85 0.90 0.90 0.91 0.98 0.91 0.89 0.97 0.99 0.97 0.93 0.95 0.99 0.96 0.92 0.98 0.89 0.94

9.2 4.9 9.5 9.8 20.3 25.2 18.9 19.3 18.0 7.7 18.4 18.1 9.0 6.2 10.0 15.8 11.6 4.8 11.4 15.8 7.9 20.3 13.1 9.2 8.4 0.91 0.86 0.92 0.90 0.85 0.92 0.90 0.90 0.85 0.85 0.87 0.86 0.89 0.89 0.93 0.89 0.89 0.88 0.92 0.88 0.91 0.91 0.89 0.91 0.90

15.5 18.6 14.7 17.0 20.9 15.1 15.0 17.0 20.8 20.5 20.0 20.0 15.0 17.1 12.0 18.2 15.7 16.8 13.8 17.8 15.3 16.0 18.4 15.7 15.2

Adults Pongo Gorilla r PE r PE

TABLE 3. Correlation coefficients (r) and prediction errors (PE, %) for long bone dimensions tested as body weight predictors Homo r PE __ 0.49 14.5 0.34 16.9 0.63 12.3 0.56 14.5 15.0 0.77 12.5 0.73 6.9 0.87 8.4 0.86 10.0 0.81 12.8 0.69 7.5 0.84 9.9 0.82 8.7 0.83 10.5 0.77 7.2 0.89 10.0 0.81 8.6 0.83 10.4 0.75 7.4 0.88 0.86 7.8 0.57 13.0 8.7 0.85 0.86 8.8 0.89 6.6 0.89 6.6

S.HARTWIG-SCHERER AND R.D. MARTIN

50

TABLE 4 . Body weight prediction equations calculated b y three statistical models1 for Pan, Gorilla, P o n ~ oand . Homo Specie2 Pan

Gorilla

Long bone parameter

Age3

Statistic

a4

b

RMA 0.82 2.73 MA 0.82 2.73 LS 0.81 2.76 SURF femur n-ad RMA 1.31 -1.01 MA 1.32 -1.05 LS 1.27 -0.86 Weight of radius n-ad RMA 0.93 3.00 MA 0.92 3.00 LS 0.89 3.04 Circumference of femur n-ad RMA 2.62 -0.19 MA 2.70 -0.33 LS 2.52 -0.02 Length of humerus n-ad RMA 2.66 -1.95 MA 2.74 -2.15 LS 2.55 -1.71 SURF tibia n-ad RMA 1.27 -0.66 MA 1.28 -0.71 LS 1.22 -0.47 Allometric reliability of predicted body weights: + 2,390 Weight of radius ad RMA 0.95 2.93 MA 0.95 2.95 LS 0.83 3.15 ad RMA 0.88 2.71 Weight of humerus MA 0.86 2.75 LS 0.76 2.98 ad RMA 0.84 0.39 VOL humerus MA 0.80 0.62 LS 0.63 1.44 Weight of femur ad RMA 0.94 2.47 MA 0.93 2.50 LS 0.73 2.94 VOL radius ad RMA 0.85 0.71 MA 0.82 0.87 LS 0.67 1.56 SURF humerus 1.42 -1.48 ad RMA MA 1.62 -2.31 LS 1.03 0.21 Allometric reliability of predicted body weights: f 16,2%? Length of tibia n-ad RMA 2.50 -1.30 MA 2.54 -1.34 LS 2.50 -1.25 SURF tibia -1.05 n-ad RMA 1.39 MA 1.39 -1.07 LS 1.37 -0.99 SURF humerus n-ad RMA 1.43 -1.57 MA 1.44 -1.60 -1.47 LS 1.41 Length of humerus n-ad RMA 2.46 -1.54 MA 2.48 -1.60 LS 2.43 -1.47 n-ad RMA 2.53 -1.47 Length of radius MA 2.56 -1.53 LS 2.49 -1.39 n-ad RMA 1.31 -1.06 SURF femur MA 1.32 -1.08 LS 1.29 -0.98 Allometric reliability of predicted body weights: f 4,5W6 ad RMA 1.09 -0.36 VOL radius MA 1.09 -0.36 LS 1.08 -0.32 Circumference of radius ad RMA 2.73 0.22 MA 2.76 0.16 LS 2.68 0.31 SURF humerus ad RMA 1.76 -3.05 MA 1.79 -3.19 LS 1.70 -2.78 Weight of femur

n-ad

r

% PE5

0.98

11.9

0.98

11.9

0.96

13.1

0.96

14.3

0.96

14.3

0.96

14.4

0.87

6.3

0.86

7.3

0.75

8.9

0.78

9.5

0.78

9.5

0.72

10.5

0.99

7.3

0.99

8.8

0.98

10.1

0.99

10.3

0.99

10.5

0.99

11.4

0.99

4.8

0.98

7.7

0.97

9.0

(continued)

PREDICTION OF BODY WEIGHT FOR HOMINOIDS

51

TABLE 4. Body weight prediction equations calculated by three statistical models1 for Pan, Gorilla, Pongo, and Homo (continued) Species2

Long bone parameter

Age3

Weight of humerus

ad

Weight of tibia

ad

SURF femur

ad

Statistic RMA MA LS RMA MA

LS

Pongo

SURF humerus Length of humerus SURF radius Length of tibia

RMA MA LS Allometric reliability of predicted n-ad RMA MA LS n-ad RMA MA LS n-ad RMA MA LS n-ad RMA MA

LS SURF femur Length of radius

SURF humerus Length of femur

n-ad

RMA MA LS n-ad RMA MA LS Allometric reliability of predicted ad RMA MA LS ad RMA MA

LsRMA MA LS ad RMA Length of radius MA LS ad RMA Length of tibia MA LS ad RMA SURF radius MA LS Allometric reliability of predicted n-ad RMA VOL tibia MA LS Circumference of tibia n-ad RMA MA LS Circumference of femur n-ad RMA MA LS Weight of femur n-ad RMA MA LS Weight of radius n-ad RMA MA LS VOL humerus n-ad RMA MA LS Allometric reliability of predicted SURF humerus

Homo

ad

a4

b

1.23 1.87 1.24 1.85 1.19 1.97 1.50 1.59 1.52 1.54 1.45 1.70 1.94 -3.81 1.98 -3.98 1.88 -3.52 body weights: k 3,4@ 1.35 -1.26 1.36 -1.26 1.35 -1.24 2.43 -1.57 2.45 -1.60 2.42 -1.53 1.44 -1.31 1.44 -1.32 1.43 -1.27 2.53 -1.41 2.55 -1.44 252 -i.37 1.41 -1.27 1.41 -1.27 1.40 -1.24 2.43 -1.57 2.45 -1.61 2.41 -0.51 body weights: i- 4,5W6 2.16 -4.44 2.26 -4.86 2.02 -3.83 4.76 -6.83 5.24 -7.99 4.29 -5.70 2.06 -4.31 2.21 -4.98 1.84 -3.36 4.93 -7.84 5.35 -8.90 4.52 -6.78 5.38 -8.08 5.96 -9.46 4.82 -6.76 1.76 -2.63 1.87 -3.11 1.56 -1.80 body weights: f 8,6u/$ 0.65 1.29 0.64 1.32 0.64 1.35 2.12 0.72 2.14 0.68 2.05 0.77 2.28 0.39 2.33 0.32 2.22 0.50 0.67 3.03 0.66 3.05 0.64 3.08 0.77 3.55 0.77 3.56 0.75 3.58 0.87 0.51 0.86 0.53 0.83 0.68 body weights: i- 3,2W6

r

W PE5

0.97

9.2

0.97

9.8

0.97

10.0

0.99

7.3

0.99

8.0

0.99

8.8

0.99

8.9

0.99

9.3

0.99

9.9

0.93

12.0

0.90

15.0

0.89

15.0

0.92

15.1

0.90

17.0

0.89

17.1

0.98

9.9

0.98

10.1

0.97

11.4

0.96

13.3

0.97

13.3

0.95

16.0

(continued)

S. HARTWIG-SCHERERAND R.D. MARTIN

52

TABLE 4. Body weight prediction equations calculated by three statistical models1 for Pan, Gorilla, Pongo, and Homo (continued) Species'

Homo

Long bone parameter Length of femur SURF femur

VOL tibia Length of tibia SURF humerus SURF radius

Age3

Statistic

ad

RMA MA LS RMA MA LS RMA MA LS RMA MA LS RMA MA LS RMA MA

a4

b

2.10 -0.82 2.31 -1.38 1.81 -0.07 ad 1.03 0.03 1.03 0.02 0.91 0.57 ad 0.58 1.55 0.54 1.88 0.50 2.08 ad 1.95 -0.29 2.15 -0.79 1.68 0.43 ad 0.88 0.93 0.86 1.03 0.73 1.59 ad 0.97 0.83 0.96 0.86 LS 0.75 1.73 Allometric reliability of predicted body weights: +_ 6,970~

r

W PE5

0.87

6.9

0.89

7.2

0.86

7.8

0.86

8.4

0.83

8.7

0.77

10.5

'RMA is recommended a s the most suitable model (see text) ". troglodytes a n d P.paniscus were combined for the given predictors (see text). :'Age range to which application is restricted; n-ad, nonadult specimens only; ad, adult specimens only. fForm of e uation log body weight = a lo (long bone dimension mm mm2 or mm") + b. "Mean preliction error (PE) in percent a n f correlation coefficient are given for each equation. bThe standard deviation of slopes (in percent) which indicates the allometric reliability of predicted body weights was determined by plotting each set of predicted body weights against a cranial dimension (see text).

&

conclusions concerning the reliability of a given variable a s a predictor. For a small sample, both the correlation coefficient and prediction errors may also reflect the accidental (and possibly distorted) distribution of data points in the limited set. An additional test was therefore performed to ensure that no bias occurred in body weights predicted with any given variable. For each species and age group separately, body weights were predicted for the entire sample available, using each of the 25 predictors. These 25 sets of predicted body weights were then plotted against a chosen cranial dimension (basicranial length) in a double logarithmic plot, and the resulting slopes and intercepts were compared. As expected, in the great majority of cases, slopes and intercepts were closely similar between the 25 sets. Nevertheless, deviating lines were found with a small number of variables, confirming that the correlation coefficient and prediction errors do not always reflect the relative quality of predictors. The variables concerned were accordingly discarded as predictors. For instance, for nonadult Gorilla (Fig. 4), tibia weight (and in consequence total bone weight) had to be excluded

as a predictor, despite its very high correlation with body weight (r = 0.99) and astonishingly low average prediction errors (2.1%)(see Table 3). Body weights predicted from this variable are greatly distorted, causing a marked overprediction for small individuals. This kind of bias results both from the small sample size available for very young individuals in making the prediction and from uncontrolled variations in bone weight. Degreasing of bones, which depends on the surface:volume ratio, renders this variable sensitive to experimental ("nonbiological") error, a s the degreasing process may be incomplete to varying degrees in the specimens investigated. Hence, bone weight can be used a s a predictor only if enough specimens covering the whole size range are available (as was the case for adult gorilla and both adult and nonadult chimpanzees and humans). Predicted body weights derived from the six best prediction sets display minimal slope differences when plotted in the manner described above. The range of the slopes is given in percent deviation (Table 4A-D) for each species and age group. This gives a n indication of possible variation of exponents determined in any subsequent allometric

PREDICTION OF BODY WEIGHT FOR HOMINOIDS

53

E E

23 5 5-

F 1 2.05 .-CI W

c

e

2

3 e

1.95

- 1.85 0

34

3.8

42

46

5.0

Y

Log,,, (predicted body weight, gm) Fig. 4. Slope deviations when a cranial dimension is plotted against predicted body weight calculated from 25 different predictors (illustrated for Gorilla; n = 63). Three predictors (indicated with small arrows) had to be discounted for body weight prediction due to distortion inherent in the small sample set available to derive the prediction equations (see discussion). The remaining 22 predictors (see Table 3) show only minor deviations (for deviation of slopes, see Table 4A-D).

TABLE 5. Correlation

of

predicted body weight and observed body weight with a cranial dimension (shown for basicranial length)’ Coefficient of determination’ Observed body weight Predicted body weight

Pan troglodytes Gorilla gorilla Pongo pygmaeus Homo sapiens

n-ad3 ALL n-ad ALL mad* ALL n-ad ALL

0.88 0.94 0.94 0.96 0.95 0.95 0.91 0.92

0.91 0.96 0.98 0.98 0.94 0.96 0.94 0.94

‘Note that, in all but one case (*), predicted body weight correlates better than observed body weight. ‘Coefficients of determination (T‘)when basicranial length is correlated with observed and predicted body weight, respectively (same individuals). jAge range: n-ad: nonadults only; ALL total age range.

study using predicted body weight a s the group have been applied for the following analyses. reference variable. Four criteria were hence applied together Advantages of predicted body weight in selecting the best predictors: 1)low preover observed body weight diction errors and high correlation coeffiWhen cranial measurements are correcients, 2) no distortion observed (test a s described above), 3 ) a selection of at least three lated with both predicted and observed body different long bones per species and age weights, predicted body weights correlate group, and 4) selection of dimensions that better than observed body weights (Table 5 ) . were as simple as possible. Combined vari- As predicted body weights are derived from ables (e.g., total SURF) have been omitted postcranial variables, cranial dimensions for this reason, although they often rank that correlate well with observed body among the best. For additional improve- weight serve as a n independent test for the ment, a combination of several prediction quality of the size variable “predicted body equations is recommended, in that it re- weight” compared with actual body weight. duces the effects of fluctuations in individ- In Table 5, coefficients of determination are ual bone dimensions. Accordingly, the mean given for double logarithmic plots of basicrapredicted body weights derived from the six nial length (which generally correlates best best predictors for each species and age with body weight across the species investi-

54

S. HARTWIG-SCHERER AND R.D. MARTIN

gated) against observed and predicted body weights, respectively. With only one exception, higher correlations are obtained with predicted body weights. This confirms the assumption that actual body weight can be greatly influenced by biological fluctuations (e.g., nutritional and pathological conditions) and developmental irregularities, while the overall size of long bones, used here to predict body weight, is inherently less variable. [Cock (1963) was able to show for chickens that body weight is much more affected than shank length by environmental fluctuations or irregularities in the developmental process.]

shows clear advantages in contrast to other reference variables, it may in fact be superior to actual body weight because of the more limited effects of environmental and developmental factors on individuals. With the exception of bone weight, the equations can be applied to fossil forms as well (Hartwig-Scherer and Martin, 1991). However, a note of caution should be added. Quite generally, prediction equations can be applied only a s long as the given fossil species closely corresponds with the extant model species. If, however, body weights are to be predicted for a species, such a s a n Australopithecus species, without any corresponding extant model, it would seem to be more appropriate to use a n interspecific approach (for instance, a combination of African apes and humans) rather than taking a single modern species as a model for comparison. However, this study has shown that the relationships between body weight and skeletal dimensions can differ greatly among the extant hominoids, so a n interspecific approach disguises rather than eliminates the profound scaling differences for certain skeletal dimensions among extant hominoid species. As a n alternative, it would be more revealing if several intraspecific models were to be applied separately to the given extinct hominid (Hartwig-Scherer, submitted), yielding a range of possible body weights instead of a compromise prediction that masks the major scaling differences between species.

CONCLUSIONS There is little doubt that body weight is, in many respects, a particularly suitable estimator of overall size for interspecific allometric studies. However, as actual body weights are commonly not available for museum specimens, various intervening variables have been used instead. This, however, may give rise to a n extreme distortion of results. Because the intervening variable itself may change in a n unknown manner with changing overall size, this may generate misleading conclusions, as has been illustrated with a number of examples in this study. Prediction of body weight as proposed here avoids this problem of intervening variables and may have major implications for future allometric studies, leading to possible reevaluation of numerous issues discussed in the literature. ACKNOWLEDGMENTS Reliable prediction of body weight for ontogenetic and static series of skeletons of This study depended above all on access to Pan, Gorilla, Pongo, and Homo with individ- specimens housed in various museum collecually recorded body weights is rendered pos- tions. For generous cooperation during work sible with the data presented in this paper. conducted by S.H.-S. a t these museums Using the equations given, body weight may thanks are expressed to Dr. Bruce Latimer be derived for any mature or immature skel- and Mr. Lyman Jellema (Cleveland Mueton of the great apes and humans, taking seum of Natural History); to Dr. Richard one or more of the long bone dimensions pre- Thorington, Dr. Jeremy Jacobs, and Ms. sented. To avoid limited applicability due to Linda Gordon of the Department of Mamthe incompleteness of the skeletal re- malogy (USMNH Smithsonian Institution); mains-important for both extant and fossil to Dr. Dwight Smith, Dr. David Hunt, and specimens-prediction equations were de- Mrs. Carol Butler of the Department of Anrived by using variables of only one long thropology (USMNH Smithsonian Institubone at a time. Results can be improved by tion); to Mr. Wolfgang Fuchs (American Muapplying several predictions to any given seum of Natural History, New York, NY);to specimen. Predicted body weight not only Mr. D. Howlett of the Powell-Cotton Collec-

PREDICTION OF BODY WEIGHT FOR HOMINOIDS

tion, (BirchingtonXent England); and to Dr. M. Louette and Dr. van Neer of the Musee de 1’Afrique Centrale (Tervuren, Belgium). Thanks are also due Bruce Latimer and three anonymous referees for helpful suggestions to improve the manuscript. The study was made possible by a grant to S.H.-S.from the A.H. Schultz-Stiftung (Zurich, Switzerland). LITERATURE CITED Aiello LC (1981a) Locomotion in the Miocene Hominoidea. In CB Stringer (ed): Aspects of Human Evolution. London: Taylor and Francis, pp. 63-97. Aiello LC (1981b)The allometry of primate body proportions. Symp. Zool. SOC. London 48:331-358. Aiello LC (1984) Applications of allometry: The postcrania of the higher primates. In H Preuschoft, DJ Chivers, WY Brockelman, and N Creel (eds): The Lesser Apes: Evolutionary and Behavioural Biology. Edinburgh: Edinburgh University Press, pp. 17G177. h e l l o LC, and Day MH (1982) The evolution of locomotion in the early Hominidae. In RJ Harrison and V Navaratnam (eds): Progress in Anatomy, Vol. 2. Cambridge: Cambridge University Press, pp. 81-97. Biegert J , and Maurer R (1972) Rumpfskelettlange, Allometrien und Korperproportionen bei catarrhinen Primaten. Folia Primatol. 27t142-156. Blaney SPA (1986) An allometric study of the frontal sinus in Gorilla, Pun and Pongo. Folia Primatol. 47:81-96. Calder WA (1984) Size, Function and Life History. Cambridge, MA: Harvard University Press. Clutton-Brock TH, Harvey PH, and Rudder B (1977) Sexual dimorphism, socionomic sex ratio and body weight in primates. Nature 269:797-800. Cochard LR (1985) Ontogenetic allometry of the skull and dentition of the rhesus monkey (Mucucu mulattu). In WL Jungers (ed):Size and Scaling in Primate Biology. New York: Plenum Press, pp. 231-255. Cock AG (1963) Genetic studies on growth and form in the fowl. 1. Phenotypic variation in the relative growth pattern of shank length and body weight. Genet. Res. 4:167-192. Cock AG (1966) Genetical aspects of metrical growth and form in animals. Q. Rev. Biol. 42:131-190. Corruccini RS, and Ciochon RL (1976) Morphometric affinities of the human shoulder. Am J. Phys. Anthropol. 45:19-38. Creel N (1986) Size and phylogeny in hominoid primates. Syst. Zool. 35t81-99. Dean MC, and Wood BA (1981)Developing pongid dentition and its use for ageing individual crania in comparative cross-sectional growth studies. Folia Primatol. 36t111-127. Dean MC, and Wood BA (1984) Phylogeny, neoteny and growth of the cranial base in hominoids. Folia Primatol. 43:157-180. Eveleth PB, and Tanner JM (1976)Worldwide Variation

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