Body size and postcranial robusticity of European Upper Paleolithic hominins

Body size and postcranial robusticity of European Upper Paleolithic hominins

Trenton W. Holliday Department of Anthropology, Tulane University, New Orleans, Louisiana 70118, U.S.A. E-mail: [email protected] Received 14 Novembe...

218KB Sizes 0 Downloads 44 Views

Trenton W. Holliday Department of Anthropology, Tulane University, New Orleans, Louisiana 70118, U.S.A. E-mail: [email protected] Received 14 November 2000 revised 10 July 2002 accepted 29 July 2002 Keywords: cortical area, bone strength, body mass, Upper Paleolithic.

Body size and postcranial robusticity of European Upper Paleolithic hominins The robust diaphyses of Pleistocene hominins are said to indicate higher activity levels in these prehistoric humans than among people today. Thus, it could be argued that the prediction of body mass from fossil lower limb diaphyseal cortical area (CA) using recent human regressions might lead to erroneously high body mass estimates. This study uses three body mass prediction formulae based on the following features: reconstructed femoral 80% (subtrochanteric) CA, femoral head diameter (FH), and bi-iliac breadth and stature (BIB-St) among European Early and Late Upper Paleolithic (EUP and LUP) and recent humans from Africa and Europe. All three methods produce similar body mass estimates for all groups studied, including recent humans. Gleaning behavioral differences from these data is more difficult, as no significant differences in CA were found among the fossil and recent Europeans. It has been suggested that the EUP had less robust diaphyses than their LUP counterparts. However, here this result is only obtained when CA is size-standardized to femoral length3 (Ruff et al., 1993, Am. J. phys. Anthrop. 91, 21–53 Trinkaus et al., 1998, in Neandertals and Modern Humans in Western Asia, pp. 391–404, New York: Plenum). This should not be interpreted as evidence for lower activity levels in the EUP, but rather as an artefact of standardization, for as Wolpoff (1999), Am. J. phys. Anthrop. 109, 416–423 points out, these standardized variables are extremely sensitive to limb length differences, and the EUP have longer limbs than their LUP counterparts. With this in mind, these data do not support a pattern of behavioral differences between EUP and LUP humans, and therefore more sensitive measures than CA may be required to detect such differences.  2002 Elsevier Science Ltd. All rights reserved.

Journal of Human Evolution (2002) 43, 513–528 doi:10.1053/jhev.2002.0590 Available online at http://www.idealibrary.com on

Introduction Long bone diaphyseal morphology has in recent years proven a treasure trove of information about Pliocene and Pleistocene hominins. In particular, the highly phenotypically plastic nature of diaphyses has lent itself to analyses of both body mass and activity levels in pre-Holocene humans (McHenry, 1988; Ruff et al., 1993; Grine et al., 1995; Trinkaus, 1997; Trinkaus et al., 1999; Pearson, 2000). In this paper, both of these features—body mass and activity levels—will be examined in European Upper 0047–2484/02/100513+16$35.00/0

Paleolithic humans, for the gleaning of each of these attributes from fossil diaphyses is intimately tied to the other. First, with regard to body mass, McHenry (1976, 1988), Aiello (1981), and Rightmire (1986) have all used some measure of lower limb diaphyseal area (either total area, cortical area, or one of its components) as a predictor of body mass among anthropoids in general and hominins specifically. From a biomechanical perspective, it makes sense that lower limb diaphyseal morphology is closely tied to body mass, since in humans the lower limb supports the body’s weight,  2002 Elsevier Science Ltd. All rights reserved.

514

. . 

and especially since during locomotion it transmits forces related to, but many times larger than, body mass (Crowinshield et al., 1978). In order to function effectively, bones in the lower limb must resist these forces and, since a bone’s strength is (at least in part) proportional to its cross-sectional area (Levangie & Norkin, 2001), one would expect greater body mass to result in even larger diaphyseal (and epiphyseal) dimensions in the lower limb. A landmark study of hip radiographs of individuals of known body mass indicates that this is in fact the case (Ruff et al., 1991). In their study, Ruff and colleagues demonstrated that among recent humans diaphyseal cortical area continues to track changes in body mass that occur long after the onset of skeletal maturity, while femoral head diameter is more tightly correlated with body mass at the onset of skeletal maturity. This suggests that diaphyseal morphology may be one of the most accurate features from which to predict body mass in prehistoric human skeletons. Yet while diaphyseal morphology is highly correlated with body mass, it is not molded by body mass alone, but rather is also influenced by the bone’s biomechanical environment, as has been demonstrated in laboratory studies (e.g., Goodship et al., 1979; Woo et al., 1981; Simkin et al., 1989; McCarthy & Jeffcott, 1992; Mosley et al., 1997; Mosley & Lanyon, 1998). Specifically, many workers have demonstrated that animals subjected to low or moderate exercise regimes tend to lay down new bone either through subperiosteal expansion, medullary cavity contraction (i.e., endosteal apposition), or both. Thus, one could predict that more active humans would tend to have larger cross-sectional areas in their lower limb bones than those of the same body mass who are less active. Importantly, however, there also appears to be a threshold exercise level, i.e., too much exercise, above which some bones respond

negatively via suppression of normal growth mechanisms (Forwood & Burr, 1993). Using this experimental research as a guide, anthropologists have tried to glean activity patterns from the diaphyseal morphology of prehistoric human skeletons. In one of the earliest such studies, Lovejoy et al. (1976) applied biomechanical principles to the tibiae of prehistoric skeletons from Libben and other sites in Ohio, as well as to medical school cadavers representative of more sedentary, ‘‘industrialized’’ humans. These workers were specifically interested in platycnemia, or antero-posterior thickening of the tibial shaft—a feature that shows up in higher frequencies in nonindustrialized human populations. Through the application of the engineering principle of beam theory to actual tibial cross-sections (from both platycnemic and nonplatycnemic bones) they argued that higher torsional and bending stresses associated with the rigors of prehistoric subsistence led to the buildup of bone along the tibia’s A–P axis. Since that original study, there has been a significant amount of research into biomechanical changes in long bones associated with the transition from foraging to agriculture in prehistoric North American groups. For example, workers such as Larsen & Ruff (1991) documented a decline in lower limb (femoral and tibial) diaphyseal strength with the abandonment of hunting and gathering and the adoption of agriculture in different regions of North America. They posited that this shift was due to a reduction in mobility and long-distance walking associated with the transition from foraging to farming. In contrast, Bridges, working with skeletons from different regions in North America, found the opposite pattern—that in general agriculturalists tended to have stronger diaphyses than the hunter-gatherer populations who preceded them in their region (Bridges, 1989, 1991). However, more recent work by these same researchers has demonstrated that the effect of the transition from foraging

     to farming on long bone diaphyseal strength was not quite so simple. For example, Bridges and colleagues have recently identified a more complex pattern, in which the adoption of agriculture in west-central Illinois led to increased humeral and femoral strength in females, but also promoted a reduction in right arm (humeral) strength in males (Bridges et al., 2000). In a similar vein, Ruff (1999, 2000a) has shown that Great Basin and other hunter-gatherer groups had more robust femora (but not humeri) than did Native American groups who practiced agriculture. The huntergatherer groups also exhibited a higher degree of sexual dimorphism in diaphyseal strength. Ruff attributes the first observation (greater femoral robusticity) to either more rugged terrain and/or greater huntergatherer mobility, and the second observation (high sexual dimorphism) to the generally higher mobility of males in hunter-gatherer societies. Yet another factor often considered in discussions of the transition from foraging to farming is whether health related to nutrition improved or declined with the rise of agriculture, with a growing consensus that it deteriorated with the advent of farming (Larsen, 1995). Obviously, then, there could be effects on farmers’ skeletons that reflect a more protein-poor diet, and diaphyseal cortical area reduction could be one of them. Yet, Bridges (1989, 1991) argued that nutritional differences alone could not be responsible for these changes because: (1) the agriculturalists, who presumably had a poorer diet, nonetheless had a tendency toward greater diaphyseal cortical areas, and (2) increases in cortical area were not consistent from bone to bone or even from section to section on the same bone. Rather, in some sections (e.g., female proximal humerus), the foragers had larger cortical areas than the agriculturalists. This suggests that activity differences (which may be site-specific) are the more likely cause of

515

robusticity (traditionally defined as diaphyseal thickness standardized to bone length; see Pearson, 2000) differences than nutrition, the effects of which one would assume to be more systematic (and see Churchill, 1996). With these data (both experimental and bioarchaeological) in mind, it would seem that the prediction of body mass from diaphyseal cross-sectional area using formulae derived from recent, less active, industrialized humans could tend to overestimate the body mass of Pleistocene foragers (as has been pointed out by Ruff et al., 1991). However, by the same token, because the diaphysis is modeled and remodeled according to its mechanical environment, one may be able to detect differences in behavior between different groups of Pleistocene foragers, such as, for example, those associated with the Upper Paleolithic. Along this line of inquiry, a question that has been addressed by workers such as Churchill & Holt (Churchill, 1994; Holt, 1998, 1999; Holt & Churchill, 2000), and Pearson (2000) has been to ascertain whether differences in behavior and/or activity levels are manifest between European Early and Late Upper Paleolithic hominins (EUP and LUP, respectively). One conclusion reached by at least some of the above workers is that humans from the Late Upper Paleolithic tend to be more robust (i.e., have greater diaphyseal bone strength and/or crosssectional size relative to bone length) than are those from the Early Upper Paleolithic. While a specific temporal boundary separating the ‘‘Early’’ vs ‘‘Late’’ Upper Paleolithic is not agreed upon by all, the current study examines femoral diaphyseal cortical area differences between Early and Late Upper Paleolithic samples, which have here been divided at 20,000 BP. The object of this study is to determine if there is a difference in lower limb diaphyseal cortical area between EUP and LUP Europeans, and if so, whether such a difference is due to body

. . 

516

mass differences, or rather to differences in behavior or activity levels. Materials and methods Femoral diaphyseal cortical area at 80% of diaphyseal length (i.e., just distal to the lesser trochanter) was reconstructed for a sample of fossil and recent humans from biplanar radiographs. These radiographs were taken by the author using a Lumix 70-II dental X-ray machine. A radio-opaque wire was used to mark the location of the 80% section. Cross-sectional cortical area was reconstructed from the radiographs in the following manner: measurements of A–P and M–L radiographs were taken and corrected for parallax by comparing the radiographic dimensions to measurements taken on the actual bone. Areas were then estimated using ellipse formulae. First, total area (TA) was estimated as (A–P breadth/ 2) · (M–L breadth/2). Medullary area (MA) was calculated as (medullary cavity A–P breadth/2) · (medullary cavity M–L breadth/ 2). Cortical area was then computed as TA–MA. This technique does not involve molding the external contours of the specimen, and therefore there may be a danger of overestimating CA using the ellipse vs molded external contour method (Ruff, personal communication). This possibility was tested by comparing the 80% sections of 22 Upper Paleolithic and Mesolithic specimens measured by the author with those reported for the same specimens in Holt (1999), who used the external contour method. The predicted CA values are fairly highly correlated (r=0·92), but, on average, the ellipse method used here produced a CA that was 9·4% larger than that produced using the molded contour method, with an associated range from 28·8% larger (Grotte des Enfants 4) to 9·4% smaller (Veyrier 1). This would seem to indicate that the two methods tend to produce different results. While the external contour method is in all

likelihood the more accurate of the two, this as yet remains uncertain. In any case, in the absence of evidence to the contrary, any bias introduced by this method will be assumed to be consistent across all groups, fossil and recent, and thus would not influence the results. Radiographs were taken on a total of 28 European Upper Paleolithic skeletons and, for comparison, 203 recent human skeletons from Europe and Africa (Table 1). For analyses not involving cortical area, postcranial osteometrics are available for an additional 18 Upper Paleolithic and 251 recent human skeletons (Table 1). In addition to femoral 80% cross-sectional cortical area, the measurements used in the analyses are femoral head diameter, femoral bicondylar and diaphyseal length, and bi-iliac breadth. All measurements were taken by the author, except where indicated otherwise in Table 1. Size-standardization procedures The investigation of cortical area (CA) and other diaphyseal variables as measures of bone strength brings with it a set of scaling problems. Let us assume one wishes to use CA as a measure of postcranial robusticity. The fact that it is so highly correlated with body mass could mean that by using raw CA as an indicator of robusticity, one is merely calling heavier individuals ‘‘robust’’. We must therefore take size into account when discussing bone strength, and it is for this reason that Ruff et al. (1993) have defined postcranial robusticity as ‘‘the strength or rigidity of a structure relative to the mechanically relevant measure of body size’’ (Ruff et al., 1993: 25). It is also for this reason (among others discussed below), that workers beginning with Lovejoy et al. (1976) have used bone length (or powers thereof) as the standard for measures of bone strength, such as CA. There are multiple means by which to size-standardize cross-sectional data,

     Table 1

Table 1

517

Upper Paleolithic and Recent human samples included in the analyses Early Upper Paleolithic specimens Barma del Caviglione 11 Cro-Magnon 1* & 2* Dolnı´ V stonice 3, 13, 14* & 16* Grotte des Enfants 4*, 5*, 6* Paglicci 25

Paviland 1* Pavlov 1* P edmostı´ 1, 3, 4, 9, 10, 142 La Rochette 1

Late Upper Paleolithic specimens Arene Candide 1*, 1 (Il Principe)*, 2*, 4*, 5*, 10* Barma Grande 2* Bichon 1* Bruniquel 24* Cap Blanc 1* Chancelade 1* Grotte Continenza 1 Grotte des Enfants 3* Neuessing 2*

Oberkassel 1* & 2* Parabita 1 & 2 Le Peyrat 5* & 6* Le Placard 16 Romito 3 & 4 St Germain-la-Rivie`re 4* San Teodoro 4 Veyrier 1*

(continued)

Recent human samples

Region/group

Females with CA/Total

Males with CA/Total

Sex Indeterminate with CA/Total

Europe Bohemia Germany Norse Romano-British French Bosnia

0/16 11/11 8/8 15/25 0/9 17/29

0/21 18/22 12/12 15/25 0/11 20/43

0/3 0 0 0 0 0

North Africa Egypt Nubia Sudan

18/36 2/7 11/18

11/31 8/13 14/29

0 0 0

0/19 3/3 0/5 2/5

0/27 6/7 0/3 12/16

0 0 0 0

Sub-Saharan Africa East Africa3 Pygmy San West Africa

*Radiographic data are available. 1 Data from Verneau (1906). 2 Data from Matiegka (1938). 3 Data courtesy of C. B. Ruff.

depending, in part, on which bone is being investigated, and whether it is weightbearing or nonweight-bearing. However, for the purposes of this paper, only one method will be used—CA will be divided by femoral length to the third power, then multiplied by 108, following Ruff et al. (1993). Ruff et al. (1993) argued that purely axial loads on

lower limb diaphyses would be proportional to body mass, and therefore CA should be scaled to body mass, or a proxy of it. In one sense, femoral length3 is expected to be a good size measure, since femoral length, as a linear measure, is theoretically proportional to body mass, a cubic measure, when the former is raised to the third power. Femoral

518

. . 

length3 may not be an ideal standardizer for reasons to be elucidated in the Discussion. Indeed, Ruff and colleagues, who first used the method, incorporated correction factors to account for differences in body shape, and later replaced the method with direct estimation of body mass (see, for example, Trinkaus et al., 1999; Ruff, 2000b). Nonetheless, the femoral length3 method remains prominent in the current anthropological literature (e.g., Bridges et al., 2000; Ledger et al., 2000; Stock & Pfeiffer, 2001). The femoral length3 method also has an advantage in that it is a simple procedure, the results of which should be somewhat consistent with other, more complex standardization methods (e.g., those found in Trinkaus, 1997; Trinkaus et al., 1998; and see Pearson, 2000). Body mass for Upper Paleolithic and recent humans was estimated using three formulae derived from the work of Chris Ruff. The first of these formulae predicts body mass from femoral 80% crosssectional cortical area (Ruff et al., 1991), the second from femoral head diameter (Ruff et al., 1997), and the third from bi-iliac breadth and stature (Ruff et al., 1997). The sex-specific formulae reported by Ruff and coworkers were used. When sex could be readily assessed from pelvic remains, body mass was predicted using the appropriate (i.e., male vs. female) formula. For individuals of unknown sex, the body mass value assigned to them was the arithmetic average of the results of the male and female predictive formulae. Stature was also predicted for all individuals in the skeletal sample, using Trotter & Gleser’s (1952, 1958) formulae for the femur. As with body mass, sex-specific formulae were used. Individuals for whom sex could not be determined were given an estimated stature that was the arithmetic mean of the male and female predicted stature estimates. Importantly, the stature of EUP skeletons was predicted using

African-American formulae, while those of the LUP humans were predicted using Euroamerican formulae. This follows from their differences in body proportions, as the EUP have a longer, more linear, African-like body shape, while the LUP more closely resemble modern-day Europeans (Holliday, 1997, 1999; Pearson, 2000). Among the recent sample, the Europeans’ stature was predicted using Euroamerican formulae, sub-Saharan Africans’ stature was predicted using African-American formulae, and the stature of North Africans was the average of their predicted stature using both formulae. Body mass predictions of the groups derived from the three predictive formulae were then compared using analysis of variance (ANOVA) and associated Scheffe´’s tests. The former test is used to determine if there is a significant difference in predicted body mass among the groups studied; the latter is used in cases where a significant difference is detected in order to determine which of the group(s) is responsible for the difference. Similar univariate tests (Student’s t tests) were applied to both CA and standardized CA for the two fossil samples. In order to maximize fossil sample sizes, and therefore statistical power, the analyses presented here are based on a combined sample of males and females; male and female subsamples yield broadly similar results. Results Table 2 shows summary statistics for the Upper Paleolithic and recent humans, including sex-specific mean body mass estimates, bi-iliac breadth and predicted stature. Note that the EUP and LUP humans are not heavier than recent Europeans based on the femoral head and bi-iliac breadth-stature methods, a result consistent with Ruff et al. (1997). Using femoral cross-sectional cortical area, only the LUP sample evinces higher (albeit not

    

519

Table 2 Means, standard deviations, and sample sizes for predicted body mass (kg), predicted stature (cm), and bi-iliac breadth (mm): fossil and recent humans CA-predicted1 7 8

Group

EUP

LUP

Europeans

North Africans

Sub-Saharan Africans

X S.D. n X S.D. n X S.D. n X S.D. n X S.D. n

Group

EUP

LUP

Europeans

North Africans

Sub-Saharan Africans

71·70 6·53 7 74·07 6·27 11 71·78 3·87 65 65·80 3·11 33 62·58 3·74 18

72·86 2·21 2 58·10 6·79 6 55·52 7·87 51 44·45 6·51 31 44·27 16·46 5

Bi-iliac breadth 7 8 X S.D. n X S.D. n X S.D. n X S.D. n X S.D. n

272·0 16·2 6 270·8 18·6 10 278·3 16·7 127 254·7 13·5 61 234·6 18·0 49

FH-predicted2 7 8

265·0 — 1 270·9 13·8 4 264·2 16·6 89 245·0 14·2 46 234·2 15·0 29

65·84 10·03 10 67·73 6·60 14 69·28 7·33 134 59·01 7·63 73 54·65 8·50 53

65·64 6·58 6 63·92 5·95 7 59·00 5·24 98 53·37 4·60 61 52·06 5·75 32

BIB-ST-predicted3 7 8 69·58 7·34 6 67·36 8·23 6 70·96 7·35 126 61·28 5·53 60 53·64 8·60 49

56·13 — 1 60·34 4·34 4 56·61 5·12 87 51·86 4·69 46 49·30 6·45 29

Predicted stature 7 8 170·0 7·8 12 168·5 7·0 15 171·6 5·8 311 167·4 5·9 75 164·7 8·2 62

157·6 3·5 6 158·4 5·6 8 157·2 5·4 171 155·3 5·0 63 152·2 7·3 47

1

Predicted from femoral 80% section cross-sectional area (CA). Predicted from antero-posterior femoral head diameter (FH). 3 Predicted from bi-iliac breadth and estimated stature (BIB-ST). 2

statistically significantly higher) mean body masses than do recent Europeans. However, this result should be taken with caution, as Ruff and colleagues (1991) strongly cautioned against using their formulae to predict body mass for other samples. Among recent humans, the Europeans are consistently found to be the heaviest group. In contrast, the sub-Saharan Africans have the lowest predicted mass based on all three

predictive methods. This result is expected, given the well-documented human adherence to Bergmann’s (1847) rule. ANOVA and associated Scheffe´’s tests show a consistent pattern among all three body mass prediction methods. Table 3 indicates that for cortical area-predicted body mass, the combined-sex recent Europeans are significantly heavier than the North Africans. The combined-sex Scheffe´’s test

. . 

520 Table 3

ANOVA and Scheffe´’s test for predicted body mass [mass predicted from femoral 80% cortical area (CA)] DF

Sum-sq.

ANOVA Table—Body mass (from CA) Among groups 4 5772·877 Within groups 226 25205·77 TOTAL

Scheffe´’s test EUP LUP Europe North Africa 1 2

Mean sq.

Fs

P

1443·219 111·53

12·94

<0·0001

230

30978·65

LUP

Euro

N. Africa

SS Africa

ns1

ns ns

Significant2 Significant Significant

Significant Significant ns ns

Not significantly different at P<0·05. Significantly different at P<0·05.

indicates recent Europeans are not significantly heavier than the sub-Saharan Africans. However, this is probably due to the male bias among individuals for whom CA was measured in the sub-Saharan African sample, since sex-specific Scheffe´’s tests find significant differences between European and sub-Saharan African males and females. With regard to the fossils, the EUP and LUP samples are significantly heavier than recent Africans, but not recent Europeans. In Tables 4 and 5, Scheffe´’s tests reveal that for femoral head-predicted (Table 4) and bi-iliac breadth/stature predicted (Table 5) body mass, we have a similar result in that the recent Africans (both in North and sub-Saharan Africa) are significantly lighter than recent Europeans and the European Upper Paleolithic samples. Note, too, that no significant difference in predicted body mass is detected between the LUP and EUP samples; the combined-sex mean body mass differs no more than 3·5% between the two fossil groups. With regard to gleaning behavior from reconstructed cortical area, recall that it has been suggested by some workers that the EUP have less robust diaphyses than their

LUP counterparts. As shown in Table 6, mean 80% cortical area values for the EUP and LUP samples are virtually identical, and thus Student’s-t test finds no significant difference between the EUP and LUP humans. However, as discussed earlier, workers rarely look at ‘‘raw’’ cortical area—rather, they routinely standardize it to a power of long bone length. Table 6 also shows Student’s t test results for cortical area standardized by cubed diaphyseal femur length. When this standardization method is used, the LUP do have significantly more robust shafts than the EUP, as indicated by the t-test. Discussion Regarding body mass, the analyses presented above demonstrate that, like recent Europeans, Upper Paleolithic Europeans are characterized by high predicted body mass, and this result is obtained via all three prediction methods, not just via analysis of cortical area. Also, while EUP and LUP humans are significantly heavier than modern-day Africans, they (the Upper Paleolithic Europeans) are not significantly heavier than Europeans today. All three

     Table 4

ANOVA and Scheffe´’s test for predicted body mass [mass predicted from femoral head diameter (FHAP)] DF

Sum-sq.

Mean sq.

ANOVA Table—Body mass (from FHAP) Among groups 4 12023·41 3005·852 Within groups 489 29445·18 60·21508 TOTAL

Scheffe´’s test EUP LUP Europe North Africa 1 2

Table 5

521

Fs

P

49·92

<0·0001

493

41468·58

LUP

Euro

N. Africa

SS Africa

ns1

ns ns

Significant2 Significant Significant

Significant Significant Significant ns

Not significantly different at P<0·05. Significantly different at P<0·05.

ANOVA and Scheffe´’s test for predicted body mass [mass predicted from stature and bi-iliac breadth (ST-BIB)] DF

Sum-sq.

Mean sq.

ANOVA Table—Body mass (from ST-BIB) Among groups 4 11915·69 2978·923 Within groups 414 31034·66 74·96294 TOTAL

Scheffe´’s test EUP LUP Europe North Africa 1 2

Fs

P

39·74

<0·0001

418

42950·35

LUP

Euro

N. Africa

SS Africa

ns1

ns ns

Significant2 Significant Significant

Significant Significant Significant Significant

Not significantly different at P<0·05. Significantly different at P<0·05.

prediction methods produce similar results, as has been reported elsewhere (Ruff et al. 1997). While it may appear from the data reported in Table 2 that the CA body mass estimates are consistently higher than those predicted by either the bi-iliac breadth-stature or femoral head size, this is an artefact of sampling. In those individuals

for which all three methods can be employed, the three methods produce nearly identical mean body mass estimates. This would seem to suggest that using equations derived from recent, more sedentary humans to predict body mass from CA are not biased to the extent that they produce erroneously high body mass estimates.

. . 

522 Table 6

Student’s t test results—80% cross-sectional cortical area, standardized and unstandardized, EUP vs. LUP Unstandardized CA EUP Mean=514·23, S.D.=109·5 LUP Mean=514·19, S.D.=120·8 Student’s t-statistic=0·0008; P=0·99; 26 d.f. (not significant) Standardized CA (CA/FL3) EUP Mean=560·0, S.D.=108·4 LUP Mean=734·0, S.D.=147·6 Student’s t-statistic= 2·655; P=0·0142, 23 d.f. (significant)

Table 7

A Comparison of Grotte des Enfants 4, an EUP specimen, with Neuessing 2, an LUP specimen—Standardized CA (CA/FL3)

Grotte de Enfants 4 Neuessing 2

CA

FL

FL3

Standardized CA

725·4 506·1

491 422

118,370,771 75,151,448

613·12 675·55

It is more difficult, however, to glean behavioral differences from these data. In particular, there is no significant difference in ‘‘raw’’ cortical area between the EUP and LUP humans. When standardized by femoral length raised to the third power, however, a significant difference is detected. In this case, I agree with Wolpoff, who has recently argued that this and similar methods of standardization are problematic (Wolpoff, 1999). First, he notes that beam theory was developed for use with structures of uniform material distribution and density—something we know not to be the case in bone. Yet more importantly, he points out that when bone length is raised to a high power, it has an undue influence on measures of bone strength standardized to it. This is particularly problematic for the question at hand, since the EUP have longer limbs than the LUP (Jacobs, 1985; Holliday, 1997, 1999; Formicola & Giannecchini, 1999), and thus, when the long limb bones of the EUP humans are cubed, this has an overarching effect on their relative cortical area. Wolpoff’s (1999) point is illustrated in Table 7. Grotte des Enfants 4, an EUP specimen, has a cortical area

some 43% larger than that of Neuessing 2, an LUP specimen. In terms of femoral diaphyseal length, the Grotte des Enfants specimen has a femur that is ca. 16% longer. However, when femoral length is cubed, the resulting enormous number has a sizable influence on the standardized cortical area, so much so that Neuessing 2 is now calculated to be more robust. This could be a real result—perhaps, once corrected for overall size, Neuessing 2 is in fact more robust than Grotte des Enfants 4. In order to address this issue we need to look at how cortical area is scaling, to see if and how it is allometric. Figure 1 shows the simple bivariate allometric relationship between the square root of cortical area regressed on the cube root of femoral head-predicted body mass. Femoral head– predicted body mass was chosen because its sample size was larger than that of the bi-iliac breadth/stature prediction (which also yields similar results). The recent human RMA line drawn on the plot indicates that this is a positive allometric relationship (slope of 2·53 vs. expected isometric slope of 1·0). This is to be expected, since bone strength is proportional to

    

523

Figure 1. Log square root of femoral 80% cortical area (mm2) regressed on log cube root of femoral head-predicted body mass (kg). Crosses=recent humans; triangles=EUP; squares=LUP. The recent human reduced major axis line is shown.

cortical area, and therefore cortical area must increase exponentially with increasing mass in order to provide sufficient strength to counteract the forces related to body mass that act upon it. Importantly, though, it has been shown with pan-primates data that despite a similarly positive allometric trend, larger primates still tend to have lower bone strength indices than smaller ones, simply as a function of overall greater size (Jungers & Burr, 1994). In other words, bone strength or robusticity cannot keep pace with increasing body size, with behavioral consequences. For example, an elephant has relatively thicker limb bone diaphyses than does my pet cat, but my cat can leap across the floor a distance easily four times his body length; an elephant cannot. With this in mind, it is theoretically possible that larger humans are less robust (i.e., have relatively weaker diaphyses) than smaller ones—an interesting avenue for future research. Recall, however, that size is unlikely to play a role among these fossil samples, as

there is no significant difference in predicted body mass between the EUP and LUP samples. Likewise, in Figure 1 there appears to be little difference in scaling between the recent humans, shown as crosses, the EUP humans, shown as triangles, and the LUP humans, shown as squares. While a higher percentage of the LUP sample falls above the recent human line than do the EUP specimens, the three groups are essentially indistinguishable from each other. While not shown in the figure, the fossil samples have slopes with wide 95% confidence limits, and are thus indistinguishable from each other and from the recent humans. Likewise, as noted earlier, EUP and LUP humans have roughly equivalent body masses, and their cortical areas are roughly equal relative to their overall size. Note, too, the position of the two specimens discussed earlier. Grotte des Enfants 4 falls above the recent human regression, while Neuessing 2 falls just below it. Recall that scaling cortical area to femoral length cubed made Neuessing 2

524

. . 

more robust than Grotte des Enfants 4, something that does not appear to be the case. The EUP/LUP comparison provides a clear example of why standardizing diaphyseal measurements to bone length (especially to powers of bone length) may provide spurious results. Bone lengths between the two roughly equal-mass groups (EUP and LUP) tend to be significantly different (with the EUP possessing longer limb bones), yet their diaphyseal dimensions, when not scaled to bone length, generally are not. Such a pattern holds for both the lower limb data presented here, and the upper limb data presented in Churchill (1994) (TH, personal observation). Thus, when one scales EUP vs. LUP humans’ diaphyseal dimensions to powers of bone length, one may very well detect a significant difference between the two groups in those ‘‘adjusted’’ diaphyseal measurements, but this difference is largely tracking limb length differences, and does not reflect diaphyseal strength per se. The work of Holt (1998; 1999) supports this assertion. In her 1998 paper, Holt argued that there was an increase in lower limb robusticity from the EUP to the LUP. Yet in 1999, Holt came to the opposite conclusion—that the EUP were in fact more robust in their lower limbs than were the LUP. This difference in results is due to Holt’s abandonment in her 1999 dissertation of the standardization procedure described above (i.e., CA/long bone length3) that she used in the 1998 paper. The above evidence thus calls into question the use of powers of bone length to standardize diaphyseal cross-sectional properties. As was demonstrated in Table 6, bone length raised to the third power is an enormous number that drives much of the variability in the resulting index, such that individuals with long limbs are consistently less robust than individuals with shorter limb bones, a point first made by Wolpoff (1999).

In the current literature one can find, other, more appropriate scaling factors for lower limb CA. For example, Ruff (2000b) and Polk et al. (2000) have both argued that in the lower limb, CA is most appropriately scaled against body mass, since CA reflects resistance to axial compressive loading of the limb. However, these same workers argue that the most appropriate scalar for J (polar moment of area) is body mass multiplied by bone length, since J reflects resistance to bending stresses, which are a function of both beam (bone) length and body mass (Polk et al., 2000; Ruff, 2000b; and see Jungers & Burr, 1994). In this case, scaling a property such as J to bone length seems appropriate. This is especially true in cross-species comparisons, where differences in limb length are often functionally related. In this regard, Kimura (1991, 1995) has argued that primates possess more robust diaphyses than other mammals, and attributed this pattern to primates’ largely arboreal adaptation; i.e., more diaphyseal strength is needed in a complex arboreal environment. However, many other orders of mammals also have a large number of arboreal species, and primates also possess longer limbs relative to their body mass than other mammals (Alexander et al., 1979). With this in mind, Polk et al. (2000) tested Kimura’s hypothesis and demonstrated that once scaled to limb length times body mass, differences in J between primates and other mammalian orders disappear. Yet standardizing cross-sectional properties by bone length in the above manner could be problematic, at least within the limited size range of a species characterized by low sexual dimorphism, such as Homo sapiens (see Ruff et al., 1993: 30). As discussed in my response to Pearson (2000), while from a beam theory perspective a longer bone is weaker in axial compressive loads and less resistant to bending than a shorter bone with the same diaphyseal

     cross-sectional properties, it remains uncertain if this is truly meaningful from a biological perspective (Holliday, 2000). For example, cold-adapted modern humans tend to be characterized by relatively foreshortened limbs, particularly, but not exclusively, in their distal segments (Trinkaus, 1981; Holliday, 1997). Therefore, an important question is whether cold adaptation (or any other factor) could bring about a change in limb bone length without a concomitant increase or decrease in diaphyseal diameter. Experimental work may provide insight into this issue. In one such study Riesenfeld (1973) exposed growing rats to either heat or cold, and found that cold-exposed rats had significantly shorter limbs than either controls or those raised in hot environments. More importantly, however, he noted that these same cold-exposed rats with foreshortened limbs had more robust limb bones than either controls or heat-exposed rats. In his study robusticity was calculated as a bone’s length divided by the cube root of the bone’s weight. What we may infer from these results is that while bone length reduced due to exposure to cold, cortical thickness (as induced from bone weight) does not appear to have experienced a concomitant decrease. While exercise levels among the rats were not controlled, this result is not due to an increase in body mass—the cold-exposed rats weighed less than controls. Therefore to speak of cold-exposed rats as ‘‘more robust’’ may not imply any specific cortical bone response to body mass or activity level, but rather is likely to be the spurious result of limb bone shortening1. These observations bring us back to exactly how one should define ‘‘robusticity’’. Robusticity has traditionally been defined as 1 An alternative interpretation, given the results of Jungers & Burr (1994) is that the smaller, cold-exposed rats are more robust as a by-product of their smaller size. Future animal research into this issue could prove particularly fruitful, especially in experimental outcomes in which cold-exposed animals evince both shorter limbs and a larger body size.

525

bone thickness relative to length (Pearson, 2000). Yet the above experimental results, as well as the seemingly false EUP–LUP dichotomy, suggest that differences in bone length, at least within a single species, where significant locomotor differences are unlikely, are often too great to make this definition meaningful. It is for this reason that a definition of robusticity (or ‘‘residual strength’’—Pearson, 2000) as bone strength relative to an appropriate measure of size (Ruff et al., 1993) is preferable to the older definition. This leaves the question of how one should scale diaphyseal cross-sectional properties such as CA. As discussed above, one could make the argument (as both Ruff, 2000b and Polk et al., 2000 have) that since lower limb resistance to axial compressive loads is reflected in CA, and since CA is so intimately tied to body mass, that body mass is the most appropriate measure against which to scale CA. While the case of the upper limb is somewhat more complex, given that in humans it is non-locomotor, Ruff (2000b) found that human humeral diaphyseal properties scaled in much the same way as their lower limb counterparts. Thus, body mass would appear to be an appropriate scale variable for both limbs. How one predicts body mass then becomes an issue. One cannot ignore the arguments of Smith (1996) that predicting body mass for fossils will increase the amount of error in one’s analysis. Yet the fact that the three methods used here provide similar estimates suggests that different methods yield comparable results, and produce mass estimates that are therefore reliable (and see Ruff et al., 1997). However, one should not use CA to predict body mass, and then scale CA to that body mass prediction, for the obvious reason that to do so would be tautological. Ruff (2000b) makes a good case for the use of nonbiomechanical (e.g., bi-iliac breadth/stature)

. . 

526

predicted body mass estimates, given the potential for circularity of argument when using lower limb measures that also respond to biomechanical forces related to body mass, such as femoral head diameter, to scale diaphyseal measures. However, bi-iliac breadth is only rarely preserved in the paleontological record; stature never is. Also, Pearson (2000) has shown that residuals from the diaphyseal–epiphyseal relationship may provide important clues into bone strength. Thus, judicious use of epiphyseal measures such as femoral head diameter to study the relative size of diaphyseal measures such as CA may in fact be appropriate (see also Ruff, 2000a). Conclusions In conclusion, these analyses do not support the hypothesis that the LUP humans had more robust femoral diaphyses (at least as reflected in CA) than did the EUP. Differences in CA between the groups are only manifest when a ratio of CA to femoral length3 is employed, and such correction factors appear to lead to erroneous results driven by limb length differences alone. The relationship of CA to predicted body mass, a more appropriate method of sizestandardization, demonstrates that there is little difference in the relationship of CA to size among recent and Upper Paleolithic humans. However, some words of caution are warranted. First, it may be that crosssectional cortical area at the 80% section is not as sensitive to biomechanical factors due to locomotion than is, say, the 50%, or midshaft section. Second, CA is a relatively crude measure of diaphyseal strength, as the same cortical area, distributed in different ways about a section’s centroid, may have very different resistance to bending stresses (Ruff, 2000b). In other words, diaphyseal shape may be more important in terms of bone strength than diaphyseal size. Therefore, more sensitive measures of bone

strength, such as polar moments of area, may provide better insight into any possible behavioral differences between EUP and LUP humans. In this regard, Holt & Churchill’s (2000) finding of significant shape differences in the midshaft femur between EUP and LUP humans may indeed reflect differences in habitual loading patterns of the lower limb (but see Demes et al., 2001). Future analyses of robusticity changes in the Upper Paleolithic are desirable, but scaling robusticity factors to exponentially increased limb bone length will probably yield unreliable results. Acknowledgements The author wishes to thank Chris Ruff for his East African data, Eric Nauman and Vance Hutchinson for a critical reading of an earlier version of this paper, and the thoughtful comments of three anonymous referees. Thanks also to many curators and museum staff who provided access to the original fossil material, including C. B. Stringer, R. Kruszynski, G. Comerford, W. J. Kennedy, H. Powell, R. Foley, M. Bellatti, A. Langaney, J.-J. Hublin, M. Sakka, G. Rossi, S. Jousse, P. Mennecier, M. Pereira, M. Cheche, H. DeLumley, S. Condemi, G. Berillon, M.-T. Barbaud, S. Lasvergnas, M.-H. Marino, D. Buisson, C. Moser, J.-J. Cleyet-Merle, R. Rousset, S. Le Sausse, E. Ladier, B. Vandermeersch, P. Murail, N. Villena, D. Rouge´, O. Delmas, J.-F. Brugne, M.D. Nivie`re, N. Rousset, C. Simon, A. Czarnetski, H. Joachim, J. Weit, G. Grupe, R. Orban, P. Cornand, H. Kritscher, H. Hartmann, G. Franzke, J. Jelı´nek, M. Oliva, M. Dockalova, J. Svoboda, F. Mallegni, S. Borgognini-Tarli, V. Formicola, G. Rossi, O. Giuggiola, G. Vicino; G. Caldo, S. Simone, J. F. Bussie`re, D. Pilbeam, L. Beck, P. Lieberson, B. Bronson, and W. Grewe-Mullins. This research was supported in part by NSF (#SBR-9321339) and the L. S. B. Leakey Foundation.

     References Aiello, L. C. (1981). Locomotion in the Miocene Hominoidea. In (C. B. Stringer, Ed.) Aspects of Human Evolution, pp. 63–97. London: Taylor & Francis. Alexander, R. M., Jayes, A. S., Maloiy, G. M. O. & Wathuta, E. M. (1979). Allometry of the limb bones of mammals from shrews (Sorex) to elephant (Loxodonta). J. Zool., Lond. 189, 305–314. Bergmann, C. (1847). Ueber die Verhaltnisse der Warmeokonomie der thiere zu ihrer grosse. Gottinger Studien 3, 595–708. Bridges, P. S. (1989). Bone cortical area in the evaluation of nutrition and activity levels. Am. J. hum. Biol. 1, 785–792. Bridges, P. S. (1991). Skeletal evidence of changes in subsistence activities between Archaic and Mississippian time periods in northwestern Alabama. In (M. L. Powell, P. S. Bridges & A. M. Mires, Eds) What Mean these Bones?: Studies in Southeastern Bioarchaeology, pp. 89–101. Tuscaloosa: University of Alabama Press. Bridges, P. S., Blitz, J. H. & Solano M. C. (2000). Changes in long bone diaphyseal strength with horticultural intensification in west-central Illinois. Am. J. phys. Anthrop. 112, 217–238. Churchill, S. E. (1994). Human upper body evolution in the Eurasian later Pleistocene. Ph.D. Dissertation, University of New Mexico. Churchill, S. E. (1996). Particulate versus integrated evolution of the upper body in Late Pleistocene humans: A test of two models. Am. J. phys. Anthrop. 100, 559–583. Crowinshield, R. D., Johnston, R. C., Andrews, J. G. & Brand, R. A. (1978). A biomechanical investigation of the human hip. J. Biomech. 11, 75–85. Demes, B., Qin, Y.-X., Stern, J. T., Jr., Larson, S. G. & Rubin, C. T. (2001). Patterns of strain in the macaque tibia during functional activity. Am. J. phys. Anthrop. 116, 257–265. Formicola, V. & Giannecchini, M. (1999). Evolutionary trends of stature in Upper Paleolithic and Mesolithic Europe. J. hum. Evol. 36, 319–333. Forwood, M. R. & Burr, D. B. (1993). Physical activity and bone mass: exercises in futility? Bone Mineral. 21, 89–112. Goodship, A. E., Lanyon, L. E. & McFie, H. (1979). Functional adaptation of bone to increased stress. J. Bone Jt. Surg. 61-A, 539–546. Grine, F. E., Jungers, W. L., Tobias, P. V. & Pearson, O. M. (1995). Fossil Homo femur from Berg Aukas, northern Namibia. Am. J. phys. Anthrop. 97, 151–185. Holliday, T. W. (1997). Body proportions in Late Pleistocene Europe and modern human origins. J. hum. Evol. 32, 423–448. Holliday, T. W. (1999). Brachial and crural indices of European Late Upper Paleolithic and Mesolithic humans. J. hum. Evol. 36, 549–566. Holliday, T. W. (2000). Comment on Pearson. Curr. Anthrop. 41, 591–592.

527

Holt, B. (1998). Lower limb skeletal structural adaptation in Upper Paleolithic and Mesolithic Europeans. Am. J. phys. Anthrop. 26 Suppl., 123. Holt, B. M. (1999). Biomechanical evidence of decreased mobility in Upper Paleolithic and Mesolithic Europe. Ph.D. Dissertation, University of Missouri. Holt, B. & Churchill, S. (2000). Behavioral changes in European Upper Paleolithic foragers: evidence from biomechanical analysis of the appendicular skeleton. Am. J. phys. Anthrop. 30 (Suppl.), 182. Jacobs, K. H. (1985). Evolution in the postcranial skeleton of Late Glacial and early Postglacial European hominids. Z. Morph. Anthrop. 75, 307– 326. Jungers, W. L. & Burr, D. B. (1994). Body size, long bone geometry and locomotion in quadrupedal monkeys. Z. Morph. Anthrop. 80, 89–97. Kimura, T. (1991). Long and robust bones of primates. In (A. Ehara, T. Kimura, O. Takenaka & M. Iwamoto, Eds) Primatology Today, pp. 495–498. New York: Elsevier. Kimura, T. (1995). Long bone characteristics of primates. Z. Morph. Anthrop. 80, 265–280. Larsen, C. S. (1995). Biological changes in human populations with agriculture. Ann. Rev. Anthrop. 24, 185–213. Larsen, C. S. & Ruff, C. B. (1991). Biomechanical adaptation and behavior on the prehistoric Georgia coast. In (M. L. Powell, P. S. Bridges & A. M. Mires, Eds) What Mean these Bones? Studies in Southeastern Bioarchaeology, pp. 102–113. Tuscaloosa: University of Alabama Press. Ledger, M., Holtzhausen, L.-M., Constant, D. & Morris, A. G. (2000). Biomechanical beam analysis of long bones from a late 18th century slave cemetery in Cape Town, South Africa. Am. J. phys. Anthrop. 112, 207–216. Levangie, P. K. & Norkin, C. C. (2001). Joint Structure and Function: A Comprehensive Analysis. 3rd edn. Philadelphia: F.A. Davis. Lovejoy, C. O., Burstein, A. H. & Heiple, G. (1976). The biomechanical analysis of bone strength: a method and its application to platycnemia. Am. J. phys. Anthrop. 44, 489–505. Matiegka, J. (1938). Homo p edmostensis II: Ostatnı´ ca´sti kostrove´. Praha: Na´kladem eska Akademie V d a Um nı´. McCarthy, R. N. & Jeffcott, L. B. (1992). Effects of treadmill exercise on cortical bone in the third metacarpus of young horses. Res. Vet. Sci. 52, 28–37. McHenry, H. M. (1976). Early hominid body weight and encephalization. Am. J. phys. Anthrop. 45, 77–84. McHenry, H. M. (1988). New estimates of body weight in early hominids and their significance to encephalization and megadontia in ‘‘robust’’ australopithecines. In (F. E. Grine, Ed.) Evolutionary History of the ‘‘Robust’’ Australopithecines, pp. 133–148. New York: Aldine de Gruyter. Mosley, J. R. & Lanyon, L. E. (1998). Strain rate as a controlling influence on adaptive modeling in

528

. . 

response to dynamic loading of the ulna in growing male rats. Bone 23, 313–318. Mosley, J. R., March, B. M., Lynch, J. & Lanyon, L. E. (1997). Strain magnitude related changes in whole bone architecture in growing rats. Bone 20, 191–198. Pearson, O. M. (2000). Activity, climate and postcranial robusticity: implications for modern human origins and scenarios of adaptive change. Curr. Anthrop. 41, 569–607. Polk, J. D., Demes, B., Jungers, W. L., Biknevicius, A. R., Heinrich, R. E. & Runestad J. A. (2000). A comparison of primate, carnivoran and rodent limb bone cross-sectional properties: are primates really unique? J. hum. Evol. 39, 297–325. Riesenfeld, A. (1973). The effect of extreme temperatures and starvation on the body proportions of the rat. Am. J. phys. Anthrop. 39, 427–460. Rightmire, G. P. (1986). Body size and encephalization in Homo erectus. Anthropos 23, 139–150. Ruff, C. B. (1999). Skeletal structure and behavioral patterns of prehistoric Great Basin populations. In (B. E. Hemphill & C. S. Larsen, Eds) Prehistoric Lifeways in the Great Basin Wetlands: Bioarchaeological Reconstruction and Interpretation, pp. 290–320. Salt Lake City: University of Utah Press. Ruff, C. B. (2000a). Biomechanical analyses of archaeological human skeletons. In (M. A. Katzenberg & S. R. Saunders, Eds) Biological Anthropology of the Human Skeleton, pp. 71–102. New York: Wiley-Liss. Ruff, C. B. (2000b). Body size, body shape, and long bone strength in modern humans. J. hum. Evol. 38, 269–290. Ruff, C. B., Scott, W. W. & Liu, A. Y.-C. (1991). Articular and diaphyseal remodeling of the proximal femur with changes in body mass in adults. Am. J. phys. Anthrop. 86, 397–413. Ruff, C. B., Trinkaus, E., Walker, A. & Larsen, C. S. (1993). Postcranial robusticity in Homo, I: temporal trends and mechanical interpretation. Am. J. phys. Anthrop. 91, 21–53. Ruff, C. B., Trinkaus, E. & Holliday, T. W. (1997). Body mass and encephalization in Pleistocene Homo. Nature 387, 173–176. Simkin, A., Leichter, I., Swissa, A. & Samueloff, S. (1989). The effect of swimming activity on bone architecture in growing rats. J. Biomech. 22, 845–851.

Smith, R. J. (1996). Biology and body size in human evolution: Statistical inference misapplied. Curr. Anthrop. 37, 451–481. Stock, J. & Pfeiffer, S. (2001). Linking structural variability in long bone diaphyses to habitual behaviors: foragers from the southern African later Stone Age and Andaman Islands. Am. J. phys. Anthrop. 115, 337–348. Trinkaus, E. (1981). Neanderthal limb proportions and cold adaptation. In (C. B. Stringer, Ed.) Aspects of Human Evolution, pp. 187–224. London: Taylor & Francis. Trinkaus, E. (1997). Appendicular robusticity and the paleobiology of modern human emergence. Proc. natl. Acad. Sci. U.S.A. 94, 13367–13373. Trinkaus, E., Ruff, C. B. & Churchill, S. E. (1998). Upper limb versus lower limb loading patterns among Near Eastern Middle Paleolithic hominids. In (T. Akazawa, K. Aoki & O. Bar-Yosef, Eds) Neandertals and Modern Humans in Western Asia, pp. 391–404. New York: Plenum. Trinkaus, E., Churchill, S. E., Ruff, C. B. & Vandermeersch, B. (1999). Long bone shaft robusticity and body proportions of the Saint-Ce´saire 1 Chaˆtelperronian Neandertal. J. Archaeol. Sci. 26, 753–773. Trotter, M. & Gleser, G. G. (1952). Estimation of stature from long bones of American whites and negroes. Am. J. phys. Anthrop. 10, 463–514. Trotter, M. & Gleser, G. G. (1958). A re-evaluation of estimation of stature based on measurements of stature taken during life and of long bones after death. Am. J. phys. Anthrop. 16, 79–123. Verneau, R. (1906). Anthropologie. In Les Grottes de Grimaldi (Baousse´-Rousse´), Vol. 2, fasc. I. Monaco: Imprimerie de Monaco. Wolpoff, M. H. (1999). Review of Neandertals and Modern Humans in Western Asia (T. Akazawa, K. Aoki & O. Bar-Yosef, Eds). Am. J. phys. Anthrop. 109, 416–423. Woo, S. L.-Y., Kuei, S. C., Amiel, D., Gomez, M. A., Hayes, W. C., White, F. C. & Akeson, W. H. (1981). The effect of prolonged physical training on the properties of long bone: A study of Wolff’s Law. J. Bone Jt. Surg. 63-A, 780–787.