Human Variation in Interlimb Proportions

The humerofemoral index (defined above) is highly correlated with another interlimb metric, the intermembral index (100 x [humerus + radius]/[femur + tibia]). Figure 9.1 is a bivariate plot of these two indices in a human skeletal sample of 314 individuals drawn from a diversity of ethnicities, climates and body sizes: African Pygmies, Andaman Islanders, Khoesan, Zulu, African Americans, Sami and Inuit. The parametric and rank order correlations are highly significant (p < 0.001) and similar in magnitude at 0.848 and 0.841, respectively. One can therefore predict the intermembral index from the humerofemoral index, but the relationship is not an isometric one. The regression in raw data space is

Intermembral Index = 0.676 x Humerofemoral

Fig. 9.1 Bivariate plot of the intermembral index against the humerofemoral index in a diverse ethnic sample of 314 modern humans. The two indices are highly correlated but not isometric because the intercept is significantly different than 0. Spearman's rank order correlation (rho) is 0.841. A nonparametric Loess line (tension = 0.5) is fit to the data.

Fig. 9.1 Bivariate plot of the intermembral index against the humerofemoral index in a diverse ethnic sample of 314 modern humans. The two indices are highly correlated but not isometric because the intercept is significantly different than 0. Spearman's rank order correlation (rho) is 0.841. A nonparametric Loess line (tension = 0.5) is fit to the data.

and the 95% confidence interval on the intercept does not include 0 (cf. Jungers et al., 1995).

Table 9.1 provides the descriptive statistics for the humerofemoral index in these samples, for the total sample, as well as additional data on small-bodied "Asian Negritos" from Martin and Saller (1959), and three fossils (A.L. 288-1, LB 1, and KNM-WT 15000). Figure 9.2 presents these data in a box-and-whiskers graphical format. A great deal of variation is apparent (although not as much as imagined by Eckhardt, 2000), and there are many significant differences among groups that are unrelated to overall body size. A one-way analysis-of-variance is highly significant (p < 0.001), and Games-and-Howell posthoc comparisons (employed due to heterogeneous variances) reveal the following:

Table 9.1 Descriptive statistics for the humerofemoral index in humans and fossil hominins

Group

N

Mean

Standard deviation

Lower 95%

Upper 95%

Minimum

Maximum

African Pygmies

24

73.7

1.5

73.1

74.4

70.2

76.3

Andaman Islanders

31

69.9

2.2

69.1

70.7

65.9

74.5

Khoesan

27

69.9

2.8

68.8

71.1

64.1

76.3

Zulu

47

70.5

1.8

70.0

71.0

66.7

75.9

African Americans

43

70.5

2.4

69.7

71.2

65.8

77.3

Sami

57

74.6

2.0

74.1

75.2

70.3

78.3

Inuit

85

72.1

2.2

71.7

72.6

66.6

77.3

Total Human Sample

314

71.8

2.7

71.5

72.1

64.1

78.3

Asian "Negritos"a

15 averages

70.5

1.7

69.5

71.4

67.6

73.3

AL 288-1

1

85.4

-

-

-

-

-

LB 1

1

86.8

-

-

-

-

-

KNM-WT15000

2 (juvenile & adult)

75.5

-

-

-

73.8 (juvenile)

77.2 (adult)

aMeans from Martin and Saller (1959), after Schebesta (1952). The "15 averages" are used as individual data points to create a mean of means, standard deviation of means and the range of means for these Asian groups of small stature.

aMeans from Martin and Saller (1959), after Schebesta (1952). The "15 averages" are used as individual data points to create a mean of means, standard deviation of means and the range of means for these Asian groups of small stature.

Knm 15000 Tibia

123456789 10 11 Group

Fig. 9.2 Box-and-whiskers plots of the humerofemoral index (HF Index) in modern humans and fossil hominins. The samples are numbered as follows: 1 - African Pygmies, 2 - Andaman Islanders, 3 - Khoesan, 4 - Zulu, 5 - African Americans, 6 - Sami, 7 - Inuit, 8 - "Asian Negritos", 9 - AL 288-1, 10 - LB 1, 11 - KNM-WT15000. Sample sizes are in Table 9.1. The bold horizontal line indicates the median value, and the "box" encompasses 50% of the data points; the "whiskers" encompass the remainder of the sample except for extreme outliers (individual circles). Both A.L. 288-1 and LB 1 fall far above all modern humans, but KNM-WT-15000 is decidedly more human-like (note that the box for KNM-WT 15000 reflects the range from juvenile to estimated adult proportions).

123456789 10 11 Group

Fig. 9.2 Box-and-whiskers plots of the humerofemoral index (HF Index) in modern humans and fossil hominins. The samples are numbered as follows: 1 - African Pygmies, 2 - Andaman Islanders, 3 - Khoesan, 4 - Zulu, 5 - African Americans, 6 - Sami, 7 - Inuit, 8 - "Asian Negritos", 9 - AL 288-1, 10 - LB 1, 11 - KNM-WT15000. Sample sizes are in Table 9.1. The bold horizontal line indicates the median value, and the "box" encompasses 50% of the data points; the "whiskers" encompass the remainder of the sample except for extreme outliers (individual circles). Both A.L. 288-1 and LB 1 fall far above all modern humans, but KNM-WT-15000 is decidedly more human-like (note that the box for KNM-WT 15000 reflects the range from juvenile to estimated adult proportions).

small-bodied groups (African Pygmies, Andaman Islanders, and Khoesan) that almost certainly contain some very small individuals comparable in adult body mass to both fossils.

It is obvious that the individual fossils represent point estimates of the species mean for the humerofemoral index, but we have no idea where any of them really fall with respect to the variation seen in the populations from which they are drawn. It is statistically possible to calculate confidence intervals for samples of N = 1, but these intervals are enormous, biologically absurd and "unlikely to be useful" (Smith, 2005). Using a human-driven model, Korey (1990) estimated the standard deviation for A.L. 288-1 at roughly 2.8; 2 standard deviations below a value of 85.4 is still outside the range observed in my heterogeneous human sample (as well as any of the many values presented in Martin and Saller (1959) for a wide variety of modern human groups). Moreover, the value of 85.4 used here is perhaps too conservative. Recent attempts at 3-D digital reconstruction of femur length in A.L. 288-1 suggest that 281 mm could well be too long (Sylvester et al., 2007). Regardless, I am unaware of any normal humans with a humerofemoral index approaching the values seen in either A.L. 288-1 or LB 1, and that includes skeletons drawn from the smallest people on earth. These observations alone render the allometric hypotheses described above as highly suspect. Direct tests described below lead to unequivocal rejection of such size-required scenarios.

• African Pygmies are significantly different from (greater than) all other groups except the Sami.

• Andaman Islanders are significantly different from (less than) African Pygmies, Sami and Inuit.

• Khoesan are significantly different from (less than) African Pygmies, Sami and Inuit.

• Zulu are significantly different from (lower than) African Pygmies, Sami and Inuit.

• African Americans are significantly different from (lower than) African Pygmies, Sami and Inuit.

• Sami are significantly different from (greater than) all groups except the African Pygmies.

• Inuit are significantly different from all other groups.

The Sami and African Pygmies have the highest humerofem-oral indices, and the Andaman Islander and Khoesan have the lowest. The mean of averages for small-bodied "Asian Negritos" (Aeta, Semang, and Senoi) is below my total sample average of 71.8 but very similar to that seen in Zulu and African Americans (70.5). KNM-WT 15000 (as a juvenile)

overlaps with several modern human groups, but the estimated adult index (using the average of 11 year-old and 12 year-old models [Ruff and Walker, 1993]) is appreciably higher; however, it can still be matched by individuals from the Sami, Inuit and African American samples. Both A.L. 288-1 and LB1 fall far above all of the human samples, including the

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