Data for the Calculation of Body Height on the Basis of Extremities of Individuals Living in Different Historical Periods in the Carpathian Basin

ANNALES HISTORICO-NATURALES MUSEI NATIONALIS HUNGARICI Volume 100 Budapest, 2008 pp. 385–397.

Data for the calculation of body height on the basis of extremities of individuals living in different historical periods in the Carpathian Basin

ZS. BERNERT

Department of Anthropology, Hungarian Natural History Museum H-1082 Budapest, Ludovika tér 2. Hungary. E-mail: [email protected]

– On the basis of individual data of several thousands of human bones excavated in the Carpathian Basin, 1) numerical correlations of the length of bones of the same individual was described. This can help us for instance when assorting bones found in ossuaries; 2) a body height calculation method considering figure and sex differences of individuals living in the Carpathian Basin was proposed; 3) tables were created showing the chances that various postcranial bones belonged to males or females based on the length; 4) stature categories were proposed corresponding to height estimation methods. With 8 tables and 5 figures.

– Age estimation, body height, Carpathian Basin, human skeletal remains, ossuary, physical anthropology, stature categories.

INTRODUCTION

In classic anthropological publications, it is almost obligatory to deal with estimated body height of ancient people. Namely, we cannot imagine how these people looked like without knowing their height. The height is often estimated on the basis of metric data of postcranial bones. In this work, I will examine length data of long bones of people living in the Carpathian Basin. Knowing the correlations of limb bones of individuals may help in comparing different populations and sorting bones found in ossuaries. At the same time, the large number of individual data can also be used for the estimation of height of people living in the historical ages of the Carpathian Basin. Similarly, it enables the creation of stature categories and the definition of biological sex.

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MATERIAL AND METHOD

The majority of data were taken from the work of KINGA ÉRY describing the dimensions of four bones (femur, tibia, humerus and radius) of several thousand individuals (ÉRY 1998). This is the most complete database of this character in the Carpathian Basin. I extended this pool of data using measurements collected from other series (Bala- tonlelle, cemetery of the medieval village of Báté, the motte of Edelény-Borsod, Fonyód- Bézsenypuszta, Gyugy, site No. 26 in the 62nd Street in Kaposvár, Kereki-Homokbánya, Kéthely-Melegoldal, Ordacsehi-Csereföld, Park Street in Öreglak, Somogyjád, Török- koppány, borderland of Vörs-Major, Vörs-Papkert B, Zselickislak-Töröcske). My results are based on the combined database including data of approximately 4,000 males and females.

RESULTS

I created empirical tables (Tables 1–2) showing individual metric data of postcranial bones, organised in rows. I arbitrarily chose the femur to be the basis of comparison. I also defined femur data categories with a range of 3 millimetres. As a result, I achieved appropriately narrow categories while the number of such classes remained transparent. I also specified the average length of matching (i.e. of the same individual) tibiae, humeri and radii as well as the number of elements.

Empirical table of matching postcranial bones of males. N = number of individuals with comparable limb bone and femur. M = average MARTIN 1 length that belongs to a given femur length group

391−393 318.33 6 286.00 7 219.50 4 394−396 332.00 4 306.57 7 228.83 6 397−399 323.92 4 294.31 8 220.07 7 400−402 328.44 16 293.39 23 215.68 14 403−405 330.84 19 300.44 18 227.60 15 406−408 337.96 23 302.02 26 229.52 23 409−411 336.28 34 300.32 39 227.03 30 412−414 337.01 41 302.05 39 228.08 36 415−417 338.78 52 303.24 49 229.52 47 418−420 344.43 45 305.84 47 229.43 40 421−423 342.23 67 306.81 67 232.26 64 424−426 347.9 77 309.29 80 235.84 70 427−429 348.4 98 312.68 94 236.22 82 430−432 350.5 110 314.15 113 237.22 98 433−435 354.36 119 316.14 120 239.05 114

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(continued)

433−435 354.36 119 316.14 120 239.05 114 436−438 355.38 128 316.15 128 240.92 111 439−441 357.48 125 318.76 122 242.87 113 442−444 360.5 152 322.06 149 243.53 135 445−447 362.78 156 324.11 155 245.47 133 448−450 365.32 142 324.49 151 246.20 130 451−453 369.06 126 326.40 134 248.01 115 454−456 369.64 158 328.10 162 248.88 133 457−459 372.23 111 331.10 114 250.91 95 460−462 376.28 123 331.97 123 251.47 106 463−465 377.88 107 332.43 101 253.61 93 466−468 378.08 91 335.10 95 254.66 80 469−471 383.42 87 337.67 95 255.29 74 472−474 383.29 77 339.01 83 257.45 67 475−477 386.21 73 340.48 69 257.98 70 478−480 389.18 59 343.38 55 259.22 57 481−483 391.77 41 346.50 36 260.98 30 484−486 395.41 47 346.12 47 261.93 41 487−489 393.68 30 348.03 30 260.23 28 490−492 402.77 26 346.48 25 266.05 21 493−495 397.67 23 350.48 20 263.72 18 496−498 401.04 13 349.73 13 265.90 10 499−501 402.54 13 354.33 12 270.08 6 502−504 412.93 7 355.31 8 270.81 8 505−507 411.11 10 354.30 9 270.83 10 508−510 421.79 7 358.08 6 275.75 6 511−513 412.33 3 360.00 3 260.50 1 514−516 425.90 5 358.33 3 286.00 3

N shows the number of individuals with comparable limb bone and femur. When thelengthofboththerightandtheleftboneofthegiventypewasknown,Iusedthe average of the two. I compared the femur category average in the table with the average length of the other four postcranial bones belonging to the same femur category. (By this method, data of the smaller number of tall and short individuals represented a greater weight.) In case of males (Table 1), the correlation was 0.997 when comparing the humerus, radius and tibia to the femur. (I have calculated only with table cells with an element number above 50). In case of females (Table 2), the correlation was 0.998 when comparing tibia to femur and humerus to femur but it was 0.990 when comparing the lengths of radius and femur. I prepared a graphic chart of data columns of Tables 1 and 2 (Figs 1–2).

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Empirical table of matching postcranial bones of females. N = number of individuals with comparable limb bone and femur. M = average MARTIN 1 length that belongs to a given femur length group

352−354 296.50 4 258.17 3 202.33 3 355−357 279.00 1 259.50 2 203.00 2 358−360 290.40 5 264.70 5 193.30 5 361−363 300.60 5 268.67 6 197.19 6 364−366 299.59 11 269.00 11 205.11 9 367−369 299.40 15 272.63 12 202.79 7 370−372 306.72 16 272.63 12 207.38 12 373−375 307.69 18 274.82 14 203.17 15 376−378 307.85 36 276.77 33 204.90 26 379−381 310.55 37 278.54 36 206.89 32 382−384 315.79 47 278.67 50 208.83 39 385−387 313.47 46 281.02 46 209.51 40 388−390 317.96 82 283.18 80 211.20 77 391−393 320.81 90 285.30 89 212.83 73 394−396 323.81 117 286.94 112 213.89 99 397−399 325.80 104 287.35 88 215.57 87 400−402 326.61 126 290.42 109 216.15 99 403−405 331.73 152 293.08 140 218.78 117 406−408 333.18 129 294.40 134 220.73 110 409−411 334.25 137 295.49 134 222.19 116 412−414 338.45 140 297.29 149 223.23 129 415−417 339.13 135 299.65 137 225.63 122 418−420 341.13 112 300.84 100 225.20 95 421−423 344.73 130 303.51 130 228.71 115 424−426 345.89 115 305.17 103 227.69 93 427−429 348.27 86 306.39 89 229.01 71 430−432 351.89 98 308.80 84 232.21 80 433−435 352.77 68 308.84 58 230.85 51 436−438 356.03 55 310.31 49 233.70 46 439−441 356.24 46 313.76 41 236.86 40 442−444 359.86 45 315.67 41 235.79 39 445−447 363.46 40 318.32 33 238.82 31 448−450 363.45 20 322.33 23 241.50 18 451−453 368.02 25 318.29 21 239.71 17 454−456 370.47 16 323.39 19 242.61 14 457−459 369.27 11 326.04 14 245.56 9 460−462 375.21 12 322.96 12 240.88 13 463−465 371.28 9 328.50 6 246.08 6 466−468 381.50 4 326.42 6 246.80 5 469−471 371.33 6 319.75 2 237.13 4 472−474 382.63 4 335.38 4 247.50 4

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Empirical correlation of the length (MARTIN 1 size) of long bones, males

Empirical correlation of the length (MARTIN 1 size) of long bones, females

Figs 1 and 2 show two important things. The one is that there is a linear correlation between the length of the thigh-bone and that of the other long bones (i.e. the longer the femur, the longer the other postcranial bones). The other is that incidental effects resulting from the lower number of elements in case of extreme values ‘wimple’ the curve.

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It can also be observed that the effect of incidental errors can be neglected in the case of cells with an element number higher than 50. Based on cells of the experimental tables with data of more than 50 individuals, we can find correlations as follows:

Males M1tibia = 0.786 × M1femur + 12.528 M1tibia = 0.773 × M1femur + 18.001 M1humerus = 0.610 × M1femur + 50.878 M1humerus = 0.594 × M1femur + 52.043 M1radius = 0.460 × M1femur + 39.438 M1radius = 0.470 × M1femur + 28.904

Based on correlations above, we can estimate the most probable length of the long bones compared to the given femur. As far as historical anthropological series are concerned, this information can be used to estimate missing dimensions and to sort bones found in ossuaries. The absolute dimension of postcranial bones is pivotal when specifying biological sex. Based on several thousands of individual data, I have calculated the probability of that a given bone length belonged to a male or a female. Results can be found in Table 3.

Calculated correlation of the length of long bones and the probability of morpho- logical sex. First column shows level of sex markedness (+2 = very masculine, +1 = masculine, 0 = neutral, –1 = feminine, –2 = very feminine). The percentage column shows the probability that a given bone length in the sample belonged to a male or a female

Sex % 3 97 4 96 4 96 4 96 4 96 -2 5 95 5 95 5 95 6 94 8 92 10 90 13 87 16 84

-1

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(continued) Sex % 0

At the same time, measurement data provide information concerning one certain component of average stature of the given period: the ratio of extremities. Certain sex differences in terms of the ratio of postcranial bones are more transparent when looking at the table (Fig. 3). The tibia dimensions of males and females have such a similar ratio that relevant data completely correspond in Fig. 3. Differences in terms of the limb ratio of males and females could be verified by the paired t test. Compared to the same femur length, both the radius and the humerus of females were significantly shorter than those of males. At the same time, there was a signifi- cant similarity of the tibia of males and females, compared to the same femur length. I have also examined the brachyalis index of males and females. According to that, the radius of females was significantly shorter when compared to the humerus than in males. Data collected in the Carpathian Basin can be used for the verification of applicabil- ity of body height estimation methods relying on the length of postcranial bones in the field of Hungarian series. When applying these height estimation methods, four major de- ficiencies can be identified.

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Calculated correlation of the length (MARTIN 1 size) of long bones

1) As a result of the differences in the limb ratios of males and females, methods using any bones not considering sex differences when estimating body height of males and females are wrong in principle. Namely, our data collected on the basis of historical anthropological series proved that the long bones of the upper extremities of females were significantly shorter than those of males when comparing male and female individuals with the same length of the femur (or tibia). 2) Methods estimating greater body height for males than for females (by several centimetres) in case of limb bones of the same length are also erroneous. Because the ratio of extremities and the torso is different: the limbs of females are shorter when compared to their torso than those of males (Table 4). This type of stature characteristics is universal, irrespective of population origin. This is mainly because growth takes longer in boys and the extremities grow faster than the limb itself during that development period. This is also true for historical ages. Therefore, only those estimation methods are correct that calculate with a greater height for females in consideration of the same length of limb bones. However, I have not found such a method in literature.

Average data of 18-year old people in Hungary

Stature (S) 175.34 162.28 Upper-extremity (UE) 76.45 69.23 UE / S × 100 43.60 42.66 Lower-extremity (LE) 98.68 89.89 LE / S × 100 56.28 55.39

Annls hist.-nat. Mus. natn. hung. 100, 2008 Data for the calculation of body height in the Carpathian Basin 393

3) By using certain body height calculation methods, we get considerably different values for the given bone types as shown in the rows of Table 2. In extreme cases, the differences of body height estimations based on the bones of the same individual can exceed 10 centimetres. This phenomenon can be explained by the fact that these methods had been elaborated on individuals strongly different than those people in our samples. Just compare data of Tables 9 and 10 in the work of MENDONCA (2000) with those found in Table 1 and 2 of this document, and it is obvious why we can query the validity of height calculation methods worked out for different distant populations. 4) I observed considerable deviation in terms of body height values when applying different estimation methods. This goes beyond figure differences mentioned above because dissimilar data collection, different age or health conditions of individuals etc. also influenced the findings of researchers when working out their calculation methods. Mainly because of these considerable deviations in terms of results given by body height calculation methods, researchers have not clearly been in favour of one or the other method. It is beyond argument that we cannot actually measure the height of ancient people. Nevertheless, mathematical formulas can be worked out for the postcranial bone database of historical populations found in the Carpathian Basin and these formulas can be used for calculations performed on further samples from the same territory as well. The idea behind is as follows: As the first step, I used the male formula to calculate male bone lengths of Table 3 by using several methods worked out for Europeans. When calculating the average body height, I applied methods worked out by the quoted authors, as specified by the following works: SJØVOLD (1990) for both genders and all the races, PEARSON &RÖSING (1988, cit. ÉRY 1992), TROTTER &GLESER (1958) for white people, TELKKA (1950, cit. OLIVIER 1960), DUPERTUIS &HADDEN (1951) for whites, BREITINGER (1938), OLIVIER (1978, cit. ÉRY 1992), DEBETS & DYRNOVO (1971). Secondly, I took the average of body heights calculated on the basis of the different types of bones per method. I continued averaging, thus, I received only one height value for each and every row of Table 3. Finally, I prepared the linear regression equations resulting in body height data as follows (Table 5). As far as females are concerned, we have to take into account that limb ratio is different in case of the two sexes. My reasoning was the following:

Formulas for calculating the body height of males Males 0.310 × M1humerus + 68.460 0.410 × M1radius + 68.045 0.189 × M1femur + 84.222 0.240 × M1tibia + 81.211 0.106 × (M1femur +M1tibia) + 82.897

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It can be observed that practically the same tibia length belongs to the same male and female femur length (Table 3). Hence, the length of the lower extremities of males and females with the same femur length is practically the same. Based on recent Hungarian body heights and averages of lower extremities (Table 4, EIBEN et al. 1991), it can be calculated that females are 1.016 times taller then males if the length of the lower limb is identical. When comparing sitting heights, it can be observed that the upper body of females is 1.020 times longer than that of males. When calculating correlations below, I used this ratio. Finally, I prepared the linear regression equations resulting in body height data as follows (Table 6): Formulas for estimating the body height of males Females 0.323 × M1humerus + 68.771 0.409 × M1radius + 73.758 0.192 × M1femur + 85.570 0.248 × M1tibia + 81.101 0.108 × (M1femur +M1tibia) + 83.621

One method for evaluating individual height data is to classify them. This is the most transparent way of data processing. We can notice in several works involving stature estimates following MARTIN’s classification that the proportion of tall individuals (tall-medium or very tall, depending on population) is extremely high. This can be observed both in case of males and females of large series. The deviation from the theoretical Gauss curve may refer to the emergence of taller populations or the selective effect of the environment. However, the cause of this phenomenon is methodological and not biological. When choosing even stature categories, we can expect the theoretical distribution even historical populations if the number of individuals in the sample is appropriately high. I took the example of the distribution of more than three thousand male femurs according to length (of people living in the Carpathian Basin in different historical periods). I chose categories of 5 millimetres from 370 mm to 539 mm (34 categories) (Fig. 4). Fig. 4 clearly shows that the distribution of length (and the stature calculated from that) follows the Gauss curve if the sample is large enough. On the basis of femurs in this figure, by using the height estimation method of SJOVOLD worked out for both sexes and different populations and assigning the calculated heights to the categories according to MARTIN’s classification, we receive the following distribution (Fig. 5). Again, the figure clearly shows the phenomenon already mentioned, namely that the distribution of stature categories does not follow the distribution of extremities, i.e. the proportion of tall individuals is too high. The explicit disharmony of distribution according to stature categories and the distribution of limb bones according to length is quite problematic because historical populations examined cannot be evaluated and compared on the basis of the distribution of stature. At this point, I would like to refer to the fact that the estimation of stature is important among others because of the transparent comparison of historical populations.

Annls hist.-nat. Mus. natn. hung. 100, 2008 Data for the calculation of body height in the Carpathian Basin 395

Distribution of male bones from the Carpathian Basin according to length

Distribution of stature values estimated on the basis of male femurs from the Carpathian Basin according to MARTIN

Thus, it is reasonable to harmonise categories and stature estimation methods because by doing that, we can identify the differences of the body height distribution of the examined series compared to the theoretical distribution. Based on the largest length data of male and female femurs in the database above, the application of height estimation formulas already mentioned will result in the following categories if the borders of categories are set at deviation values 1, 2 and 3 (Tables 7–8).

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Proposed stature categories based on examined bones from the Carpathian Basin Category Males Females Femur Stature Femur Stature Below very short Very short Short Short -medium Medium Tall-medium Tall Very tall Above very tall 518− 182.04− 475− 176.68−

Basic data of calculations above

N 3554.00 3160.00 Vmax 538.00 478.50 Vmin 372.00 349.00 M 448.95 411.89 SD 23.03 20.19 SD/M 5.13 4.90

Instead of a comparison according to body height, metric data of postcranial bones alone are enough and appropriate for comparison. The only advantage of comparison based on estimated height is that it generates a higher number of cases than the comparison by the most measurable bone.

REFERENCES

BREITINGER, E. 1938: Zur Berechnung der Körperhöhe aus den langen Gliedmassen- knochen. – Anthropologische Anzeiger : 249–174. DEBETS,G.F.&DYRNOVO, J. A. 1971: Fizicheskoe razvitie lyudey epohi eneolita v yuzhnoy Turkmenii. [Physical development of eneolitic people in southern Turkmenia.] – Sovyetskaya Etnographia : 26–35. DUPERTUIS,C.W.&HADDEN, J. A. 1951: On the reconstruction of stature from long bones. – American Journal of Physical Anthropology : 15–53. EIBEN, O. G., BARABÁS,A.&PANTÓ, E. 1991: The Hungarian National Growth Study. – Humanbiologia Budapestiensis : 1–123. ÉRY, K. 1998: Length of limb bones and stature in ancient populations in the Carpathian basin. – Humanbiologia Budapestiensis : 1–96.

Annls hist.-nat. Mus. natn. hung. 100, 2008 Data for the calculation of body height in the Carpathian Basin 397

MENDONCA, M. C. 2000: Estimation of Height from the Length of Long Bones in a Portu- guese Adult Population. – American Journal of Physical Anthropology : 39–48. OLIVIER, G. 1960: Pratique Anthropologique. – Vigot Freres, Paris 299 pp. SJØVOLD, T. 1990: Estimation of stature from long bones utilizing the line of organic correlation. – Human Evolution : 431–447. TROTTER,M.&GLESER, G. C. 1952: A re-evaluation of estimation of stature based on measurements of stature taken during life and of long bones after death. – American Journal of Physical Anthropology : 79–123.

Annls hist.-nat. Mus. natn. hung. 100, 2008