Eody Proportions, Population Structure and
Height Pr
e
diction
JESPER L. BOLDSEN
Institute of Community Health Department of Social Medicine University of Odense, Odense, Dernnark
VÜCUT ORANLARI, TOPLUM YAPıSı VE BOY UZUNLUGU TAHMİNİ
Özet
Bazı sonuçların elde edilmesi için insau iskeleti kalıntıların incelenmesi YÖf\temi adli antropoloji ve biyo
-lojik antropolojinin ana ilkelerindendir. Toplumların yapılarını incelemek amacıyla geliştirilmiş olan regres
-yon analizi tekniği bu tür çalışmalarda en sık kullanılan yöntemdir. Uzun kemik boylarının, boy uzunluğu ilc oldukça sıkı bir uyum göstermesi dikkati çekmiştir. Buna göre, vücut oranlarının boy uzunluğu ile ilişkileri gözönüne alınarak toplumların fizik özellikleri üzerinde araştırmalar yapılabilmektedir.
Bu çalışmada, özellikle bacakları oluşturan uzun kemiklerin yardunıyla hesaplanan boy uzunlukJarına ait regresyon formüllerinin, toplumların karşılaştırılması amacıyla kullanılmasının uygulanabilirliği araştırılmıştır. Incelenen toplumlar, eldeki bilgilerin ışığında, vücut bölümlerindeki yapısal farklılıklar açısından birbirleriyle karşılaştırıldı.lncelediğimiz materyal, Danimarka'nın Batı Jutland bölgesindeki Erken Ortaçağ (M.S. ıo-l ı. yüzyıl) dönemine ait bir kilise mezarlığından elde edilmiş iskeletler üzerinde yapıldı. Bu iskeletlerde, uzun kemik boylarının ve boy uzunluğunun ölçümü sonuçlarının analizi yapıldı. Belirli bir sayıdaki iskelette bütünlük bozulmadığı için Boldsen (3) yöntemi kullanılarak, kişinin hayattaki boyunun uzunluğu saptanabildi. Iskeletlerin tümünde uzun kemiklerin boylarının yanısıra kraniyumda iki ayrı ölçüm yapıldı. Regresyon analizinde standard istatistiksel tekniğin uygulanması için GLlM (8) bilgisayar programından yararlanıldı.Yapılan analizlerden elde edilen verilerin sağlamaları Cox-Small istatistik test yöntemiyle yapıldı. Ortaçağ başlarında yaşamış olan bu toplumun boyortalamalan erkeklerde 165.9 cm, kadınlarda ise 154.8 cm olarak saptandı. Bu tür işlemlerde, klasik formüllerin kullanılmasıyla boy uzunluk-lannın sistematik olarak çok fazla bulunduğu görüldü. Sonuç olarak, belirli bir toplum için hazırlanmış olan regresyon fonnülleri kullanarak başka bir topluma ait birey boy uzunluğunun hesaplanmaSL'lda çok dikkatli davranılması gerekliliği ortaya çıktı. Bireyin genelik geçmişi ile yaşadığı toplumun sanık yapısı, bu tür çalışmaJarın sonuçlarını eıkileyen sapmaJardaki başlıca faktörler olarak belirlendi.
Summary
The simultaneous distribution of the length of the long bones and the measured height of Medieva! Danes are analysed. It is shown that the classic formulae predict the height systematical1y ıoo large. A closer analysis of these data reveals that this is partly due to deviations from the assumptions behind the regression analysis (simuItaneous nonnaliıy). it appearsthat the deviation from simuhaneous normality in a rural Medieva! Dan-ish sample is due to a major factor acting on the body proportions. This major factor associaıes wiıh ıhe gc -netic background of the individuals and thus with breeding structure of the community. The conciuston of ıhis study is that heights predicted by means of regression formulae should only be used very cauıiously if the for
-mula is not derived fromthe very population to which the person is question belonged.
Kcy words : Heighl prediction - Populalion structure -Length of the long bones -Genetic backgrourıd
AdliTıpOerg., 6, 157 -165 (1990)
İ TIP DERGİSİ Journal of Forensic Medicine
158 1. L. BOLDSEN
INTRODUCTION
Calcıılation of individual height of people only known fron. their skeletal remains is considered to he apoint of essential importance both in fmensic medicine and in biological anıhropology. Pearson (1) introduced the use of regression analysis in the
attempt to predict the height of such people. His example was fnllnwed by numerous other scientists. Telkka (2) and Boldsen (3) have so far been the onlyone who did so working on Nordic materia1. However, for three decades the work of Trotter and Gleser (4,5) has fonne.ı the background for height predierjan in the Nordie area.
The length of the long bones are generally muttlally very highly cnrrelated. The
correlation coefficients for the relationship between individual bone lcngths and height are usually more moderate (0.7-0.8). This means that very lilllc is gainecl in tcrms of reduction of the precliction variance from including several bones in the regression.
The application of regression formulae derived from one population to skeletons derived from anaıher population implies an assumplion about a certain type of regularity of the distribution of bocly proportions. This assumption has been shown not
to be fulfılled (3).
This paper sets out to investigate the cross-populational applicabiliıy of regressioıı formıılae for the predietion of height from the lengıb of long bones. Emphasis is plaeed
on the analysis of aspects of the distribution of body size which İs not strangIy correlatecl to the length of the Jong honcs of ıhe Jeg. The stnıcture of differenccs in body
proportions are interpreıated in the light of knowiedge about the sımetme of the popuJations from which the analyzed samplcs were drawn.
MATERIAL AND METHOD$
The materral analyzed in this commnnicaıion wa, excavated in 1984 uncler the supervisıon and active panicipation of the author from an abıındond Early Medieva! Churchya"d a few kilomeıers west of the town }]orsens-Eastem Tutland, Dcnmark. The cemetery served as bıırtal p!ace for the inhabitants of a smail nıral
community. The villa~e to whi.ch the chureh and churchyard helongec! LS not known from writlen sources bUl old field names in the area mdicawc! that Ihe name of the community was Tirup. ViUages with this type of nanie are generaUy founded ın the Late Viking Age or Early Middle Ages-i Oth to i Ith century A.D. (6).
The excayation yielded evidenee of 619 burials - some of thwı only indieattod by color dtüerences in the earth. However, il was possible to mcasure the living height of a considerable number of ,keletoIls using the method described by !1ofdsEn (3) (~ppendix 1). The length of the long bones and two cranial measurements were measured in accord wiıh the standard procedures as gi\ien by Martin and Sal/er (7) (femur and tibia MI).
The sıatistiea! standard tcchniqucs of regression analysts-using the GLL\1 (8) program systcm-wen; uscJ ıo .:sıimaıe the parameters of the fonnul.ae for the predietion of hcight from the lenglh of L~e Jang bones of the !eg. The assumptions bdıind ıhese regression analysis was chccked usiııg the Cox-Sınal1ıest (9,10). Probiı
diııgram, are used to check [or Ilonnal distribution of univariate vanabksboth raw measurcmcnlS and ıesidu~k
Body Propol1ions, Population Stnıelllfe and Height PredicLion 159
RESULTS
The Early Mcdieval Tirup populalion had a fairly stature. The average height was
165.9 cm for males (n==80, sd.==7.6) and 154.8 cm for females (n;:;:55, sd::=6.0) The descriptive statistics [or the simultaneous distribution of heighı and the length or one long bone(feınur or tibia) are given in Table i along with the Cox-Srnall lest sLatlstics cvaIuating whethcr the regression of the two margina! variables up on each other is rectilinear. Evielently, the regrcssion of living height upon ıhe length of bOıh of the two long bones conformed to the hypothesis.
Table L The dcscriptive statisttcs for the simultaneous distribution of height and femoral or ıibia Icngıh ın
the twc sexe. in the skeletal sılInpks from Tinıp. The Cox-SmaU IIc.sı eVJlnnt~s ıh~ dr:viaıion from rectiline-ar of ıhe regrcssıon of the one vMiabk upon the oıher thesc 5taıist'cs have (n-3) dcgrccs cf fr~donı
Sex FCInm' x lkight Tibia x Height
l\1ales n 59 50 X. 46.78 166.66 37.41 166.46 s2 6.58 51.78 4.84 51.52 2.56 7.20 2.20 7.13 0.80 0.87 covanance 14.83 13.71 Cox-Smallt-test 1.25 0.05 1.03 0.29 - - - _ . _ . _ . _ - - - - 0_--- - - - --".--- -Females il 36 32 X. 43.58 155.94 35.04 155.88 S~ '337 34.05 2.04 3398 184 5.1\4 1.43 5.83 (L? ı 0.76 covananee 7.62 634
Cox-Smali I-test O.08ns O.96ns rı.19rıs O.52ns
The covariance mal.rices for the simnltaneous distribution of hcighl and bone lengıhs
of the Tirup skeletons do not differ statistically significant when diffcrcntiated by sex
(8=4.63, dr.:::3 for the height-femorallength covariance mıılıiC'es, 8==6.90, df.=3 for the
height-tibia Iength covariance matriees, B is the generalized Bartlctt's test statistie). These combined cavariance matrices are not significantly eliffercnt from the ones
Boldsen (3) found to deseribe the patterns of eovartation in several populations of European extracıion (height-femur: B;:;:l.4g, df.:=:3; heigbt-tibia: B=g.l6, dL=3 ). These
160 J.L. BOLDSEN
equalities of covariance matrices means that height in the samples analyzed by Boldsen (3) and in the Tirup skeletal sampIe can be predicted as:
2.3182
*
femoral length (in cm) + Csf and2.4172
*
tibia length (in cm) + Cstwhere Csf and Cst are the sample, sex and bone dependent constants of the regression
formulae. The values of the C's are given in TabIe II. Boldsen (3) has already repofted the C's to be statisticaIly significant different among the three samples from
populations of European descent which he analyzed. The differences of the C-values by sex do not differ between the two Medieval Jutland populations-Tirup and LilIc Set. Mikkelsgadc (t=0.44 (df=1462) when the femur is uscd for the prediction and t=-O.71 (df=1549) when tibia is used).
Tablc II. The va1ues of the constant part of the rcgression fomıu1ae (the C's) for ılıe three
samples analyzed by Boldsen (3) and the Tirup sample.
Fcmur Tihia
Males Females Males Females
Tirup 58.16 54.91 76.03 71.18
Lille Set.
Mi.kkelsgade 62.50 59.69 81.98 76.10
Finns 63.92 59.90 81.90 76.79
White Americans 65.63 62.03 82.04 78.72
Table II elearly demonstrates the very large difference between the C-values from the
two Mcdieval J utland populations. As it just has been shown that the sexual differenees are the same in the two populations it can be concIuded that members of the Tirup population were on average around 5 em shorter than members of the Lille Set. Mikkelsgade population with the same bone lengths(femur: differenee=5.44, t=7.45,
df=1462; tibia: differenee=4.70, t=6.94, df=1549). It is interesting to note that these differences are not statistieaııy signifieant differentiated by the bone used for the
predietion of height (differenee=5.04, u=0.74 - note that the t-test eould not be used in this case as the variance of the observed differences for each bone can not be assumed to be equal-further the observations are not independent, consequently, the given test is
Eody Proportions. Population Strueture and Height Predietion 161
These findings elearly indicates that the difference in the relationship between bone
length and height among the two Medieval Jutland samples does not rdate to possible differences of the relative length of the two long bones of the leg. As the same patterns appear whether tibia or femur is taken as the independent variable and whether males or females are analyzed we have chosen to give illustrations of the relationship between
femur and height among females. The structure of covariation is very much the same for tibia and femur and for males and females.
480 460 f
e
440m
u r 420 (mm) + Tirup - females + + 145 155 165 175 he ight (cm)Figure ı. Seatter plot illustrating the simultaneous distribution of height and femoral length in the female sample from Tirup. The dashed line is the regression of height upon femoral length estimated from the Lille SeL. Mikkelsgade female sample. Figures ı. 2 and 3 indicate three subsamples of skeletons dcfined by the solid lines. The interpretation of these subsamples is discussed in the text.
Figure ı iHustrates the simultaneous distribution of height and femorallength in the Tirup female sample. The dotted line indicate the regression of height upon the length of the femur based on the estimates from the Lille Set. Mikkelsgade females. The solid lines divide the points in the plane into three subsamples (1, 2 and 3). It is obvious that the regression line estimated from the Lille Set. Mikkelsgade skeletons fits group 1
fairly well whereas the members of group 2 are substantially and systematically shorter than should be expected from their femoral lengths. Group 3 probably consist of a mixture of members of groups 1 and 2.
162 J.L. BOLDSEN In ord er to illuminate this difference abit further wc have defined il new variable-the torso length. The torso lcngıh İs in the present conıext defined as the measured height mİnııs the length of the long bones of the leg (fernur and tibia). This variable conıains
probably smail variance components describing variatian in the height of the foot and descrihing the height of the skull. However, as the foot and skuıı heighı<; only form vcry minor parts of the torso length the varianee of this variable must be heavi!y
doıninated by the distance from the hip to ıhe basi-craniul11. Wc have chosen this
directly measurable variable rather than the rcgression residual to illustrate our points
about the struetme of the population because we did nol wish to rday on urlIıccessarily
complicated variables. f e m " r (mm) Tirup females 400
i
+ + 460+
+ + ı + ı + ı 440..l-ı ı 420t
+ i ı + ii
+ + + + + 400+--- --- -- ---- -
--t 70 75 + + + + + + + + + + + t t + - - - j , - - - I 80 8S torso (cm)Figııre 2. Scatter plot iliustrating ·,.he sim1l1taneolls distnbution of the torso length and the lcngth of the femur. The. correIation be.lween ıhese two measıırements ıs evidentıy sm~1I and the. deviaıion from simultaneous nOlma] distributi0n is considerable.
Figure 2 illustrates the simultaneous distribution of this [orso lengıh and the Icngth of the femur. This plot c!early indicates that the length of the femur has very lıtlıe or
none bearing upon tJ1C length of the torso. It is clcar from inspection of l11is figore that the length of the torso does not follow a normal distribution it can more readily be understood as a mixture of two normal distributions.
Body Proportions. Population Strueıure and Heighı Predietlon 163
DISCUSSION
In spite of the r.ather rigorous numerical testing of the assumptions behind the
regressİon approach to hcight prcdiction (simultaneous normal distribution of the companent variables) I.he graphic analysis of the distribution of ıhe torso Jength elem!y shows that height and femoral length cannat be simultancausly narmally distributed in the Tirup female population. The same type of graphic analysis has heen carried out for the skeletal sample from Lille Sel. Mikkelsgade (not shown in this paper). This analysis clearly indicated that this populatian canformed rathe! well to the assumption
about simultaneous normal distribution of height and bone lengths.
The observcd pattem of coyariaLion of bone Iengtlıs and height in the Tirup medieva!
popıılation indicates that this population consists of lwo subpopulalion with re.latively large differenccs in body proportions. The torso length must be highly corrclatcd to the sitting heigllt of living persons. In living persons it is generally possible by the unaidcd
eye to distinguish peapk on the basis of both relative and absolute sitting height. This
ıneans that ardinary people in the Middle Ages werc able to teil most Tural from most urban persons on the basis of theİr overt body proportions. Further. the inhomogeneity
of the body proporlions of the Tirup populalian must have been obvious to observant members of the eommunİty.
Population structure, i.e., the leyeI of inbrceding, is generallv believed to have relatively liule inflııencc on stat.urc. However, Cavalli-Sforw and Bodmer (ll) in
summarizing several studies on the anthropometric conscqucnccs of inbreeding find that
the effects of inbreeding is most el early visible on the dimensions of the thorax. This means that the observed pattern of morphoIogical differences within the Tirup population and between tlıe Tirup and the Lille Set. Mikkelsgadc populations small differences in the lengths of the femur and the tibia and large differences in the length of
the tOl'so-is the one which would be expeeted if tlıe subpopulations of tlıe Tinıp
community differed in average leyel of inbreeding and if the Tİrııp population was more
highly inbred than the Lille Set. Mikkelsgade population.
The Tirup Early Medieval populalion was a rural peasant population whcrcas the Lille Set. Mikkelsgade populalian was an urban population from the ımportant
Merlieval eity of Viborg in the center for Juılancl. Doldsen (12) and Kieffer-Olsen el al
(13) have shown that the mortality profile differed widcly between urban (Lille Sel. ivllkkelsgade) and rural (Tirup and Lddckpinge) Mcdieva! skeleta! saınplcs. The urban
morLQlity profile intlicaıes II large iınmign:ııion surplus of young adult pecpk -mostıy
females. This pattem can not be scen in the ıural mortality profiles. The immtgralion into ıhe lown,S and cil.ies effeelive!y prevented inbrecding in the urban communities.
Tirup was a rather smail parish wiıh only around 80 inhabltants. The majority of thc:se were children who died befüre rcaching adulıhood and ıhus die! not contribuıc 10 the reproduction of the community. In communities wilh such smail size of the breeding popularinn the genetic slruclUre is likely to change quickly. However, Meclieval rules
164 J,L. 130LDSE~
for the avoidance of ineestuous marriages were comprchcnsive. These rules füreed a sizeabIe fraction of the rnembers of sıııall communilies to find their spouse outside Ihe parish.
The demographic strııetııre of the Tirup comınunity and Medi,wal maıriırıorıia!
legislation have formed the background for a simulation study of the development of the genetic stnıclurc of smail rural comnıunities in Medieval Juıtand, II was found that on average around a third of all marriages involved a spoııse who was not natiye to the community. The average level ofinbreeding rosc quitc quickly and reached arather high
level. However, the people who were children of an immigrant parent were not inbred at all kaving the rest of the population tü be even more highly inbred.
The simulation study indieatcd that a rural community likc the Tirup parish was likcly tO consist of a mixture of highly inbred majorityand a large minority of randomly bred individuals. Randomly brcd rnembcrs of small rural eoınrnunilics are, of curse, expected morphologically to resemble other randomly bred members of the
Medicval JutIane! population. This means thal the large minority of the small rural population is expected to resemble the urban population from the same main provincc and general period.
The resemblance of the long tarsocd subpopulation in the Tirup skelctal sampk to the body proporliOllS of the urban Lil1e Set. Mikkelsgade eommunity cloes not prove the suggestcd interpretation. However, the hypothcsis that this aspeet of the genetie populatian stnınure is the reason for the morphological dierıotonıy in the Tinıp
community does gain crcdibility by the fact that twü independent lincs of evidence and inrerpretation leads to the same conclusion.
The prediction variance for hcights predieted in the Tirup population is larger than should be expeeted from the common cQvarianee matrix. This IS due to the
morphological inhomogcneity of the skeletal sampk. However, if it bccomes possible to determine whieh of the !Wo subpopulations a given skeleton belongs to, the prediction error in the Tirup communiıy would drop to a level considerably below that
expcct.ed from the eommon covariance matrix.
The variance of the torso length estimatee! from the comrnon covarianee matrix and
the height prediction variance estimated from the same covariance matrix are nearly equaL The correlation between the sum of femoral and tibia lengths and the [OrSO lengtlı is law (r=0.23). This means that ıhese long bones only explain so me 5.5% of the varianee of the torso lengıll.
In general there are two problems in height prediction bath for forensic purposes and for the sake of general human biologieal studies. The regression formuıae are too inaecurate and theyare only applieable to the population from which they have been derived viz. the diffcrence in body proporıions beıween the Tirup anel the Lille Set. Mikkclsgade popuJations and within the Tirup sample.
The finding anel deseription of a ınajor varianee eomponent for the distribution of height whieh is unrclatcd to the boncs which are most commonly used for height
prcdie-Body Proportiorıs, Population Stmeture and He:ight Prediction 165
tion is a starıing poim for research into the pOlentials for the iınproveınent of forınulac
used for height prediction. We are presently working on the coIlection of measurements
which might independently correlate with the length of the torsü. Extremely preliminary results (hased on around! O skeletons) indicate that j[ might he possible to reduce the
prediction variance by up to 50% and simultaneously widen the applicabilüy of the derived formuıne.
REFERENCES
Pearson, K. (1899) Plıi/os. Trans. R. Soc. Sa., A 192, 1- 128. 2 Telkkli, A. (1950) Acla Anaı., 9, IOJ-l 17.
3 Boldsen, J.L. cı 984) Am. J. Phys. Anılıropol., 65, 305 311.
4 Trotter, M., Gleser, G.c. (1952) Am. J. Phys. Anllıropol., LO, 463-514. 5 Trotter, M., Gleser, G.C. (1958) Am. J. Phys. A.nıhropol .. 16, 79123. 6 Boldsen, I.L, Kreffcr-Olsen, l, Pentz, P. (1985) Skı:ılk, 1985, no. 4, 6-LO.
7 Martin, R., Sa ller, K. (1957) Lehrbııch der Anlhropologie in systemaıische Dars/el/ımg. Ve.r!.ag Gustaf Fisher, Bundesrepuhlik Deutschland.
8 Payne, CD. 1(87) The GUM System Release 3.'i'l, Royal Staııstical Socıeıy, London 9 Cox, DJ., Sma!!, N. J. H. (1978) Biomeırika, 65,263-272.
LO Boldsen, l.!.., Sorensen, M. (1984) Ossa. 9-11,13-28.
11 Cava!lı-Sforza, L.L., Bodmcr, W.F. (1971) The Genel/es of Human Pnpu!ations. freeman, San francisco.
12 Bold,en, ).1.. (191\4) Meddelandenfrn Lunds Universitets Historıska Museum. New series, S, 10'/-! 15. 13 Kieffer-Olsen, J, Boldsen, J.L., Pentz, P. (1986) Vejie Amls rbog. 1986,24-5L.
Rcprints requ{;sl to Dr. ksper L. Boldsen Institute of Communiıy Health Dcpanmcnt of Social MedLcine University of OdellSe
1.11 Winslowsvej 17 DK 5000 Odcnsc C Derunark
