Introduction
Stature provides one aspect of an individual’s physiognomy and one piece of information that may be an aid in individual identification. In situations where the corpse is severely mutilated, decomposed or represented by skeletal remains only, the stature of the individual may be estimated by means of measurements of the skeleton, in certain cases after necessary maceration at a forensic laboratory. Suchestimation is based on the relations between skeletal elements and stature. As a rule of thumb, the larger the skeletal element, the taller the individual. This means that, theoretically, any measurement of any bone or measurements of combinations of bones of an individual reflect that individual’s stature. Because of individual variation, however, a stature estimate is always hampered with a probable error, although each method of estimating stature from skeletal measurements aims at estimating the stature as exactly as possible.
Most methods of estimating stature from the skeleton are based on the long bones of the upper and lower extremities. Others deal with stature estimation from parts of the skeleton, either single bones or combinations of bones. Yet others estimate stature from incomplete bones, normally parts of long bones.
Bones recovered in forensic situations may either have been lying on the surface, in the ground or in water. The six long bones of the skeleton are generally composed of a shaft forming a tube of compact bone with a marrow cavity along the middle of the tube, whereas the interior of the bone ends has a rigid, spongy structure, covered by a thin layer of compact bone. Even the compact bone consists of a complicated, microscopic system with a number of pores for small vessels for blood supply and transportation. Therefore, if not completely fresh, a bone is generally more or less moist when recovered, particularly if it has been exhumed from the ground or from water. If it has not been lying exposed for a sufficiently long period of time so that it has become dry, it may tend to break, although this also depends on the amount of organic matter left in the bone. Even compact bone may tend to break, and the thin, compact bony layer at the bone ends may easily be damaged if not handled with care. It is self-evident that an undamaged bone facilitates further investigation. Every bone should be handled carefully when removed from a forensic site, to ensure that it is as complete as possible for measurements specified for stature estimation to be taken.
Considerations regarding age, sex and ethnicity may be made when estimating stature from the skeleton. Ethnicity may be understood either in terms of Caucasoid, Mongoloid or African origin or descent, or as inhabiting a particular country, or both. An argument for this is that an individual’s stature is a result of both genetic and environmental (including nutritional) factors in a way which is not fully understood. Differences in skeletal body proportions in relation to stature may depend on each of these factors in combination.
Stature increases during childhood and through puberty, until all bone growth has ceased after adulthood is reached. Growth during this period is variable, and there is an individually more or less accentuated ‘growth spurt’. Before estimating stature, it is therefore necessary first to determine if the individual is an adult from the point of view of skeletal growth. As for different ethnic groups, body proportions may vary because of selective adaptation to different kinds of climatic zones characteristic of each group.
Some words of caution should be given when estimating stature from the skeleton or judging the quality of a given method. Humans of the same population vary in body proportions, even individuals know to have the same stature. This means that for every given stature there are individuals with long trunks and short extremities or short trunks and long extremities, although the proportions are centered around mean population values. Because of this, for every estimate of stature from skeletal measurements there is an uncertainty because of the variability within the population. In general, the higher the correlation between the skeletal measurement(s) and the stature, the more accurate an estimate of the stature may be. In particular, this applies to the long bones or combinations of long bones. Conversely, if the part of the skeleton measured is small, greater uncertainty may be expected because of the lower correlation between stature and skeletal measurement. If the whole skeleton can be measured, or at least measurements of the single bones adding up to the skeletal height, allowing for the missing soft tissue, this may be preferable. Indeed, stature calculated from skeletal height has been used to represent stature when developing formulas for estimating stature from long bones (see Methods below).
In some cases methods have been tested in actual forensic cases when positive identifications have been established by means of other evidence. If the deviation between the estimate and the known stature is found to be small, this is taken to be a good property of the method. However, this may not mean that such a method is bad if there are larger deviations. It should be borne in mind that a particular method aims at a good result on average, which may not necessarily mean an optimum result will be achieved in each individual case. For every method of estimating stature from the skeleton, there will be a smaller or greater difference between estimated stature and actual stature. Ideally, this difference should be zero; that is, that the estimate of the stature is exact. What is sought therefore is a method where bias is as small as possible.
Stature as a Concept
Stature is not a fixed value for any individual at any age but is influenced by different factors. Every individual’s stature tends to decrease during the period from getting up to going to bed. This decrease is due to the elasticity and compression of intervertebral disks and joint cartilage and load carried by the body during walking upright or sitting. Such a load may be due to both the body weight and the actual loads carried or lifted. Extreme reduction of stature as a result of carrying of heavy loads have been reported – up to some 10 cm in some cases – although a decrease of 12 cm may be regarded as normal. The time lapse or repeatability of exposure to the load is an important factor in the decrease, as is the period of rest for the body to restore the amount of vertical elasticity. The possible decrease in stature may also be related to stature itself: during the period out of bed, a tall and obese individual may have greater potential for stature decrease than a short and slender individual.
Another important factor is age, because the elasticity of the intervertebral disks and cartilage decrease by age. With increasing age there is a general tendency towards stature decrease. The decrease is generally regarded to be approximately 6 mm per decade after the age of 30. When estimating stature, the age factor may be accounted for by first calculating the maximum stature attained by the individual and then adjusting for decrease due to age; however, stature decrease due to age may not be completely regular, and individual variation occurs. For instance, in old age stature decrease may be substantial during a short period of time, owing to changes in posture or gait that may affect some individuals more than others. This means that information of stature given in, for example, passports, driving licences or military records are at most fair approximations of a feature which is not exactly fixed. Sometimes, recorded stature may not even have been measured but entered on the basis of oral information. Nevertheless, stature or estimates of stature provide important information for identification purposes.
Materials for Stature Estimation Methods
All methods of estimation of stature from the skeleton are based on different kinds of samples from the populations they are regarded as representing, or from combinations of samples from different populations. Knowledge of some sort of stature and bone length is always required in order to develop any method for stature estimation, although in most connections direct information is only known for one of the two kinds of data, either stature or bone length. The main effect of this is that, if one kind of data is not known but has to be estimated, the correlations between stature and bone length tend to be underestimated, leading to a slightly higher standard error of stature estimates in comparison to methods based on both known stature and known bone lengths. The idea of stature estimation is, however, to provide an estimate of the maximum stature attained by an individual, which may be adjusted depending on information about the age of missing persons from whom the skeletal remains may derive. Five different kinds of source materials are encountered among existing methods for stature estimation:
1. In the ideal case, both (maximum) stature when living and bone lengths after death. Only a few cases exist where this condition is satisfied, mostly related to victims and repatriation of identified individuals temporarily buried during the World War II, although there are other cases where for some reason both stature during life and bone lengths after death have been recorded. Reported forensic cases where positive identification has been successful, where documented stature and bone measurements exist, provide additional data for a databank for further development of the methodology. For this kind of method both stature and bone lengths are primary data.
2. Dissection-room materials, that is cadavers and corresponding macerated bones measured. In this case, cadaver length has to be converted to stature by subtraction of postmortem extension of the length of the cadaver. Cadavers are known to increase in length after rigor mortis, due to the loosening of the intervertebral disks and slackening of the vertebral curvature. This increase is considered to be of the magnitude of 2-2.5 cm. In some cases the cadavers have been mounted, restoring the spinal curvature in order to approximate standing posture when living, and in other cases the lengths of cadavers have been measured on a dissection-room table. Although in the first case the stature of the mounted cadaver has been regarded as a measurement of the individual’s stature, age effects may not be completely ruled out. However, as for cases where cadavers have been measured in a supine position, the mean age of individuals making up such samples is generally fairly high, and it may be argued that reduction in stature due to age may to a large degree be compensated by the postmortem extension of cadaver length. For this kind of method stature is not primary data, whereas bone lengths are.
3. Somatometric materials, that is stature of individuals have been measured and their physical extremity proportions measured. The extremity proportions are converted to bone lengths by means of mathematical conversion formulas. For this kind of method stature is primary data, whereas bone lengths are not.
4. Somatometric materials using X-ray, that is living individuals measured and their extremities X-rayed. This is a variation of (3), as measurements of the bones on the radiographs are used. The method has the drawback that the X-ray beam must be positioned precisely in relation to the bone for each individual in order to produce the measurement aimed at, a problem that may create additional, random variation. Using X-ray methods, the degree of magnification of bone lengths is a function of the distance of the X-ray film to the bone and the X-ray source. The X-ray beam also has to be positioned in exactly the same way for every new application. For this kind of method stature is primary data, whereas bone lengths are not.
5. Methods where stature has been estimated from skeletal height, and bone measurements have been taken from the same skeleton. For this kind of method bone lengths are primary data, whereas stature is strictly speaking not.
Methods for Stature Estimation
The methods in use may be divided into four categories based on:
• least squares regression equations;
• other regression principles;
• stature:bone length ratios;
• skeleton height and adjustment for missing soft tissue.
For each of these methods sex and race may also be a matter of concern. These two factors become particularly important when sex or race or both are unknown, a situation which may frequently be encountered in forensic cases, particularly when only skeletal remains have been recovered. The ultimate aim, however, is to be able to produce an estimate of the stature which is as close to the actual stature of the unknown individual as possible.
A large number of studies on stature estimation have been published. Most of these concern stature estimation based on measurements of the long bones of the extremities. An important reason for that is that such methods minimize the error caused by biological variability. Although methods have also been developed using other bones, the uncertainty tends to grow so that the accuracy becomes too unsatisfactory. The same concerns stature estimation of children, where methods have been developed based on immature skeletal parts. Even in this case there are large uncertainties that depend on the rate of skeletal development of the children. Therefore these aspects are not discussed further here, although the general considerations made are also applicable in such cases, and the reader is referred to the Further Reading list for more information. The only method discussed that is not based on measurements of the long extremity bones concerns stature estimation based on skeletal height.
Stature estimation from long bones based on least squares regression
Most methods for estimating stature from long bones are based on this principle. It implies that the standard error is as small as possible from a mathematical point of view. The method is based on the principle that it minimizes the sum of squared deviations from the individual stature:bone length values which represent the sample used for calculating the formula for estimating the stature. This kind of method has both advantages and disadvantages. An advantage is that the errors are minimized when regarding a large number of individuals from the population on which the method is based. On the other hand, a disadvantage is that these methods, strictly speakng, should not be used for individuals from another population, and the longest bone does not reproduce the tallest individual nor the shortest bone the shortest individual, but tend to underestimate the tallest and overestimate the shortest. Experience has also shown that secular trends in a population may cause problems because of alterations of stature:bone length proportions in the population, so that measurements of individuals of a later generation may become incompatible with the proportions on which the original method was based. Significant changes of this nature are known to have taken place, for example in the USA between World War II and the Korean War.
The term ‘population’ in this connection is, however, not a true biological concept. The only inference that may be made is that a sample used for any method for stature estimation consists of humans displaying certain relations between stature and bone measurements, which may be given in terms of sample size, mean values, standard deviations and correlations.
Another way of looking at the deviation between estimated and actual is to regard the confidence contours of the regression line slope. This takes into account that each method is based on a sample, from which the regression line is calculated. However, since sample bias may exist, the slope of the regression line is also determined with some uncertainty, and may be allowed to vary, that is be less steep or steeper than the slope calculated from the regression line. Since the regression line passes through the mean value of the sample, estimates close to the mean value are connected with the smallest probable errors. The further away from the mean value, the larger the probable error. The reason is that every estimate is related to the population from which the sample used for the method derives, which means that every new case applied to a regression equation is formally regarded as belonging to the same population.
Least squares regression may also be presented in terms of multiple regression, by means of which stature may be estimated based on several bone lengths, taking the correlation between the bones into consideration. When the most efficient bones are incorporated into a multiple regression formula, the standard error of estimate may be further reduced. The number of bones successfully incorporated in a regression formula in order to estimate stature has, however, a limit. This limit is determined by the amount of information about the stature which is provided by the bone measurements. If still more bones are added, the standard error tends to increase compared with its minimum value, because more variability than information is introduced. In most cases, this limit is reached by means of two or three bone measurements.
Because the mean stature of males is higher than that of females in every population, regression equations have to be developed for both males and females. Different regression equations for males and females are also needed because the body proportions of males and females differ. These differences are partly due to differences in mean stature, but may also be due to female skeletal adaptations of the pelvic girdle in order to be able to give birth, broadening the pelvic inlet, and adapting the inclination of the shaft of the femur to the broadened pelvis.
Most methods for stature estimation based on skeletal parts other than the long extremity bones are based on least squares regression (see Further Reading).
Stature estimation based on other regression principles
Since regression tends to overestimate the stature of the shortest individuals and underestimate the stature of the tallest individuals, an alternative has been to use a so-called regression II model, also known as the reduced major axis. The line calculated is related to least squares regression, and may be denoted least triangles regression. It minimizes the sum of triangles formed by looking at the deviation from the line for all individual stature:bone length values in the sample, with one side formed by the deviation from the line along the stature axis and the other at a right angle along the bone length axis, with the line itself forming the third side of the triangle. Theoretically, using this method, the longest bone reproduces the tallest stature and the shortest bone reproduces the shortest stature.
A generalization of this method based on information on mean stature and mean long bone lengths from worldwide populations is called the weighted line of organic correlation because differences in sample size are taken into consideration, so that a large sample is given more weight than a small sample. This kind of method has even been shown to be independent of sex because differences in stature: bone length proportions between males and females as expressed by sample mean values appear to be primarily related to stature differences; a similar argument may also be applied with regard to ethnicity. The changes in proportions among females because of skeletal adaptation for giving birth appear to be negligible in comparison. Because of the regularity of the stature and long bone mean values for random, worldwide populations, the method also aims to cover changes in stature of a population over time due to secular trends, and may also be used if race and ethnicity are unknown. On the other hand it is clear that, if ethnicity is known, a method based on that ethnic group will be better than a method based on worldwide populations.
Stature estimation based on stature: bone length ratios
Another worldwide survey of the relationship between mean stature and mean femur lengths has shown that this relationship appears to be rather stable throughout the world. Though presented as a femur:stature ratio, it is actually the stature:femur ratio that is used for stature estimation of an unknown individual. The stature:femur ratio is derived as 3.74, corresponding to a femur:stature ratio of 26.75, based on maximum length of femur (see Measurements below). Therefore stature may be estimated using this ratio instead of using more complicated formulas when the femur is available. It is argued in favor of such a method that every regression method has an error, so using a simple ratio instead will most likely provide a stature estimate that is within the standard error of a regression formula. Tests of this principle on skeletons of identified war casualities have shown it to do better than least squares regression; that is, estimates with less deviation from the known stature for tall individuals than the corresponding least squares regression equation.
Although in the beginning it was assumed that such a ratio would be independent of sex and ethnicity, tests have shown that this is not strictly the case, and different ratios may be applied depending on sex. As for differences between ethnic groups, tests have furthermore shown that when the ethnicity is not known, which is frequently the case when only skeletal remains of an individual are recovered, the error made when using a generalized ratio is less than when using a ratio for a certain ethnic group if it later turns out that the individual belonged to another ethnic group than the one on which the ratio was based. So far, however, the standard error of this ratio has not been derived, though it may be expected that it is larger than that of the reduced major axis. In comparison to regression and the weighted line of organic correlation, use of the stature:femur ratio will rather tend to overestimate the stature of the tallest individuals and underestimate the stature of the shortest. Furthermore, the stature:femur ratio represents a line that passes through the origin, whereas both regression and the weighted line of organic correlation are lines adapted only to the data, and is not forced to pass through the origin as well. In the last major study by the group dealing with the ratio, however, it was found that a generic regression based on worldwide data, almost identical to the corresponding equation based on the weighted line of organic correlation, performed even better than the ratio, meaning that mean body proportions change when stature changes. This fact was even noted by the Frenchman Leon Manouvrier in 1892, who was the first to publish a method on stature estimation from the skeleton for general use, although it is now only of historical interest.
Stature estimation based on skeletal height
Regarding the skeletal elements adding to stature, it may be claimed that, standing upright, stature comprises the height of the skull, the height of the vertebral column, the sacrum to the level of the top of the femoral head, the length of the femur in its natural position, the physiological length of the tibia, and the height of the articulated talus and calcaneus from the foot, to which is added the thickness of soft tissue.
The height of the articulated calcaneus and talus of the foot is measured as in the standing position, the physiological length of the tibia is measured from the distal articular surface to the proximal articular surface, and the length of the femur in the natural (bicondylar) position is measured as defined under Measurements below. Since it is difficult to reconstruct the curvature of the vertebral column from a disarticulated skeleton, the height of the anterior (ventral) side of all vertebral bodies, from the first sacral vertebra to the second cervical vertebra, including the odontoid process (dens axis), may be regarded as the length of the vertebral column. The first cervical vertebra (atlas) is excluded because ontogenetically the body of the atlas is assimilated with that of axis to form the odontoid process of the axis. The height of the skull is measured as the distance between the basion and the bregma. This measurement is regarded as the height of the skull because it is easy to measure and because there are individual variations as to how to define the height of the skull when regarding a living individual. To the accumulated sum of measurement is added 10 cm if the sum is less 153.5 cm, 10.5 cm if it is between 153.5 cm and 163.4 cm and 11.0 cm if it is 163.5 cm or more, to compensate for the net thickness of missing soft tissue.
Stature estimation formulas based on least squares regression have even been developed for parts of the elements included in the skeletal height, although the methods make the application population-specific, and they are therefore not discussed further here.
Measurements
Apart from the measurements described in connection with the estimation of stature from skeletal height, all measurements should be made with an osteometric board. The measurements described are those normally used for the six long bones.
• Humerus, maximum length. The distance from the medial margin of the trochlea to the highest point of the humeral head. The humeral head is placed against the vertical wall of the osteometric board and the block at the medial margin of the trochlea. The bone is moved in any direction until maximum length is obtained.
• Radius, maximum length. The greatest distance from the tip of the styloid process to the margin of the radial head, measured by the same procedure as for the humerus.
• Ulna, maximum length. The maximum distance between the highest point of the olecranon and the most distal point of the styloid process, measured by the same procedure as for the humerus.
• Femurmax, maximum length. The distance between the highest point of the femoral head and the most distal point of the medial condyle while the bone is lying on the osteometric board with the medial condyle touching the vertical wall. The bone is rotated until maximum length is obtained.
• Femurphys, physiological length, length in the natural position (bicondylar length). The vertical distance from the femoral head to the vertical wall of the osteometric board when both condyles are placed against the vertical wall.
• Tibia, total length. The distance from the tip of the medial malleolus to the lateral part of the lateral condyle. The tibia is placed with the dorsal side on the osteometric board with the apex of the malleolus against the vertical wall, the longitudinal axis of the bone at right angles to the vertical wall, and the block placed against the lateral part of the lateral condyle. The measurement should not be confused with the maximum length, which includes the intercondylar eminences.
• Tibiaphys, physiological length. The distance from the center of the proximal, medial articular surface and the base of the medial malleolus, at the articulation with the talus. Measured with a large spreading caliper.
• Fibula, maximum length. The direct distance between the most proximal and the most distal points of the fibula. Note, however, that when drying, the fibula may tend to bend to a curve, in which case this measurement is no longer possible.
In the German literature, following the measuring system of Rudolf Martin, all measurements are measurement no. 1 for each particular bone, except for the bicondylar length of femur and the physiological length of tibia, which are measurements no. 2. In Appendix 1, the latter measurements are indicated by the subscript ‘phys’.
