STABLE POPULATIONS AND SKELETAL AGE

A common procedure in paleodemography is to use meon skeletal age to estimate the expectation of life at birth in a population. This paper shows that skeletal age and expectation of life at birth are not equivalent unless the population is stationary. This assumption is not justified for most real populations. We show that mean skeletal age is approximately equivalent to the reciprocal of the birth rate and is not correlated with the death rate. Thus, the practice of inferring changes in life span and death rates from changes in mean age at death is not reliable and most conclusions of paleodemographic studies should be revised. On the other hand, skeletal age may provide high-quality information about fertility in archaeological populations. Several published paleodemographic studies are reinterpreted in light of the model presented. A COMMON PROCEDURE in paleodemography is to use mean skeletal age to estimate the expectation of life at birth of a population. The validity of this method depends upon the assumption of a stationary population in which birth and death rates are equal and population size remains constant. This assumption is not justified for most real populations-in most cases mean age at death and expectation of life at birth are somewhat different. For example, for the stable population corresponding to the vital rates of Sweden in 1778-1782 the mean age at death was 32.7 years, while the expectation of life at birth was 38.5 years (Keyfitz and Flieger 1971). This random example of a premodern, moderately growing population (p - .006) shows that the practice in paleodemography of using mean skeletal age to estimate expectation of life deserves careful examination. We wish to show with simple models and with empirical data that (a) for moderately growing or declining populations the effect of a change in mortality on age at death is nearly nil, while changes in birth rate lead to proportional changes at age at death, and (b) the appropriate inference from mean age at death is that it is the inverse of the birth rate. Thus when, in a temporal series, mean skeletal age increases it means that the birth rate decreased, not that the expectation of life increased. With present methods skeletal ages provide no useful information about mortality or growth rate. The traditional interpretation of mean age at death as expectation of life proceeds from the assumption of a stationary population. In a stationary stable population the mean age at death is equal to the inverse of the birth rate and to the inverse of the death rate as well as to the expectation of life at birth. Stationary populations are rare, however, and under conditions of population growth or decline these statistics are no longer equivalent to each other. In general mean age at death (hence mean skeletal age) tracks the inverse of the birth rate and is effectively independent of the expectation of life and of the crude death rate. Skeletal age reflects expectation of life only if the death rate happens to be precisely equal to the birth rate. This is not very likely. This conclusion is not intuitive to us. The relations among demographic statistics are complex, and we have found no single simple and elegant way to relate skeletal age to other demographic parameters. We present instead in this paper two approaches to assessing the implications of skeletal age for paleodemography. First, we will examine an oversimplified and unrealistic model of a stable population characterized by a uniform age-specific death rate. This particular model is amenable to algebraic analysis, and we hope that the results of analyzing such an oversimplified