PALEODEMOGRAPHY

Paleodemography attempts to reconstruct past population structure using samples of human skeletons, either freshly excavated or stored in museum collections, from archaeological sites. Its chief claim to legitimacy is that it provides demographic information–albeit of a limited, indirect, and uncertain sort–about the many human populations in the past that left no written records. In principle, paleodemography also allows the reconstruction of demographic trends over time spans that are unattainable by any other branch of population science. Because of persistent methodological problems, however, paleodemographic analysis has achieved only limited credibility among mainstream demographers. Yet while it is fair to say that past paleodemographic analyses were often too crude to be believable, it is also true that recent methodological advances, not yet known to most demographers, have moved paleodemography to a firmer scientific footing. The most important such advances have been in the areas of age estimation, mortality analysis, and adjustments for the effects of demographic non-stationarity on skeletal age-at-death distributions.

Age Estimation

Osteologists have made great progress in identifying reliable skeletal markers of age. Information on age at death is provided by skeletal features such as dental development, annual increments in dental cementum, closure of long-bone epiphyses and cranial sutures, and changes in the articular surfaces of the pelvis. Ages based on such features are subject to differing degrees of error arising from the inherent variability of the underlying processes of maturation and senescence. The age of juveniles can be estimated much more reliably than that of adults, and younger adults more reliably than older adults. But all paleodemographic age estimates are inherently error-prone and always will be. However much osteologists work to reduce these errors and identify new age indicators, a large degree of aging error will always be a part of paleodemography.

The most difficult problems of paleodemographic age estimation are statistical rather than purely osteological. In addition to a target sample (the archaeological skeletons whose ages are to be estimated), the paleodemographer needs access to a reference sample of skeletons whose ages at death are known. Several well-known reference samples–for example, the Hamman-Todd and Terry Collections–provide reasonably accurate data on the joint distribution of c and a, where is a vector of skeletal traits that provide information on age and a is age itself. For the target sample, however, researchers know only the marginal distribution of c, from which they hope to estimate the marginal distribution Pr(a) of ages at death. One of several parametric or non-parametric methods can be applied to data from the reference sample to estimate the conditional probability density or mass function Pr(c | a). If these estimates are to be used in estimating ages of archaeological skeletons, one needs to make an "invariance assumption" that the joint distribution of c and a is identical in the two populations from which the reference and target samples were drawn. It is by no means clear that this assumption is warranted for many skeletal traits, and an ongoing goal of paleodemography is to identify indicators that are both informative about age and reasonably invariant across human populations.

Insofar as the invariance assumption is correct, it would seem to make sense to combine data on Pr(c) in the target sample and the joint distribution of a and c in the reference sample to estimate Pr(a | c) for each individual skeleton. But according to Bayes' theorem:

where Pr(a) is the age-at-death distribution in the target sample, which is unknown.

A procedure for estimating Pr(a) was recently developed by Hans-Georg Müller and his colleagues(2002). Briefly, Pr(a) is specified as a Gompertz-Makeham or similar parametric model, Pr(a | θ),with parameters θ which can be estimated from the reference sample using a maximum-likelihood technique. Once the parameters of Pr(a | θ) have been estimated, the expected ages of individual skeletons can be found by a straightforward application of Bayes's theorem. This approach to age estimation is called the Rostock protocol because it grew out of a series of workshops held at the Max Planck Institute for Demographic Research in Rostock, Germany.

It will seem strange to orthodox paleodemographers that they need to estimate the entire age-at-death distribution before they can estimate individual ages–the reverse of their usual procedure. But the Rostock protocol actually solves a number of problems that have long plagued paleodemography, including the "age mimicry" problem first noted by Jean-Pierre Bocquet-Appel and Claude Masset in 1982. In addition, the method can be used to obtain not just point or interval estimates of age, but the entire error structure of the age estimates. Important statistical problems remain to be solved, such as whether to use discrete categories or "staged" traits versus more continuous age indicators, and how best to use multivariate skeletal data when traits are correlated in their age trajectories. But these problems can all be attacked within the framework of the Rostock protocol.

Mortality Analysis

For years paleodemographers have used skeletal ageat-death data to compute life tables based on some simple modifications of conventional life-table techniques originally developed by the Hungarian demographer and archeologist Gy. Acsádi and J. Nemeskéri. Though this approach is still a common one, the paleodemographic use of life tables can be criticized on several grounds. First, paleodemographic studies do not produce the kinds of data needed to compute life-table mortality rates using standard methods–specifically, paleodemographers lack the numbers of deaths among people at each (known) age and the number of person-years of exposure to the risk of death at that age during some well-defined reference period. Second, the use of fixed age intervals in the life table implies that the ages of all skeletons are known within the same margin of error, including those of fragmentary skeletons that exhibit only a few unreliable indicators of age. Third, the life table is a wasteful way to use the small samples typical of paleodemographic studies–samples that are often on the order of a few dozen or a few hundred skeletons. In computing a life table demographers need to estimate one parameter (an age-specific mortality rate) for every age category by sex in the table. Few paleodemographic samples will support such a data-hungry approach to estimation.

The Rostock protocol supports an alternative approach to paleodemographic mortality analysis. If unbiased estimates of the parameters of Pr(a | θ) can be obtained for the target population of interest–and if the effects of demographic non-stationarity can be removed (see below)–the parameter estimates can be used to derive the survival function, the age-specific probability of death, life-expectancies, and anything else one might hope to learn from life-table analysis.

Demographic Non-stationarity

Another shortcoming of traditional paleodemographic life-table analysis is that it assumes that the population under investigation was stationary: that it was closed to migration, and had an intrinsic rate of increase equal to zero, age-specific schedules of fertility and mortality that were unchanging over time, and a balanced age distribution generated by those age-specific birth and death rates. Only in this special case is the empirical age distribution of skeletons expected to have a simple, straightforward relationship to the cohort age-at-death column in the life table. This problem was recognized by Larry Angel, one of the early practitioners of paleodemography, and remains a concern.

As demographers have long realized, the age structure of a non-stationary population–and thus the number of its members at risk of death at each age–is more sensitive to the level of fertility than to the level of mortality. Thus, age-at-death distributions from different populations are at least as likely to reflect fertility differences as genuine differences in mortality. This incontrovertible fact of demography has given rise to the odd notion that paleodemographic age-at-death estimates are more informative about fertility than mortality. In fact all demographers can ever hope to estimate about fertility from such data is the crude birth rate, which is scarcely a measure of fertility at all. But if paleodemographers could correct for demographic non-stationarity, they could extract quite a bit of information about age-specific mortality from skeletons, and perhaps even estimate the population's growth rate.

Let f₀(a) be the expected age-at-death distribution for a single birth cohort in the target population. If the target population was stationary, the same distribution holds for all deaths occurring in the population. But even if the population cannot be assumed to have been stationary, it may be reasonable to assume that it was stable. That is, demographers may be able to make all the assumptions listed above for the stationary population, with the exception that they should allow for the possibility of a non-zero growth rate. (The assumption of stability is much less restrictive than that of stationarity: even when fertility and mortality rates are changing and migration is occurring, most human populations still closely approximate a stable age distribution at any given time.) In a stable but non-stationary population, the age-at-death distribution is only partly a function of age-specific mortality; it is also influenced by the number of living individuals at risk of death at each age, which is influenced in turn by population growth. More precisely, the probability density function for ages at death in a stable population with growth rate r, f_r(a), can be expressed in terms of the target population age-at-death distribution, f₀(a), by:

As David Asch showed in 1976, this expression also applies to all the skeletons accumulated by a stable population over some more or less extended span of time–for example, the period over which skeletons were deposited in a cemetery. In principle, then, f_r(a) can be treated as the Pr(a | θ) function in the Rostock protocol, and r can be estimated as an additional parameter of the model, if the population can be assumed to be stable. And if it was not stable, at least approximately, paleodemographers have probably reached the limits of what they can ever hope to learn about age-specific mortality from skeletal samples.

Prospects

The most important recent developments in paleodemography from the perspective of the early twenty-first century have been methodological, not substantive. But now that paleodemographic methods have become more sophisticated, there is every reason to expect that important empirical results will be forthcoming. It is likely, too, that the findings of paleodemography will be strengthened by the study of DNA extracted from ancient bones–a field that is already starting to provide insights into the ancestry and kinship structure of past populations, as well as the pathogens that infected them. There is also a new and encouraging movement to bring archaeological settlement studies, long an established approach to past population dynamics, into the purview of paleodemography. Another useful development has been the study of historical graveyards where cemetery records or parish registers exist to cross-check the osteological results. While mainstream demographers were once justified in dismissing the field of paleodemography, it may be time for them to rethink their skepticism.

See also: Archaeogenetics; Evolutionary Demography; Prehistoric Populations.

bibliography

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James W. Wood