The approach to population structure followed in this work is that of stable population theory as developed by A. J. Lotka and others. An early exposition of this theory is found in Lotka (1956); more recently it has been summarized by Coale (1972), Keyfitz (1968), and Shryock and Siegel(1971).

The theory of stable populations requires that a population is infinite in size, has no net immigration or outmigration, and has fixed rates of fertility and mortality at each age. These assumptions are often approximated closely enough by real populations for the theory to be useful. Given the stated conditions, a population is described by its age distribution, or the number of individuals at each age. Since the theoretical population is infinite, the age distribution is defined in terms of relative numbers or percentages rather than finite numbers of individuals at each age.

The age structure is determined by the rates of mortality and fertility. It has been proved by Lotka that, no matter what the initial age distribution, a population under these assumptions approaches a certain age distribution which is determined by those rates. The result is the so-called stable age distribution since it will no longer change if mortality and fertility remain fixed. In fact, a temporary perturbation in these rates will only temporarily disturb the age distribution, which will quickly return to the stable form. Human populations approach the stable age distribution in well under 100 yr after the rates become fixed.

Our model life tables are based on data from censused primitive populations and from aged skeletal populations ranging from early lithic to medieval European cultures.

Censuses among relatively unacculturated primitive populations are rare. Most of the censused groups have long been contacted and affected by Europeans. They have been exposed to European diseases and medicine, affected by trade and technology, or influenced by missions and schooling among Europeans. Many live in reservation areas, or are otherwise confined by industrial populations which have invaded their former territories. It is difficult to isolate from published accounts the precise effect of contact on the population censuses utilized for this work, this source of “error”—that is, demography not representative of aboriginal conditions—is difficult to control. Yet, this work is not intended for use solely with primitive populations; were this the case, it should have been published 50 yr ago when there were more “aboriginals” remaining. Rather, it is intended to apply to any populations of interest to anthropologists, regardless of their degree of acculturation or development, so long as they can be said to approximate stable population assumptions.

To utilize skeletal populations, one must assume stable population conditions at the time of deposition of the skeletons; one must also assume that the sample is representative of the population, and that it is free from systematic aging error. In this chapter, we assume that the studies used satisfy these conditions.

The procedure for calculating mortality rates based on assigned ages of skeletons is simple and straightforward. Table 1 provides an example, the Illinois Hopewell Indians (Blakely 1971). There are 294 specimens distributed over 8 age classes including children. Assuming that this represents the stable mortality experience of any cohort in a non-growing population, a survivorship schedule can be derived.

The mortality between adjacent age classes can be estimated from the survivorship schedules derived in Chapter 3. The data, however, differ in each case in the number, size, and age limits of the age classes; therefore, it is not possible to derive strictly comparable information from the data sets. Further, it is not yet possible to define the internal mortality structure of each age class which must be known for the computation of many elements of the life table.

If we assume, as is commonly done in demography, that human mortality patterns follow some function of age, then we can fit our 50 source populations to that function and assume that deviations from that fit are merely stochastic. This process of curve fitting is called graduation, and it is a powerful and useful smoothing operation for mortality or survivorship data.

Chapter 4, and particularly Table 4, indicate a relatively narrow range of values for E(15), the life expectancy at age 15. This range, 12.3 to 34.6, just overlaps the lowest life expectancies in national censuses of the past 2 centuries (Arriaga 1968; Keyfitz and Flieger 1968). Even in the model life tables of Coale and Demeny (1966), “West” series, which are most applicable to pre-industrial populations, the lowest E(15) is 31.16. This particular value is found in a table which is an extrapolation of their regression lines well beyond the range of data on which the regressions were based.

Before the stable population can be fully characterized, the age-specific fertility rates needed to satisfy equation (1-4a) must be determined. For most anthropological data (and certainly for archaeological data) this information is not available. A method must be devised to estimate the rates of B(X), based on the assumption of a growth rate r and the mortality information.

The relative amount of fertility in females at each age during the childbearing period follows a generally similar pattern for most human populations: fertility begins at a relatively low rate at the age of menarche—in fact, there is generally a period of adolescent sterility (Montagu 1957), then it rises rapidly to a maximum from age 20 to age 30, after which it falls gradually to a minimum just before menopause. This general pattern is virtually universal among human females. We can use this degree of similarity to model our anthropological fertility rates.

The model life tables for stationary populations, together with the mortality and fertility schedules, are presented in Appendix C. This chapter annotates all of the elements in the tables: the names are given as they appear in our tables together with their standard denotation in the demographic literature, all elements are defined, and the formulas or algorithms for their derivation are presented. Since the tables apply only to stationary populations, the calculation of the table elements for growing populations is also outlined. Our notational format is somewhat different from standard notation to allow for computer printout and to better fit the goals of this work. For further details on the life table elements, the reader should consult Barclay (1958) or Shryock and Siegel (1971).

The model life tables should be compared to various data to illustrate their applicability. The comparative data should be independent of the populations used in the construction of the tables so that they can serve as controls for the models.

Russell (1958) carried out a comprehensive study of human mortality in late ancient and medieval times. The life table material in his work derives from ungraduated and unsmoothed raw data in the Corpus Inscriptionum Latinarum which lists tombstone inscriptions from ancient Roman areas. These data, together with some medieval British life expectancies also from Russell, are summarized in Tables 13 through 15. The mortality and life expectancy values closely approximate in range and pattern the values in our model life table series.

Many authors have written comparative articles on the history of human mortality and life expectancy; for example, see Acsádi and Nemeskéri (1970), Angel (1969), Brothwell (1971), Gejvall (1960), Genovés (1969), Goldstein (1953), Howells (1960), Kobayashi (1967), Russell (1958), Şenyürek (1951), Todd (1927), Vallois (1937, 1960). These studies are based on skeletal or historical material. Many of these studies have been used as data sources earlier in this work, and in fact several of the same data series are used by many of these authors.

Drawing on many of these sources, Deevey (1960) has recently analyzed the history of human life expectancies. This article has been reprinted and cited more than the others combined, and the life expectancies given by Deevey are used in many textbooks of ecology and anthropology. Deevey acknowledges the poorness of his source data, in particular the lack of juvenile skeletons. He also stresses that his life expectancies are only the adult mean ages at death. Yet, since Deevey's values are frequently taken as representative of total life expectancy, it seems appropriate to reexamine them in the light of this work and of material published since his paper. The life expectancies given by Deevey are shown in Table 22.

Biologists have long been concerned with the processes by which animal populations regulate their growth. The biological factors ultimately responsible for this regulation are fertility and mortality; their relative effectiveness in keeping growth within tolerable limits, and generally at, or cyclically around, zero, has been examined in several ways.

This and the following chapters will deal with the practical application of our life tables to anthropological data. In order to fit field data to a model, one must be confident that the data are as accurate and reliable as possible. This is difficult with anthropological data, especially if one is working from the literature. In this chapter the methods and common problems associated with the aging and sexing of anthropological populations are discussed. This discussion may help the reader to recognize questionable aspects of his data and to correct them prior to fitting a model table.

There is always the problem of the representativeness of the sample. If there is no direct evidence to suspect one’s sampling, the sample of skeletons or the census of a living population are usually assumed to be representative of stable processes. This is necessary to the application of our models. If a skeletal series is taken from a biased sample of burials, then of course it is not representative of the population from which it came. This is often true for juveniles (Schwidetzky 1965), and some means have been developed to make up for this deficiency. Where an unbiased, representative sample or census cannot be assumed, further demographic analysis is not likely to be productive.

The model life tables are constructed for field data which are fragmentary, incomplete, or lacking in detail. If a few gross measures can be determined which reflect the pooled experience of many elements of the population and hence are freer of stochastic variation, and if the stationary population assumptions are at all justified, a reasonable fit to a model can be expected with a minimum of work.

This work deals almost exclusively with stationary populations whose fertility function is assumed to be approximated by the K(X) values developed in Chapter 6. It is appropriate to consider how the shape of the fertility function may be adjusted to fit unusual field situations. Then we can show how the models can be adapted for populations with nonzero growth rates.

The models discussed so far have been, effectively, asexual.We have considered fertility in terms of females and their daughters, but we have used pooled survivorship data to derive model mortalities. In so doing, we have assumed an equal sex ratio at birth and equal sex-specific mortality rates. This introduces some error, and the direction is probably known: pre-industrial males have generally a higher adult survivorship than females, although the sex ratio may vary from age to age and from group to group (Weiss 1972b). Given our purpose and the quality of data available to anthropologists it is doubtful that the error introduced in this way is significant. A fieldworker who insists on constructing 2-sex models must have a larger data sample, so that the stochastic variations in age-class representation are minimized. But if the data seem sufficient and a 2-sex demographic model is desired, this chapter will present the methods by which such a model can be constructed.