By Griffith Feeney
Formal demographic concepts have myriad applications both within and beyond the study of human populations. The object of this paper is to explore systematically the nature and limits of this generality. `Populations' are defined in a way that leaves the nature of the entities comprising them entirely arbitrary. It is shown that most tools and concepts of demographic analysis apply in this completely general setting. Recognition of the full generality of `demographic' analysis is a powerful tool for understanding because it reveals limitations as well as capabilities. The implications of these results for our understanding of the technique and substance of demography are discussed.
The range of formal demographic concepts is extraordinary. One of Alfred J. Lotka's earliest contributions to mathematical demography is a 1907 paper on the population dynamics of `material aggregates'. Kenneth Boulding provided the first formal definition of `population' and applied it to the theory of capital (1934) and to the automobile population of the United States (1955). Norman B. Ryder has detailed the application of population concepts to social as distinct from demographic aggregates (1964b), a theme continued in Ford and De Jong (1970). Hartshorn (1975) has applied life table and matrix population dynamics concepts to the study of tree populations in tropical rain forests. James R. Carey has spent much of the past decade developing the discipline of- with apologies to etymological purists- `insect demography' (1982, 1983, 1984, 1985).
It would not be difficult to extend this list with more diverse and exotic applications. For most demographers, however, the important issues lie closer to home, in the application of familiar methods to new demographic situations. Life table ideas were developed for the study of human mortality, but they have long been applied in the most diverse corners of the field, including the study of marriage and divorce, birth intervals, and contraceptive use. Reflecting on this diversity, we find certain common elements. In every case we deal with one or more subpopulations of a given human population; in every case certain events signify entry to and exit from the subpopulation; and in every case the entry and exit events are formally analogous to birth and death, allowing the introduction of life table concepts.
The object of this paper is explore systematically the nature and limits of generality of formal demographic concepts. I begin by proposing a formal, set-theoretic definition of the population concept, a definition that strips away any vestige of reference to the particular nature of the entities that comprise the population. `Population analysis' is then taken to be the study of those propositions that hold for populations in general, whatever their members may be. I proceed ask how much of what is generally recognized as formal demographic analysis may be derived from this definition. The answers are surprising and instructive, both for how much of what we think of as 'demographic' analysis is in fact entirely general, and for how much more there is to demography than population analysis.
Mathematics teaches that abstraction sharpens understanding. The formalization of population analysis provides a striking case in point. The familiar concept of a population closed to migration seems an unlikely subject for intellectual (as opposed to definitional) subtlety, but its extension to subpopulations requires some unexpectedly sharp thinking. Life table concepts are centuries old, the last place one would expect to find unanswered questions, but determined abstraction yields at least one. The very definition of 'population' provides insights into the mundane but important problem of organizing demographic data.
Disciplining ourselves to think abstractly about familiar ideas enables us to think more clearly and deeply about certain aspects of them. This is not to deny that our ultimate concerns are more complex, nor that there will always be a time to move from the abstract to the particular. It is simply to say that we are likely to get further in complex matters if we have first mastered some of their simpler aspects.