Abstract.
A canonical/lognormal model for human demography is established, specifying the net maternity function and the age distribution for mothers of new-borns using a single macroscopic parameter vector of dimension five. The age distribution of mothers is canonical, while the net maternity function normalizes to a lognormal density. Comparison of an actual population with the model serves to identify anomalies in the population which may be indicative of phase transitions or influences from levels outside the demographic. Tracking the time development of the parameter vector may be used to predict the future state of a population, or to interpolate for data missing from the record. In accordance with classical theoretical considerations of Backman, Prigogine, et al., it emerges that the logarithm of a mother’s age is the most fundamental time variable for demographic purposes.
Similar content being viewed by others
References
Andresen, B., Shiner, J.S., Uhliger, D.E.: Allometric scaling and maximum efficiency in physiological eigen time. Proc. Nat. Acad. Sci. 99, 5822–5824 (2002)
Athreya, K.B., Smith, J.D.H.: Canonical distributions and phase transitions. Discuss. Math. Prob. Stat. 20, 167–176 (2000)
Backman, G.: Lebensdauer und Entwicklung. Arch. für Entwicklungsmechanik 140, 90–123 (1940)
von Bertelanffy, L.: General System Theory. Braziller, New York, 1968
Crow, E.L., Shimizu, K.: Lognormal Distributions. Marcel Dekker, New York, 1988
Demetrius, L.: Growth rate, population entropy and perturbation theory. Math. Biosci. 93, 159–180 (1989)
Demetrius, L.: Directionality principles in thermodynamics and evolution. Proc. Nat. Acad. Sci. 94, 3491–3498 (1997)
Keyfitz, N.: Introduction to the Mathematics of Population. Addison-Wesley, Reading, MA, 1968
Keyfitz, N.: Applied Mathematical Demography. 2nd ed., Springer, New York, 1985
Keyfitz, N., Flieger, W.: World Population Growth and Aging. University of Chicago, Chicago, 1990
Lotka, A.J.: Théorie Analytique des Associations Biologiques II: Analyse Démographique avec Application Particulière á l’Espèce Humaine. Hermann, Paris, 1939
Mosimann, J.E. Campbell, G.: Applications in biology: simple growth models. In: ‘‘Lognormal Distributions’’ E.L. Crow and K. Shimizu, (eds.), Marcel Dekker, New York, 1988, pp. 287–302
Prigogine, I.: Etude Thermodynamique des Phénomènes Irréversibles. Dunod, Paris, 1947
Shannon, C.E.: A mathematical theory of communication. Bell System Tech. J. 27, 623–656 (1948)
Smith, J.D.H.: Competition and the canonical ensemble. Math. Biosci. 133, 69–83 (1996)
Smith, J.D.H.: Demography and the canonical ensemble. Math. Biosci. 153, 151–161 (1998)
Tuljapurkar, S.D.: Why use population entropy? It determines the rate of convergence. J. Math. Biol. 13, 325–337 (1982)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Smith, J. A macroscopic approach to demography. J. Math. Biol. 48, 105–118 (2004). https://doi.org/10.1007/s00285-003-0231-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-003-0231-9