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Relationships in a simple harmonic mean two-sex fertility model. (English) Zbl 0532.92019
The paper examines relationships in a continuous time two-sex stable population model that is not specific for age and which follows the harmonic mean consistency condition for the two sexes. The stable population intrinsic growth rate and the sex composition are derived, and the process of stabilization is investigated. For the discrete time case, an explicit algebraic solution is presented and used to describe the trajectory to stability of several hypothetical populations. For the continuous model, a closed form expression for the trajectory to stability can only be found under the assumption of no mortality.
Reviewer: V.Abel

MSC:
92D25 Population dynamics (general)
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[1] Goodman, L. A.: Population growth of the sexes. Biometrics 9, 212-225 (1953)
[2] Granville, W. A., Smith, P. R., Longley, W. R.: Elements of the differential and integral calculus (rev.ed.). Boston: Ginn 1941 · JFM 67.0151.08
[3] Kendall, D. G.: Stochastic processes and population growth. J. R. Statist. Soc. Ser. B 11, 230-264 (1949) · Zbl 0038.08803
[4] Keyfitz, N. The mathematics of sex and marriage. Proceedings of the sixth Berkeley symposium on mathematical statistics and probability, vol. IV, pp. 89-108. Berkeley: Univ. of California Press 1971
[5] Pollard, J. H.: Mathematical models for the growth of human populations. London: Cambridge University Press 1973 · Zbl 0295.92013
[6] Schoen, R.: The harmonic mean as the basis of a realistic two-sex marriage model. Demography 18 (May), 201-216 (1981)
[7] Schoen, R.: Generalizing the life table model to incorporate interactions between the sexes. pp 385-443 in Kenneth, C. L. and Andrei, Rogers (eds.), Multidimensional mathematical demography, New York: Academic Press 1982 · Zbl 0583.92014
[8] Schoen, R., Land, K. C.: A general algorithm for estimating a Markov-generated increment-decrement life table with applications to marital-status patterns. J. Am. Statist. Assoc. 74 (Dec), 761-776 (1979) · Zbl 0423.62084
[9] U.S. National Center for Health Statistics. Births, Marriages, Divorces, and Deaths for March 1982. Monthly Vital Statistics Report, 31 (3) (June 21); 1, 7 (1982)
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