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The solution of time-dependent population models

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  • Nan Li
  • Shripad Tuljapurkar
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    Abstract

    We analyze the dynamics of age-structured population renewal when vital rates make a transition in a finite time interval from arbitrary initial values to any specified final values. The general solution to the renewal equation in such cases is obtained. This solution describes the birth sequence explicitly, and also leads to a general formula for population momentum. We show that the duration of the transition determines the complexity of the solution for the birth sequence. For transitions that are completed in a time smaller than the maximum age of reproduction, we show that the classical Lotka solution found in every textbook also applies, with a small modification, to the time-dependent case. Our results substantially extend previous work that has often focused on instantaneous transitions or on slow and infinitely persistent change in vital rates.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/08898480009525464
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Mathematical Population Studies.

    Volume (Year): 7 (2000)
    Issue (Month): 4 ()
    Pages: 311-329

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    Handle: RePEc:taf:mpopst:v:7:y:2000:i:4:p:311-329

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    Related research

    Keywords: Population model; Time-dependent; General solution;

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    Cited by:
    1. Thomas Espenshade & Analia Olgiati & Simon Levin, 2011. "On Nonstable and Stable Population Momentum," Demography, Springer, vol. 48(4), pages 1581-1599, November.
    2. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.

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