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Renewal and stability in populations structured by remaining years of life

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  • Timothy Riffe

    (Max Planck Institute for Demographic Research, Rostock, Germany)

Abstract

The Lotka-Leslie renewal model is the core of formal demography. This model is structured by chronological age, and it does not account for thanatological age. I derive a specification of the classic renewal equation that is structured by thanatological age rather than by chronological age. I give both continuous and discrete variants of the derived model, and relate these to the Lotka-Leslie renewal model. In stability, the thanatological and chronological renewal models are commensurable, implying identical intrinsic growth rates. I demonstrate approximate symmetry be- tween chronological and thanatological age structure in stability when subject to intrinsic growth rates equal magnitude and opposite sign. Birth-death renewal processes can be expressed as death-birth processes, and vice versa. The thanatological renewal model offers a new perspective on population renewal, and it is valid more generally as an aspect of birth-death processes.

Suggested Citation

  • Timothy Riffe, 2015. "Renewal and stability in populations structured by remaining years of life," MPIDR Working Papers WP-2015-007, Max Planck Institute for Demographic Research, Rostock, Germany.
    • Handle: RePEc:dem:wpaper:wp-2015-007
    DOI: 10.4054/MPIDR-WP-2015-007
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    References listed on IDEAS

    as
    1. Tim Riffe, 2015. "The force of mortality by life lived is the force of increment by life left in stationary populations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(29), pages 827-834.
    2. W. Arthur, 1982. "The Ergodic Theorems of Demography: a Simple Proof," Demography, Springer;Population Association of America (PAA), vol. 19(4), pages 439-445, November.
    3. James W. Vaupel, 2009. "Life lived and left: Carey’s equality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 20(3), pages 7-10.
    4. Timothy Riffe & Pil H. Chung & Jeroen J. A. Spijker & John MacInnes, 2015. "Time-to-death patterns in markers of age and dependency," MPIDR Working Papers WP-2015-003, Max Planck Institute for Demographic Research, Rostock, Germany.
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    More about this item

    Keywords

    stable population;

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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