Renewal and stability in populations structured by remaining years of life

Timothy Riffe
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Timothy Riffe: Max Planck Institute for Demographic Research, Rostock, Germany

No WP-2015-007, MPIDR Working Papers from 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.

Keywords: stable; population (search for similar items in EconPapers)
JEL-codes: J1 Z0 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2015
New Economics Papers: this item is included in nep-age and nep-pr~
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Persistent link: https://EconPapers.repec.org/RePEc:dem:wpaper:wp-2015-007

DOI: 10.4054/MPIDR-WP-2015-007

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