MPIDR Working Paper

Renewal and stability in populations structured by remaining years of life

MPIDR Working Paper WP-2015-007, 31 pages.
Rostock, Max Planck Institute for Demographic Research (November 2015)
Open Access


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
The Max Planck Institute for Demographic Research (MPIDR) in Rostock is one of the leading demographic research centers in the world. It's part of the Max Planck Society, the internationally renowned German research society.