# Exploring Stable Population Concepts from the Perspective of Cohort Change Ratios: Estimating the Time to Stability and Intrinsic r from Initial Information and Components of Change

• David A. Swanson
• Lucky M. Tedrow
• Jack Baker
Chapter
Part of the The Springer Series on Demographic Methods and Population Analysis book series (PSDE, volume 39)

## Abstract

Cohort Change Ratios (CCRs) appear to have been overlooked in regard to a major canon of formal demography, stable population theory. CCRs are explored here as a tool for examining the transient dynamics of a population as it moves toward the stable equivalent that is captured in most formal demographic models based on asymptotic population dynamics. We employ simulation and a regression-based approach to model trajectories toward this stability. This examination is done in conjunction with the Leslie Matrix and data for 62 countries selected from the US Census Bureau’s International Data Base. We use an Index of Stability (S), which defines stability as the point when S is equal zero (operationalized as S = 0.000000). The Index also is used to define initial stability for a given population and four subsequent “quasi-stable” points on the temporal path to stability (S = .01, S = .05, S = .001, and S = .0005). The regression-based analysis reveals that the initial conditions as defined by the initial Stability Index along with fertility and migration play a role in determining time to stability up until the quasi-stable point of S = .0005 is reached. After this point, the initial conditions are no longer a factor and mortality joins the fertility and migration components in determining the remaining time to stability. Overall all, we find that fertility and mortality have an inverse relationship with time to stability while migration has a positive relationship. The initial Stability Index has an inverse relationship with time to quasi-stability at S = .01, S = .005, S = .001, and S = .0005. We also find that a regression model works very well in estimating the intrinsic rate of increase from the initial rate of increase, but that this model can be improved by adding the components of change. We also compare time to stability and intrinsic r as estimated using the CCR Leslie Matrix approach to, respectively, estimates of time to stability and intrinsic r found using analytic methods and find that the former are consistent with the latter.

## Keywords

Leslie matrix Stability index Initial conditions

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© Springer International Publishing Switzerland 2016

## Authors and Affiliations

• David A. Swanson
• 1
Email author
• Lucky M. Tedrow
• 2
• Jack Baker
• 3
1. 1.Department of SociologyUniversity of California RiversideRiversideUSA
2. 2.Department of SociologyWestern Washington UniversityBellinghamUSA
3. 3.Geospatial and population StudiesUniversity of New MexicoAlbuquerqueUSA