Volume 23 - Article 19 | Pages 531–548  

Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates

By Hal Caswell

This article is part of the ongoing Special Collection 8 "Formal Relationships"

Abstract

The population growth rate, or intrinsic rate of increase, measures the potential rate of growth of a population with specified and fixed vital rates.The sensitivity of population growth rate to changes in the vital rates can be written in terms of the stable stage or age distribution and the reproductive value distribution. If the vital rate measures the rate of production of one type of individual by another, then the sensitivity of growth rate is proportional to the reproductive value of the destination type and the representation in the stable stage distribution of the source type. This formal relationship exists in three forms: one limited to age-classified populations, a second that applies to stage- or age-classified populations, and a third that uses matrix calculus. Each uses a different set of formal demographic techniques; together they provide a relationship that beautifully cuts across different types of demographic models.

Author's Affiliation

Other articles by the same author/authors in Demographic Research

The formal demography of kinship V: Kin loss, bereavement, and causes of death
Volume 49 - Article 41

The contributions of stochastic demography and social inequality to lifespan variability
Volume 49 - Article 13

How does the demographic transition affect kinship networks?
Volume 48 - Article 32

The formal demography of kinship IV: Two-sex models and their approximations
Volume 47 - Article 13

The formal demography of kinship III: Kinship dynamics with time-varying demographic rates
Volume 45 - Article 16

Healthy longevity from incidence-based models: More kinds of health than stars in the sky
Volume 45 - Article 13

The formal demography of kinship II: Multistate models, parity, and sibship
Volume 42 - Article 38

The formal demography of kinship: A matrix formulation
Volume 41 - Article 24

The sensitivity analysis of population projections
Volume 33 - Article 28

Lifetime reproduction and the second demographic transition: Stochasticity and individual variation
Volume 33 - Article 20

Demography and the statistics of lifetime economic transfers under individual stochasticity
Volume 32 - Article 19

A matrix approach to the statistics of longevity in heterogeneous frailty models
Volume 31 - Article 19

Why do lifespan variability trends for the young and old diverge? A perturbation analysis
Volume 30 - Article 48

Perturbation analysis of nonlinear matrix population models
Volume 18 - Article 3

Most recent similar articles in Demographic Research

Dynamics of the coefficient of variation of the age at death distribution
Volume 49 - Article 38    | Keywords: lifespan inequality, mathematical demography, sensitivity analysis, threshold age

Migration’s contribution to the urban transition: Direct census estimates from Africa and Asia
Volume 48 - Article 24    | Keywords: migration, population growth, urbanization

The formal demography of kinship III: Kinship dynamics with time-varying demographic rates
Volume 45 - Article 16    | Keywords: family, kinship, matrix population models, population projection, Sweden

The role of reductions in old-age mortality in old-age population growth
Volume 44 - Article 44    | Keywords: cohort analysis, mortality, population growth, survival, variable-r method

Impact of delayed effects on human old-age mortality
Volume 40 - Article 41    | Keywords: delayed effects, DOHaD, older age mortality patterns, senescence

Cited References: 43

Download to Citation Manager

PubMed

Google Scholar

Volume
Page
Volume
Article ID