Volume 33 - Article 20 | Pages 561–588

Lifetime reproduction and the second demographic transition: Stochasticity and individual variation

By Silke van Daalen, Hal Caswell

Print this page  Facebook  Twitter


Date received:17 Dec 2014
Date published:16 Sep 2015
Word count:4100
Keywords:fertility, fertility transition, individual stochasticity, lifetime reproduction, Markov chains
Additional files:33-20 supplementary figures (pdf file, 312 kB)


Background: In the last half of the previous century many developed countries went through a period of decreasing fertility rates, referred to as the second demographic transition. This transition is often measured using the Total Fertility Rate (TFR), which gives the mean number of children produced by a woman surviving through her reproductive years. The TFR ignores effects of mortality and, as a mean, provides no information on variability among individuals in lifetime reproduction.

Objective: Our goal is to quantify the statistics (mean, variance, standard deviation, coefficient of variation, and skewness) during the second demographic transition. We compare these statistical properties as functions of age, time, and developmental indices.

Methods: We used Markov chains with rewards to compute the moments of lifetime reproductive output (LRO) based on age-specific mortality and fertility rates for 40 developed countries, two hunter-gatherer populations and a group of North-American Hutterites. The analysis uses a Markov chain to model individual survival, and treats reproduction as a Bernoulli-distributed reward with probability equal to the age-specific fertility.

Results: All statistical properties of lifetime reproduction changed during the transition. The mean and standard deviation of LRO declined, and the coefficient of variation and skewness increased. By 2000, these statistics were tightly correlated across countries, suggesting that the entire distribution of LRO shifted, not just the mean.

Conclusions: We find that developed countries adhere to a seemingly universal distribution in LRO, during and after the second demographic transition. This distribution becomes more apparent when development improves health circumstances and decreases mortality.

Author's Affiliation

Silke van Daalen - Universiteit van Amsterdam, the Netherlands [Email]
Hal Caswell - Universiteit van Amsterdam, the Netherlands [Email]

Other articles by the same author/authors in Demographic Research

» 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

» 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

» Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates
Volume 23 - Article 19

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

Most recent similar articles in Demographic Research

» “Everyone tries to avoid responsibility” The attenuating role of financial obligations in fertility change among Yorùbá farmers of southwestern Nigeria
Volume 43 - Article 26    | Keywords: fertility, fertility transition

» Forty years of fertility changes in the Sahel
Volume 41 - Article 46    | Keywords: fertility, fertility transition

» Fertility compression in Niger: A study of fertility change by parity (1977–2011)
Volume 39 - Article 24    | Keywords: fertility, fertility transition

» Measuring and explaining the baby boom in the developed world in the mid-twentieth century
Volume 38 - Article 40    | Keywords: fertility, fertility transition

» Demography and the statistics of lifetime economic transfers under individual stochasticity
Volume 32 - Article 19    | Keywords: individual stochasticity, Markov chains