Journal Article

The formal demography of kinship VI

Caswell, Hal

2024

Overview

Although the matrix model for kinship networks includes many demographic processes, it is deterministic. It provides values of age-stage distributions of kin, but no information on (co)variances. Because kin populations are small, demographic stochasticity is expected to create appreciable inter-individual variation. To develop astochastick in ship model that includes demographics to chasticity and projects (co)variances of kin age distributions, and functions thereof. Kin populations are described by multitype branching processes. Means and covariances are projected using matrices that are generalizations of the deterministic model. The analysis requires only an age-specific mortality and fertility schedule. Both linear and nonlinear transformations of the kin age distribution are treated as outputs accompanying the state equations. The stochastic model follows the same mathematical framework as the deterministic model, modified to treat initial conditions as mixture distributions. Variances in numbers of most kin are compatible with Poisson distributions. Variances for parents and ancestors are compatible with binomial distributions. Prediction intervals are provided, as are probabilities of having at least one or two kin of each type. Prevalences of conditions are treated either as fixed or random proportions. Dependency ratios and their variances are calculated for any desired group of kin types. An example compares Japan under 1947 rates (high mortality, high fertility) and 2019 rates (low mortality, low fertility).

• Publisher: Max-Planck-Gesellschaft zur Foerderung der Wissenschaften,Max Planck Institute for Demographic Research
• Subject: Demographic aspects / dependency ratios / Kinship / matrix models / Methods / multitype branching processes / prevalence / Research Article / Social networks / Stochastic analysis / stochastic models