Probabilistic projections of distributions of kin over the life course
Joe Butterick, Jason Hilton, Jakub Bijak, Peter W. F. Smith, Erengul Dodd · bioRxiv (Cold Spring Harbor Laboratory) · 2025
Abstract BACKGROUND Mathematical kinship demography is an expanding area of research. Recent papers have explored the expected number of kin a typical individual should experience. Despite the uncertainty of the future number and distributions of kin, just one paper investigates it. OBJECTIVE To develop a new method for obtaining the probability that a typical population member experiences one or more of some kin at any age through the life course. METHODS We use combinatorics and matrix algebra to construct and project a discrete probability distribution of kin. Our model requires as inputs, age-specific mortality and fertility. CONCLUSIONS We derive probabilities of kin-number for fixed age of kin and over all possible ages of kin. We derive expected numbers and variance of kin. We demonstrate how kinship structures are conditional on familial events. CONTRIBUTION The paper presents the first analytic approach allowing the projection of a full probability distribution of the number of kin of arbitrary type that a population member has over the life course.