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A mathematical framework for time-variant multi-state kinship modelling

Year: 2025
Type: article
Abstract: Recent research on kinship modelling in demography has extended age-structured models (i) to include additional characteristics, or “stages” (multi-state kinship), and (ii) to time-variant situations. A wide variety of population structures can affect kinship networks. However, only one prior model has comprehensively considered such effects, and under specific assumptions relating to the nature of individuals’ stages. As such, the leading multi-state framework for kin is theoretically limited in scope, and moreover, has yet to be implemented under time-variant demographic rates. Generalising kinship models to encompass arbitrary population characteristics and extending them to time-dependent processes remain open challenges in demography. This research proposes a methodology to extend multi-state kinship. We present a model which theoretically accounts for any stage, both in time-variant and time-invariant environments. Drawing from Markov processes, a concise mathematical alternative to existing theory is developed. The benefits of our model are illustrated by an application where we define stages as spatial locations, exemplified by clusters of local authority districts (LADs) in England and Wales. Our results elucidate how spatial distribution – a demographic characteristic ubiquitous across (and between) societies – can affect an individual’s network of relatives. • A time-variant formulation of multi-state kinship is proposed. • The model is valid for arbitrary population structures. • The model introduces time-variant genealogical Markov chains and validates their use. • A salient application based on spatial demographics is presented.
DOI: 10.1016/j.tpb.2025.02.002
Language: English
Subfield: Demography
Open Access status: hybrid
Estimated APC paid: $2,840
OpenAlex ID: W4408220944
FWCI: 9.356
Cites: 33
Cited by: 4
Related to: 10