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

Author

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  • Butterick, Joe W.B.
  • Smith, Peter W.F.
  • Bijak, Jakub
  • Hilton, Jason

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.

Suggested Citation

  • Butterick, Joe W.B. & Smith, Peter W.F. & Bijak, Jakub & Hilton, Jason, 2025. "A mathematical framework for time-variant multi-state kinship modelling," Theoretical Population Biology, Elsevier, vol. 163(C), pages 1-12.
    • Handle: RePEc:eee:thpobi:v:163:y:2025:i:c:p:1-12
    DOI: 10.1016/j.tpb.2025.02.002
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    References listed on IDEAS

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    1. Hal Caswell, 2022. "The formal demography of kinship IV: Two-sex models and their approximations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 47(13), pages 359-396.
    2. Xi Song & Robert D. Mare, 2019. "Shared Lifetimes, Multigenerational Exposure, and Educational Mobility," Demography, Springer;Population Association of America (PAA), vol. 56(3), pages 891-916, June.
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    6. Thomas Pullum, 1982. "The Eventual Frequencies of Kin in a Stable Population," Demography, Springer;Population Association of America (PAA), vol. 19(4), pages 549-565, November.
    7. Hal Caswell & Xi Song, 2021. "The formal demography of kinship III: Kinship dynamics with time-varying demographic rates," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 45(16), pages 517-546.
    8. Hal Caswell, 2024. "The formal demography of kinship VI: Demographic stochasticity and variance in the kinship network," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 51(39), pages 1201-1256.
    9. Hal Caswell, 2019. "The formal demography of kinship: A matrix formulation," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(24), pages 679-712.
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