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

Joe W B Butterick1, Peter W F Smith1, Jakub Bijak1

  • 1Department of Social Statistics and Demography, University of Southampton, Southampton SO17 1BJ, United Kingdom.

Theoretical Population Biology
|March 7, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new demographic model for kinship, allowing for any individual characteristic and time-varying rates. The model reveals how spatial distribution influences an individual's relatives.

Keywords:
Age×stage-structured populationsKinshipMarkov processMathematical demographyMatrix projections

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Area of Science:

  • Demography
  • Mathematical Biology
  • Sociology

Background:

  • Kinship modeling in demography has advanced with multi-state and time-variant approaches.
  • Existing multi-state kinship models have theoretical limitations in scope and adaptability.
  • Generalizing kinship models for arbitrary characteristics and time-dependent processes is an open challenge.

Purpose of the Study:

  • To propose a generalized methodology for extending multi-state kinship models.
  • To develop a flexible model accommodating any individual stage and demographic rates.
  • To address the limitations of current kinship modeling frameworks in demography.

Main Methods:

  • Developed a novel methodology to extend multi-state kinship modeling.
  • Utilized Markov processes to create a concise mathematical framework.
  • Applied the model to a spatial demographic scenario in England and Wales.

Main Results:

  • The proposed model theoretically accommodates any stage in time-variant and time-invariant settings.
  • Demonstrated the model's utility by defining stages as spatial locations (LADs).
  • Elucidated the impact of spatial distribution on kinship networks.

Conclusions:

  • The developed methodology offers a significant advancement in demographic kinship modeling.
  • The model provides a flexible and theoretically robust approach for diverse population structures.
  • Spatial distribution is a key demographic factor influencing an individual's network of relatives.