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The formal demography of kinship VII: Lifetime kin overlap within and across generations

Author

Listed:
  • Hal Caswell

    (Woods Hole Oceanographic Institute)

  • Lotte de Vries

    (Universiteit Leiden)

Abstract

Background: Interactions among kin have important consequences, including resource transfers, allo-parenting, health care, and economic support. Some interactions require that the lives of the interacting relatives overlap. The overlap over a lifetime (lifetime kin overlap, LKO) depends on mortality (longer lives give more opportunity for overlap) and fertility (higher fertility produces more kin with which to overlap). Here we provide a general solution to the problem of calculating lifetime kin overlap. Objective: Our objective is to develop a demographic model for the mean and variance of the lifetime overlap of any types of kin over the life of a focal individual. Methods: The matrix kinship model is used to provide the age distribution of kin as an age-specific property of Focal. The mean and variance of lifetime overlap with kin of any type are then calculated using Markov chains with rewards. Results: The analysis provides the mean and variance of the remaining lifetime overlap with any kind of kin at every age of a focal individual. It may be measured in terms of numbers, numbers in chosen age ranges, or numbers weighted by prevalence, or by the presence of at least one kin. Overlap is defined both prospectively and retrospectively. and includes simultaneous overlap with two or more types of kin (‘sandwiched kin’). Contribution: It is now possible to compute the mean and variance of the projected LKO with any type of kin, in one-sex or two-sex models based on age or combinations of age and stage.

Suggested Citation

  • Hal Caswell & Lotte de Vries, 2025. "The formal demography of kinship VII: Lifetime kin overlap within and across generations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 53(5), pages 123-174.
    • Handle: RePEc:dem:demres:v:53:y:2025:i:5
    DOI: 10.4054/DemRes.2025.53.5
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    References listed on IDEAS

    as
    1. Sha Jiang & Wenyun Zuo & Hal Caswell & Zhen Guo & Shripad Tuljapurkar, 2023. "How does the demographic transition affect kinship networks?," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 48(32), pages 899-930.
    2. Xi Song & Robert D. Mare, 2017. "Short-Term and Long-Term Educational Mobility of Families: A Two-Sex Approach," Demography, Springer;Population Association of America (PAA), vol. 54(1), pages 145-173, February.
    3. Rachel Margolis & Ashton M. Verdery, 2017. "Older Adults Without Close Kin in the United States," The Journals of Gerontology: Series B, The Gerontological Society of America, vol. 72(4), pages 688-693.
    4. 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.
    5. Hal Caswell, 2020. "The formal demography of kinship II: Multistate models, parity, and sibship," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 42(38), pages 1097-1146.
    6. Olivia Healy & Rachel Dunifon, 2025. "Grandchildren’s spatial proximity to grandparents and intergenerational support in the United States," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 52(34), pages 1097-1110.
    7. Hal Caswell & Fanny Annemarie Kluge, 2015. "Demography and the statistics of lifetime economic transfers under individual stochasticity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(19), pages 563-588.
    8. Mirkka Lahdenperä & Khyne U. Mar & Virpi Lummaa, 2016. "Short-term and delayed effects of mother death on calf mortality in Asian elephants," Behavioral Ecology, International Society for Behavioral Ecology, vol. 27(1), pages 166-174.
    9. Emilio Zagheni & Brittney Wagner, 2015. "The impact of demographic change on intergenerational transfers via bequests," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(18), pages 525-534.
    10. Robert Mare, 2011. "A Multigenerational View of Inequality," Demography, Springer;Population Association of America (PAA), vol. 48(1), pages 1-23, February.
    11. Rachel Margolis & Xiangnan Chai & Ashton M Verdery & Lauren Newmyer, 2022. "The Physical, Mental, and Social Health of Middle-Aged and Older Adults Without Close Kin in Canada," The Journals of Gerontology: Series B, The Gerontological Society of America, vol. 77(7), pages 1350-1360.
    12. Mariana Amorim & Rachel Dunifon & Natasha Pilkauskas, 2017. "The magnitude and timing of grandparental coresidence during childhood in the United States," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 37(52), pages 1695-1706.
    13. 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.
    14. Silke van Daalen & Hal Caswell, 2015. "Lifetime reproduction and the second demographic transition: Stochasticity and individual variation," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(20), pages 561-588.
    15. Xi Song, 2016. "Diverging Mobility Trajectories: Grandparent Effects on Educational Attainment in One- and Two-Parent Families in the United States," Demography, Springer;Population Association of America (PAA), vol. 53(6), pages 1905-1932, December.
    16. 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.
    17. Hal Caswell & Rachel Margolis & Ashton Verdery, 2023. "The formal demography of kinship V: Kin loss, bereavement, and causes of death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 49(41), pages 1163-1200.
    18. Hal Caswell, 2011. "Beyond R0: Demographic Models for Variability of Lifetime Reproductive Output," PLOS ONE, Public Library of Science, vol. 6(6), pages 1-21, June.
    19. Rachel Margolis & Ashton M. Verdery, 2019. "A Cohort Perspective on the Demography of Grandparenthood: Past, Present, and Future Changes in Race and Sex Disparities in the United States," Demography, Springer;Population Association of America (PAA), vol. 56(4), pages 1495-1518, August.
    20. 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.
    21. Hal Caswell & Silke van Daalen, 2021. "Healthy longevity from incidence-based models: More kinds of health than stars in the sky," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 45(13), pages 397-452.
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    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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