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

BackgroundInteractions among kin have important consequences, including resource transfers, alloparenting, 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. ObjectivesTo 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. MethodsThe 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. ResultsWe obtain the statistics of LKO with numbers of kin, with selected age classes of kin, and with at least one kin, in both prospective and retrospective directions, for each sex separately and with sexes combined. Simultaneous overlap with two or more types of kin (e.g., parents and children) describes sandwich generations. We provide an example comparing Japan under 1947 rates (low survival, high fertility) and 2019 rates (high survival, low fertility). ContributionIt 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.