The Formal Demography of Kinship: Descendants, Generations, and the Persistence of Lineages

Hal Caswell , University of Amsterdam

Given a set of demographic rates, the matrix kinship model projects the entire kinship network, or as much of it as desired, over the life of a Focal individual. One subset of that network, of particular demographic, social, and historical interest, comprises the generations of descendants of Focal (her children, grandchildren, etc.). Focusing on this lineage, I report here an extension of the matrix kinship model that projects the numbers and age distributions of as many generations of descendants as desired. Both one-sex and two-sex lineages are included. Because the lineage model is jointly structured by both age and generation, it (1) provides age-specific overlap of generations, (2) shows growth or decline of lineages, (3) can incorporate generation-specific variation in rates, and (4) can incorporate within- and between-generation interactions and transfers. But there's more. The generation model is the expected value operator of a large multi-type branching process. This stochastic version of the model leads to a solution to the extinction problem, giving the probabilities of extinction as functions of both calendar time and generation number. It includes both one-sex and two-sex lineages. It permits free choice of originator of the lineage: a single individual of a specified age; a collection of individuals; or an individual and their kin at the origin of the lineage. Example results will be shown, contrasting a decreasing and an increasing lineage.

See extended abstract

 Presented in Session 16. Modelling Kinship and Fertility Processes