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The formal demography of kinship and family

Periodic Reporting for period 1 - FORMKIN (The formal demography of kinship and family)

Reporting period: 2018-06-01 to 2019-11-30

Any individual is surrounded by a network of kin (parents and children, siblings, aunts, nieces, cousins,...). This network is shaped by the schedules of mortality and fertility in the population. The goal of this project is to develop and apply a formal demographic theory for kinship networks based on demographic information.

Kinship and family structures are critical and rapidly changing components of society. Relatives provide and receive services and support from each other; think of grandparents helping to care for grandchildren, or of inter-generational bequests, or of the need for families to care for their elderly parents, grandparents, and other relatives. These types of family structures have changed dramatically in recent history. Yet, there have been only partial solutions to the problem of how kinship structures are determined.

The overall objectives of the project are (1) to develop the necessary theory for kinship dynamics, using new classes of population models, (2) to extend those models to include aspects of kinship not previously calculated, and (3) to apply the new models to data that will permit comparisons among countries, historical periods, ethnic groups, and economic conditions.
As of February 2020, progress has centered on the theoretical developments:

Individual kin dynamics (task 1.1): The basic model has been completed and a major paper published.

Characteristics of kin (task 1.2): This methodology is included in the paper describing task 1.1 with applications published to disease prevalence and economic dependency.

Loss and deaths of kin (task 1.3): This methodology forms part of the paper describing task 1.1; examples considered there include the analysis of experienced and cumulative deaths.

Demographic stochasticity (task 1.4): The model structure developed for task 1.1 is now ready for this analysis. Two approaches are now possible: novel applications of multitype branching processes, or numerical stochastic solutions of the equations. These will be developed in the next phase.

Multistate kinship analysis (task 1.5): The model structure needed for this important extension has been developed and applied to parity dynamics, and a major manuscript in final preparation. A very general two-sex kinship model has been developed using this structure and will be the topic of the next methodological paper. A multistate genetic model has been completed and papers published; this will provide the basis for an analysis of relatedness of kin.

Sensitivity analysis (task 1.6): Methods for sensitivity analysis of multistate models have been developed and published.

Combining types of kin (task 1.7): A generalized kinship network model has been developed; it will provide the basis for this task.

Cohort distribution of kin (task 2.1): Variance decomposition methods needed for this task have been developed and are ready for application.

Lifetime exposure to kin (task 2.2): Probability of exposure and incorporation in Markov chain models developed.

Kinship structure of populations (task 3.1) and population projections (task 3.2): results of task 1.1 and task 1.5 will provide the framework for these tasks. In addition to publications and manuscripts in preparation, results of the project to date have been presented at national and international conferences and scientific meetings.
The model structure describing kinship dynamics is a totally new development of matrix population models; it expresses the age structure of the kinship network as a coupled set of matrix difference equations for the kin at every age of a focal individual. The multistate version of the model combines age structure with other criteria, such as sex, parity, or health status.

The next phase of the project will involve applying the model to demographic data from national and international statistical offices and from surveys, in order to compare consequences for kinship structure of differences in mortality and fertility. Workshops will be organized to bring together researchers involved in various aspects (demographic, anthropological) of kinship studies.
Portion of the kinship network surrounding a focal individual.