Apr 3, 2014

The formal demography of kinship. II. Multistate models, parity, and sibship

BioRxiv : the Preprint Server for Biology
Jesse D Bloom

Abstract

Background: Recent kinship models focus on the age structures of kin as a function of the age of the focal individual. However, variables in addition to age have important impacts. Generalizing age-specific models to multistate models including other variables is an important and hitherto unsolved problem. Objectives: Our aim is to develop a multistate kinship model, classifying individuals jointly by age and other criteria (generically, ''stages''). Methods: We use the vec-permutation method to create multistate projection matrices including age- and stage-dependent survival, fertility, and transitions. These matrices operate on block-structured population vectors that describe the ageXstage structure of each kind of kin, at each age of a focal individual. Results: The new matrix formulation is directly comparable to, and greatly extends, the recent age-classified kinship model of Caswell (2019). As an application, we derive a model that includes age and parity. We obtain, for all types of kin, the joint ageXparity structure, the marginal age and parity structures, and the (normalized) parity distributions, at every age of the focal individual. We show how to use the ageXparity distributions to calculate the distributions of s...Continue Reading

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