Projecting kinship networks through time in variable environments

Christophe F.D. Coste , Samuel Pavard

Kinship networks shape key biological and social processes, yet their dynamics under changing environments remain poorly understood. Like population abundances, kinship structures are determined by past vital rates. Matrix population models provide a powerful framework for projecting population abundances through time and analysing the effects of environmental change on population dynamics, but no comparable framework exists for kinship networks. Here we develop a general projection framework for kinship networks in one-sex populations structured by any number of traits (e.g. age, stage, location, body mass, or genotype) under varying environments. We derive the kinship projection equation, which tracks through time the expected number of all kin, up to an arbitrary genealogical distance, structured by kin category and by the traits of both ego and its kin. By embedding kinship within the same matrix projection framework used for population dynamics, our approach provides a computationally simple and theoretically tractable tool for analysing how environmental change reshapes kinship networks. We demonstrate its analytical power by studying asymptotic, transient, and periodic kinship dynamics. Finally, we illustrate the framework by analysing how India’s demographic transition has reshaped - and will continue to reshape - kinship networks.