The stable doubly infinite pedigree process of supercritical branching populations

Summary An individual is sampled randomly from a supercritical general branching population and the pedigree process, which centers around this ego-individual, is studied. The process describes not only lineage backwards and forwards, but also the lives of all individuals involved. Under mild conditions and in several senses, the process is shown to stabilize, as time passes. The limit is a doubly infinite population process, which generalizes the stable age distribution of branching processes and demography. It displays a nice independence structure, and can easily be constructed from the original branching law. The results are applied to certain kin-number problems, the process of ego's ancestors' births, and to the FLM-curve of cell kinetics.