title: The birth process with immigration, and the genealogical structure of large populations.
abstract: This paper studies a version of the birth and immigration process in which families are followed in the order of their appearance. This age structure is related to a number of results from population genetics, in particular the genealogical structure of the infinitely-many neutral alleles model. The asymptotic behavior of this genealogy is an easy consequence of the structure of the age-ordered family size process.
mesh_terms: D001699:Biometry; D001723:Birth Rate; D004641:Emigration and Immigration; D005190:Family; D005828:Genetics, Population; D006801:Humans; D008957:Models, Genetic; D013269:Stochastic Processes