From Size to Age and Type Structure Dependent Branching: A First Step to Sexual Reproduction in General Population Processes

Classical branching processes, even the most general, share the property that individuals are supposed to multiply independently of one another, at least given some environment that in its turn is supposed to be unaffected by the population. Only more recently have birth-and-death and branching processes been considered which allow individual reproduction to be influenced by population size. The first results, due to Klebaner, deal with Galton-Watson processes. Work on general, age-structured processes and habitats with a threshold, a so called carrying capacity, came only decades later, inspired by deterministic population dynamics. Multi-type such processes have only been analysed recently. It turns out that a two-type population (males, females) where only the latter can give birth, their fecundity however influenced by the number of males present, provides an approach to sexual reproduction without mating assumptions, like random mating, which are artificial in genereral branching processes