Branching processes as population dynamics

Abstract

Branching processes were once born out of a question from (human) population dynamics. Lately the driving forces have been, and continue to be, more of pure mathematical nature. Nevertheless, the resulting theory turns out to solve many classical problems from general, usually deterministic, population dynamics. These will be reviewed, with an emphasis on basic structure and on problems of the rate of population growth and the ensuing population composition. Special attention will be paid to possible interaction between individuals, or between the environment or population as a whole and individual reproduction behaviour. But the framework will remain the general model without explicit special assumptions about the form of interactions, lifespan distribution or reproduction.