Branching Processes

Kapitel i bok, 2006

Branching processes are stochastic population models based on explicit descriptions of individual life and reproduction. The basic assumption is that individuals live and multiply independently. This can, however, be relaxed. Individuals may be of various types and have varying life spans. In the simple branching processes, there is only one type of individual and life span is determistic (one year or season) or exponentially distributed, yielding Markov processes, and as simple special cases, birth-and-death processes. But more general branching processes allow complex reproduction patterns as well as arbitrary life distributions. The main results are that no finite population can persist forever. It either dies out or it grows, usually at the exponential rate postulated by Euler and Malthus. However, recent results show that if population size can influence individual reproduction, other growth modes, like linear, can also occur. In exponential growth, the age-distribution, and population composition generally, stabilize.