Chapter 8 - Branching Processes and Population Growth

Abstract

This chapter reviews the branching process and population growth. A branching process is a special-structured Markov chain used in determining a species' spatial propagation and transference of species characteristics at a given population size. There are numerous examples of Markov branching processes that arise naturally in various scientific disciplines; some notable ones are electron multipliers, neutron chain reactions, survival of family names, and survival of mutant genes. The branching process may experience variations such as multiple branching processes, branching process related to immigration, and branching processes with killings, etc. For branching processes involving multitypes with interactions when the expected growth rate exceeds one, extinction does not happen with certainty, and for a realization where extinction does not occur, the population actually grows at an exponential rate. Finally, the renewal theorem and generating functions also play a role in the analysis of a simple deterministic model of population growth that takes into account the age structure of the population.