Chapter 8 - Branching Processes and Population Growth

Abstract

This chapter discusses the definitions, terminologies, and examples involved in the branching processes and population growth. There are numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The lists of some prominent cases that arise consist of electron multipliers, neutron chain reaction, survival of family names and survival of mutant genes. The chapter provides an overview of the mean and variance of a branching process, extinction probabilities, branching processes and generating functions, and discusses some conditional limit theorems of geometrically distributed offspring, variations on branching processes like multiple branching processes, branching processes with immigration and branching processes with killing, and some stochastic models of plasmid reproduction and plasmid copy number partition like the replication process and random lines of descent. The multiple and permanent mapping in population growth processes with interacting types and deterministic population growth with age distribution including a simple growth model and the model with age structure is reviewed.