Chapter

Simple Markov population processes

Eric Renshaw

in Stochastic Population Processes

Published in print February 2011 | ISBN: 9780199575312
Published online September 2011 | e-ISBN: 9780191728778 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199575312.003.0002
Simple Markov population processes

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This chapter explains the basic principles which underlie the concept of stochastic population dynamics by considering some simple types of population structure. Suppose that individuals develop completely independently from each other, and may either enter a population (i.e., immigrate) randomly at rate α 〉 0, depart (i.e., emigrate) at rate β, reproduce at rate λ or die at rate μ. Then combining these different types of behaviour generates a variety of interesting processes, each with its own characteristics. The chapter examines six specific combinations in roughly increasing order of mathematical complexity. It covers simple Poisson process, pure death process, pure birth process, simple birth-death process, simple immigration-birth-death process, simple immigration-emigration process. Batch events are also considered.

Keywords: stochastic population dynamics; simple Poisson process; pure death process; pure birth process; simple birth-death process; simple immigration-birth-death process; simple immigration-emigration process

Chapter.  37678 words.  Illustrated.

Subjects: Applied Mathematics

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