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Stochastic Population ProcessesAnalysis, Approximations, Simulations$
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Eric Renshaw

Print publication date: 2011

Print ISBN-13: 9780199575312

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199575312.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 19 September 2021

Simple Markov population processes

Simple Markov population processes

Chapter:
(p.31) 2 Simple Markov population processes
Source:
Stochastic Population Processes
Author(s):

Eric Renshaw

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199575312.003.0002

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

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