Simple Markov population processes
Eric Renshaw · Oxford University Press eBooks · 2011
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.