Probability for Physicists pp 347-359 | Cite as

# Stochastic Population Modeling

Chapter

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## Abstract

One way to analyze the time evolution of discrete populations is to develop models of birth, death and other mechanisms that influence the size of the population, as well as interactions between two or more populations. Modeling of births and deaths is introduced, followed by a discussion of a combined birth-death model representable in matrix form. The existence of equilibrium states is questioned and the time evolution of population distribution moments is presented.

## Keywords

Extinction Probability Extinction Time Initial Population Size Rabbit Population Independent Poisson Process
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## References

- 1.J.H. Matis, T.R. Kiffe,
*Stochastic Population Models. A Compartmental Perspective*. Lecture Notes in statistics, vol. 145 (Springer, Berlin, 2000)Google Scholar - 2.L.J.S. Allen,
*Stochastic Population and Epidemic Models*(Springer, Cham, 2015)Google Scholar - 3.L.M. Ricciardi, in:
*Biomathematics Mathematical Ecology*, eds. by T.G. Hallam, S.A. Levin. Stochastic Population Theory: Birth and Death Processes, vol 17 (Springer, Berlin, 1986) p. 155Google Scholar - 4.L.M. Ricciardi, in:
*Biomathematics Mathematical Ecology*, eds. by T.G. Hallam, S.A. Levin. Stochastic Population Theory: Birth and Death Processes, vol 17 (Springer, Berlin, 1986) p. 191Google Scholar - 5.gsl_ran_poisson in GSL library, http://www.gnu.org/software/gsl/, or poidev in
*Numerical Recipes*, eds. W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling. Numerical Recipes: The Art of Scientific Computing, 3rd edn. (Cambridge University Press, Cambridge, 2007)

## Copyright information

© Springer International Publishing Switzerland 2016