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Environmental versus demographic stochasticity in population growth

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Workshop on Branching Processes and Their Applications

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 197))

Abstract

Demographic stochasticity (sampling variation in births and deaths) and environmental stochasticity (effect of random environmental fluctuations on growth rate) in population growth are usually modeled using different approaches. Branching processes or birth and death processes (BDP) are used to model the effect of demographic stochasticity but do usually assume a constant environment. Stochastic differential equations (SDE) are used to model environmental stochasticity but usually ignore demographic stochasticity. We shall examine the similarities and the differences between these approaches in what concerns extinction and local behavior, using as a benchmark the particular case of the Malthusian (density-independent) models, namely the Galton–Watson process, the simple BDP and the Malthusian SDE model. For SDE density-dependent growth models, we then present a review of the results on extinction and existence of stationary densities. Such results are robust with respect to the form of density-dependence since we use general models (rather than specific models like the logistic). It would be worth studying the results for corresponding general density-dependent demographic stochasticity models.

Mathematics Subject Classification (2000): 92D25, 60J70, 60J85

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References

  1. Anderson, W.J.: Continuous-time Markov Chains. An Applications-Oriented Approach. Springer, New York (1991)

    Google Scholar 

  2. Arnold, L.: Stochastic Differential Equatios: Theory and Applications. Wiley, New York (1974)

    Google Scholar 

  3. Braumann, C.A.: Threshold crossing probabilities for population growth models in random environments. J. Biol. Syst. 3, 505–517 (1995)

    Article  Google Scholar 

  4. Braumann, C.A.: Applications of stochastic differential equations to population growth. In: Bainov, D. (ed.) Proceedings of the Ninth International Colloquium on Differential Equations, pp.47–52. VSP, Utrecht (1999)

    Google Scholar 

  5. Braumann, C.A.: Variable effort fishing models in random environments.Math. Biosci. 156, 1–19 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Braumann, C.A.: Variable effort harvesting models in random environments:generalization to density-dependent noise intensities. Math.Biosci. 177&178, 229–245 (2002)

    Article  MathSciNet  Google Scholar 

  7. Braumann, C.A.: Itô versus Stratonovich calculus in random population growth. Math. Biosci. 206, 81–107 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  8. Braumann, C.A.: Harvesting in a random environment: Itô or Stratonovich calculus.J. Theoret. Biol. 244, 424–432 (2007)

    Article  MathSciNet  Google Scholar 

  9. Braumann, C.A.: Growth and extinction of populations in randomly varying environments. Comput. Math. Appl. 56, 631–644 (2008)

    MATH  MathSciNet  Google Scholar 

  10. Carlos, C., Braumann, C.A.: Tempos de extinção para populações em ambiente aleatório e cálculos de Itô e Stratonovich. In: Canto e Castro, L., Martins, E.G., Rocha, C., Oliveira, M.F., Leal, M.M., Rosado, F. (eds.) Ciência Estatística, pp. 229–238. Edi÷ões SPE, Lisboa (2006)

    Google Scholar 

  11. Haccou, P., Jagers, P., Vatutin, V.A.: Branching Processes. Variation, Growth and Extinction of Populations.Cambridge University Press, Cambridge (2005)

    Google Scholar 

  12. Hull, D.M.: A survey of the literature associated with the bisexual Galton-Watson branching processes. Extracta Math. 18, 321–343 (2003)

    MATH  MathSciNet  Google Scholar 

  13. Karlin, S., Taylor, H.M.: A First Course in Stochastic Processes, 2nd edition. Academic Press, New York (1975)

    MATH  Google Scholar 

  14. Karlin, S., Taylor, H.M.: A Second Course in Stochastic Processes. Academic Press, New York (1981)

    Google Scholar 

  15. Levins, R.: The effect of random variations of different types on population growth. Proc. Nat. Acad. Sci. USA. 62,1062–1065 (1969)

    Article  MathSciNet  Google Scholar 

  16. Øksendal, B.: Stochastic Differential Equatios: An Introduction with Applications, 6th edition. Springer, New York (2003)

    Google Scholar 

Download references

Acknowledgements

The author is member of the Centro de Investigação em Matemática e Aplicações (CIMA), a research center financed by FCT (Fundação para a Ciência e a Tecnologia, Portugal). This work is also related to the research project PTDC/MAT/64297/2006, financed by FCT as well.

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Authors and Affiliations

  1. Department of Mathematics, Universidade de Évora, Rua Rom ãao Ramalho 59, 7000-671, Évora, Portugal

    Carlos A. Braumann

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  1. Carlos A. Braumann
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Correspondence to Carlos A. Braumann .

Editor information

Editors and Affiliations

  1. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Miguel González Velasco

  2. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Inés M. Puerto

  3. Universidad de Extremadura, Avda. Virgen del Puerto, Plasencia, 10600, Spain

    Rodrigo Martínez

  4. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Manuel Molina

  5. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Manuel Mota

  6. Facultad de Veterinaria, Universidad de Extradura, Avda Universidad s/n, Caceres, 10071, Spain

    Alfonso Ramos

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Braumann, C.A. (2010). Environmental versus demographic stochasticity in population growth. In: González Velasco, M., Puerto, I., Martínez, R., Molina, M., Mota, M., Ramos, A. (eds) Workshop on Branching Processes and Their Applications. Lecture Notes in Statistics(), vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11156-3_3

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