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Part of the book series: Mathematical Biosciences Institute Lecture Series ((STOCHBS,volume 1.4))

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Abstract

In the previous sections, the models that we considered described a homogeneous population and could be considered as toy models. A first generalization consists in considering multitype population dynamics. The demographic rates of a subpopulation depend on its own type. The ecological parameters are functions of the different types of the individuals competiting with each other. Indeed, we assume that the type has an influence on the reproduction or survival abilities, but also on the access to resources. Some subpopulations can be more adapted than others to the environment.

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References

  1. B. Bolker, S.W. Pacala. Using moment equations to understand stochastically driven spatial pattern formation in ecological systems. Theor. Pop. Biol. 52, 179–197, 1997.

    Google Scholar 

  2. B. Bolker, S.W. Pacala. Spatial moment equations for plant competition: Understanding spatial strategies and the advantages of short dispersal. Am. Nat. 153, 575–602, 1999.

    Google Scholar 

  3. P. Cattiaux and S. Méléard. Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction. J. Math. Biology 6, 797–829, 2010.

    Article  Google Scholar 

  4. N. Champagnat, R. Ferrière and S. Méléard: Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theor. Pop. Biol. 69, 297–321, 2006.

    Article  MATH  Google Scholar 

  5. S. N. Evans, A. Hening & S. Schreiber. Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments. In press, Journal of Mathematical Biology.

    Google Scholar 

  6. N. Fournier and S. Méléard. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14, 1880–1919 (2004).

    Google Scholar 

  7. J. Hofbauer and K. Sigmund. Evolutionary Games and Population Dynamics. Cambridge Univ. Press (2002).

    Google Scholar 

  8. E. Kisdi. Evolutionary branching under asymmetric competition. J. Theor. Biol. 197, 149–162, 1999.

    Article  Google Scholar 

  9. R. Law, D. J. Murrell and U. Dieckmann. Population growth in space and time: Spatial logistic equations. Ecology 84, 252–262, 2003.

    Google Scholar 

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Bansaye, V., Méléard, S. (2015). Population Point Measure Processes. In: Stochastic Models for Structured Populations. Mathematical Biosciences Institute Lecture Series(), vol 1.4. Springer, Cham. https://doi.org/10.1007/978-3-319-21711-6_6

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