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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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.
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.
P. Cattiaux and S. Méléard. Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction. J. Math. Biology 6, 797–829, 2010.
N. Champagnat, R. Ferrière and S. Méléard: Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theor. Pop. Biol. 69, 297–321, 2006.
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.
N. Fournier and S. Méléard. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14, 1880–1919 (2004).
J. Hofbauer and K. Sigmund. Evolutionary Games and Population Dynamics. Cambridge Univ. Press (2002).
E. Kisdi. Evolutionary branching under asymmetric competition. J. Theor. Biol. 197, 149–162, 1999.
R. Law, D. J. Murrell and U. Dieckmann. Population growth in space and time: Spatial logistic equations. Ecology 84, 252–262, 2003.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-21711-6_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21710-9
Online ISBN: 978-3-319-21711-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)