Skip to main content
Top

2015 | OriginalPaper | Chapter

6. Population Point Measure Processes

Authors : Vincent Bansaye, Sylvie Méléard

Published in: Stochastic Models for Structured Populations

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
13.
go back to reference 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. Using moment equations to understand stochastically driven spatial pattern formation in ecological systems. Theor. Pop. Biol. 52, 179–197, 1997.
14.
go back to reference 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. 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.
20.
go back to reference P. Cattiaux and S. Méléard. Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction. J. Math. Biology 6, 797–829, 2010.CrossRef P. Cattiaux and S. Méléard. Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction. J. Math. Biology 6, 797–829, 2010.CrossRef
21.
go back to reference N. Champagnat, R. Ferrière and S. Méléard: Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theor. Pop. Biol. 69, 297–321, 2006.MATHCrossRef N. Champagnat, R. Ferrière and S. Méléard: Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theor. Pop. Biol. 69, 297–321, 2006.MATHCrossRef
34.
go back to reference 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. 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.
35.
go back to reference N. Fournier and S. Méléard. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14, 1880–1919 (2004). N. Fournier and S. Méléard. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14, 1880–1919 (2004).
39.
go back to reference J. Hofbauer and K. Sigmund. Evolutionary Games and Population Dynamics. Cambridge Univ. Press (2002). J. Hofbauer and K. Sigmund. Evolutionary Games and Population Dynamics. Cambridge Univ. Press (2002).
49.
go back to reference E. Kisdi. Evolutionary branching under asymmetric competition. J. Theor. Biol. 197, 149–162, 1999.CrossRef E. Kisdi. Evolutionary branching under asymmetric competition. J. Theor. Biol. 197, 149–162, 1999.CrossRef
54.
go back to reference R. Law, D. J. Murrell and U. Dieckmann. Population growth in space and time: Spatial logistic equations. Ecology 84, 252–262, 2003. R. Law, D. J. Murrell and U. Dieckmann. Population growth in space and time: Spatial logistic equations. Ecology 84, 252–262, 2003.
Metadata
Title
Population Point Measure Processes
Authors
Vincent Bansaye
Sylvie Méléard
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-21711-6_6