Stochastic competition between two populations in space

  • Simone Pigolotti
  • Roberto Benzi
  • Mogens H. Jensen
  • Prasad Perlekar
  • Federico Toschi
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 553)


We present a model describing spatial competition between two biological populations. Individuals belonging to the two populations diffuse in space, reproduce, and die as effect of competitions; all these processes are implemented stochastically. We focus on how the macroscopic equations for the densities of the two species can be derived within the formalism of the chemical master equations. We also compare the case in which the total density of individuals is kept fixed by constraint with a case in which it can fluctuate.


Langevin Equation Spatial Competition Neutral Case Chemical Master Equation Local Population Size 
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Copyright information

© CISM, Udine 2014

Authors and Affiliations

  • Simone Pigolotti
    • 3
  • Roberto Benzi
    • 4
  • Mogens H. Jensen
    • 5
  • Prasad Perlekar
    • 6
  • Federico Toschi
    • 1
    • 2
  1. 1.Department of Physics, Department of Mathematics and Computer Science, and J.M. BurgerscentrumEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.CNR-IACRomeItaly
  3. 3.Dept. de Fisica i Eng. NuclearUniversitat Politecnica de Catalunya Edif. GAIATerrassaSpain
  4. 4.Dipartimento di FisicaUniversità di Roma “Tor Vergata” and INFNRomaItaly
  5. 5.The Niels Bohr InstitutUniversity of CopenhagenCopenhagenDenmark
  6. 6.Tata Institute of Fundamental ResearchCentre for Interdisciplinary SciencesHyderabadIndia

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