Chapter

Collective Dynamics from Bacteria to Crowds

Volume 553 of the series CISM International Centre for Mechanical Sciences pp 105-117

Stochastic competition between two populations in space

  • Simone PigolottiAffiliated withDept. de Fisica i Eng. Nuclear, Universitat Politecnica de Catalunya Edif. GAIA
  • , Roberto BenziAffiliated withDipartimento di Fisica, Università di Roma “Tor Vergata” and INFN
  • , Mogens H. JensenAffiliated withThe Niels Bohr Institut, University of Copenhagen
  • , Prasad PerlekarAffiliated withTata Institute of Fundamental Research, Centre for Interdisciplinary Sciences
  • , Federico ToschiAffiliated withDepartment of Physics, Department of Mathematics and Computer Science, and J.M. Burgerscentrum, Eindhoven University of TechnologyCNR-IAC

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Abstract

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.