Population Formulation of Adaptative Meso-evolution: Theory and Numerics

Part of the Mathematics and Biosciences in Interaction book series (MBI)


The population formalism of “adaptive evolution” has been developed in the last twenty years along ideas presented in other chapters in this volume. This mathematical formalism addresses the question of explaining how selection of a favorable phenotypical trait in a population occurs. In the language of Metz’s Chapter, it refers to meso-evolution. It uses models based, usually, on integro-differential equations for the population structured by a phenotypical trait. A self-contained mathematical formulation of adaptive evolution also contains the description of mutations and leads to partial differential equations. Then the complete evolution picture follows from the model ingredients mostly driven by the changing adaptive landscape.


Adaptive evolution Lotka-Volterra equation Darwinian evolution Hamilton-Jacobi equation Viscosity solutions Dirac concentrations MonteCarlo simulations Finite differences 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis LionsUPMC Univ Paris 06, UMR 7598ParisFrance
  2. 2.Laboratoire Jacques-Louis LionsInstitut Universitaire de France & UPMC Univ Paris 06, UMR 7598ParisFrance

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