Theory in Biosciences

, Volume 135, Issue 4, pp 187–200 | Cite as

On discrete evolutionary dynamics driven by quadratic interactions

  • N. GrosjeanEmail author
  • T. Huillet
  • G. Rollet
Original Paper


After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or train) algebras. In this setup, any quadratic offspring interaction can produce any type of offspring and after the use of specific changes of basis, we study the evolution and possible stability of some examples. We also consider some examples that cannot be treated using the framework of genetic algebras. Among these are bistochastic matrices.


Evolutionary dynamics Quadratic interactions Genetic algebras Polymorphism Bistochastic interaction 



T. Huillet acknowledges support from the Project Basal PFB 03 of the CONICYT of Chile, from the “Chaire Modélisation mathématique et biodiversité” and together with N. Grosjean, from the labex MME-DII Center of Excellence (Modèles mathématiques et économiques de la dynamique, de l’incertitude et des interactions, ANR-11-LABX-0023-01 project).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique et ModélisationCNRS-UMR 8089 et Université de Cergy-PontoiseCergy-PontoiseFrance

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