title: On discrete evolutionary dynamics driven by quadratic interactions.
abstract: 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.
authors.affiliation: Laboratoire de Physique Théorique et Modélisation, CNRS-UMR 8089 et Université de Cergy-Pontoise, 2 Avenue Adolphe Chauvin, 95302, Cergy-Pontoise, France. Nicolas.Grosjean@u-cergy.fr.
authors.forename: N
authors.initials: N
authors.lastname: Grosjean
authors.affiliation: Laboratoire de Physique Théorique et Modélisation, CNRS-UMR 8089 et Université de Cergy-Pontoise, 2 Avenue Adolphe Chauvin, 95302, Cergy-Pontoise, France.
authors.forename: T
authors.initials: T
authors.lastname: Huillet
authors.affiliation: Laboratoire de Physique Théorique et Modélisation, CNRS-UMR 8089 et Université de Cergy-Pontoise, 2 Avenue Adolphe Chauvin, 95302, Cergy-Pontoise, France.
authors.forename: G
authors.initials: G
authors.lastname: Rollet
mesh_terms: D000465:Algorithms; D000483:Alleles; D005075:Biological Evolution; D004171:Diploidy; D005838:Genotype; D008957:Models, Genetic; D011995:Recombination, Genetic; D012641:Selection, Genetic; D013269:Stochastic Processes
keywords: Bistochastic interaction; Evolutionary dynamics; Genetic algebras; Polymorphism; Quadratic interactions