title: Adaptive dynamics of saturated polymorphisms.
abstract: We study the joint adaptive dynamics of n scalar-valued strategies in ecosystems where n is the maximum number of coexisting strategies permitted by the (generalized) competitive exclusion principle. The adaptive dynamics of such saturated systems exhibits special characteristics, which we first demonstrate in a simple example of a host-pathogen-predator model. The main part of the paper characterizes the adaptive dynamics of saturated polymorphisms in general. In order to investigate convergence stability, we give a new sufficient condition for absolute stability of an arbitrary (not necessarily saturated) polymorphic singularity and show that saturated evolutionarily stable polymorphisms satisfy it. For the case [Formula: see text], we also introduce a method to construct different pairwise invasibility plots of the monomorphic population without changing the selection gradients of the saturated dimorphism.
authors.affiliation: Department of Mathematics and Statistics, University of Helsinki, PO Box 68, 00014, Helsinki, Finland. eva.kisdi@helsinki.fi.
authors.forename: Éva
authors.initials: É
authors.lastname: Kisdi
authors.affiliation: Department of Mathematics and Statistics, University of Helsinki, PO Box 68, 00014, Helsinki, Finland.
authors.forename: Stefan A H
authors.initials: SAH
authors.lastname: Geritz
mesh_terms: D000818:Animals; D017753:Ecosystem; D019143:Evolution, Molecular; D025461:Feedback, Physiological; D020387:Food Chain; D005828:Genetics, Population; D054884:Host-Pathogen Interactions; D055641:Mathematical Concepts; D008957:Models, Genetic; D011110:Polymorphism, Genetic
keywords: Adaptive dynamics; Coevolution; Competitive exclusion principle; Environmental feedback; Saturated community