Adaptive dynamics of saturated polymorphisms

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http://hdl.handle.net/10138/173477

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Kisdi , E & Geritz , S A H 2016 , ' Adaptive dynamics of saturated polymorphisms ' Journal of mathematical biology , vol. 72 , no. 4 , pp. 1039-1079 . DOI: 10.1007/s00285-015-0948-2

Title: Adaptive dynamics of saturated polymorphisms
Author: Kisdi, Eva; Geritz, Stefan A.H.
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2016-03
Language: eng
Number of pages: 41
Belongs to series: Journal of mathematical biology
ISSN: 0303-6812
URI: http://hdl.handle.net/10138/173477
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 , we also introduce a method to construct different pairwise invasibility plots of the monomorphic population without changing the selection gradients of the saturated dimorphism.
Subject: Adaptive dynamics
Coevolution
Competitive exclusion principle
Environmental feedback
Saturated community
STRUCTURED POPULATION-MODELS
TRADE-OFF GEOMETRIES
EVOLUTIONARY DYNAMICS
COMPETITIVE-EXCLUSION
BIFURCATION-ANALYSIS
STRATEGIES
STABILITY
COEVOLUTION
COEXISTENCE
VIRULENCE
111 Mathematics
1181 Ecology, evolutionary biology
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