Adaptive dynamics of saturated polymorphisms

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 dem...

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Bibliographic Details
Published in:Journal of mathematical biology 2016-03, Vol.72 (4), p.1039-1079
Main Authors: Kisdi, Éva, Geritz, Stefan A. H.
Format: Article
Language:English
Subjects:
Animals
Applications of Mathematics
Ecosystem
Evolution, Molecular
Feedback, Physiological
Food Chain
Genetics, Population
Host-Pathogen Interactions
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Genetic
Polymorphism, Genetic
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Summary: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 n = 2 , we also introduce a method to construct different pairwise invasibility plots of the monomorphic population without changing the selection gradients of the saturated dimorphism.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-015-0948-2