Construction of multiple trade-offs to obtain arbitrary singularities of adaptive dynamics

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http://hdl.handle.net/10138/262548

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Kisdi , E 2015 , ' Construction of multiple trade-offs to obtain arbitrary singularities of adaptive dynamics ' , Journal of mathematical biology , vol. 70 , no. 5 , pp. 1093-1117 . https://doi.org/10.1007/s00285-014-0788-5

Title: Construction of multiple trade-offs to obtain arbitrary singularities of adaptive dynamics
Author: Kisdi, Eva
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2015-04
Language: eng
Number of pages: 25
Belongs to series: Journal of mathematical biology
ISSN: 0303-6812
URI: http://hdl.handle.net/10138/262548
Abstract: Evolutionary singularities are central to the adaptive dynamics of evolving traits. The evolutionary singularities are strongly affected by the shape of any trade-off functions a model assumes, yet the trade-off functions are often chosen in an ad hoc manner, which may unjustifiably constrain the evolutionary dynamics exhibited by the model. To avoid this problem, critical function analysis has been used to find a trade-off function that yields a certain evolutionary singularity such as an evolutionary branching point. Here I extend this method to multiple trade-offs parameterized with a scalar strategy. I show that the trade-off functions can be chosen such that an arbitrary point in the viability domain of the trait space is a singularity of an arbitrary type, provided (next to certain non-degeneracy conditions) that the model has at least two environmental feedback variables and at least as many trade-offs as feedback variables. The proof is constructive, i.e., it provides an algorithm to find trade-off functions that yield the desired singularity. I illustrate the construction of trade-offs with an example where the virulence of a pathogen evolves in a small ecosystem of a host, its pathogen, a predator that attacks the host and an alternative prey of the predator.
Subject: Critical function analysis
Evolutionary branching
Evolutionarily singular strategy
Coexistence
Trade-off
Host-pathogen-predator system
STRUCTURED POPULATION-MODELS
COMPETITIVE-EXCLUSION
PATHOGEN VIRULENCE
EVOLUTIONARY
COEXISTENCE
STRATEGIES
GEOMETRIES
PREDATION
STABILITY
PRINCIPLE
111 Mathematics
1181 Ecology, evolutionary biology
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