NDLI: An extension of the classification of evolutionarily singular strategies in Adaptive Dynamics

Content Provider	Springer Nature Link
Author	Boldin, Barbara Diekmann, Odo
Copyright Year	2013
Abstract	The existing classification of evolutionarily singular strategies in Adaptive Dynamics (Geritz et al. in Evol Ecol 12:35–57, 1998; Metz et al. in Stochastic and spatial structures of dynamical systems, pp 183–231, 1996) assumes an invasion exponent that is differentiable twice as a function of both the resident and the invading trait. Motivated by nested models for studying the evolution of infectious diseases, we consider an extended framework in which the selection gradient exists (so the definition of evolutionary singularities extends verbatim), but where the invasion fitness may lack the smoothness necessary for the classification à la Geritz et al. We derive the classification of singular strategies with respect to convergence stability and invadability and determine the condition for the existence of nearby dimorphisms. In addition to ESSs and invadable strategies, we observe what we call one-sided ESSs: singular strategies that are invadable from one side of the singularity but uninvadable from the other. Studying the regions of mutual invadability in the vicinity of a one-sided ESS, we discover that two isoclines spring in a tangent manner from the singular point at the diagonal of the mutual invadability plot. The way in which the isoclines unfold determines whether these one-sided ESSs act as ESSs or as branching points. We present a computable condition that allows one to determine the relative position of the isoclines (and thus dimorphic dynamics) from the dimorphic as well as from the monomorphic invasion exponent and illustrate our findings with an example from evolutionary epidemiology.
Ending Page	940
Page Count	36
Starting Page	905
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	4
Volume Number	69
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-08-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Evolutionarily singular strategy One-sided ESS Invasion exponent Adaptive dynamics Mathematical and Computational Biology Evolutionary branching Superinfection Ecology Applications of Mathematics Evolutionary arms race Epidemiology Problems related to evolution
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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