Continuously stable strategies as evolutionary branching points

Journal of Theoretical Biology
Michael Doebeli, Iaroslav Ispolatov

Abstract

Evolutionary branching points are a paradigmatic feature of adaptive dynamics, because they are potential starting points for adaptive diversification. The antithesis to evolutionary branching points are continuously stable strategies (CSS's), which are convergent stable and evolutionarily stable equilibrium points of the adaptive dynamics and hence are thought to represent endpoints of adaptive processes. However, this assessment is based on situations in which the invasion fitness function determining the adaptive dynamics have non-zero second derivatives at CSS. Here we show that the scope of evolutionary branching can increase if the invasion fitness function vanishes to higher than first order at CSS. Using classical models for frequency-dependent competition, we show that if the invasion fitness vanishes to higher orders, a CSS may be the starting point for evolutionary branching. Thus, when invasion fitness functions vanish to higher than first order at equilibrium points of the adaptive dynamics, evolutionary diversification can occur even after convergence to an evolutionarily stable strategy.

References

Jan 1, 1996·Journal of Mathematical Biology·U Dieckmann, R Law
Jul 27, 2001·Proceedings. Biological Sciences·S A Geritz, E Kisdi
Jan 17, 2003·Nature·Michael Doebeli, Ulf Dieckmann
Oct 19, 2007·Journal of Mathematical Biology·Michel DurinxGéza Meszéna
Jul 1, 1997·The American Naturalist·M Kirkpatrick, N H Barton
Jun 1, 1992·Trends in Ecology & Evolution·J A MetzS A Geritz

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Citations

Sep 27, 2015·Journal of Evolutionary Biology·C Koykka, G Wild
Jan 3, 2016·Journal of Theoretical Biology·Fabio Dercole, Stefan A H Geritz
Aug 6, 2021·ELife·Rodrigo CaetanoMichael Doebeli

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