Function-valued adaptive dynamics and the calculus of variations

Parvinen K, Dieckmann U, & Heino M (2006). Function-valued adaptive dynamics and the calculus of variations. Journal of Mathematical Biology 52 (1): 1-26. DOI:10.1007/s00285-005-0329-3.

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Abstract

Adaptive dynamics has been widely used to study the evolution of scalar-valued, and occasionally vector-valued, strategies in ecologically realistic models. In many ecological situations, however, evolving strategies are best described as function-valued, and thus infinite-dimensional, traits. So far, such evolution has only been studied sporadically, mostly based on quantitative genetics models with limited ecological realism. In this article we show how to apply the calculus of variations to find evolutionarily singular strategies of function-valued adaptive dynamics: such a strategy has to satisfy Euler's equation with environmental feedback. We also demonstrate how second-order derivatives can be used to investigate whether or not a function-valued singular strategy is evolutionarily stable. We illustrate our approach by presenting several worked examples.

Item Type: Article
Uncontrolled Keywords: Adaptive dynamics; Infinite-dimensional traits; Reaction norms; Calculus of variations; Euler's equation
Research Programs: Evolution and Ecology (EEP)
Bibliographic Reference: Journal of Mathematical Biology; 52(1):1-26 (January 2006)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:19
Last Modified: 24 Feb 2016 14:49
URI: http://pure.iiasa.ac.at/7893

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