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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/5038 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/5038 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/5038 archive 351 disk0/00/00/74/10 2016-01-15 02:17:12 2021-08-27 17:18:49 2016-01-15 02:17:12 monograph show 3 Parvinen K. 7727 0000-0001-9125-6041 Dieckmann U. 1668 0000-0001-7089-0393 Heino M. 7602 0000-0003-2928-3940 pub iis_mod iis_ecl prog_adn Adaptive dynamics; infinite-dimensional traits; reaction norms; calculus of variations; Euler's equation 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. 2004-11 published IR-04-038 IR-04-038 2852 66 122 public interim_report IIASA, Laxenburg, Austria 28 FALSE info:eu-repo/semantics/book