A1 Refereed original research article in a scientific journal

Function-valued adaptive dynamics and the calculus of variations




AuthorsParvinen K, Dieckmann U, Heino M

PublisherSPRINGER

Publication year2006

JournalJournal of Mathematical Biology

Journal name in sourceJOURNAL OF MATHEMATICAL BIOLOGY

Journal acronymJ MATH BIOL

Volume52

Issue1

First page 1

Last page26

Number of pages26

ISSN0303-6812

DOIhttps://doi.org/10.1007/s00285-005-0329-3(external)


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.



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