A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Function-valued adaptive dynamics and the calculus of variations
Tekijät: Parvinen K, Dieckmann U, Heino M
Kustantaja: SPRINGER
Julkaisuvuosi: 2006
Journal: Journal of Mathematical Biology
Tietokannassa oleva lehden nimi: JOURNAL OF MATHEMATICAL BIOLOGY
Lehden akronyymi: J MATH BIOL
Vuosikerta: 52
Numero: 1
Aloitussivu: 1
Lopetussivu: 26
Sivujen määrä: 26
ISSN: 0303-6812
DOI: https://doi.org/10.1007/s00285-005-0329-3
Tiivistelmä
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.
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.
Turun yliopiston Tutkimustietojärjestelmän portaali