A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Function-valued adaptive dynamics and optimal control theory
Tekijät: Kalle Parvinen, Mikko Heino, Ulf Dieckmann
Kustantaja: SPRINGER
Julkaisuvuosi: 2013
Journal: Journal of Mathematical Biology
Tietokannassa oleva lehden nimi: JOURNAL OF MATHEMATICAL BIOLOGY
Lehden akronyymi: J MATH BIOL
Numero sarjassa: 3
Vuosikerta: 67
Numero: 3
Aloitussivu: 509
Lopetussivu: 533
Sivujen määrä: 25
ISSN: 0303-6812
DOI: https://doi.org/10.1007/s00285-012-0549-2
Tiivistelmä
In this article we further develop the theory of adaptive dynamics of function-valued traits. Previous work has concentrated on models for which invasion fitness can be written as an integral in which the integrand for each argument value is a function of the strategy value at that argument value only. For this type of models of direct effect, singular strategies can be found using the calculus of variations, with singular strategies needing to satisfy Euler's equation with environmental feedback. In a broader, more mechanistically oriented class of models, the function-valued strategy affects a process described by differential equations, and fitness can be expressed as an integral in which the integrand for each argument value depends both on the strategy and on process variables at that argument value. In general, the calculus of variations cannot help analyzing this much broader class of models. Here we explain how to find singular strategies in this class of process-mediated models using optimal control theory. In particular, we show that singular strategies need to satisfy Pontryagin's maximum principle with environmental feedback. We demonstrate the utility of this approach by studying the evolution of strategies determining seasonal flowering schedules.
In this article we further develop the theory of adaptive dynamics of function-valued traits. Previous work has concentrated on models for which invasion fitness can be written as an integral in which the integrand for each argument value is a function of the strategy value at that argument value only. For this type of models of direct effect, singular strategies can be found using the calculus of variations, with singular strategies needing to satisfy Euler's equation with environmental feedback. In a broader, more mechanistically oriented class of models, the function-valued strategy affects a process described by differential equations, and fitness can be expressed as an integral in which the integrand for each argument value depends both on the strategy and on process variables at that argument value. In general, the calculus of variations cannot help analyzing this much broader class of models. Here we explain how to find singular strategies in this class of process-mediated models using optimal control theory. In particular, we show that singular strategies need to satisfy Pontryagin's maximum principle with environmental feedback. We demonstrate the utility of this approach by studying the evolution of strategies determining seasonal flowering schedules.
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