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The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle.

In English

Författare

Summary, in English

This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013) are chosen such that they avoid a number of the problems that one gets in this most relevant of applications, (2) derive the fitness gradient occurring in the CE from simple fitness return arguments, (3) show explicitly that setting said fitness gradient equal to zero results in the classical marginal value principle from evolutionary ecology, (4) show that the latter in turn is equivalent to Pontryagin's maximum principle, a well known equivalence that however in the literature is given either ex cathedra or is proven with more advanced tools, (5) connect the classical optimisation arguments of life history theory a little better to real biology (Mendelian populations with separate sexes subject to an environmental feedback loop), (6) make a minor improvement to the form of the CE for the examples in Dieckmann et al. and Parvinen et al.

Publiceringsår

2015-11-19

Språk

Engelska

Sidor

1125-1152

Publikation/Tidskrift/Serie

Journal of Mathematical Biology

Volym

74

Issue

4

Dokumenttyp

Artikel i tidskrift

Förlag

Springer

Ämne

  • Bioinformatics and Systems Biology

Nyckelord

  • Function valued traits
  • Pontryagin’s maximum principle
  • Age-dependent resource allocation
  • Mendelian take on life history theory
  • Evolution in periodic environments

Status

Published

Forskningsgrupp

  • Theoretical Population Ecology and Evolution Group

ISBN/ISSN/Övrigt

  • ISSN: 1432-1416