The canonical equation of adaptive dynamics for life histories: from fitnessreturns to selection gradients and Pontryagin's maximum principle.
(2015) In Journal of Mathematical Biology 74(4). p.11251152 Abstract
 This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370389, 2006) and Parvinen et al. (J Math Biol 67: 509533, 2013). Our goal is, using little more than highschool 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 241:370389, 2006) and Parvinen et al. (J Math Biol 67: 509533, 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... (More)
 This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370389, 2006) and Parvinen et al. (J Math Biol 67: 509533, 2013). Our goal is, using little more than highschool 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 241:370389, 2006) and Parvinen et al. (J Math Biol 67: 509533, 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8235082
 author
 Metz, Johan A Jacob ; Staňková, Kateřina and Johansson, Jacob ^{LU}
 organization
 publishing date
 20151119
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Function valued traits, Pontryagin’s maximum principle, Agedependent resource allocation, Mendelian take on life history theory, Evolution in periodic environments
 in
 Journal of Mathematical Biology
 volume
 74
 issue
 4
 pages
 1125  1152
 publisher
 Springer
 external identifiers

 pmid:26586121
 scopus:84958124373
 wos:000370269200014
 pmid:26586121
 ISSN
 14321416
 DOI
 10.1007/s0028501509384
 language
 English
 LU publication?
 yes
 id
 349ff2f879a74d839eee6c9a32cd7b27 (old id 8235082)
 date added to LUP
 20160401 13:03:11
 date last changed
 20220306 03:28:37
@article{349ff2f879a74d839eee6c9a32cd7b27, abstract = {{This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370389, 2006) and Parvinen et al. (J Math Biol 67: 509533, 2013). Our goal is, using little more than highschool 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 241:370389, 2006) and Parvinen et al. (J Math Biol 67: 509533, 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.}}, author = {{Metz, Johan A Jacob and Staňková, Kateřina and Johansson, Jacob}}, issn = {{14321416}}, keywords = {{Function valued traits; Pontryagin’s maximum principle; Agedependent resource allocation; Mendelian take on life history theory; Evolution in periodic environments}}, language = {{eng}}, month = {{11}}, number = {{4}}, pages = {{11251152}}, publisher = {{Springer}}, series = {{Journal of Mathematical Biology}}, title = {{The canonical equation of adaptive dynamics for life histories: from fitnessreturns to selection gradients and Pontryagin's maximum principle.}}, url = {{http://dx.doi.org/10.1007/s0028501509384}}, doi = {{10.1007/s0028501509384}}, volume = {{74}}, year = {{2015}}, }