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

11276 9 33401 2 71531 document 33401 The canonical equation of adaptive dynamics for life.pdf application/pdf 6d7669ad41176afefb28527ea2ba76c7 MD5 669799 2016-02-22 08:51:21 https://pure.iiasa.ac.at/id/eprint/11276/1/The%20canonical%20equation%20of%20adaptive%20dynamics%20for%20life.pdf 11276 1 1 application/pdf text en public cc_by

The canonical equation of adaptive dynamics for life.pdf

published 33403 2 71542 document 33403 lightbox.jpg image/png 529bbbf33a5ea03562c5fb8fb11717d0 MD5 35462 2016-02-22 09:01:40 https://pure.iiasa.ac.at/id/eprint/11276/2/lightbox.jpg 11276 2 2 image/png other Thumbnails conversion from text to thumbnail_lightbox en public

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/33401 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/33401 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/33401 archive 351 disk0/00/01/12/76 2016-01-15 08:52:28 2021-08-27 17:39:49 2016-01-15 08:52:28 article show Metz J.A.J. 7506 Stankova K. Johansson J. The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle pub iis_ecl prog_eep age-dependent resource allocation; canonical equation of adaptive dynamics; evolution in periodic envronments; function valued traits; Mendelian take on life history theory; Pontryagin's maximum principle 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 24:370.389, 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 argument, (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. 2016-03 published Springer 10.1007/s00285-015-0938-4 XJ-15-377 Journal of Mathematical Biology; Article in press (Published online 19 November 2015) [doi:10.1007/s00285-015-0938-4] 206 public Journal of Mathematical Biology 72 4 1125-1152 TRUE 1432-1416 FALSE no info:eu-repo/semantics/article