Adaptive dynamics for physiologically structured population models

Durinx M, Metz JAJ, & Meszena G (2008). Adaptive dynamics for physiologically structured population models. Journal of Mathematical Biology 56 (5): 673-742. DOI:10.1007/s00285-007-0134-2.

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Abstract

We develop a systematic toolbox for analyzing the adaptive dynamics of multidimensional traits in physiologically structured population models with point equilibria (sensu Dieckmann et al. in Theor. Popul. Biol. 63:309-338, 2003). Firstly, we show how the canonical equation of adaptive dynamics (Dieckmann and Law in J. Math. Biol. 34:579-612, 1996), an approximation for the rate of evolutionary change in characters under directional selection, can be extended so as to apply to general physiologically structured population models with multiple birth including second order terms, in the distances of the trait vectors to the singularity) for a community of N coexisting types near an evolutionarily singular point has a rational form, which is model-independent in the following sense: the form depends on the strategies of the residents and the invader, and on the second order partial derivatives of the one-resident fitness function at the singular point. This normal form holds for Lotka-Volterra models as well as for physiologically structured population models with multiple birth states, in discrete as well as continuous time and can thus be considered universal for the evolutionary dynamics in the neighbourhood of singular points. Only in the case of one-dimensional trait spaces or when N = 1 can the normal orm be reduced to a Taylor polynomial. Lastly we show, in the form of a stylized recipe, how these results can be combined into a systematic approach for the analysis of the (large) class of evolutionary models that satisfy the above restrictions.

Item Type: Article
Uncontrolled Keywords: Adaptive dynamics; Evolutionary modelling; Multitype branching processes; Multivariate evolutionarily singular strategies; Physiologically structured populations
Research Programs: Evolution and Ecology (EEP)
Bibliographic Reference: Journal of Mathematical Biology; 56(5):673-742 (May 2008)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:41
Last Modified: 24 Feb 2016 14:49
URI: http://pure.iiasa.ac.at/8554

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