A new proof for the convergence of an individual based model to the trait substitution sequence

Gupta A, Metz JAJ, & Tran VC (2013). A new proof for the convergence of an individual based model to the trait substitution sequence. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-13-034

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Abstract

We consider a continuous time stochastic individual based model for a population structured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is large, the mutations are rare and the process is viewed in the timescale of mutations. Using averaging techniques due to Kurtz (in Lecture Notes in Control and Inform. Sci., vol. 177, pp. 186-209, 1992), we give a new proof of the convergence of the individual based model to the trait substitution sequence of Metz et al. (in Trends in Ecology and Evolution 7(6), 198-202, 1992), first worked out by Dieckman and Law (in Journal of Mathematical Biology 34(5-6), 579-612, 1996) and rigorously proved by Champagnat (in Theoretical Population Biology 69, 297-321, 2006): rigging the model such that "invasion implies substitution", we obtain in the limit a process that jumps from one population equilibrium to another when mutations occur and invade the population.

Item Type: Monograph (IIASA Interim Report)
Uncontrolled Keywords: Birth and death process; Structured population; Adaptive dynamics; Individual based model; Averaging technique; Trait substitution sequence
Research Programs: Evolution and Ecology (EEP)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:49
Last Modified: 20 Oct 2016 18:06
URI: http://pure.iiasa.ac.at/10728

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