Open Access
December 2019 Crossing a fitness valley as a metastable transition in a stochastic population model
Anton Bovier, Loren Coquille, Charline Smadi
Ann. Appl. Probab. 29(6): 3541-3589 (December 2019). DOI: 10.1214/19-AAP1487


We consider a stochastic model of population dynamics where each individual is characterised by a trait in $\{0,1,\ldots,L\}$ and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation towards neighbouring traits at each reproduction event. We choose parameters such that the induced fitness landscape exhibits a valley: mutant individuals with negative fitness have to be created in order for the population to reach a trait with positive fitness. We focus on the limit of large population and rare mutations at several speeds. In particular, when the mutation rate is low enough, metastability occurs: the exit time of the valley is an exponentially distributed random variable.


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Anton Bovier. Loren Coquille. Charline Smadi. "Crossing a fitness valley as a metastable transition in a stochastic population model." Ann. Appl. Probab. 29 (6) 3541 - 3589, December 2019.


Received: 1 January 2018; Revised: 1 February 2019; Published: December 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07172341
MathSciNet: MR4047987
Digital Object Identifier: 10.1214/19-AAP1487

Primary: 37N25 , 60F15 , 60J27 , 60J80 , 92D15 , 92D25

Keywords: birth and death process with immigration , competitive Lotka–Volterra system with mutations , coupling , Eco-evolution , selective sweep

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.29 • No. 6 • December 2019
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