# Crossing a fitness valley as a metastable transition in a stochastic population model

@article{Bovier2019CrossingAF, title={Crossing a fitness valley as a metastable transition in a stochastic population model}, author={Anton Bovier and Loren Coquille and Charline Smadi}, journal={The Annals of Applied Probability}, year={2019} }

We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0,1,...,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…

## 11 Citations

### From adaptive dynamics to adaptive walks.

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This work considers an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event, and modelled as a measure-valued Markov process.

### A general multi-scale description of metastable adaptive motion across fitness valleys

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This work develops the framework of a meta graph that is constituted of ESCs and possible metastable transitions between those, and proves the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability.

### Stochastic models for adaptive dynamics: Scaling limits and diversity

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I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation…

### Stochastic individual-based models with power law mutation rate on a general finite trait space

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The theorem 3.2 of [Bovier, Coquille, Smadi, 2018] is generalised to any finite mutation graph, and a series of examples describing surprising phenomena arising from the geometry of the graph and/or the rate of mutations are illustrated.

### Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer

- BiologyThe Annals of Applied Probability
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The goal is to analyze the trade-off between natural evolution to higher birth rates and transfer, which drives the population towards lower birth rates, and implies that negligible sub-populations may have a strong contribution to evolution.

### Filling the gap between individual-based evolutionary models and Hamilton-Jacobi equations

- Mathematics
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We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a ﬁnite grid of the torus, and with mutation and selection. Traits are vertically…

### Balancing selection and the crossing of fitness valleys in structured populations: diversification in the gametophytic self-incompatibility system

- BiologybioRxiv
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Numerical simulations in a finite island population genetics model suggest that population subdivision can act in two opposite directions: it renders S-haplotypes diversification easier, although it also increases the risk that the self-incompatibility system is lost.

### On Λ-Fleming–Viot processes with general frequency-dependent selection

- MathematicsJournal of Applied Probability
- 2020

This multidimensional model aims for the generality of adaptive dynamics and the tractability of population genetics, and provides a natural bridge between two of the most prominent modelling frameworks of biological evolution: population genetics and eco-evolutionary models.

### Competing evolutionary paths in growing populations with applications to multidrug resistance

- BiologyPLoS Comput. Biol.
- 2019

This work focuses on the setting where cells at the root vertex have the highest fitness and transition rates are small, and develops simple formulas derived for the time to reach the target vertex and for the probability that it is reached along a given path in the graph.

### Multidimensional $\Lambda$-Wright-Fisher processes with general frequency-dependent selection.

- Mathematics
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We construct a constant size population model allowing for general selective interactions and extreme reproductive events. It generalizes the idea of (Krone and Neuhauser 1997) who represented the…

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