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

TL;DR

This paper models population dynamics with trait-based fitness landscapes, analyzing how populations transition across fitness valleys under stochastic effects, especially in large populations with rare mutations, revealing metastable behaviors.

Contribution

It introduces a stochastic population model with trait-dependent fitness and mutation, analyzing metastability and transition times across fitness valleys in large populations.

Findings

Metastability occurs with exponential distribution of exit times.

Population transitions across fitness valleys depend on mutation rates.

Large population limits reveal metastable transition behaviors.

Abstract

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. 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 random, exponentially distributed.