The emergence of a birth-dependent mutation rate: causes and consequences

TL;DR

This paper demonstrates that in asexual populations, mutation rates naturally depend on birth rates, leading to new evolutionary dynamics and trade-offs between birth and survival optima, contrasting with standard models.

Contribution

The study introduces a model showing the emergence of birth-dependent mutation rates and analyzes its impact on evolutionary trajectories and population adaptation.

Findings

Birth-dependent mutation rate naturally emerges at the population level.

A new trade-off arises between birth and survival optima due to mutation dependence.

Population trajectories show initial attraction to birth optimum, then convergence to survival optimum.

Abstract

In unicellular organisms such as bacteria and in most viruses, mutations mainly occur during reproduction. Thus, genotypes with a high birth rate should have a higher mutation rate. However, standard models of asexual adaptation such as the 'replicator-mutator equation' often neglect this effect. In this study, we investigate the emergence of a positive dependence between the birth rate and the mutation rate in models of asexual adaptation and the consequences of this dependence. We show that it emerges naturally at the population scale, based on a large population limit of a stochastic timecontinuous individual-based model with elementary assumptions. We derive a reaction-diffusion framework that describes the evolutionary trajectories and steady states in the presence of this dependence. When this model is coupled with a phenotype to fitness landscape with two optima, one for birth, the other one for survival, a new trade-off arises in the population. Compared to the standard approach with a constant mutation rate, the symmetry between birth and survival is broken. Our analytical results and numerical simulations show that the trajectories of mean phenotype, mean fitness and the stationary phenotype distribution are in sharp contrast with those displayed for the standard model. Here, we obtain trajectories of adaptation where the mean phenotype of the population is initially attracted by the birth optimum, but eventually converges to the survival optimum, following a hook-shaped curve which illustrates the antagonistic effects of mutation on adaptation.