PCI Math Comp Biol

107

Title *

The emergence of a birth-dependent mutation rate in asexuals: causes and consequencesuse asterix (*) to get italics

Authors *

Florian Patout, Raphaël Forien, Matthieu Alfaro, Julien Papaïx, Lionel RoquesPlease use the format "First name initials family name" as in "Marie S. Curie, Niels H. D. Bohr, Albert Einstein, John R. R. Tolkien, Donna T. Strickland"

Year *

2021

Picture *

Abstract *

<p style="text-align: justify;">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 generation-time 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 time-continuous 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. The reason for this is that the usual weak selection limit does not hold in a complex landscape with several optima associated with different values of the birth rate. 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.</p>

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Keywords (optional)

Generation-time effect; PDE models; Stochastic models; Evolutionary trade-off; Fertility; Survival

Methods that require specific expertise (optional)

NonePlease indicate the methods that may require specialised expertise during the peer review process (use a comma to separate various required expertises).

Thematic fields *

Dynamical systems, Evolutionary Biology, Probability and statistics, Stochastic dynamics

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Submission date

2021-06-12 13:59:45

Recommender

Yuan Lou

Reviewers

Anonymous, Hirohisa Kishino

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