  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.
