Evolution of an ensemble of mutator strains towards an equilibrium mutation rate

Mutation rates are fundamental parameters for evolutionary processes in general. If they are excessively low, populations may not adapt fast enough to environmental changes and go extinct. If they are excessively fast, deleterious mutations may reach levels unbearable to life as well. Thus, equilibrium mutation rates commonly found in nature must be compatible with the very existence of the populations they are measured in. Based on a though experiment by Fisher, we investigate the establishment of an equilibrium mutation rate reached after competition within an ensemble of asexual lineages that differ only by a mutator gene which regulate genomic mutation rates in scenarios such as under adaptation or not, and if mutator genes are directly selected or not. Our model consists initially of $L$ wild genes which can become beneficial with a selective advantage $s$, and by a genic favorable mutation rate $r$, a constant depletion of the population of a lineage that represents the genomic deleterious mutation rate $d$, and a single mutator gene that sets the multiplicative factor $m$ to all mutation rates of the strain. We show and discuss here analytical and numerical results for the distribution of the ensemble and for the fitness of the ensemble over time, paralleling them from the distinct scenarios, assessing the effect of the different parameters over the evolution of the ensembles, and comparing the latter with data from a long term evolution experiment. This work is supported by CAPES, CNPq, and FAPEMIG.