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A model is presented relating the evolution of genomic GC content over timeto AT$\rightarrow$GC and GC$\rightarrow$AT mutation rates. By employing It\^ocalculus it is shown that if mutation rates in asexually reproducing organismsare subject to random perturbations that can vary over time severalimplications follow. For instance, an extra Brownian motion term appearsinfluencing nucleotide variability; the greater the variability of the randomperturbations on the mutation rates the stronger the impact of the Brownianmotion term. Reducing the influence of the random perturbations, to limitfitness decreasing and deleterious mutations, will likely imply divestingresources to genomic repair systems. The stable mutation rates seen in manyorganisms could thus be an evolved strategy to reduce the influence of theBrownian motion term. Furthermore, if change to genomic GC content, i.e. the GCcontent of variable sites or single nucleotide polymorphisms (SNPs), is just aslikely to increase as to decrease, something that resembles knockout of repairenzymes and removal of selective pressures seen in evolutionary laboratoryexperiments, the species genome will likely decay unless infinite resources areavailable. These implications are solely a consequence of allowing randomperturbations affect AT- and GC mutation rates and not obtainable usingstandard non-stochastic methodology. Finally, a connection between the modelfor genomic GC content evolution and the classical Luria-Delbr\"uck mutationmodel is presented in a stochastic setting.

A simple model describing evolution of genomic GC content with random perturbations in asexually reproducing organisms