A simple stochastic model describing genomic evolution over time of GC content in microbial symbionts

•Mathematical model describing evolution of GC content in microbial symbionts over time.•Model allows for random perturbation of mutation rates.•Muller’s ratchet: abrupt extinction process may have been initiated early in the organisms’ history.•Species must continuously devote resources to reduce effects of random mutations. An organism’s genomic base composition is usually summarized by its AT or GC content due to Chargaff’s parity laws. Variation in prokaryotic GC content can be substantial between taxa but is generally small within microbial genomes. This variation has been found to correlate with both phylogeny and environmental factors. Since novel single-nucleotide polymorphisms (SNPs) within genomes are at least partially linked to the environment through natural selection, SNP GC content can be considered a compound measure of an organism’s environmental influences, lifestyle, phylogeny as well as other more or less random processes. While there are several models describing genomic GC content few, if any, consider AT/GC mutation rates subjected to random perturbations. We present a mathematical model that describes how GC content in microbial genomes evolves over time as a function of the AT → GC and GC → AT mutation rates with Gaussian white noise disturbances. The model, which is suited specifically to non-recombining vertically transmitted prokaryotic symbionts, suggests that small differences in the AT/GC mutation rates can lead to profound differences in outcome due to the ensuing stochastic process. In other words, the model indicates that time to extinction could be a consequence of the mutation rate trajectory on which the symbiont embarked early on in its evolutionary history.