In this paper we study the effect of rare mutations, driven by a marked point process, on the evolutionary behavior of a population. We derive a Kolmogorov equation describing the expected values of the different frequencies and prove some rigorous analytical results about their behavior. Finally, in a simple case of two different quasispecies, we are able to prove that the rarity of mutations increases the survival opportunity of the low fitness species.
Amadori, A. L., Calzolari, A., Natalini, R., & Torti, B. (2015). Rare mutations in evolutionary dynamics. Journal of Differential Equations, 259(11), 6191–6214. https://doi.org/10.1016/j.jde.2015.07.021