Rare Mutations in Evolutionary Dynamics

TL;DR

This paper investigates how rare mutations, modeled by a marked point process, influence evolutionary dynamics, showing that rarity can enhance the survival chances of less fit species.

Contribution

It introduces a mathematical framework for analyzing rare mutations' effects on evolution and proves that rarity can favor low fitness species in simple models.

Findings

Rare mutations increase survival chances of low fitness species.

Derived a Kolmogorov equation for expected population frequencies.

Proved analytical results about the behavior of populations with rare mutations.

Abstract

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.