The interplay between population genetics and diffusion with stochastic resetting

Abstract

In this work we analyze the connection between the theory of diffusion with stochastic resetting and the theory of the Ohta–Kimura continuous ladder model. A first hint of this connection is readily given by the equivalence between the models’ partial differential equations for their distribution probabilities. In addition, it turns out that Fleming–Viot processes play a central role in connecting these theories. As an unfolding thereof, it is expected that relevant results obtained for one model can be translated to the other model framework. This is illustrated in this article by obtaining the mean first-passage time for the Ohta–Kimura continuous ladder model and by establishing the correlation between particles in the stochastic resetting model. We also study the non-equilibrium stationary distribution for two interacting resetting particles. In addition we make a brief excursion into another particle interaction model that does not have stationary distribution.