A non-local rare mutations model for quasispecies and prisoner's dilemma: Numerical assessment of qualitative behaviour

Abstract

An integro-differential model for evolutionary dynamics with mutations is investigated by improving the understanding of its behavior using numerical simulations. The proposed numerical approach can handle also density dependent fitness, and gives new insights about the role of mutation in the preservation of cooperation.

A rare mutation model in a spatial heterogeneous environment

“…In the same paper [2], a Kolmogorov integro-differential equation describing the expected frequencies is derived and investigated analytically, with particular attention to the long term equilibrium. Analytical investigation is satisfactory in the case of constant fitness (quasispecies equation), but there are some gaps concerning variable fitness, that has been tackled by a numeric approach in the subsequent paper [3]. In the present work we are mainly concerned with Monte-Carlo simulations.…”

“…This aspect is well-suited especially within the framework of social dilemma, or more generally when the type E i are read as strategies more then species or phenotypes. See also the numerical paper [3], focused on Prisoner's Dilemma. In this paper we take a step further and address our attention to the environment, seen as a place where individuals can evolve but also as a factor that can influence the dynamics of interaction between strategists.…”

“…This aspect is well-suited especially within the framework of social dilemma, or more generally when the type E i are read as strategies more then species or phenotypes. See also the numerical paper [3], focused on Prisoner's Dilemma.…”