On diffusive stability of Eigen's quasispecies model

TL;DR

This paper analyzes the stability of Eigen's quasispecies model with spatial diffusion, showing that positive eigenvalues in the diffusion matrix ensure convergence to equilibrium and that spatial interactions do not alter the error threshold.

Contribution

It provides a mathematical proof that spatial diffusion with positive eigenvalues does not affect the stability or error threshold of Eigen's quasispecies model.

Findings

Solutions converge to local equilibrium under positive diffusion eigenvalues

Spatial interactions do not modify the error threshold

Diffusive stability is established for globally regulated systems

Abstract

Eigen's quasispecies system with explicit space and global regulation is considered. Limit behavior and stability of the system in a functional space under perturbations of a diffusion matrix with nonnegative spectrum are investigated. It is proven that if the diffusion matrix has only positive eigenvalues then the solutions of the distributed system converge to the equilibrium solution of the corresponding local dynamical system. These results imply that the error threshold does not change if the spatial interactions under the principle of global regulation are taken into account.