Numerical study on error catastrophe of adaptive mutants and their stability

Abstract

We study an error catastrophe of a self-replicating system, in which a number of bit strings with variable mutation rate compete to survive in a given rugged fitness landscape. The error catastrophe is known as a phase transition from an ordered state to a disordered state when a mutation rate increases. As a control parameter, we choose a selection pressure rather than a mutation rate. We find that our system shows the error catastrophe when the selection pressure decreases. An order parameter is introduced and the error catastrophe is studied for three types of mutant; (a) each bit has a fixed mutation rate, (b) each bit has a common variable mutation rate, and (c) each bit has a variable mutation rate. We also analyze stability of the system on the basis of the eigenvalue and the eigenvector of the transition matrix.