Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution

TL;DR

This paper maps Eigen's equations of biological evolution to a polymer depinning transition on a hypercubic lattice, providing exact solutions that confirm error catastrophe as an inherent consequence, questioning the adequacy of these models for complex evolution.

Contribution

It offers an exact solution to a mapped model of Eigen's equations, revealing fundamental limitations in their ability to describe complex biological evolution.

Findings

Error catastrophe arises naturally from the equations

Eigen's model equations are inadequate for complex evolution

Exact solutions confirm qualitative predictions

Abstract

In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We reexamine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a ``genotype'' space represented by a unitary hypercubic lattice. The exact solution of the model shows that error catastrophe arises as a direct consequence of the equations involved and confirms some previous qualitative results. The physically relevant consequence is that such equations are not adequate to properly describe evolution of complex life on the Earth.