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

In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We re-examine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a 'genotype' space represented by a unitary hypercubic lattice {0, 1}(d). 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.