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

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

1996-01-20

arxiv.org/abs/cond-mat/9601088v1

Physics

Condensed Matter

10 pages in LaTeX. Figures are available from the authors. stefano.galluccio@unifr.ch (e-mail address)

Scientific paper

10.1088/0305-4470/29/10/005

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.

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