Error Threshold for Spatially Resolved Evolution in the Quasispecies Model

The error threshold for quasispecies in 1, 2, 3, and $\infty$ dimensions is investigated by stochastic simulation and analytically. The results show a monotonic decrease in the maximal sustainable error probability with decreasing diffusion coefficient, independently of the spatial dimension. It is thereby established that physical interactions between sequences are necessary in order for spatial effects to enhance the stabilization of biological information. The analytically tractable behavior in an $\infty$-dimensional (simplex) space provides a good guide to the spatial dependence of the error threshold in lower dimensional Euclidean space.