Phase diagram for the Eigen quasispecies theory with a truncated fitness landscape

Abstract

Using methods of statistical physics, we present rigorous theoretical calculations of Eigen's quasispecies theory with the truncated fitness landscape which dramatically limits the available sequence space of information carriers. As the mutation rate is increased from small values to large values, one can observe three phases: the first (I) selective (also known as ferromagnetic) phase, the second (II) intermediate phase with some residual order, and the third (III) completely randomized (also known as paramagnetic) phase. We calculate the phase diagram for these phases and the concentration of information carriers in the master sequence (also known as peak configuration) x0 and other classes of information carriers. As the phase point moves across the boundary between phase I and phase II, x0 changes continuously; as the phase point moves across the boundary between phase II and phase III, x0 has a large change. Our results are applicable for the general case of a fitness landscape.