Error thresholds for molecular quasispecies as phase transitions: From simple landscapes to spin-glass models

The correspondence between Eigen’s model [Naturwissenschaften 58, 465 (1971)] for molecular quasispecies and the equilibrium properties of a lattice system proposed by Leuthäusser [J. Chem. Phys. 84, 1884 (1986); J. Stat. Phys. 48, 343 (1987)] is used to characterize the error thresholds for the existence of quasispecies as phase transitions. For simple replication landscapes the error threshold is related to a first-order phase transition smoothed by the complete wetting of the time surface. Replication landscapes based on the Hopfield Hamiltonian for neural networks allow for the tuning of the landscape complexity and reveal the existence of two error thresholds, bracketing a region of spin-glass quasispecies between the simple quasispecies and the fully disordered mixture of sequences.