Solvable biological evolution models with general fitness functions and multiple mutations in parallel mutation-selection scheme

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Abstract
In a recent paper [Phys. Rev. E 69, 046121 (2004)], we used the Suzuki-Trottere formalism to study a quasispecies biological evolution model in a parallel mutation-selection scheme with a single-peak fitness function and a point mutation. In the present paper, we extend such a study to evolution models with more general fitness functions or multiple mutations in the parallel mutation-selection scheme. We give some analytical equations to define the error thresholds for some general cases of mean-field-like or symmetric mutation schemes and fitness functions. We derive some equations for the dynamics in the case of a point mutation and polynomial fitness functions. We derive exact dynamics for two-point mutations, asymmetric mutations, and the four-value spin model with a single-peak fitness function. The same method is applied for the model with a royal road fitness function. We derive the steady-state distribution for the single-peak fitness function. DOI: http://dx.doi.org/10.1103/PhysRevE.70.041908 © 2004 The American Physical Society