title: Solvable biological evolution models with general fitness functions and multiple mutations in parallel mutation-selection scheme.
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.
authors.affiliation: Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan.
authors.forename: David B
authors.initials: DB
authors.lastname: Saakian
authors.forename: Chin-Kun
authors.initials: CK
authors.lastname: Hu
authors.forename: H
authors.initials: H
authors.lastname: Khachatryan
mesh_terms: D005075:Biological Evolution; D003198:Computer Simulation; D017753:Ecosystem; D014644:Genetic Variation / Q000502:physiology*; D008954:Models, Biological; D009154:Mutation; D011157:Population Dynamics; D012641:Selection, Genetic; D016019:Survival Analysis