Mathematical Models of Quasi-Species Theory and Exact Results for the Dynamics.
We formulate the Crow-Kimura, discrete-time Eigen model, and continuous-time Eigen model. These models are interrelated and we established an exact mapping between them. We consider the evolutionary dynamics for the single-peak fitness and symmetric smooth fitness. We applied the quantum mechanical methods to find the exact dynamics of the evolution model with a single-peak fitness. For the smooth symmetric fitness landscape, we map exactly the evolution equations into Hamilton-Jacobi equation (HJE). We apply the method to the Crow-Kimura (parallel) and Eigen models. We get simple formulas to calculate the dynamics of the maximum of distribution and the variance. We review the existing mathematical tools of quasi-species theory.
A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, 2 Alikhanian Brothers St., Yerevan, 375036, Armenia. saakian@yerphi.am.
David B
DB
Saakian
Institute of Physics, Academia Sinica, Nankang, Taipei, 11529, Taiwan.
Chin-Kun
CK
Hu
D019143:Evolution, Molecular; D008957:Models, Genetic; D008962:Models, Theoretical; D009154:Mutation