Variational ansatz for quasispecies in the Eigen model
نویسندگان
چکیده
We investigate the error threshold for the emergence of quasispecies in the Eigen model. By mapping to an effective Hamiltonian ruled by the “imaginary-time” Schrödinger equation, a variational ansatz is proposed and applied to calculate various properties associated with the quasispecies. The variational ansatz gives correct prediction for the survival population of the wild-type sequence and also reveals an unexpected universal scaling behavior near the error threshold. We compare the results from the variational ansatz with that from numerical methods and find excellent agreement. Though the emergence of the scaling behavior is not yet fully understood, it is remarkable that the universal scaling function reigns even for relatively short genome length such as L = 16. Further investigations may reveal the mechanism of the universal scaling and extract the essential ingredients for the emergence of the quasispecies in molecular evolution.
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