Schwinger Boson Formulation and Solution of the Crow-Kimura and Eigen Models of Quasispecies Theory

Abstract

We express the Crow-Kimura and Eigen models of quasispecies theory in a functional integral representation. We formulate the spin coherent state functional integrals using the Schwinger Boson method. In this formulation, we are able to deduce the long-time behavior of these models for arbitrary replication and degradation functions. We discuss the phase transitions that occur in these models as a function of mutation rate. We derive for these models the leading order corrections to the infinite genome length limit.

37 pages; 4 figures; to appear in J. Stat. Phys

References in corpus (2)

• Quasispecies Theory for Multiple-Peak Fitness Landscapes
• Quasispecies evolution in general mean-field landscapes

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• Anderson Localization, Non-linearity and Stable Genetic Diversity
• Growing Probability of Additional Offspring with a Beneficial Reversal Allele in the Decoupled Continuous-time Mutation-selection Model