Solution of quasipecies models using coherent states

Quasispecies models describe the evolution of an asexually reproducing population subject to random mutation and selection. Individuals are labelled by a DNA-like string of letters of a fixed length N, and the population is described by a distribution function on the set of possible strings. Quasispecies models are a popular starting point for theoretical studies of molecular evolution, and have recently been applied to studies of virus-immune system interactions, evolution in changing environments, and extended to include sexual reproduction.

Two of the most commonly studied quasispecies models can be mapped onto a quantum spin system similar to the one-dimensional quantum Ising model, which allows the application of several techniques from statistical physics. Here I present a new method for calculating the dynamics and equilibrium population distribution in these quasispecies models by constructing a spin coherent-state path integral representation of the evolution operator. In the large N limit a semi-classical approximation gives a description in terms of a classical Hamiltonian function on a sphere. Using this method I will present several new results relevant to biological systems including evolution of the mutation rate, adaptation in changing environments, and a model of escape from adaptive conflict.