糖心TV Complexity Science Events
Complexity Centre and MathSys CDT events carry priority over room D1.07.
To book D1.07 please email Sheetal dot Sharma at warwick dot ac dot uk
Please note that your event booking is for D1.07 only. The adjacent common room is a private area for the MathSys Centre that cannot used as part of your booking.
Mark Ancliff: Solution of quasispecies models using spin coherent states
Abstract
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.