Understanding clustering in type space using field theoretic techniques

Abstract

The birth/death process with mutation describes the evolution of a population, and displays rich dynamics including clustering and fluctuations. We discuss an analytical `field-theoretical' approach to the birth/death process, using a simple dimensional analysis argument to describe evolution as a `Super-Brownian Motion' in the infinite population limit. The field theory technique provides corrections to this for large but finite population, and an exact description at arbitrary population size. This allows a characterisation of the difference between the evolution of a phenotype, for which strong local clustering is observed, and a genotype for which distributions are more dispersed. We describe the approach with sufficient detail for non-specialists.Comment: Accepted, Bulletin of Mathematical Biolog