Understanding clustering in type space using field theoretic techniques.
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.
Lawson
Daniel John
DJ
Biomathematics and Statistics Scotland, Macaulay Institute, Aberdeen, AB15 8QH, UK. daniel@bioss.ac.uk
Jensen
Henrik Jeldtoft
HJ
D005075:Biological Evolution; D016000:Cluster Analysis; D040961:Genetic Drift; D005828:Genetics, Population; D005838:Genotype; D008433:Mathematics; D008957:Models, Genetic; D010641:Phenotype; D013269:Stochastic Processes