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.
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Lawson, D.J., Jensen, H.J. Understanding Clustering in Type Space Using Field Theoretic Techniques. Bull. Math. Biol. 70, 1065–1081 (2008). https://doi.org/10.1007/s11538-007-9290-1
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DOI: https://doi.org/10.1007/s11538-007-9290-1