The frequency spectrum of a mutation, and its age, in a general diffusion model.
General formulae are derived for the probability density and expected age of a mutation of frequency x in a population, and similarly for a mutation with b copies in a sample of n genes. A general formula is derived for the frequency spectrum of a mutation in a sample. Variable population size models are included. Results are derived in two frameworks: diffusion process models for the frequency of the mutation; and birth and death process models. The coalescent structure within the mutant gene group and the non-mutant group is considered.
Griffiths
R C
RC
Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK. griff@stats.ox.ac.uk
D000483:Alleles; D001723:Birth Rate; D005787:Gene Frequency; D005828:Genetics, Population; D008433:Mathematics; D008957:Models, Genetic; D009026:Mortality; D009154:Mutation / Q000235:genetics* / Q000502:physiology; D011156:Population Density; D011336:Probability; D012098:Reproduction