title: SpectralTDF: transition densities of diffusion processes with time-varying selection parameters, mutation rates and effective population sizes.
abstract: In the Wright-Fisher diffusion, the transition density function describes the time evolution of the population-wide frequency of an allele. This function has several practical applications in population genetics and computing it for biologically realistic scenarios with selection and demography is an important problem.
  
  
  
  We develop an efficient method for finding a spectral representation of the transition density function for a general model where the effective population size, selection coefficients and mutation parameters vary over time in a piecewise constant manner.
  
  
  
  The method, called SpectralTDF, is available at https://sourceforge.net/projects/spectraltdf/
  
  
  
  yss@berkeley.edu
  
  
  
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003, USA.
authors.forename: Matthias
authors.initials: M
authors.lastname: Steinrücken
authors.affiliation: Department of Statistics.
authors.forename: Ethan M
authors.initials: EM
authors.lastname: Jewett
authors.affiliation: Department of Statistics, Department of EECS, Department of Integrative Biology, University of California, Berkeley, CA 94720, USA, Department of Mathematics and Department of Biology, University of Pennsylvania, Philadelphia, PA 19104, USA.
authors.forename: Yun S
authors.initials: YS
authors.lastname: Song
mesh_terms: D005828:Genetics, Population; D008957:Models, Genetic; D009154:Mutation; D059645:Mutation Rate; D012641:Selection, Genetic