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 (TDF) 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 TDF 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/ .