SpectralTDF

SpectralTDF computes the transition density function (TDF) of the Wright–Fisher diffusion to model allele-frequency dynamics under diploid selection and recurrent mutation.

Key Features:

• Transition Density Function Computation: Computes the TDF to quantify temporal evolution of allele frequencies under genetic drift, selection, and mutation.
• Diffusion Approximation: Implements the diffusion approximation of the Wright–Fisher process to represent genetic drift in continuous time.
• Spectral Representation Methodology: Uses a spectral representation approach to evaluate TDFs, enabling computation for models with temporally piecewise-constant effective population size, selection coefficients, and mutation rates.
• General Model Adaptability: Supports general Wright–Fisher models with diploid selection and recurrent mutation allowing piecewise-constant parameter regimes.

Scientific Applications:

• Population Genetics: Analyzes allele-frequency evolution under genetic drift, selection, and mutation.
• Modeling Selection and Mutation: Enables investigation of effects of diploid selection coefficients and recurrent mutation on allele trajectories.
• Demographic Studies: Models consequences of varying effective population size over time on genetic variation.

Methodology:

Applies the diffusion approximation of the Wright–Fisher process and constructs a spectral representation of the transition density function to compute TDFs for models with piecewise-constant effective population size, selection coefficients, and mutation rates.