Scaling the discrete-time Wright-Fisher model to biobank-scale datasets

Area of Science:

• Population Genetics
• Computational Biology
• Bioinformatics

Background:

• The discrete-time Wright-Fisher (DTWF) model is fundamental for understanding allele frequency evolution due to genetic drift, mutation, and selection.
• Current computational methods for DTWF likelihoods are limited by scalability, failing for large sample sizes common in exome sequencing.
• Diffusion approximations, while computationally tractable, become inaccurate with large samples or strong selection.

Purpose of the Study:

• To develop a scalable algorithm for approximating the DTWF model with provably bounded error.
• To enable accurate population genetics inference for biobank-scale datasets (millions of individuals).
• To assess the impact of increasing sample sizes on estimating selection coefficients, particularly for loss-of-function variants.

Main Methods:

• Leveraged two key DTWF properties: approximate sparsity of transition probabilities and closeness of transition distributions for similar allele frequencies.
• Developed an approximate matrix-vector multiplication technique achieving linear time complexity.
• Extended these principles to Hypergeometric distributions for efficient subsampling likelihood computations.

Main Results:

• The novel algorithm accurately approximates the DTWF model and scales to population sizes in the tens of millions.
• Theoretical and practical demonstrations confirm the high accuracy of the approximation.
• Analysis indicates that sample sizes beyond current large exome sequencing cohorts offer diminishing returns for estimating selection coefficients, except for genes with extreme fitness effects.

Conclusions:

• The developed scalable algorithm overcomes previous computational limitations in population genetics.
• This facilitates rigorous, large-scale inference, including biobank-level analyses.
• Findings suggest current large exome sequencing efforts are near the point of diminishing returns for selection coefficient estimation in most genes.