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

Area of Science:

• Population genetics
• Computational biology
• Statistical genetics

Background:

• The Discrete-Time Wright Fisher (DTWF) model is fundamental for population genetics, describing allele frequency changes due to drift, mutation, and selection.
• Existing computational methods for DTWF model likelihoods struggle with large sample sizes common in modern exome sequencing.
• Diffusion approximations for the DTWF model fail with large sample sizes or strong selection.

Approach:

• Developed a novel algorithm approximating the DTWF model with provably bounded error.
• Leveraged properties of Binomial distributions (sparsity, closeness of similar distributions) to approximate the DTWF transition matrix as low-rank.
• Enabled linear-time matrix-vector multiplication and fast likelihood computation for subsamples using Hypergeometric distribution properties.

Key Points:

• The algorithm achieves linear time complexity with respect to population size, overcoming quadratic scaling limitations.
• Approximation accuracy is proven theoretically and demonstrated empirically.
• Scales to population sizes in the billions, facilitating biobank-scale population genetic inference.

Conclusions:

• The new algorithm enables rigorous population genetic inference at unprecedented scales.
• Increasing sample sizes beyond current exome sequencing cohorts offers diminishing returns for estimating selection coefficients, except for variants with extreme fitness effects.