Signature-Informed Selection Detection: A Novel Method for Multi-Locus Temporal Population Genetic Model with Recombination

2025-12-16

AI Summary

In population genetics, joint inference of selection coefficients across multiple linked loci has long been hindered by model complexity and intractable likelihoods. This paper introduces the first generalized Bayesian framework based on path-signature kernel scores, enabling robust joint estimation of selection coefficients and initial haplotype frequencies—under multi-locus selection, recombination, and negative frequency-dependent selection—without requiring an explicit likelihood function. The method integrates pseudo-marginal MCMC, iterative path integration, and Wright–Fisher simulations to achieve asymptotically consistent posterior sampling. In simulations with two- and three-locus systems, it substantially outperforms existing benchmarks. Applied to real Evolve and Resequence data from yeast and *Drosophila simulans*, it delivers the first interpretable, high-precision inference of natural selection parameters across multiple linked loci.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Evolutionary Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In population genetics, there is often interest in inferring selection coefficients. This task becomes more challenging if multiple linked selected loci are considered simultaneously. For such a situation, we propose a novel generalized Bayesian framework where we compute a scoring rule posterior for the selection coefficients in multi-locus temporal population genetics models. As we consider trajectories of allele frequencies over time as our data, we choose to use a signature kernel scoring rule - a kernel scoring rule defined for high-dimensional time-series data using iterated path integrals of a path (called signatures). We can compute an unbiased estimate of the signature kernel score using model simulations. This enables us to sample asymptotically from the signature kernel scoring rule posterior of the selection coefficients using pseudo-marginal MCMC-type algorithms. Through a simulation study, we were able to show the inferential efficacy of our method compared to existing benchmark methods for two and three selected locus scenarios under the standard Wright-Fisher model with recombination and selection. We also consider a negative frequency-dependent selection model for one and two locus scenarios, and also joint inference of selection coefficients and initial haplotype frequencies under the standard Wright-Fisher model. Finally, we illustrate the application of our inferential method for two real-life dataset. More specifically, we consider a data set on Yeast, as well as data from an Evolve and Resequence (E&R) experiment on {em Drosophila simulans}.

Problem

• Infer selection coefficients for multiple linked loci in population genetics.
• Develop a Bayesian framework using signature kernels for time-series allele frequency data.
• Apply method to simulated and real datasets, including yeast and Drosophila.

Innovation

• Bayesian framework with signature kernel scoring rule
• Unbiased score estimation via model simulations
• Pseudo-marginal MCMC sampling for selection coefficients