Leveraging FracMinHash Containment for Genomic d N / d S

Increasing availability of genomic data demands algorithmic approaches that can efficiently and accurately conduct downstream genomic analyses. These analyses, such as evaluating selection pressures within and across genomes, can reveal developmental and environmental pressures. One such commonly used metric to measure evolutionary pressures is based on the ratio of non-synonymous and synonomous substitution rates, $d_N/d_S$ . Conventionally, the $d_N/d_S$ ratio is used to infer selection pressures employing alignments to estimate total non-synonymous and synonymous substitution rates along protein-coding genes. However, this process can be time consuming and not scalable for larger datasets. Recently, a fast, approximate similarity measure, FracMinHash containment, was introduced and related to average nucleotide identity. In this work, we show how FracMinHash containment can be used to quickly estimate $d_N/d_S$ enabling alignment-free estimations at a genomic level. Through simulated and real world experiments, our results indicate that employing FracMinHash containment to estimate $d_N/d_S$ is scalable, enabling pairwise $d_N/d_S$ estimations for 85,205 genomes within 5 hours. Furthermore, our approach is comparable to traditional $d_N/d_S$ methods, representing sequences subject to positive and negative selection across various mutation rates. Moreover, we used this model to evaluate signatures of selection between Archaeal and Bacterial genomes, identifying a previously unreported metabolic island between Methanobrevibacter sp. RGIG2411 and Candidatus Saccharibacteria bacterium RGIG2249. We present, FracMinHash $d_N/d_S$ , a novel alignment-free approach for estimating $d_N/d_S$ at a genome level that is accurate and scalable beyond gene-level estimations while demonstrating comparability to conventional alignment-based $d_N/d_S$ methods. Leveraging the alignment-free similarity estimation, FracMinHash containment, pairwise $d_N/d_S$ estimations are facilitated within milliseconds, making it suitable for large-scale evolutionary analyses across diverse taxa. It supports comparative genomics, evolutionary inference, and functional interpretation across both synthetic, and complex biological datasets.