Beyond Invariable Sites: Using Evolutionary Stasis to Map Multi-Layered Constraints on the Evolution of Viral and Mammalian Genomes

The quantification of genomic conservation has progressed from foundational statistical modeling of evolutionary rates to state-of-the-art deep learning architectures. However, a major resolution gap remains at the zero-rate origin, where standard selection inference tools fail to distinguish between sites that are invariant due to chance (stochastic invariance) or low substitution opportunity, and those that are invariant due to extreme purifying selection. We present B-STILL (Bayesian Significance Test of Invariant Low Likelihoods), a hierarchical Bayesian framework designed to resolve the selective landscape of protein-coding genes near the zero-rate limit. By leveraging gene-level rate distributions (prior calibration) and modeling codon-site specific substitution opportunities (determined by genetic code degeneracy and nucleotide substitution biases), B-STILL quantifies the statistical significance of observed stasis. We define a rate-based stasis threshold to identify Evolutionary Stasis Anchors (ESAs)-sites where the upper bound on the evolutionary rate is statistically constrained relative to the background rate of the gene due to extreme purifying selection. Validation against clinical and pathogen datasets confirms that ESAs are strong predictors of biological fitness and pathogenicity. Applying B-STILL across viral and mammalian genomes, we identify thousands of significantly clustered ESAs that map to known functional domains and uncharacterized structural motifs. These results establish B-STILL as a scalable, statistically rigorous framework for high-resolution genomic annotation, converting previously uninformative invariant sites into precise markers of extreme evolutionary constraint.