Poster #31 - Nicholas Paradis

A Closed-Form Estimator of Selection Strength from Substitution-Mutation Ratios: Theory and a SARS-CoV-2 Case Study

Paradis, N., PhD Candidate, Dept. of Chemistry and Biochemistry, Rowan University, Glassboro, NJ, 08028. Wu, C., Associate Professor, Dept. of Chemistry and Biochemistry, Dept. of Molecular & Cellular Biosciences, Rowan University, Glassboro, NJ, 08028.

Classical fixation probability (Pfix) formulations are central to population genetics but are analytically non-invertible, hindering genome-scale selection inference from sequence data and efficient sampling of sequence space in simulations. Using a well-known invertible surrogate, P_fix=e^(S⁄2)/N_e, we yield a closed-form estimator from the substitution-to-mutation rate ratio S=2ln⁡(c/μ). This log-ratio framework preserves Halpern-Bruno equilibrium landscapes, improves barrier-crossing efficiency with exponential speedup (e^(|S⁄(2|))/|S|) relative to Halpern-Bruno's Pfix formulation, and avoids transcendental functions, enabling rapid, site-specific fitness inference. Applied to SARS-CoV-2 with 9711 codons, the surrogate (i) generated fitness profiles nearly identical to Halpern-Bruno's but at ~1000-fold lower computational cost to convert c/μ into S; (ii) improves barrier-crossing efficiency by ~2-fold per codon site, suggesting potentially enormous speedup for the whole codon sequence. Distributions of fitness effects across coding and noncoding regions consistently showed L-shaped patterns dominated by deleterious mutations with rare adaptive substitutions, inconsistent with Neutral, Nearly Neutral, or Selectionist theories. Instead, the data supports a Near-Neutral Selectionist Theory (NNST), in which balancing weakly beneficial and weakly deleterious mutations sustain a molecular clock, while imbalance collapses it. This tractable framework bridges theory with practice, enabling scalable evolutionary inference across viral and larger genomes (Gb) and speed up the sequence-space simulations.