Phylospect: a spectral operator framework for detecting episodic selection in codon evolution.

Detecting episodic positive selection along individual phylogenetic branches is a central goal of molecular evolution. The dominant approach, PAML's branch-site likelihood ratio test, is powerful under correctly specified models but inflates type I error under multinucleotide mutations (MNMs), which occur at 1-3% of substitution events in mammalian genomes and cannot be represented by standard codon substitution models. We present PHYLOSPECT (Phylogenetic Spectral Operator-based Codon Testing), a likelihood-free, operator-based framework for branch-specific selection detection. Branch-specific codon substitution rate matrices are estimated via stochastic mapping and the Nonsynonymous Operator Excess (NOE), the signed mean deviation from a pooled background across nonsynonymous single-nucleotide codon pairs is evaluated against a parametric bootstrap null. Simulations demonstrate calibrated null behaviour: Kolmogorov-Smirnov p = 0.815, false positive rate = 0.058 at α = 0.05 across 30 neutral replicates. Power increases monotonically with alignment length and selection intensity, reaching 95% at ω = 3.0 and 3,000 codons. Under 3% MNM site contamination, a pessimistic stress test exceeding realistic biological rates, PAML's false positive rate reached 1.00 while PHYLOSPECT's was 0.30, a 3.3-fold reduction. PHYLOSPECT runs 5-10 × faster per branch than PAML. Application to primate lysozyme and CD2 illustrates complementary detection regimes: PAML is sensitive to site-localised selection; PHYLOSPECT detects branch-coherent rate elevation. PHYLOSPECT is best suited as a fast, calibrated pre-screening tool for genome-scale surveys, complementing rather than replacing likelihood-based confirmatory tests.