BABAPPAΩ: Diagnosing the Identifiability of Episodic Selection under Branch–Site Evolution Using Likelihood-Free Neural Inference

Episodic positive selection acting on specific evolutionary lineages is a longstanding yet intrinsically difficult target of molecular inference. Classical branch–site methods formulate this problem as hypothesis testing under explicit codon substitution models, implicitly assuming that episodic selection is statistically identifiable from finite alignments. Under biologically realistic conditions—including recombination, epistasis, transient fitness shifts, and alignment uncertainty—this assumption may fail, leading to unstable or uninterpretable results. BABAPPAΩ reframes branch–site analysis as a problem of statistical measurement rather than binary detection. Instead of estimating dN/dS or conducting likelihood ratio tests, the method produces continuous, scale-preserving summaries that quantify the measurability of lineage-specific evolutionary deviation under observed data conditions. Inference is likelihood-free and performed using a frozen neural model trained on forward-time mutation– selection simulations, without estimating substitution rates or codon model parameters. Simulation-based calibration shows that under strict neutrality (ω = 1), outputs remain diffuse, bounded, and structurally uninformative across phylogenies ranging from 8 to 64 taxa, with decreasing variance and no reproducible high-ranking branches or sites. In addition, a tree-conditional Monte Carlo calibration procedure provides a gene-level Episodic Identifiability Index (EII), standardized relative to neutral expectations and accompanied by an empirical p-value. Imposed episodic structure produces monotonic but saturating responses, consistent with continuous measurement rather than threshold behavior. Permutation tests eliminate inferred structure, whereas bootstrap and taxon jackknife analyses demonstrate stability under realistic perturbations. These results establish BABAPPAΩ as a conservative diagnostic framework for assessing when episodic selection is statistically resolvable, at what scale, and with what uncertainty, complementing rather than replacing likelihood-based branch–site methods.