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

concise to single paragraph:Episodic positive selection acting on specific evolutionary lineages is a longstanding but intrinsically difficult target of molecular evolutionary inference. Classical branch–site approaches formulate this problem as hypothesis testing under explicit codon substitution models, implicitly assuming that episodic selection is statistically identifiable from finite alignments. Under evolutionary processes that are biologically realistic—including recombination, epistasis, transient fitness perturbations, and alignment uncertainty—this assumption frequently fails. A likelihood-free inference framework, BABAPPAΩ, is introduced in which branch–site analysis is reframed as estimation of latent episodic selection burden rather than hypothesis testing. A forward-time mutation–selection simulator grounded in population-genetic theory is used to generate training and benchmarking data with exact ground truth defined at the level of site- and branch-specific fitness landscapes. A neural inference model is trained to quantify branch- and site-conditioned deviations from background evolutionary patterns without estimating likelihoods or substitution-rate parameters. Genome-scale simulations spanning neutral to heavily selected regimes demonstrate that episodic selection becomes statistically identifiable at aggregate (gene-level) scales long before it becomes identifiable at individual sites. Under strict neutrality, inferred burden remains unstructured, indicating correct calibration rather than detection bias. BABAPPAΩ is not intended as a replacement for likelihood-based branch–site tests. Instead, it provides a diagnostic framework for assessing when episodic selection is measurable at all and at what scale, offering a principled approach to studying the limits of identifiability in branch–site evolution.