A hybrid Ornstein–Uhlenbeck–Branching framework unifies microbial and pediatric tumor evolution

Introduction: Pediatric tumors can relapse despite low mutation burdens, suggesting hybrid evolutionary dynamics shaped by stochastic variability and stabilizing forces. We develop a hybrid Ornstein-Uhlenbeck (OU)-Branching framework that couples mean-reverting stochastic trait dynamics with demographic birth-death processes to model lineage diversification under effective stabilizing constraints. Methods: Using Escherichia coli long-term evolution experiment (LTEE) lineages (WT, priA, recG), we parameterized the equilibrium mean (μ), mean-reversion strength (θ), and diffusion scale (σ) on the log10 mutation-frequency axis via replicate-grouped likelihood inference. We performed forward simulations for predictive envelopes, uncertainty quantification, phase-plane dynamics, and OU-Branching lineage networks. We also ran illustrative in silico therapy simulations under fixed OU parameters with exposure-modulated birth/death rates. Results: The fitted model recapitulated lineage-specific mutation dynamics and branching architectures. priA exhibited elevated stochastic dispersion and drift-prone behavior consistent with a high-plasticity regime, whereas recG showed constrained diversification and increased lineage turnover consistent with a collapse-prone regime. Illustrative therapy simulations generated oscillatory trait trajectories, suppression-rebound population dynamics, clonal pruning, and extinction-versus-persistence regimes. Discussion: Although Y is directly observed as log10 mutation frequency in LTEE, in tumors Y can represent a longitudinally measurable phenotypic state (e.g., drug-tolerance scores from single-cell data, MRD/VAF-derived burden proxies, or pathway activity states). The balance between stabilizing strength (θ) and stochastic variability (σ) provides a quantitative axis governing plasticity and persistence, motivating future calibration to clinical longitudinal data for evolution-aware, patient-specific modeling.