Data Sheet 1_A hybrid Ornstein–Uhlenbeck–Branching framework unifies microbial and pediatric tumor evolution.pdf

IntroductionPediatric 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.
MethodsUsing 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.
ResultsThe 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.
DiscussionAlthough 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.