Modeling constrained tumor evolution through hybrid Ornstein–Uhlenbeck and branching dynamics

Pediatric leukemias evolve under developmental and therapeutic constraints that can limit phenotypic dispersion while allowing stochastic lineage diversification. Here, we evaluate a hybrid Ornstein-Uhlenbeck (OU)-Branching framework that couples mean-reverting continuous-state dynamics with discrete lineage branching, death, and extinction. By treating Brownian motion as the zero-attraction limiting case of OU dynamics, the model tests whether stabilizing attraction improves the description of longitudinal tumor-state trajectories. We benchmarked Brownian diffusion, OU diffusion, a Markov-emission benchmark, a branching-only drift proxy, and an OU-Branching jump-diffusion proxy using likelihood-based case-level model comparison. Applied to longitudinal targeted-sequencing variant-allele-frequency trajectories from pediatric KMT2A-rearranged acute leukemia, OU diffusion, OU-Branching, and Brownian diffusion were preferred in six, six, and four of 16 evaluable patients, respectively. These results support patient-level heterogeneity among constrained mean reversion, branching-like reconfiguration, and near-Brownian drift, positioning OU-Branching as an interpretable scaffold for evolution-aware precision oncology.