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.