Bayesian and computational modelling for evolutionary cancer dynamics: from coarse dynamics to single-cell resolution

Biological systems such as cancer evolve across multiple scales, from macroscopic growth dynamics observable in longitudinal measurements to molecular alterations captured at single-cell resolution. Understanding these processes requires statistical and computational frameworks that adapt to increasing data richness, heterogeneity, and granularity. This dissertation introduces three complementary methods that collectively span this spectrum, offering principled, scalable, and interpretable models for studying biological evolution across levels of resolution. At the macroscopic scale, biPOD models sparse, noisy, and heterogeneous longitudinal measurements to identify dynamic transitions in growth or decay. It detects changepoints and fits piecewise parametric trajectories within a Bayesian framework that infers both the number and timing of transitions, providing interpretable summaries of latent dynamics. Although motivated by tumour growth data, biPOD applies broadly to systems exhibiting regime shifts, such as ecological populations or patient biomarker trajectories. At a higher molecular resolution, DEVIL provides a scalable framework for differential expression analysis in multi-patient single-cell transcriptomics datasets. It disentangles within-patient cellular variation from between-patient heterogeneity through a hierarchical Bayesian model combining variational inference, GPU acceleration and robust covariance estimation. DEVIL enables efficient inference across millions of cells and flexible experimental designs involving replicates and covariates, extending beyond cancer biology to developmental and immunological contexts. At the most granular scale, BRIDGES reconstructs evolutionary relationships from single-cell copy-number profiles by integrating mechanistic insights into a distance-based phylogenetic algorithm. This yields biologically faithful trees that capture complex rearrangement patterns and enable inference of ancestral genomes, bridging mechanistic realism and computational efficiency. Together, these frameworks establish a unified computational perspective for modelling biological evolution across scales, progressing from coarse-grained population dynamics to molecular reconstruction at single-cell resolution. Collectively, they demonstrate how methodological innovation enables coherent inference across heterogeneous datasets, advancing our ability to decode the multi-scale complexity of evolving biological systems.