Clonal haematopoiesis (CH) is an age-associated process in which hematopoietic stem cells (HSCs) acquire somatic mutations that may confer a selective advantage, driving clonal expansion and elevating malignancy risk. Although sequencing studies have catalogued recurrent driver mutations, the evolutionary dynamics that govern their emergence, competition, and clinical impact remain poorly understood. Current models often assume exponential growth, yet such formulations neglect homeostatic constraints and competition that necessarily limit clonal expansion. Thus, more mechanistic and predictive frameworks are needed. We propose an integrated modeling strategy that combines deterministic logistic growth with stochastic Moran process simulations to study CH progression. The Moran process and its extension capture the balance of selection and drift under fixed or variable HSC pool sizes. This aligns with adult homeostasis, but can also reflect reduced compartments under stressors such as chemotherapy. Our simulations demonstrate that cytotoxic therapy contracts the HSC pool, amplifying stochastic drift and random variation in clonal prevalence. Under these conditions, mutants with modest fitness advantages expand more readily, reflecting context-dependent evolutionary success. These predictions parallel clinical observations: in a cohort breast cancer including 171 patients with serial peripheral blood samples collected before and after treatment (chemotherapy, radiation, hormone therapy, or combined modalities), the 22 patients with positively selected CH exposed to chemotherapy or chemoradiation showed significant allelic populations contractions, suggesting that therapeutic depletion of wild-type cells is a key driver of observed fitness. On the deterministic side, quantification of the differences in fitness with this improved assumption of longitudinal variant allele frequency (VAF) trajectories from the largest, publicly available dataset of CH (Bolton et al. 2020) shows that logistic growth provides a superior fit compared to exponential models. Exponential assumptions systematically underestimate clonal fitness, while logistic models capture saturation effects and more realistic growth dynamics. By unifying stochastic (Moran) and deterministic (logistic) approaches, our framework enables more accurate inference of clonal fitness and allows classification of positively versus negatively selected clones, which directly links to patient survival outcomes. This combined modeling approach establishes a mathematically rigorous foundation for quantifying CH dynamics, bridging mechanistic predictions with clinical data. It advances our ability to identify high-risk clones, forecast progression, and ultimately improve the predictive power of CH as a biomarker for patient management.