Stem cells and their derivatives represent a renewable source of cells for therapeutic applications. However, the inability to quantitatively integrate and exploit the effects of multiple parameters on the fate of stem cells limits their use in clinical applications. To address this, we developed a computational model that combines probabilistic, individual-cell and deterministic cell-population parameters to simultaneously calculate the specific effects of exogenous and endogenous factors on the overall population-dynamics behaviour. The model tracks the progeny trajectory of individual cells over several generations as a threshold function of ligand-receptor signalling interactions. Simulations in silico were validated against an Oct 4-promoter-driven green-fluorescent-protein-expressing murine embryonic stem cell line, and used to understand the effects of key parameters on the clonal evolution of stem versus differentiated cells in this system. Our approach demonstrated the ability to distinguish between individual-cell and population-averaged parameters with respect to their effects on governing dynamic behaviour. Moreover, we could discriminate between digital versus graded regulation of the Oct 4 transcription factor in accounting for experimental observations. Finally, we showed that our approach could be generalized to other stem-cell systems, in particular the previously characterized intestinal crypt system, in elucidating relative contributions of stem and progenitor cells to population output. On the basis of all these results, we believe that our iterative experimental and computational approach has been found to be useful for the study of various stem-cell systems.