Mathematical modelling of cancer cell evolution and plasticity

In this review, we argue that mathematical modelling is an essential tool for understanding cancer cell evolution and phenotypic plasticity. We show that mathematical models enable us to reconstruct time-dependent tumour evolutionary dynamics from temporally-restricted biological data. In their ability to capture complex biological processes, they also serve as a means for in silico experimentation. In particular, they allow us to investigate different biological hypotheses and generate experimentally-testable predictions about underlying mechanisms of phenotype evolution and treatment resistance. Finally, mathematical models can reveal which biological data is informative, and, in combination with our understanding of which biological hypotheses need to be tested, they can guide experimental and clinical trial design.