Stochastic clonal dynamics and genetic turnover in exponentially growing populations

We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a birth-death process to analytically calculate the probability that the parent of a given genotype will go extinct. We compare the results with numerical simulations and show how this turnover of genetic clones can be used to infer the rates underlying the population dynamics. Our work is motivated by growing populations of tumour cells, the epidemic spread of viruses, and bacterial growth.