0 0.2 0.4 0.6 0.8 1 y 0 0.2 0.4 0.6 0.8 1 P F Population (log scale) Time FIG. 8: Fixation probability for the competition between two populations in the presence of drug. Squares correspond to the competition with a population capable of undergoing quiescence whereas circles correspond to the competition with a population that cannot undergo quiescence/ Solid line corresponds to the analytical expression of P$_{F}$ ( y ) for the latter case FIG. 9: This plot illustrates the phenomenon of persistence. After introducing a drug (typically, an antibiotic), there is an initial period of fast decay of the population followed by a cross-over after which the rate of population decays is much slower. In bacterial populations such as E. Coli , this is thought to be due to a phenotype switch: Cells switch to a slow growing phenotype that is more resilient to the effect of the grug than the normal phenotype. This phenomenon cannot be of genetic origin, as cells regrown from the persistent population upon removal of the drug are sensitive to it [22]. very relevant to the important issue concerning population dynamics of cancer cells and the competition mechanisms between cancer cells and their normal counterparts. In particular our model addresses issues related to the response of cancer cells to oxygen starvation [11, 15]. The mechanism involved in quiescence-dependent escape is in essence simple: it provides a buffer for the population to be safe from the hostile environment. I.e. in cases where 13