the competition between sub-populations exhibiting different behaviour, can be extended to study this type of bacterial persistence. Another issue in which our model differs from previous work on bacterial persistence is the following. We are consider different populations adopting different strategies, namely, a wild-type population which thrives in the absence of drug composed of two subpopulations: one that is capable of undergoing quiescence and another one that is not. By adopting this scenario we can study the evolutionary dynamics of these populations and analyse which strategy is evolutionary stable and which one is susceptibel to be invaded. In that respect, our analysis goes beyond, for example, the population models proposed by [22]. Within the context of the problem of how the hypoxic sub-population affects the dynamics of the whole tumour, our model sheds further light on this issue. It is commonly thought that hypoxia increases the probability of survival of the tumour by providing a selective pressure that favours the evolution and survival of more aggresive phenotypes [11]. Our model shows that quiescence by itself is enough to increase the survival probability of the population without further increase in the phenotypic variety of the population. Obviously, the residual population provides a springboard for these evolutionary processes to ensue. TA and HJJ gratefully acknowledge the EPSRC for funding under grant EP/D051223. In this appendix we briefly describe the method we have used to produce our simulation results. Our simulations start with one single individual of type 1. Its offspring is the determined by the probabilities of producing descendants as prescribed by the generating functions given in Tables I, II, and III, corresponding to Models A, B, and C, respectively. In general, the coefficients of the Taylor expansion of G$_{i}$ ( ⃗x ) = ∑ l,n,m $_{=0}$P$_{i}$$_{;}$$_{lnm}$ x l $_{1}$x n $_{2}$x m 3 are the probabilities per generation per indvidual (of type i ) that an type i -individual produces l descendants of type 1, n descendants of type 2, and m descendants of type 3. In subsequent generations, we go over all the individuals in existance in the last generation and the numbers and types of their descendants within the next generation are calculated in the same way. Simulations are run over 1000 realisations of 1000 generations each. The survival probability P [ N > 0] is calculated as the ratio between the number of simulations such that N ( T = 1000) > 0 and the total number of realisations. Appendix A: Simulations 15