0 0.2 0.4 0.6 0.8 1 r$_{31}$ 0.005 0.01 0.015 0.02 0.025 0.03 P[N>0] Model B FIG. 2: Simulation results for r$_{12}$ = 0 . 5. Black circles correspond to r$_{13}$ = 0 . 5 and red squares to r$_{13}$ = 0 . 25. Other parameter values: µ = 0 . 001, ϵ = 10 − $^{5}$, and α = 1. well as resistance to radio- and chemo-therpay [15]. We now present the results of simulations of the survival probability for the three different scenarios represented by model A, B and C. Simulation results. Numerical simulations of the underlying multi-type branching process (see Appendix A for details) confirm that, in fact, the presence of a quiescent population as a mechanism for escape to harsh conditions is indeed feasible. Fig. 2 shows how the survival probability depends on the probability of an indvidual of type (1) to become quiescent, r$_{13}$ . We can see that as r$_{13}$ decreases the threshold for survival in terms of r$_{31}$ , i.e. the probability of a quiescent individual to revert to type (1), moves towards smaller values of the parameter r$_{31}$ . This means that, following a decrease in the flux of individuals from the type (1) population to type (3), survival is only possible by reducing the inverse flux. This observation reveals that the mechanism by which quiescence helps escape is by acting as a reservoir where part of the population can be safely “stored”. If the flux from type (3) back to type (1) is too big, it effectively increases the flux from type (1) to type (2), thus increasing lethality. This behaviour, however, is sensitive to the decay rate of type (3) individuals, ϵ : as this parameter increases the survival probability decreases (see Fig. 4). This means that the death rate of quiescent individuals being small is an instrumental factor for quiescence-induced escape from harsh environments. Fig. 3 shows that as r$_{12}$ increases further into the regime where Eq. (1) predicts sure extinction of the (2)-type population, survival is only possible by decreasing r$_{31}$ , i.e. by increasing the average time individuals spent in the quiescent state. To test further this scenario, we perform simulations in which the following situation is 6