where Δ r ≡ r$_{q}$ − r , Δ σ 2 = σ 2 q − σ $^{2}$, with r$_{q}$ ( r ) is the growth rate of the quiescence (normal) population, and σ 2 q ( σ $^{2}$) is the variance of the quiescent (normal) population, 〈 N 〉 is the average stationary population. The demographic parameters (i.e. r , σ $^{2}$, r$_{q}$ , and σ 2 $_{q}$) can be estimated from the evolu- tionary formalism (see [18, 19]). The growth rates are given by r = log λ$_{0}$ , where λ$_{0}$ is the dominant eigenvalue of the of the matrix A = ( a$_{ij}$ ) = ( ∂$_{j}$G$_{i}$ ( ⃗ x ) |$_{⃗}$ x $_{=1}$). In [18], it is shown that the parameter σ 2 can be obtained by slightly perturbing the parameters that determine the dynamics of the system, i.e. the mean-field dynamics being given by A ( δ ) = ( a 1+ δ ij ), and then doing an expansion for small δ . Accordingly, σ 2 is given by: Hence, in the linear approximation with H ( δ ) given by H ( δ ) = H + δH$_{δ}$ , we have that σ $^{2}$( γ ) = − H$_{δ}$ , which is given by: where π$_{i}$ ( δ ) = π$_{i}$ + δπ ( δ ) i and p$_{ij}$ ( δ ) = p$_{ij}$ + δp ( δ ) ij are the corresponding linear approximations to π and P = ( p$_{ij}$ ) when we take A ( δ ) = ( a 1+ δ ij ) δ << 1. The details of how these quantities are actually calculated is given in Appendix A of [19]. In order to show that this formalism can be used to analyse the invasion of a population possessing a dormant type, we have done simulations where one population, which is sensitive to the drug, competes with two different population: one capable of undergoing quiescence and another one which is unable to enter such state. We compare the numerics with the analytical results obtained from Eq. (6) in Fig. 8. Both analytical and numerical results show that whereas in the former case the quiescent population takes over the sensitive population almost surely, in the latter case is unlikely that the non-resident population takes over the resident one. It is worth remarking that the good agreement between simulations and analytical result seen in Fig. 8 implies that the evolutionary formalism developed by Demetrius and coworkers [17, 18] is able to make the invasion problem considered here analytically tractable. Summary and Discussion. We have shown that quiescence is a feasible mechanism for biological populations to escape hostile environments. This mechanism is expected to be σ 2 = − dH ( δ ) dδ ∣ δ =0 (8) H$_{δ}$ = − ∑ i,j π ( δ ) i p$_{ij}$ (1 + log p$_{ij}$ ) + π$_{i}$p ( δ ) ij log p$_{ij}$ (9) 12