Competing evolutionary paths in growing populations with applications to multidrug resistance - Fig 7

(a) Illustration of the paths to multidrug resistant cells arising in the region containing both drugs A and B, as in Fig 6. Note a spatial location exists containing only drug A. The red, dashed path is an example of stepwise evolution, where multidrug resistant cells come to exist in the sanctuary via the region containing only a single drug. The vertex labels display the fitness cost (increase to the cellular death rate) of cells in that state. (b) Exploration of the median time to resistance as the size of the drug A region increases relative to the sanctuary size. Here we plot t1/2, as given in Table 1, for the system displayed in (a). We observe that, for a subset of the parameter space, the existence of a single drug region can decrease the time to resistance, despite diminishing the sanctuary size. If both drugs penetrate the majority of the system and the drugs have a greater effect than the cost of resistance, this subset of parameter space is identified by the inequality (16). Within this parameter subset, resistance is fastest at a particular size of single drug compartment, given by (17). Parameters; (top) ν = 10−6, m = 0.05, d = 0.9, s = 10−3, λ = 0.4, α = 0.3, nTot = 107, nDD = 0.9nTot, γ = 10−3; (bottom) all same except s = 10−2.