(A) Evolutionary dynamics reflect a combination of collateral effects, drug interactions, and mutational structure. (B) Phenotypes are defined by relative resistance (R) or sensitivity (S) to each of two drugs, leading to four possible phenotypes: SS , RS , SR , or RR . Mutations can occur via direct paths (B), where each mutant phenotype is accessible directly from the fully sensitive ancestor, or via sequential paths (C), where the doubly resistant mutant (RR) is only accessible from single mutants (RS or SR). Entries of the mutation matrix (heatmaps) reflect the probability of mutating from state (rows) to state (columns) given that a mutation occurs in state . (D) Main panel: contour plot of growth surface in ancestral (SS) cells. For a specific choice of drug dosages, SS cells experience the true dosage combination (; blue circle, SS) while single mutants (black x, RS; and black square, SR) and double-resistant mutants (RR) experience decreased effect concentration of one or more drugs. Dashed lines show mean trajectories () for direct (red) and sequential (blue) mutational structures. Inset: mean growth rate for direct (red) and sequential (blue) mutational structures. (E, F) Population frequencies for single mutants (panel D; xs are RS, squares are SR) and double mutants (panel E) under direct (red) or sequential (blue) mutational structures. See also Figure 6—figure supplements 1–4.