Fig 4. Optimal tradeoffs in the presence of phages.

For all panels, we set N_S = 599, N_V = 5, and λ = 0.017 min⁻¹ in line with the strain used in [26] carrying the EcoRI system, and without loss of generality we fix l/ρv = 1min such that n_s and λ_e/p_V are the same up to units. Note that for these results, we used a biologically realistic number of restrictions sites on the bacterial DNA as opposed to the small value of N_S that was used for illustration purposes earlier in the paper. (a) Pareto front (thick line) for expected growth until phage escape, n_s(r, m, k), and effective growth rate, λ_e (r, m, k), traced out by varying m, r, and the number of RM systems, k (different colors; dotted lines show individual Pareto fronts at fixed k); c = c_r = c_m = 10⁻⁵. Examples with specific parameter values are marked on k = 1 front with crosses. (b) Optimal enzyme activities, r_opt and m_opt (in min⁻¹), on Pareto fronts for different k (color as in a), as a function of effective growth rate, λ_e. (c) Pareto fronts for different replication rates, λ, and cost c = c_r = c_m ≈ 3.7 · 10⁻⁷ chosen to make E. coli in [26] lie on the front (black dot, also in panel d); only k ≤ 6 are considered. (d) Pareto fronts for different cost c = c_r = c_m at fixed λ = 0.017 min⁻¹.