Extended Data Fig. 3: Numerical simulations of the batch culture dynamics.
From: Strain displacement in microbiomes via ecological competition
Multiple numerical solutions of batch culture dynamics are presented where the variable toxin investment and variable availability of private nutrient (panels A-D), variable toxin potency and variable availability of private nutrient (panels E-H), variable toxin investment and both invader and resident have variable availability of private nutrients (panels I-L), and variable toxin potency and both invader and resident have variable availability of private nutrients (panels M-P). Toxin investment is varied between values \(z=0\) ((panels A, B, I, J) and \(z=0.5\) (panels C, D, K, L), while toxin potency is varied between values \(p=0\) (panels E, F, M, N) and \(p=1\) ((panels G, H, O, P). Similarly, the availability of the invader’s private nutrient is varied between initial values mI = 0 (panels A, C, E, G) and mI = 1 (panels B, D, F, H), while the private nutrients of both invader and resident are varied between initial values mI = mR = 0 (panels I, K, M, O) and mI = mR = 1 (panels J, L, N, P). Moreover, the initial abundance of the shared nutrient is always set to a value m = 1. After the resident strain, introduced at initial abundance of NR = 0.001, reaches an equilibrium, the invader strain is introduced at abundance NI = 0.001 and the resulting dynamics is plotted. Solid lines indicate the abundance of strains (resident in blue, invader in red), the dotted red line indicates the abundance of the invader toxin, and the dashed lines indicate the abundance of nutrients (shared nutrient in grey, private nutrient for the resident in blue, private nutrient for the invader in red). Baseline parameter values used for simulating the invasion dynamics from Eq. 3(Methods): \(m={m}_{R}={m}_{I}=0,\delta =D=d=0,{R}_{R}=\)\({r}_{R}={R}_{I}={r}_{I}=1,{C}_{R}={c}_{R}={C}_{I}={c}_{I}=\)\(1,s=1,{k}_{R}={k}_{I}=1,{K}_{R}={K}_{I}=\)\(K=10,g=1,p=0.7,z=0.5\).
