Extended Data Fig. 5: Numerical simulations of the spatially explicit model.
From: Strain displacement in microbiomes via ecological competition
Extension of Fig. 1 to spatially explicit contexts. Numerical simulated spatial profiles of Eq. S27 are shown in different rows at specified timepoints (t=0, 75, 150, 250). Different panels correspond to the invader that has not invested in the production of a toxin and has no private nutrient (panel A; mI=0, z=0), has not invested in the production of a toxin but has an abundant private nutrient (panel B; mI=1, z=0), has invested in a toxin but has no private nutrient (panel C; mI=0, z=0.5), and has both invested in a toxin and has an abundant private nutrient (panel D; mI=1, z=0.5). 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). In panel B, the lines corresponding to residents and invaders are on top of each other, which is indicated by the word “co-exist.” Parameter values used for simulating the invasion dynamics from Eq. S27: \(m={m}_{R}=1,\delta =D=d=0.15,{R}_{R}={r}_{R}=\)\({R}_{I}={r}_{I}=1,{C}_{R}={c}_{R}={C}_{I}={c}_{I}=1,s=\)\(1,{k}_{R}={k}_{I}=1,{K}_{R}={K}_{I}=K=10,g=1,\)\(p=0.7,{M}_{NR}={M}_{NI}=0.0001,{M}_{x}=\)\({M}_{xI}={M}_{xR}=0.01,{M}_{y}=0.001\).
