Open-loop control of the human microbiome.

(a) Background of clustering analysis for α = 1.6 from Fig 2, but with Euclidean distance used so that a projection matrix could be found to show the trajectories in the 2D principle coordinate plane (S1 Text Sec. 5.6). We aim to steer a local community (denoted as LC*, shown in magenta) in the blue cluster to the orange cluster. Three different scenarios are presented, per the three numbers above the arrows. Scenario 1: SISs swap. The SISs (23 and 81) of LC* were replaced by the SISs present in the orange cluster (60 and 51). The initial abundances of species 60 and 51 were drawn from , resulting in and altered community (green dot), and the GLV dynamics were simulated until the steady state was reached (white dot), which is located in the orange cluster as desired. Scenario 2: Dominating Species (DS) swap. The six most abundant species in LC* were removed and replaced by the six most abundant species from a local community in the orange cluster, with the initial condition after the switch of species shown as the red dot, and the dynamics were simulated until steady state was reached (white dot). Scenario 3: Fecal Microbiota Transplantation (FMT). The two SISs and 18 of the most abundant species (for a total of 20) were removed from LC* with the initial condition shown in blue (post-antibiotic state). Then the GLV dynamics were simulated (gray line) and the system converged to the black dot (CDI state). Then 1% of the steady abundances from an arbitrary LC in the orange cluster were added to the CDI state (gray dot, emulating oral capsule FMT) and the dynamics were then simulated until steady state was reached. (b) The SISs swap process was repeated ten times, each time the initial abundances of species 60 and 51 were randomly drawn from . Nine of the simulations are shown in black and the simulation that pertains to Fig 4a is shown in maroon. (c) The same analysis as for Fig 5a, in terms of SISs swap, but for α = 2. (d) The same analysis as for Fig 5a, in terms of SISs swap, but for α = 3.