  The generalized Lotka-Volterra (gLV) equations model the microbiome as a
collection of interacting ecological species. Here we use a particular
experimentally-derived gLV model of C. difficile infection (CDI) as a case
study to generate methods that are applicable to generic gLV models. We examine
how to transition gLV systems between multiple steady states through the
application of direct control protocols, which alter the state of the system
via the instantaneous addition or subtraction of microbial species. Then, the
geometry of the basins of attraction of point attractors is compressed into an
attractor network, which decomposes a multistable high-dimensional landscape
into web of bistable subsystems. This attractor network is used to identify
efficient (total intervention volume minimizing) protocols that drive the
system from one basin to another. In some cases, the most efficient control
protocol is circuitous and will take the system through intermediate steady
states with sequential interventions. Clinically, the efficient control of the
microbiome has pertinent applications for bacteriotherapies, which seek to
remedy microbiome-affiliated diseases by directly altering the composition of
the gut microbiome.
