Before revision:  Using only two ranked tables  with microbes' nutrient preferences and  competitive abilities, we can determine all the stable states as well as the specific perturbations driving a community from one state to another. Using an example of 7 Bacteroides species utilizing 9 polysaccharides common to the human gut  , we predict that mutual complementarity in nutrient preferences enables these species to coexist at high abundances.
After revision:  Using only two ranked tables with microbes' nutrient preferences and competitive abilities, we can determine all the stable states as well as predict inter-state transitions, triggered by the removal or addition of a specific nutrient or microbe. Further, using an example of 7 Bacteroides species utilizing 9 polysaccharides common to the human gut , we predict that mutual complementarity in nutrient preferences enables these species to coexist at high abundances.