Optimal control and Bayes inference applied to complex microbial communities.

Interactions between species are essential in ecosystems, but sometimes competition dominates over mutualism. The transition between mutualism-competition can have several implications and consequences, and it has hardly been studied in experimental settings. This work studies the mutualism between cross-feeding bacteria in strains that supply an essential amino acid for their mutualistic partner when both strains are exposed to antimicrobials. When the strains are free of antimicrobials, we found that, depending on the amount of amino acids freely available in the environment, the strains can exhibit extinction, mutualism, or competition. The availability of resources modulates the behavior of both species. When the strains are exposed to antimicrobials, the population dynamics depend on the proportion of bacteria resistant to the antimicrobial, finding that the extinction of both strains is eminent for low levels of the resource. In contrast, competition between both strains continues for high levels of the resource. An optimal control problem was then formulated to reduce the proportion of resistant bacteria, which showed that under cooperation, both strains (sensitive and resistant) are immediately controlled, while under competition, only the density of one of the strains is decreased. In contrast, its mutualist partner with control is increased. Finally, using our experimental data, we did parameters estimation in order to fit our mathematical model to the experimental data.