Ecological mechanisms of direct and indirect bacteriotherapies in generalized Lotka-Volterra systems*

Over the last two decades, an association between microbiome composition and some human diseases has been unambiguously established. The correlation between gut microbe composition and these diseases has prompted medical interest into bacteriotherapies, which seek to modify the gut microbiome composition in the hopes of treating the correlated disease. In this work we use generalized Lotka-Volterra (gLV) models to probe the ecological mechanisms through which these bacteriotherapies function. We first describe direct bacteriothapies, which drive a microbiome to a target state via an instantaneous influx of foreign microbes (e.g. probiotics or fecal microbiota transplantation). Then, we present a novel control framework for indirect bacteriotherapies, which drive a microbiome to a target state by deliberately modifying its environment (e.g. diet, acidity, or nutrients). These dual control methods for gLV systems, interpreted as bacteriotherapies, could eventually inform personalized medicine for the microbiome.