Optimizing microbial intake helps to maintain the gut microbiome diversity

The animal gut holds a myriad of microbes with demonstrated importance for the host's health. Properties of this microbiome have been studied in different host conditions in search of the best biomarkers for practical medical interventions. One well-studied quantity is the $\alpha$-diversity, which usually correlates with lower values and pathological status. Diet plays an important part in the gut microbiome assembly. While its nutritional content has been extensively investigated, we ask instead how can the microbial content of food impact the gut alpha-diversity, taking into account the intermittent nature of feeding. We design a simple model that isolates the effect of intermittent microbial migration, for which we are able to develop an analytical treatment. Specifically, we find that there is a set of feeding parameters (feeding interval and food microbial content) that maximizes the time-averaged observed Shannon diversity, which we call the Optimal Feeding Strategy. Using a combination of numerical and analytical techniques, we show that, in the optimal scenario, diversity converges to that of the food, and that the optimal feeding rate converges to the average clearance rate. As probiotics become more and more widely used, we hope this work can help assess how quantitative ecological control can be used to improve intake protocols of live biotherapeutic products.