The interrelationships between our diets and the structure and operations of our gut microbial communities are poorly understood. A model community of 10 sequenced human gut bacteria was introduced into gnotobiotic mice, and changes in species abundance and microbial gene expression were measured in response to randomized perturbations of four defined ingredients in the host diet. From the responses, we developed a statistical model that predicted over 60% of the variation in species abundance evoked by diet perturbations, and we were able to identify which factors in the diet best explained changes seen for each community member. The approach is generally applicable, as shown by a follow-up study involving diets containing various mixtures of pureed human baby foods.