A major open question in microbiome research is whether we can predict how the components of a diet collectively determine the taxonomic composition of microbial communities. Motivated by this challenge, here we ask whether communities assembled in a mixed nutrient environment can be predicted from those assembled in every single nutrient in isolation. To that end, we first formulate a quantitative null model of community assembly in a mixture of nutrients that recruit species independently. We then test the model predictions by assembling replicate communities in synthetic environments that contain either a pair of nutrients, or each nutrient in isolation. We find that the null, naturally additive model generally predicts well the family-level community composition. However, we also identify systematic deviations from the additive predictions that reflect generic patterns of nutrient dominance at the family-level of taxonomy. Pairs of more-similar nutrients (e.g. two sugars) are on average more additive than pairs of more dissimilar nutrients (e.g. one sugar and one organic acid). A simple dominance rule emerges, where we find that sugars generally dominate organic acids. This simple dominance rule extends to most families and most sugar-organic acid pairs in our experiment. Our results suggest that regularities in the ways nutrients interact may help us predict how microbial communities respond to changes in nutrient composition.