<p>Understanding the composition of microbial communities in their environment remains a challenge due to the complex interplay of factors like inter-species interactions and nutrient availability. In this context, it has become an established approach to use overlap in functional subsets of metabolic networks as indices of synergy and competition among microorganisms. Here, we show that this idea can actually be reduced to a much simpler principle. Leveraging the agent-based community modeling software BacArena and natural co-occurrence patterns in the human gut microbiome for a systematic comparison, we find that simple set-theoretical indices explain interactions to a similarly high degree as more sophisticated, established approaches based on network topology. Furthermore, we observe that the performance of most indices decreases substantially for patients diagnosed with obesity or inflammatory bowel disease, suggesting a systemic decline in the microbiome.</p>