How many dimensions (trait-axes) are required to predict whether two species interact? This unansweredquestion originated with the idea of ecological niches, and yet bears relevance today for understanding whatdetermines network structure. Here, we analyse a set of 200 ecological networks, including food webs,antagonistic and mutualistic networks, and find that the number of dimensions needed to completelyexplain all interactions is small ( < 10), with model selection favouring less than five. Using 18 high-qualitywebs including several species traits, we identify which traits contribute the most to explaining networkstructure. We show that accounting for a few traits dramatically improves our understanding of the structureof ecological networks. Matching traits for resources and consumers, for example, fruit size and billgape, are the most successful combinations. These results link ecologically important species attributes tolarge-scale community structure.