Understanding the relationship between biodiversity and ecosystem functioning has so far resulted from two main approaches: the analysis of species' functional traits, and the analysis of species interaction networks. Here we propose a third approach, based on the association between combinations of species or of functional groups, which we term assembly motifs, and observed ecosystem functioning. Each assembly motif describes a biotic environment in which species interactions have particular effects on a given ecosystem function. Clustering species in functional groups generates a classification of ecosystems based on their assembly motif. We evaluate the quality of each species clustering, that is its ability to predict an ecosystem function, by the coefficient of determination of the ecosystem classification. An iterative process then enables identifying the species clustering in functional groups that best accounts for the functioning of the observed ecosystems. We test this approach using experimental and simulated datasets. We show that our combinatorial analysis makes it possible to identify the combinations of functional groups of species whose interactions govern ecosystem functioning without any a priori knowledge of the species themselves or their interactions. Our combinatorial approach reproduces the associative learning of empirical ecologists, and proves to be powerful and parsimonious.