Quantifying the effects of species interactions is key to understanding the relationships between biodiversity and ecosystem functioning but remains elusive due to combinatorics issues. Functional groups have been commonly used to capture the diversity of forms and functions and thus simplify the reality. However, the explicit incorporation of species interactions is still lacking in functional group-based approaches. Here, we propose a new approach based on an a posteriori clustering of species to quantify the effects of species interactions on ecosystem functioning. We first decompose the observed ecosystem function using null models, in which species diversity does not affect ecosystem function, to separate the effects of species interactions and species composition. This allows the identification of a posteriori functional groups that have contrasting diversity effects on ecosystem functioning. We then develop a formal combinatorial model of species interactions in which an ecosystem is described as a combination of co-occurring functional groups, which we call an assembly motif. Each assembly motif corresponds to a particular biotic environment. We demonstrate the relevance of our approach using datasets from a microbial experiment and the long-term Cedar Creek Biodiversity II experiment. We show that our a posteriori approach is more accurate, more efficient and more parsimonious than a priori approaches. The discrepancy between a priori and a posteriori approaches results from the way each clustering is set up: a priori approaches are based on ecosystem or species properties, such as ecosystem size (number of species or functional groups) or species' functional traits, whereas our a posteriori approach is based only on the observed interaction and composition effects on ecosystem functioning. Our findings demonstrate that an a posteriori approach is highly explanatory: it identifies who interacts with whom, and quantifies the effects of species interactions o