Fig. 1: Conceptual framework.

(see also Table 1 for a glossary of terms). Ecosystems are multidimensional complex systems whose interactions are captured by a rank-3 resource-consumer-function (RCF) tensor (here, a plant-animal/fungus ecological interaction tensor) with entries \({f}_{ix}^{\alpha }\). This tensor can be visualized as a multilayer (multifunctional) ecological network (see Fig. 2) when identifying the indices i and x with resource and consumer nodes, respectively, and index α with ecological function layers. Integrating consumers out (see Eq. (1) in the text and Methods), we obtain a resource-function matrix P (Fig. 3) that encapsulates how plant species and functions are intertwined in the ecosystem. Further projections of this matrix yield function-function networks Φ (Fig. 4) that characterize how each plant species connects different functions (phytocentric embedding) and plant-plant networks Π (Fig. 5) that characterize how each ecological function connect different plant species (function-centric embedding). Inspection of these networks allows us to rank species and functions based on how they participate and connect within the ecosystem. Created in BioRender⁹⁹.