Species interactions are ubiquitous in ecological systems, and range from direct predator-prey hierarchies to indirect relationships mediated by the environment. There are multiple proposals for empirical measures of interactions. However, understanding how different interaction measures relate, their informativeness, and their limitations in general ecosystem analysis remains challenging. This study focuses on the empirical interaction matrix, a commonly used measure, examining it from three perspectives: predicting experimental outcomes using models, inferring mathematical models from empirical values, and linking it to other interaction measures in the literature. We derive analytical expressions for the interaction matrix at short and long times, showing that changes in interaction signs can result from experimental conditions or intrinsic oscillations, even in pure competitive systems. We also check that our inference method based on measures of interactions successfully retrieves the original multi-species models used to generate synthetic data. Lastly, we demonstrate its connection with other measures of interactions.
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