Observational studies have not yet shown that environmental variables can explain pervasive non-linear patterns of species abundance, because those patterns could result from (indirect) interactions with other species (competition), and models only estimate direct responses. We developed a bio-physical approach to quantify the environment-species interactions that govern community change. By embedding dynamic ESI within a time-series framework that admits data for species gathered on different scales, we quantify responses that are induced indirectly through ESI. A hierarchical framework provides probabilistic uncertainty in parameters, model specification, and data. Simulation demonstrates that effects of environment on movement, population growth, and species interactions are needed for accurate interpretation. Applications include published data sets on lake food webs and the breeding bird survey. For NEON ground beetles, small mammals, and bird data we integrate remote sensing, including lidar and hyperspectral data from the airborne observation platform. Analytical analysis demonstrates how non-linear responses arise even when all direct species responses to environment are linear. Applications to experimental lakes and BBS yield contrasting estimates of ESI. In closed lakes, interactions involving phytoplankton and their zooplankton grazers play a large role. By contrast, ESI are weak in BBS, as expected where year-to-year movement degrades the link between local population growth and previous species abundances. In both cases, non-linear responses are induced by interactions between species. Stability analysis shows stability in the closed-system lakes and instability in BBS. NEON analysis is underway to evaluate how canopy condition and habitat structure mediate food web interactions. The probabilistic framework also has direct application to conservation planning that must weigh risk assessments for entire habitats and communities against competing interests.