Observational studies have not yet shown that environmental variables can explain pervasive nonlinear patterns of species abundance, because those patterns could result from (indirect) interactions with other species (e.g., competition), and models only estimate direct responses. The experiments that could extract these indirect effects at regional to continental scales are not feasible. Here, a biophysical approach quantifies environment– species interactions (ESI) that govern community change from field data. Just as species interactions depend on population abundances, so too do the effects of environment, as when drought is amplified by competition. By embedding dynamic ESI within framework that admits data gathered on different scales, we quantify responses that are induced indirectly through other species, including probabilistic uncertainty in parameters, model specification, and data. Simulation demonstrates that ESI are needed for accurate interpretation. Analysis demonstrates how nonlinear responses arise even when their direct responses to environment are linear. Applications to experimental lakes and the Breeding Bird Survey (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 species interactions. In both cases, nonlinear responses to environmental gradients are induced by interactions between species. Stability analysis indicates stability in the closed-system lakes and instability in BBS. The probabilistic framework has direct application to conservation planning that must weigh risk assessments for entire habitats and communities against competing interests.

观测研究尚未表明，环境变量可以解释物种丰富度的普遍非线性模式，因为这些模式可能是由于与其他物种的（间接）相互作用（例如竞争）产生的，并且模型仅估计了直接响应。可能无法在区域到大陆范围内提取这些间接影响的实验。在这里，一种生物物理方法可以量化环境与物种之间的相互作用（ESI），该相互作用通过实地数据来控制社区的变化。正如物种之间的相互作用取决于种群的数量一样，环境的影响也是如此，就像干旱由于竞争而加剧一样。通过将动态ESI嵌入允许以不同规模收集的数据的框架中，我们可以量化由其他物种间接诱导的响应，包括参数，模型规格和数据中的概率不确定性。仿真表明，需要ESI才能进行准确的解释。分析表明，即使对环境的直接响应是线性的，非线性响应也是如何产生的。在实验湖泊中的应用和“鸟类繁殖调查”（BBS）得出了ESI的对比估计。在封闭的湖泊中，涉及浮游植物及其浮游动物放牧者的相互作用起着很大的作用。相比之下，正如预期的那样，BBS中的ESI较弱，因为逐年移动会降低本地人口增长与物种相互作用之间的联系。在两种情况下，物种之间的相互作用都会引起对环境梯度的非线性响应。稳定性分析表明封闭系统湖泊中的稳定性和BBS中的稳定性。