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In nature, virtually no living organism exists in isolation. Yet stochastic descriptions of single-species dynamics with no ecology work remarkably well at quantitatively explaining several observed patterns such as species abundance fluctuations. I will show how these descriptions can be understood as emerging from the action of a large number of interacting species continually affecting, and affected by, a shared environment. I will highlight how such a coarse-grained dynamical mean-field theory can be used to extract more information from ecological time-series in a principled way, such as environmental variation and species interactions. I will also show how this framework can be used to address other important problems in high-dimensional ecology, such as predicting the impact of ecological invasions and understanding the effects of evolution. I will end by highlighting the challenges facing the formulation of a complete and self-consistent statistical physics of evolving ecosystems. |