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This lecture series presents a comprehensive overview of community ecology from a statistical physics perspective, focusing on two main mathematical frameworks: Consumer Resource Models and generalized Lotka-Volterra models. The work demonstrates unexpected connections between ecological dynamics and constrained optimization problems, and shows how high-dimensional ecosystems with many species can be analyzed using statistical physics tools like the cavity method and Random Matrix Theory originally developed for disordered systems.
Why it matters
Understanding ecosystem dynamics through statistical physics methods could improve predictions about biodiversity, stability, and responses to environmental changes. These theoretical frameworks may help inform conservation strategies and ecosystem management by revealing general principles governing how complex communities of species organize and persist.
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⚠️ Preprint – Noch nicht peer-reviewed
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Abstract: Ecosystems are among the most interesting and well-studied examples of self-organized complex systems. Community ecology, the study of how species interact with each other and the environment, has a rich tradition. Over the last few years, there has been a growing theoretical and experimental interest in these problems from the physics and quantitative biology communities. Here, we give an overview of community ecology, highlighting the deep connections between ecology and statistical physics. We start by introducing the two classes of mathematical models that have served as the workhorses of community ecology: Consumer Resource Models (CRM) and the generalized Lotka-Volterra models (GLV). We place a special emphasis on graphical methods and general principles. We then review recent works showing a deep and surprising connection between ecological dynamics and constrained optimization. We then shift our focus by analyzing these same models in “high-dimensions” (i.e. in the limit where the number of species and resources in the ecosystem becomes large) and discuss how such complex ecosystems can be analyzed using methods from the statistical physics of disordered systems such as the cavity method and Random Matrix Theory.
Source: Les Houches Lectures on Community Ecology: From Niche Theory to Statistical Mechanics