In a seminal paper in 1972, Robert May studied complex ecosystems using Random Matrix Theory. Nearly fifty years later, the rise of quantitative microbial ecology makes it possible to test and refine this approach. Random matrix models successfully capture a wide range of large-scale patterns observed in real microbial communities, including functional and family-level reproducibility, compositional clustering by environment, enterotypes, dissimilarity-overlap correlations, decreased diversity in harsh environments, compositional nestedness, succession dynamics and modularity. After describing the computational model we have developed to reproduce all these patterns, I will present a set of analytic results that explain why this works in the real world. Adding even a small amount of noise to a sufficiently diverse community induces a phase transition to a “typical” phase, where community-level properties such as diversity and rank-abundance curves are indistinguishable from those of a completely random ecosystem. I will explain how the properties of this phase are governed by “susceptibilities” describing the linear response of the ecosystem to small changes in population sizes or resource concentrations. These susceptibilities can be obtained from Random Matrix Theory, in the spirit of May’s paper, and can also be measured by subjecting a community to controlled perturbations.

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