Statistical physics of high-dimensional resource competition

One classic way to link composition and function is provided by MacArthur's resource competition model from the late 60's. It was extensively studied for N = 1 and N = 2 resources, in particular by Tilman, who developed a highly influential geometric intuition.

In natural communities, however, the number of relevant metabolites is in the dozens. Remarkably, the high-diversity regime of the MacArthur model can be solved analytically, using methods of statistical physics of disordered systems. This exactly solvable model provides a rich platform to investigate the implications of high dimensionality for both ecological and evolutionary dynamics. One particularly interesting question — when and why can community properties be predicted by coarse-grained models?

Moran & Tikhonov (2024). Emergent predictability in microbial ecosystems. arXiv preprint
Moran & Tikhonov (2022). Defining coarse-grainability in a model of structured microbial ecosystems. PRX
Bergelson et al. (2021) Functional biology in its natural context: A search for emergent simplicity. eLife
Goldford, Lu et al. (2018) Emergent simplicity in microbial community assembly. Science
Tikhonov & Monasson (2018) Innovation rather than improvement: a solvable high-dimensional model highlights the limitations of scalar fitnessJ Stat Phys
Tikhonov & Monasson (2017) Collective phase in resource competition in a highly diverse ecosystem. PRL


Coarse-graining ecosystems: theory vs practice

Many ecosystems appear to be at least partially “coarse-grainable” — while the underlying complexity is enormous, some properties can nevertheless be predicted by models that omit much of this complexity. Understanding this is a fascinating question for ecological theory (starting by rigorously defining what we mean by coarse-grainability…) But it also presents a natural practical or computational question — building coarse-grained models for real systems, and developing methods to help us identify useful coarse-graining schemes in a data-driven way.

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Other recent and ongoing projects cover a diverse set of topics, including: