Timescale of environmental fluctuations determines dimensionality of microbial community response.

Microbial communities display a wide range of collective properties, from driving global nutrient cycles in the biosphere to supporting the immune function of human hosts. It is critical, therefore, to understand the way that the collective properties of microbial communities are driven by their composition. However, natural microbial communities are high-dimensional at the species level, complicating the relationship between species present and collective properties. Here, we ask whether a description at the level of the phenotypic traits of species can provide a lower-dimensional description, simplifying this relationship. We use a consumer-resource model framework to demonstrate that communities assembled in rapidly fluctuating environments exhibit low-dimensional community structure in which species with similar phenotypes have correlated abundances, whereas in slowly fluctuating environments, abundances of similar phenotypes are anti-correlated. As a corollary, we show that the transient response to environmental perturbation reveals coarse-grained similarities in species traits, whereas long-time responses reveal fine-grained differences. Our results relate the timescale of environmental fluctuations to extant structure in natural microbial communities, suggest experimental procedures to measure this structure, and provide a path forward for elucidating the relationship between community composition and collective properties.