Stabilization of extensive fine-scale diversity by spatio-temporal chaos

It has become recently apparent that the diversity of microbial life extends far below species level to the finest scales of genetic differences. Remarkably, extensive fine-scale diversity can coexist spatially. How is this diversity stable on long timescales despite selective or ecological differences and other evolutionary processes? Most work has focused on stable coexistence or assumed ecological neutrality. We present an alternative: extensive diversity maintained by ecologically-driven spatio-temporal chaos, with no assumptions about niches or other specialist differences between strains. We study generalized Lotka-Volterra models with anti-symmetric correlations in the interactions inspired by multiple pathogen strains infecting multiple host strains. Generally, these exhibit chaos with increasingly wild population fluctuations driving extinctions. But the simplest spatial structure, many identical islands with migration between them, stabilizes a diverse chaotic state. Some types (sub-species) go globally extinct, but many persist for times exponentially long in the number of islands. All persistent types have episodic local blooms to high abundance, crucial for their persistence as, for many, their average population growth rate is negative. Snapshots of the distribution of abundances show a power-law at intermediate abundances that is essentially indistinguishable from the neutral theory. But the dynamics of the large populations are much faster than birth-death fluctuations. We argue that this spatio-temporally chaotic \"phase\" should exist in a wide range of models, and that even in rapidly mixed systems, longer lived spores could similarly stabilize a diverse chaotic phase.