  Microbial ecosystems carry out essential functions for global climate, human
health, and industry. These complex communities exhibit a surprising amount of
functionally relevant diversity at all levels of taxonomic resolution,
presenting a significant challenge for most modeling frameworks. A
long-standing hope of theoretical ecology is that some patterns might persist
despite community complexity -- or perhaps even emerge because of it. A deeper
understanding of such "emergent simplicity" could enable new approaches for
predicting the behaviors of the complex ecosystems in nature. However, most
examples described so far afford limited predictive power, as they focused on
reproducibility rather than prediction. Here, we propose an
information-theoretic framework for defining, nuancing and quantifying emergent
simplicity in empirical data based on the ability of simple models to predict
community-level functional properties. Applying this framework to two published
datasets, we demonstrate that the majority of properties measured across both
experiments exhibit robust evidence of emergent predictability: surprisingly,
as community richness increases, simple compositional descriptions become more
predictive. We show that this behavior is not typical within the standard
modeling frameworks of theoretical ecology, and argue that improving our
ability to predict and control natural microbial communities will require a
shift of focus: away from complexity of _ecosystems_, and towards prediction
complexity of _properties_ of ecosystems.
