Complexity-stability trade-off in empirical microbial ecosystems

May's stability theory, which holds that large ecosystems can be stable up to a critical level of complexity, a product of the number of resident species and the intensity of their interactions, has been a central paradigm in theoretical ecology. So far, however, empirically demonstrating this theory in real ecological systems has been a long-standing challenge with inconsistent results. Especially, it is unknown whether this theory is pertinent in the rich and complex communities of natural microbiomes, mainly due to the challenge of reliably reconstructing such large ecological interaction networks. Here we introduce a computational framework for estimating an ecosystem's complexity without relying on a priori knowledge of its underlying interaction network. By applying this method to human-associated microbial communities from different body sites and sponge-associated microbial communities from different geographical locations, we found that in both cases the communities display a pronounced trade-off between the number of species and their effective connectance. These results suggest that natural microbiomes are shaped by stability constraints, which limit their complexity.