Complexity-stability relationship in empirical microbial ecosystems

May’s stability theory [1, 2], 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 [3–7]. So far, however, empirically demonstrating this theory in real ecological systems has been a long-standing challenge, with inconsistent results [8]. 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 [9–11]. Here, we introduce a novel 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 [12] and sponge-associated microbial communities from different geographical locations [13], 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.