Top-down analysis of the complexity of environmental and human-associated microbial ecosystems*

According to May's half-century-old theory, ecological systems can be stable up to a critical level of complexity, which is a product of the number of resident species and their interactions.
So far, however, this theory has not been empirically demonstrated for large microbial ecosystems which typically exhibit long-term stability, mainly due to the difficulty of reliably inferring their ecological network of inter-species interactions. Here, we introduce a computational method to approximate the effective connectance of microbial ecosystems by analyzing their assemblage-abundance relations. We show that in numerical models of ecological systems in which species interact at random this method can accurately assess the effective connectance. We used this method to study human-associated and environmental microbial communities of wide range of sizes, from tens up to hundreds of microbial species, and unknown {\it a priori} ecological networks. We found that large microbial communities tend to have weaker effective connectance compared with smaller microbial communities. These results suggest that the complexity of microbial communities is governed by stability constraints.