Biogas productivity of anaerobic digestion process is governed by a core bacterial microbiota

•A microbiota-functionality nexus is revealed by 138 samples out of 20 AD reactors.•A core bacterial microbiota prevailed across all the six types of AD reactors.•The core bacterial microbiota strongly correlates with the biogas productivity.•The analysis of a decomplexified OTU network shows apparent community divergence.•The AD microbiotas are neither functionally redundant or plastic.