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The gut microbiome is a complex ecosystem characterized not only by its marginal taxonomic composition but also by its emergent properties. Bacteria develop local interactions to form coherent functional communities, whose effects on health and diseases cannot be predicted from the behavior of individual members. Understanding the factors underlying variability in these communities may therefore provide critical insights on the biological links between the gut microbiome and human phenotypes. Here, we examined the effect of a range of host factors, including demographics, medical history, and dietary habits, on these communities in 938 healthy individuals using MANOCCA, a covariance-based approach developed to address existing limitations. Increased age and smoking were associated with a significant overall decrease in co-abundance, and conversely a higher body mass index was associated with increased co-abundance. At the taxon level, a core of 200 genera were systematically impacted in their co-abundance with other taxa, suggesting a central role in structuring the network. Finally, we demonstrate that our approach offers a powerful framework for prediction purposes, with taxa co-abundance being able to predict the age of participants with an accuracy three-fold higher than a model based on abundance only.