Conjugative plasmids can mediate the spread and maintenance of diverse traits and functions in microbial communities. This role depends on the plasmid's ability to persist in a population. However, for a community consisting of multiple populations transferring multiple plasmids, the conditions underlying plasmid persistence are poorly understood. Here, we describe a plasmid-centric framework that makes it computationally feasible to analyze gene flow in complex communities. Using this framework, we derive the 'persistence potential': a general, heuristic metric that predicts the persistence and abundance of any plasmids. We validate the metric with engineered microbial consortia transferring mobilizable plasmids and with quantitative data available in the literature. We believe that our framework and the resulting metric will facilitate a quantitative understanding of natural microbial communities and the engineering of microbial consortia.