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Small‐scale fisheries often involve weak management regimes with limited top‐down enforcement of rules and minimal support from legal institutions, making them useful model systems for investigating the role of social influence in determining economic and environmental outcomes. In such regimes, interpersonal relationships are expected to have a strong effect on a fisher's catch portfolio, the set of fish species targeted by an individual fisher. Here, we test three competing hypotheses about social influence using belief propagation network models and show that a peer‐to‐peer information‐sharing social network is key to explaining catch portfolios at a small‐scale fishery in Jamaica. We find that experience dictates the direction of influence among fishers in the social network, with older fishers and information brokers having distinct roles in shaping catch patterns for large‐ and small‐sized fish species, respectively. These findings highlight concrete opportunities for harnessing social networks in natural resource management. Our new approach to modelling social influence is applicable to many social–ecological systems with minimal legal and institutional support or those that rely heavily on bottom‐up participatory processes. [ABSTRACT FROM AUTHOR]