The presence of territorial damselfish predicts choosy client species richness at cleaning stations.

Mutualisms are driven by partners deciding to interact with one another to gain specific services or rewards. As predicted by biological market theory, partners should be selected based on the likelihood, quality, reward level, and or services each partner can offer. Third-party species that are not directly involved in the interaction, however, may indirectly affect the occurrence and or quality of the services provided, thereby affecting which partners are selected or avoided. We investigated how different clients of the sharknose goby () cleaner fish were distributed across cleaning stations, and asked what characteristics, relating to biological market theory, affected this distribution. Through quantifying the visitation and cleaning patterns of client fish that can choose which cleaning station(s) to visit, we found that the relative species richness of visiting clients at stations was negatively associated with the presence of disruptive territorial damselfish at the station. Our study highlights, therefore, the need to consider the indirect effects of third-party species and their interactions (e.g., agonistic interactions) when attempting to understand mutualistic interactions between species. Moreover, we highlight how cooperative interactions may be indirectly governed by external partners.