1. Approximately 300 pelagic fish species naturally aggregate around floating objects (FOBs) at the surface of the oceans. Currently, more than 50% of the world catch of tropical tuna comes from the industrial tuna fisheries around drifting FOBs. Greater understanding of the complex decision-making processes leading to this aggregation pattern and the impact of the massive release of artificial FOBs by fishermen on the spatial distribution and management of tuna is needed. 2. We analyse how the interplay between social (relationships between individuals) and non-social (responses to the environment) behaviours may affect the spatial distribution of a population in a multi-FOB environment. Taking the example of tropical tunas associating with FOBs and using differential equations and stochastic simulations, we examine how, when increasing the number of FOBs, fish aggregation dynamics and the distribution of the population among patches are affected by the population size, level of sociality and the natural retentive and/or attractive forces of FOBs on individual tuna. 3. Our model predicts that, depending on the species' level of sociality, fish will be scattered among FOBs or aggregated around a single FOB based on the number of FOBs deployed in a homogeneous oceanic region. 4. For social species, we demonstrated that the total fish catch is reduced with increasing FOBs number. Indeed, for each size of population, there are a number of FOBs minimizing the total population of fish associated with FOBs and another number of FOBs maximizing the total population of associated fish. 5. Synthesis and applications. In terms of fisheries management, the total catch volume is directly linked to the total number of floating objects (FOBs) for non-social species, and any limit on the number of sets would then result in a limit on the total catch. For social species (e.g. tuna), however, increasing the number of FOBs does not necessarily lead to an increase in the total catch, which is a non-intuitive result. Indeed, our model shows that, for specific values of the parameters, deploying a greater number of FOBs in the water (all other parameters being constant) does not necessarily help fishermen to catch more tuna, but does increase the level of fishing effort and bycatch.