Characterizing the vulnerability of both target and non-target (bycatch) species to a fishing gear is a key step towards an ecosystem-based fisheries management approach. This study addresses this issue for the tropical tuna purse seine fishery that uses fish aggregating devices (FADs). We used passive acoustic telemetry to characterize, on a 24 h scale, the associative patterns and the vertical distribution of skipjack (Katsuwonus pelamis), yellowfin (Thunnus albacares), and bigeye tuna (Thunnus obesus) (target species), as well as silky shark (Carcharhinus falciformis), oceanic triggerfish (Canthidermis maculata), and rainbow runner (Elagatis bipinnulata) (major non-target species). Distinct diel associative patterns were observed; the tunas and the silky sharks were more closely associated with FADs during daytime, while the rainbow runner and the oceanic triggerfish were more closely associated during the night. Minor changes in bycatch to catch ratio of rainbow runner and oceanic triggerfish could possibly be achieved by fishing at FADs after sunrise. However, as silky sharks display a similar associative pattern as tunas, no specific change in fishing time could mitigate the vulnerability of this more sensitive species. For the vertical distribution, there was no particular time of the day when any species occurred beyond the depth of a typical purse seine net. While this study does not provide an immediate solution to reduce the bycatch to catch ratios of the FAD-based fishery in the western Indian Ocean, the method described here could be applied to other regions where similar fisheries exist so as to evaluate potential solutions to reducing fishing mortality of non-target species.