The conventional view of the reproductive ecology of bluefin tunas (Thunnus thynnus, Thunnus orientalis, Thunnus maccoyii) leads to a conceptual paradox. Simple arithmetic yields an expectation for wide variation in annual reproductive success. However, the historical record does not support this prediction. A conclusion would seem to be that a much stronger than usual density dependence must be acting. It is here argued that this strong density dependence may likely occur within small strongly convergent segments of energetically forced ocean eddy structures. Success of the implied ecological scenario requires spawning schools of sufficient size to generate sufficiently copious reproductive product to circumvent resident predator pits, while exerting sufficient predatory loss on resident predators to facilitate this circumvention. This in turn implies existence of a dangerous ‘precipice’ in the form of self-enhancing feedback loop, lurking unperceived beyond the range of historical experience, and a need for a particular degree of precaution in managing the exploitation of this iconic species.