Scientists shocked many in the industry last month when they warned that unless catch levels are sharply reduced, stocks of the fatty, fast-swimming predator could crash within a decade or two.
Less iconic than Atlantic bluefin but more valuable as an industry, bigeye (Thunnus obesus) one of several so-called tropical tunas is prized for sashimi in Japan and canned for supermarket sales worldwide.
An internal report by 40-odd scientists working under the inter-governmental International Commission for the Conservation of Atlantic Tunas (ICCAT) showed in October that populations have fallen to less than 20 percent of historic levels.
"This species is in the red," said Daniel Gaertner, specialist in tropical tunas at France's Institute for Research and Development, which helps track bigeye stocks.
States are due to decide at the summit, which begins Monday in the Croatian seaside city of Dubrovnik, whether to renew bigeye quotas or revise them downward.
Three years ago, ICCAT introduced a 65,000-tonne catch limit for the seven largest fishers of bigeye, and a moratorium in certain areas of ocean.
But other countries are not bound by the quotas, and bigeye hauls last year topped 80,000 tonnes far too high to begin replenishing stocks.