Under-reporting of catch is an issue, as evidenced by the gap between reported catch and total catch; as is a lack of information on illegal fishing operations.
Another part of the problem is overcapitalization of the fishery - boats have far more capacity to catch tuna than the quotas allow. "Many Mediterranean fleets acquired new, more powerful purse seine boats in 2005-6; and having invested in them, owners now need to catch above quota to break even".
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Follow up with an earlier story on the Atlantic bluefin tuna here.