HOPEDALE, La. — The brave little oyster boats chug out daily from the dock here, but their richest harvest may actually be sitting in the office towers of downtown New Orleans, 60 miles west of this remote spot where marsh, sky and water converge.

In an arrangement that is a Louisiana seafood specialty, though one that can’t be fried or covered in sauce, an oysterman here in the nation’s top oyster-producing state can make as much, if not more, collecting damage settlements from oil companies as from harvesting the bivalves themselves, according to a recent study by two Louisiana State University economists.

Such payments often flow to an oysterman even in cases where there are no oysters to be damaged, said the report, which has infuriated the oyster community here, eliciting complaints that the conclusions are simply lies.

The authors say that while the number of oysters per acre has been in decline over the last four decades — a trend that they attribute to a vast increase in the acreage harvested — revenue from the oil companies that grudgingly share the rich bottomlands with the oystermen is increasing, thanks to a peculiar accommodation that coastal Louisiana has whispered about for years but nobody had quantified until now.