With their rows of sharp buck teeth, their downturned mouths, and both eyes on one side of their curiously flat bodies, summer flounder might seem beautiful only to one another.

But this delicately flavored flatfish is the pinup girl, the heart's desire, of thousands of New Jersey's recreational fishermen — and has long been the source of many millions of dollars in tourism revenue each summer. For that reason the state has petitioned a federal commission to reverse its new restrictions on catching summer flounder in state waters in 2017.

"If you talk to any recreational angler they'll tell you how important flounder is in New Jersey," explained Larry Hajna, a spokesman for the state Department of Environmental Protection.  He said summer flounder, also called fluke, is one of the top draws to the state's $1.5 billion recreational fishing industry.

Flounder's popularity is no secret, however, to the Atlantic States Marine Fisheries Commission based in Arlington, Va. Its website describes the species as "highly prized in the recreational  fishery" because they are easily caught with hook and line from beaches, piers, and boats.

But this federal body, which monitors and protects commercial fish populations from Maine to Florida, has determined that the species has been drastically overfished in recent years and needs a chance to repopulate.  Recreational landings that were 38 million pounds in 1980 fell to 3 million in 1989, according to the website, and were 7.4 million pounds in 2014.

The commission, a subsidiary of the National Oceanic and Atmospheric Administration composed of three representatives from each state on the Atlantic coast, in February ordered a 34 percent reduction in catches for 2017, even after a 27 percent reduction in 2016.

To achieve its goal the commission has increased the recreational "keep" size of summer flounder caught in New Jersey's coastal waters this year from 18 to 19 inches, and reduced the number of flounder that an angler may possess in one day from five to three. It could also shorten this year's fishing season for flounder, which typically runs from mid-May to mid-September. Flounder caught in Delaware Bay may be kept if they are 18 inches or larger.

Kirby Rootes-Murdy, manager of the commission's summer flounder management program, last week said it was reviewing New Jersey's request to relax its 2017 restrictions. Its chairman, vice chairman, and another official will review the request and "decide if it meets the criteria for an appeal." If it does, he said, they will present it to the commission's police board for review at its May meeting in Arlington.

Rootes-Murdy described this year's restrictions as a "difficult decision" that the commission knew would be unpopular with the fishing public and tourism industries. But he said restrictions are being imposed in all nine states where summer flounder are heavily fished.

Size and keep limits nevertheless vary from region to region along the coast, said Rootes-Murdy, so that while anglers in New York and Connecticut must abide by the 19-inch, three-fish-per-day rule, Delaware's limit is 17 inches and a four-fish possession limit. These variations are based, he said, on annual surveys of the flounder populations and average fish size in each region.

But New Jersey contends in its appeal that the commission has not applied sound science in its restrictions. Because the female fluke tends to be larger than the male, it argues the 19-inch limit means those that are kept will "overwhelmingly be reproductive females."

The appeal, assuming a 10 percent mortality rate in fish returned to the waters, also argues that the three-fish keep limit will also result in anglers "having to throw more fish back into the water than they can keep to eat." Such measures are "not sound fishery management," write the authors of the appeal, the three New Jersey representatives on the commission.

Hajna also called the restrictions an "economic disadvantage" for New Jersey because so many families spend time and money at the Shore so that some members — typically male — can go fishing.

"They're lured here by certain species, like striped bass and flounder," he said. "They might not be by dogfish or something else."

Hajna said the state is urging the commission to cancel its size and catch limits for 2017 and "start from scratch" by conducting a new study of the flounder population and fish size in New Jersey's waters.

"Look. If we do a benchmark study and find things don't go our way," he said, "we'll do what we have to do next year."

Rootes-Murdy said the commission already has an annual process for studying marine fishery populations, but it starts in the fall. Based on the data it collects, he said, the commissioners will decide "whether to maintain the same management program for an additional year or do something different."