Bert Jongerden walked through the refrigerated display room at the city-owned fish auction house Tuesday, where 3,000 to 4,000 pounds of cod were packed in ice and waiting for buyers, a significant amount for an allegedly doomed fishery.

“Look at it all. It’s beautiful,” said Jongerden, general manager of the Portland Fish Exchange.

But all that cod should not be there, according to a report last month by the National Oceanic and Atmospheric Administration that found the number of cod of reproductive age in the Gulf of Maine has hit an all-time low – only 3 percent to 4 percent of what’s needed for a sustainable fishery.

That’s a sharp decline from an estimated 13 to 18 percent in 2013. Those grim numbers will put pressure on fishery managers to make major cuts to the amount of cod that fishermen can take and that, in turn, would make it harder for fishermen to go after healthy stocks of other groundfish that swim in the same fishing grounds. It is difficult to catch those species without catching cod in the same nets.

Jongerden and fishermen in Maine say landings data in Portland and what they have seen for themselves indicate that scientists are using mathematical models that don’t reflect what’s going on in the ocean. Fishermen have landed nearly twice the amount of cod in the first four months of this season as they did during the same period last year.

But scientists stand by these numbers, explaining that they are based on trawl surveys of the entire Gulf of Maine, not just fishing grounds off the coasts of Maine and New Hampshire.

Moreover, they say, it appears that the few cod left in the Gulf of Maine may be aggregating in a relatively small area – a warning that cod stocks in Maine waters may be repeating what happened in Newfoundland in the late 1980s and early ’90s, when cod populations surged in one small area off its coast, but were thin elsewhere. The entire stock crashed the following year, resulting in a fishing moratorium that devastated the province’s fishing industry. Stocks there have never recovered.

When populations of schooling fish species, such as cod, plummet, the survivors “hyper-aggregate” in a concentrated area, creating the impression of abundance there while vanishing everywhere else, said Graham Sherwood, a fisheries ecologist with the Gulf of Maine Research Institute.

He said it’s difficult for scientists to understand what’s happening to Gulf of Maine cod stocks because they have never been so low.

“It’s uncharted territory for us,” he said.

Russell Brown, the deputy science and research director of NOAA’s Northeast Fisheries Center, said the stock assessment included the results of a bottom trawl survey done last spring in an area from Cape Cod to beyond Canadian waters, as well as data from surveys of coastal waters conducted by the states of Maine and Massachusetts.

He said the surveys show not only record-low levels of abundance but also low numbers of juveniles, which indicates poor reproduction success. Also, there are low numbers of larger, older fish, indicating that a large percentage of cod are dying prematurely from unknown causes.

Roger Fleming, an Earth Justice attorney who specializes in fisheries law, said the stock assessment is based on the best and longest-running trawl data program in the nation. He said fishermen have lost credibility on the issue because they seem to always criticize stock assessments when they show declining numbers of fish.

“Stock assessments and data have consistently shown for years the same thing – that stocks are declining,” he said. “Every time we get bad news about a stock of fish – cod in particular because it’s happening every year – this is part of what we hear from certain parts of the fishing industry.”

But the fishermen say what they are seeing is real – that cod stocks appear to be rebounding. The fishermen say they are encountering relatively large schools of cod while trying to catch other fish, such as pollock and hake.

“It concerns us that what they are saying and what we are seeing is such a contrast,” said Brian Pearce, 45, of North Yarmouth, who fishes out of Portland with his 45-foot gillnetter Danny Boy. “It’s frustrating, and it’s completely out of our hands. Who sees more fish in the ocean than the fishermen? Nobody.”

The Portland Fish Exchange, which sells virtually all of the groundfish landed in Maine and a portion of those landed by New Hampshire fishermen, has numbers to back up the fishermen’s observations. Since the fishing season began on May 1, 153,000 pounds of Gulf of Maine cod have been sold in the auction house, an 80.3 percent increase over the 84,834 pounds caught over the same period last year. The increase in cod landings occurred even though there were 93 fewer fishing trips out of Portland this year than last.

The problem is that scientists are using a mathematical model that is “corrupted” by the use of cod-landings data that does not take into account increasingly stringent regulations that make it harder for fishermen to catch cod, Pearce said. As a result, the smaller catch volumes reflect the impact of those regulations rather than the numbers of cod.

“I am not saying that codfish are in great shape, and I am not saying that we should ignore the scientists,” he said. “But let’s find an assessment model that is better suited for the job that needs to be done.”

The New England Fisheries Management Council will consider the scientists’ report in late September and early October. The council may use the report to take emergency action or to craft new regulations for the fishery.

Ben Martens, executive director of the Maine Coast Fishermen’s Association, said the fishermen are anxious because the stakes are so high for their livelihoods.

“It is scary when their businesses are on the line with this,” he said. “Their businesses, their families and their communities are going to take a hit.”