With numbers shrinking industry­wide, scientists' counting formulas are all the more crucial. But often, politics is part of the equation as well.

Braced against a stiff wind, Paul Piavis, Butch Webb and Keith Whiteford hauled a net heavy with fish from the Choptank River into their motorboat and spilled them into a tub. Flapping among dull­colored catfish, yellow perch gleamed like tarnished gold. The biologists, in camouflage gear and heavy boots, looked like any other anglers, but they were fishing for science.

Back in their barracks­style office at the Maryland Department of Natural Resources, they would plug statistics about the fish they caught into mathematical models, taking a measure of the yellow perch population.

With nets and divers, sonar and surveys, scientists around the world grapple with one of Earth's great unknowables: how many fish in the sea.

Fish counts are the science behind regulations from Virginia's Northern Neck to the South Pacific, dictating a charter boat's take and an island nation's diet. But this is a science so inexact that some call it an art. And when the counting ends, the fighting often has just begun.

That's what happened this winter when Maryland tried to open the Choptank River to commercial yellow perch netters for the first time in nearly two decades. Counts had documented a 530 percent increase in the Eastern Shore river since 1988, Piavis said.

But sport anglers disputed those findings in raucous public hearings, questioning how the fish could be so plentiful when they have trouble catching their limit of five. The department withdrew the proposal.

"Science is only one part of the equation," Piavis said. "Who gets the fish . . . is a whole other equation."

What is clear is that over the past century, the world's fish stocks have shrunk. The U.N. Food and Agriculture Organization says that one­quarter of the world's marine stocks are overfished, or harvested faster than the fish can reproduce to replace them, and another half are approaching that point.

Nearly half of the two dozen fisheries managed by the Atlantic States Marine Fisheries Commission are listed as depleted or unknown, including the American lobster, red drum and river herring.

The loss of a stock even temporarily, scientists say, can cost the industry hundreds of millions of dollars and echo throughout the ecosystem, affecting humans, too.

But measuring nature's bounty remains a challenge. Where science leaves a gap, politics rushes in.

In 1992, the collapse of the North Atlantic cod fishery, which devastated Canadian and American fishermen and uprooted entire towns, came about partly because politicians ignored dismal harvest figures in favor of more optimistic forecasts, scientists say

"Managing fisheries is not managing fish," said Serge Garcia, director of fishery resources for the U.N. organization. "It is managing the activity of people."

"That's part of the problem," agreed Larry Jennings, a recreational angler and Greater Washington Chapter president of the Coastal Conservation Association, a nationwide group. "It's all politics, run by people who have a vested interest . . . and people who are pushing harder and harder to maximize what they get."

Scientists are experimenting with futuristic ocean sonar and lasers, but the high cost ensures that fish counting, or stock assessment, usually means "dragging a net through the water, translating technical data into what an underfunded, understaffed agency can do," said James Uphoff Jr., a biologist on Maryland's natural resources staff.

In smaller bodies of water, "electrofishing" stuns fish, which then float to the top long enough for an estimate. Biologists trawl for samples. And they scramble atop towers and dams to count fish on spawning runs.

To refine the picture, researchers measure and age fish. They can learn about one fish from another by analyzing stomach contents. Or they can count the creatures that live off of that fish. Some believe that the number of red knot, a migratory shorebird, has declined along with the horseshoe crab because red knot feed on the crab's eggs.

But often, anglers are the most important source of data. Dockside, fisheries managers assess what is unloaded from boats and what was thrown back. The National Oceanic and Atmospheric Administration calls thousands of seacoast households, asking anglers how often they fished, what they caught and how big the catches were.

Researchers then plug all this data into elaborate formulas and forecast the future of a fish.

"Fishery stock assessment is a much more mature science than a lot of people like to think it is," said Steve Murawski, chief scientist for the            National Marine Fisheries Service. "If you have a high harvest rate and you have a good accounting, you know what's going on."

But dozens of factors, including fish habits and fishing trends, environmental change and human nature make the numbers fallible.

In a chandeliered hotel conference room in Arlington County a month ago, scientists, fisheries managers and fishing interests from 15 coastal states at the Atlantic States Marine Fisheries Commission's meeting sat down to learn what little is known about the American eel.

The session was a lesson in the weakness of science when pitted against the human need to make a living from the sea.

At the head of the room, Matt Cieri, a stock assessment scientist at the Maine Department of Marine

Resources, and David Secor, a biologist at the University of Maryland's Chesapeake Biological Laboratory, reviewed eel data. Some studies were small, others were incomplete, but they all showed "a decline, many of which are at their historic lows," Cieri said.

Eels are harvested as bait for fish and crab pots, and in the past three decades, they have fed a booming market led by exports to Asia and Europe. Harvests have plunged since 1980, raising fears about overfishing. So much of the eels' habitat has disappeared that the federal government is considering listing the snakelike fish as endangered.

As the last slide faded from the screen, Cieri concluded: "There's a realistic possibility that this species will not maintain a healthy and viable population throughout its historic range."

George Lapointe of Maine's marine resources department took the side of the fish, arguing that the commission should move forward on a limit to eel fishing.

In the back of the room, Barry Kratchman, president of the Delaware Valley Fish Co., nudged his attorney, Charles Sensiba, who rose to read a statement.

"We are concerned . . . with some of the comments today suggesting that we should move forward now," he read. "Delaware Valley strongly believes that it would be inappropriate to make any decision that would impact the lives and livelihoods of many people when the support for such action has not yet been identified."

Maine's Lapointe said, "In saying I think we need to move forward, I don't want to move forward rashly."