On the muddy edge of the Wicomico River, where tall grass hides all sorts of vermin, Stephen Kendrot and his patrol of federal wildlife biologists tracked the dirty rat that’s destroying precious Chesapeake Bay marsh.

A near-decade-long federal and state effort to get rid of nutria, or swamp rats, killed 13,000 of the giant rodents but failed to eradicate them from the Delmarva Peninsula. So Kendrot and his team at the Blackwater National Wildlife Refuge got strict final orders last week: Find the last survivors. Kill them all. And when it looks like they’re gone, go back and make sure.

Standing in a wobbly johnboat near Salisbury, Kendrot, the ­nutria project leader for the U.S. Department of Agriculture’s Wildlife Services — which has a little-known SWAT team of professional animal killers — spotted a telltale sign of the beast and called to his men. “Is that a tail drag there?” Kendrot asked, looking at the bank.

Up ahead, biologist Mario Eusi followed some smudged tracks and hit pay dirt: depressions in the mud where a clan of swamp rats had fed. As always, they had ripped up plants by the root, eroding the land that supports the marsh that nurtures blue crabs and juvenile fish.

“If you like crab cakes,” Ken­drot said, “you ought to be worried about nutria.”

Eradicating this semiaquatic invasive species native to South America is easier said than done. Not only do they look like rats — with twin buckteeth and long tails — they also breed like them.

Female nutria give birth to litters of up to 13 and go back into heat in two days. Basically, they’re pregnant all year, every year, until they die of old age at 8 to 10. They have nipples on their backs so the young can feed while the mother is swimming.

In the days since the new eradication order was handed down, Kendrot and his team have seen evidence of several nutria colonies along the 24-mile Wicomico River, spotting ripped out plants and droppings in places where swamp rats had never been seen.

The biologists can’t set traps along the river until homeowners in the area grant them permission. The rusty traps are square like a slice of bread and quite effective, said USDA wildlife biologist Daniel Dawson, who demonstrated how to set one.

Dawson made a bed of cordgrass the way the nocturnal rodent likes it. To make it even more appealing, he scented it with several drops of swamp rat urine he kept in a sports drink bottle. Finally, he set the trap at the entrance to the bed.

“When they climb through and hit the trigger — bang,” Dawson said as the trap snapped shut with a hard, metallic pop. A perfect strike instantly breaks the rodent’s neck.

The USDA hopes to eradicate the animal in the Delmarva Peninsula — which stretches from north of Dover, Del., to near Virginia Beach — by the end of 2015.

The Blackwater National Wildlife Refuge in Cambridge, Md., has about a dozen of the rodents in cages, candidates to wear radio tracking devices that lead to colonies. An unfortunate worker swabs their anal glands for scent markings that can lure nutria into traps.

Wildlife biologists believe Maryland has the largest nutria population in the United States after Louisiana, based on the number of sightings. Louisiana has formed hunting parties and sponsored nutria recipe contests — “Heart Healthy ‘Crock-Pot’ Nutria” is said to be yummy — but can’t kill them all.

“There’s no hope of eradicating them” in the Louisiana bayou, said Jacoby Carter, an ecologist who manages the nutria research program for the U.S. Geological Survey’s National Wetlands Research Center in Lafayette.

Maryland nutria are pitted against the USDA Wildlife Services, a formidable killer of invasive animals.

Using guns, traps and poisons, the agency killed 4.1 million animals, including nearly 3,000 nutria, in fiscal 2009. It’s not something that officials in a department of animal lovers like to talk about. But the toll is detailed on its Web site under “killed/euthanized.”

The agency poisoned roosts of marauding starlings that flew to dairy farms, pecked at cow feed in troughs and defecated in the food.

Iguanas were taken out when they crawled under houses in Florida. Vultures have been shot when they wintered in cities such as Staunton, Va.

Along with state natural resources agencies, the USDA has an exemption from the Migratory Bird Act to eliminate fowl.

Starlings caught the worst of it; 1.2 million were killed. Pigeons were next at 96,000 kills. Pike­minnows, fish that prey on salmon, were reduced by 57,000. Raccoons, squirrels, beavers and mice also got death sentences.

Swamp rats have long had it coming, officials say. The voracious plant eater was imported to the Chesapeake Bay region and other areas in the 1930s and 1940s by fur farmers who wanted to sell their pelts.

The business didn’t fare well, and the semiaquatic rodent, which has webbed feet, escaped from farms. Colonies became established along the Atlantic Coast from Maryland to Georgia, all along the Gulf Coast and on the West Coast in Oregon.

The Delmarva Peninsula was green with marsh before nutria arrived. Now, after years of being fed upon by the nutria, much of the marsh has disappeared, replaced with cloudy water that can’t support life.

In 2003, the Maryland congressional delegation, state officials and federal agencies started the Chesapeake Bay Nutria Eradication Project, which removed 13,000 of the animals from 150,000 acres of marshland.

But as the project wore down, people continued to spot isolated nutria, and vegetation kept disappearing. That’s why orders went out and Kendrot and two wildlife biologists sped from the wood docks at the Green Hill Yacht and Country Club in Salisbury on a cool and sunny Wednesday.

Eusi led them into shallow branches of the river called guts. Mixed with the native muskrat and raccoon tracks were dead-giveaway webbed swamp rat prints.

As the afternoon ended, Robert Colona, a U.S. Fish and Wildlife biologist who tagged along, complimented Eusi on his find in the hidden canals of the Wicomico River.

“There’s a ton of tracks through here,” Colona said. “There’s a lot of nutria here.”