It seems like a simple proposition: American lakes, rivers and offshore waters are filling up with destructive fish and crustaceans originally from other parts of the world, and many of them are potential sources of food.

So why not control these invasive populations by getting people to eat them?

The idea gained momentum recently when lionfish, which invaded the Gulf of Mexico, were successfully marketed to restaurants and appear to be in decline.

But businesses and scientists have struggled to repeat this apparent triumph with other species. Some, such as Asian carp, are not appetizing to Americans. Others, such as feral hogs, reproduce too quickly for the strategy to make a dent. And then there’s the question of whether turning the animals into sought-after cuisine undermines the larger goal of eliminating them.

“Eating invasive species is not a silver bullet,” said Laura Huffman, the Nature Conservancy’s director in Texas. But it can still be “a way to get people engaged in the topic and in the solution.”

The lionfish, a striped saltwater species with a flowing mane of venomous spines, is native to the Indo-Pacific Ocean and was first spotted in parts of the gulf and off the East Coast a little more than 10 years ago. The skilled predators damage reefs and devour native fish, and they are eaten only by sharks — or larger lionfish.

People soon learned that beneath the lionfish’s spiky skin lies a buttery, flaky meat that is perfect for ceviche or as an alternative to lobster. After a few years of intense fishing and brisk fillet sales, the population is dropping.

But similar efforts targeting feral hogs, Asian carp and the Himalayan blackberry have been far less successful.

Damage from invasive species extends beyond the environment. A Cornell University study concluded that they cause more than $120 billion in economic harm annually. Feral hogs cost Texas alone about $52 million in agricultural damage every year, according to a study by Texas A&M University.

Asian carp were introduced to the United States about 30 years ago. They have infested dozens of waterways, including the Mississippi River. The Army Corps of Engineers is weighing options to try to keep the voracious eaters out of the Great Lakes, where they could threaten other marine life and the fishing industry.

In China, carp are a delicacy and are threatened in the Yangtze River. But they have attracted little interest among U.S. consumers, and the few Americans who make a living on carp export most of their catch.

“The fish are good eating if they’re healthy, which they’re not always,” said Duane Chapman, a research fish biologist with the U.S. Geological Survey in Columbia, Mo., noting that this is an issue in the Missouri River. “Here the fish are pretty much not edible, because they’re so skinny.”

In Chicago, a group fed the fish to the homeless, an attempt to deal with hunger and help combat the invasion problem. A southern Illinois company had hoped to start packaging frozen Asian carp. And Kentucky organized a commercial fishing tournament to encourage anglers to go after them.

But none of those efforts was enough to stir demand for the creatures.

Another obstacle is concern that a successful carp industry could derail the original goal of getting rid of the fish.

“We’d all be better off in terms of economics if we could sell our native fish,” Chapman said.

The lionfish and the giant tiger prawn, a crustacean with a massive appetite that can grow to be a foot long, proved to be more palatable, Chapman said.

The tiger prawn has been found in the northern Gulf of Mexico, where scientists fear it could harm the multimillion-dollar crab, shrimp and oyster markets.

Like the lionfish, this prawn has been successfully turned into gourmet food, because it is similar to shrimp, Huffman said.

Similar practicalities can affect invasive plants. The Himalayan blackberry is known for crowding out other shrubs and reducing the size of pastures. Although it is delicious, it’s also thorny and requires time-consuming hand-picking that makes large-scale harvesting difficult.

Feral hogs can also be tasty, but they reproduce so quickly that hunting doesn’t make a dent in the population.

Jean-Philippe Gaston, chef at Haven and Cove Restaurant in Houston, started serving lionfish because he wanted to help reduce its population in the gulf. Now the taste alone keeps it on the menu.

“It’s light and airy and fluffy,” said Gaston, who especially likes to use lionfish in ceviche and other raw-fish dishes because it blends well with spices and marinades. “People are scared of fishy fish. This one in particular is very mild, very easygoing on the palate.”

But lionfish are hard to catch, and the dwindling population means that Gaston and other restaurateurs have not been able to get any for weeks.

The fish are individually speared and can be sold for about $16 a pound, said David Johnson, founder and owner of Traditional Fisheries, one of the few U.S. lionfish suppliers. Yet Johnson said he can’t keep up with demand, especially since many Mexican restaurants replace lobster with lionfish during the crustacean’s offseason.

In fact, an event at the Texas State Aquarium had to be canceled last month when organizers couldn’t find enough lionfish for the 100-person dinner.

So Johnson, who lives in Way­zata, Minn., is designing a “smart trap” that will allow fishermen to catch lionfish without netting other species. He hopes the traps will be in use by year’s end.

“Locally, we’ve proven that it does work,” Johnson said of the effort to turn lionfish into a delectable dish. “In Cozumel, for example, we’re having trouble finding lionfish because they’ve fished so many.”