Mr. Chadderton, however, said that DNA shed directly from a fish was likely to be more widespread and longer-lasting than anything that had passed first through a bird’s digestive system. “That plume of DNA is going to be far easier to detect than a single dropping by a cormorant that has lower-quality DNA,” he said.

A single positive hit would be less worrisome were there not other clues that at least some carp have sneaked into the lakes. Fishermen caught three bighead carp in Lake Erie in the 1990s and in the early part of the last decade. The catches were originally dismissed as flukes (insignificant accidents, that is, not flatfish), Mr. Chadderton said, but bone analyses indicated later that they had lived in the lake — and apparently thrived — for at least several years.

In 2009, experts turned up several carp DNA samples in Lake Michigan just south of downtown Chicago, at the mouth of the Calumet River. The Calumet flows into the Illinois River, a Mississippi River tributary that has been home to carp for decades. Since 2010, state workers have hauled more than 115,000 carp from a stretch of the river that ends about 30 miles southwest of Lake Michigan.

Should silver carp establish themselves in the lake, it could be cause for concern. The fish are insatiable consumers of plankton, the same food that sustains perch, walleye and whitefish during parts of their life cycles, and those fish are linchpins of the lakes’ $7-billion-a-year fishing industry.

Because the carp reproduce so quickly and eat so much — they eat up to 10 percent of their weight daily and can grow as large as 60 pounds — they could crowd out those and other species native to the lakes.

Originally brought from China to clean up algae-ridden fishponds, the carp escaped, were first sighted in the Arkansas River in 1976 and have been moving steadily up the Mississippi toward the lakes ever since. Besides its tendency to upend the ecological balance in places it invades, the silver carp is best known for its spectacular and bizarre habit of leaping well out of the water by the hundreds when riled by motorboats or other disturbances. Flying carp have on occasion smacked into passing boaters and even injured them.

In the end, the question of whether silver carp have made it into Lake Michigan is likely to be settled in one of two ways: obtaining a multitude of positive samples from one spot or actually catching a fish.