LOS ANGELES — In the war against pests, the lowly cockroach makes for a fearsome adversary. It can go weeks without water, survive decapitation for a time — and, like any proper supervillain, can send humans screaming from a room.

Now researchers have found how some roaches have eluded humans’ once-infallible traps: They have evolved so that glucose-sweetened bait tastes bitter.

The discovery, published in Friday’s edition of the journal Science, solves a 20-year mystery even as it sheds light on the cockroach’s powerful ability to adapt.

“These roaches are unbelievable,” said Walter Leal, a chemical ecologist at the University of California, Davis. “There’s an arms race here.”

Cockroaches are an inevitable companion to human civilization. They infest dark corners of homes, feed on all types of food — not to mention hair, glue and soap — and skitter away quickly when spotted. They can fill homes in the tens of thousands.

Exterminators once responded to the onslaught by spraying a home’s baseboards with strong insecticide, but this risked exposing children and pets to harsh chemicals.

The baited trap solved this dilemma in the mid-1980s. Placed under sinks and in cupboards, the traps lured in hungry cockroaches with sugary temptations and then poisoned them quickly with insecticide.

But by 1993, exterminators started noticing something strange: The traps seemed to have lost their power. Somehow, cockroaches were thriving in baited homes.

Jules Silverman, an entomologist, got on the case. His employer at the time, The Clorox Company, owned a bait-making business, and he began taking the traps apart, testing the ingredients one by one on Blattella germanica, the German cockroach.

Silverman could see that the pesticides still killed the roaches; clearly, the problem had to be with the sweet baits. They were sweetened with a formulation of high-fructose corn syrup that was about 55 percent fructose and about 45 percent glucose — a simple sugar that serves as standard energy currency in living things.

Companies switched baits to favor fructose, and the traps have seemed to work since. But the cause of cockroaches’ glucose boycott remained a mystery.

Silverman revisited the question two decades later, after he had joined the faculty of North Carolina State University in Raleigh. Using a network of cockroach collectors around the world who picked up samples from infested homes in the U.S., Puerto Rico and Russia, he and his colleagues gathered 19 different populations of German cockroaches and tested the bugs for the anti-sweet-tooth.

This was easy enough: Normal cockroaches will gladly dig into a batch of sweet, sticky jelly, while glucose-averse roaches will jump back, as if repulsed.

Sure enough, the glucose-haters cropped up in seven of the populations studied, said Coby Schal, an entomologist at NCSU and senior author of the Science study.

“It’s really interesting how they jump away from it,” he said. “It’s like an electric shock, almost.”

The cockroach’s taste system is much more decentralized than that of humans, Schal said. They have taste buds on several facial appendages, and even on their feet.

The researchers focused on the paraglossae, which sit closest to the cockroach mouth and allow the critters to taste objects before eating them. The paraglossae are lined with hair-like sensilla, just a few micrometers long, that contain taste receptor neurons.

The researchers stuck tiny glass electrodes onto these sensilla and then had the cockroaches taste a variety of sweet and bitter compounds, including fructose (the sugar found in fruit) and caffeine (whose bitterness is used by plants to deter predators). Then they watched the electrical signals the neurons sent to the brain. Signals for “sweet” had a very different shape than those for “bitter,” Schal said. That gave the scientists a fingerprint of each taste.

Next they fed the cockroaches a glucose-laced solution and watched the electrical signals. For normal cockroaches, glucose triggered a “sweet” signal. But in the glucose-averse cockroaches, the solution triggered both “sweet” and “bitter” signals.

Mystery solved: the warning was coming straight from the tips of their taste buds.

“We were elated,” Schal said.

Losing a function in sight or taste is not uncommon in the animal kingdom, – in fact, many marine mammals have lost their ability to taste sweet things, perhaps because they don’t encounter it in their fishy diet. But adding sensory information – setting off a “bitter” alarm for a sweet food – is another story.

“It’s incredibly rare,” Schal said. “We don’t know any other example where instead of having a loss of function, you had a gain of a new function – and that’s what happened in this cockroach.”

There are some disadvantages to glucose aversion, the authors pointed out: Glucose-averse cockroaches tended to grow and reproduce more slowly than their sweeter-toothed brethren. But in a trap-filled home, perhaps slow growth was a fair price to pay to stay alive.

The findings could have implications for research on obesity and diabetes in humans, said Grzegorz Buczkowski, an urban entomologist at Purdue University in West Lafayette, Ind., who was not involved in the study. Perhaps there’s a way to induce this type of evolutionary change to make harmful substances less appealing – even repellent.

“Maybe we would have fewer health problems because of obesity and diabetes – maybe even addiction to alcohol and drugs,” he said. “If we could induce aversion to different materials that harm people, maybe that has implications for human health overall.”