Most people thought the problem of polychlorinated biphenyls — known as PCBs — had been solved. Some countries began banning the toxic chemicals in the 1970s and 1980s, and worldwide production was ended with the 2001 Stockholm Convention.

But a new study based on modeling shows that they’re lingering in the blubber of killer whales — and they may end up wiping out half the world’s population of killer whales in coming decades.

“It certainly is alarming,” said Jean-Pierre Desforges, a post-doctoral researcher at Aarhus University in Denmark and the lead author on the new study published Thursday in the journal Science.

Whales sit at the top of their food chain. Chemicals like PCBs are taken up by plankton at the base of the food chain, then eaten by herring and other small fish, which are themselves eaten by larger fish, and so on. At each step in this chain, PCBs get more and more concentrated. The most at-risk killer whales are those that eat seals and other animals that are themselves fairly high on the food chain and quite contaminated, Dr. Desforges said.