A new study shows killing wolves to protect livestock is counterproductive and leads to more dead sheep and cattle the following year.

Researchers found that for every wolf killed through shooting or trapping, the odds of dead livestock increased significantly, and the trend of rising depredations continues until 25 percent of the wolves in the area are killed, Washington State University reported.

"[That rate of wolf mortality] is unsustainable and cannot be carried out indefinitely if federal re-listing of wolves is to be avoided," the researchers wrote in their study, which is published in a recent edition of the journal PLOS ONE.

Gray wolves were delisted as endangered species in 2012, but the effectiveness of protecting livestock through lethal control has been largely untested. To make their findings, researchers looked at 25 years' worth of control data and found killing one wolf increases the odds of depredations by 4 percent for sheep and 5 to 6 percent for cattle; this means killing 20 wolves could double the rate of cattle deaths.

Researchers believe this phenomenon occurs because killing a wolf disrupts the "cohesion" of the pack. Intact breeding pairs will keep young wolves from mating, but if these relationships are disrupted it can increase the amount of pregnant females. Once these pairs have pups, they cannot travel as far, and can only hunt the animals present in the immediate region.

In replacement of lethal interventions, researchers suggest tactics such as "guard dogs, "range riders" on horseback, flags, spotlights and "risk maps" that discourage grazing animals in "hard-to-protect, wolf-rich areas."

"The only way you're going to completely eliminate livestock depredations is to get rid of all the wolves and society has told us that that's not going to happen," said WSU wildlife biologist Rob Wielgus.