When predators clash with humans, debate grows fierce. Wolves, heralded as iconic North American animals, also draw the ire of ranchers who have to deal with the ones that kill their livestock. Wolf hunts are one way of dealing with animals that inevitably cross human-drawn lines, but—as the authors of a new study observe—there isn’t much research that looks into whether those hunts actually reduce livestock deaths.

The answer to that question might seem intuitive, but the new findings run counter to that expectation: Washington State University researchers found that when wolves were killed one year, more livestock were killed by wolves in the next. They published their research in PLOS One.

The researchers looked at the number of wolves killed as well as the number ofcattle and sheep killed by wolves (called depredation) over a period of 25 years in Montana and 17 years in Idaho and Wyoming. (Wolf hunts are currently allowed in Alaska, Idaho, Montana and Minnesota but on hold in Wyoming.) For each wolf killed the previous year, the odds of depredation increased by 4 percent for sheep and 5 to 6 percent for cattle.

Of course, when many wolves are killed, that story changes. When more than 25 percent of wolves in the area were killed, livestock kills also went down. However, the researchers point out that 25 percent is the magic number because it exceeds the rate of wolf population growth. At that rate of wolf killing, all the wolves would quickly disappear.

Those numbers might seem like a straightforward argument against wolf hunts, but the story gets more complicated. The researchers don’t know exactly why the statistics shake out this way. The lead author of the study, WSU biologist Rob Wielgus, explains one hypothesis in Rich Landers blog for The Spokesman-Review:

Wielgus said wolf killings likely disrupt the social cohesion of the pack. While an intact breeding pair will keep young offspring from mating, disruption can set sexually mature wolves free to breed, leading to an increase in breeding pairs. As they have pups, they become bound to one place and can’t hunt deer and elk as freely. Occasionally, they turn to livestock.

The inspiration for this explanation is that approximately 5 percent increase in depredation matched up with a 5 percent increase in breeding pairs for each wolf killed, reports ABC News. Similar research on livestock killed by bears and cougars also backs it up.

Seattle-based KUOW reports that a better strategy might be to use non-lethal control measures like guard dogs, light and sounds that deter wolves. "It really underscores the need to prevent conflict between wolves and livestock in the first place," Chase Gunnell, of the advocacy group Conservation Northwest, told reporter Courtney Flatt.

Wolf kills make up a very small percentage of overall livestock deaths in these regions. However, for the ranchers who depend on livestock, any death by predators seems like a frustratingly preventable tragedy. Certainly some strategy is needed to keep wolves in the boundaries humans place around them, but the only way we can figure out what will work is to look at the data.