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The saying "safety in numbers" is typically a phrase associated with animals considered prey.

The idea being: More eyes and ears in a group help alert wildlife to approaching predators. And the more animals in a group, the less likely a specific individual will fall during the hunt.

As it turns out, the saying means something very different when it comes to predators and could be changed to "success in numbers," particularly when applied to the wolves and bison of Yellowstone National Park.

In a research project published on the peer-reviewed Public Library of Science website Tuesday, Utah State University's Department of Wildland Resources and Ecology Center researchers found wolf hunting behavior changes based on pack numbers and terrain.

Elk are the preferred prey of wolves in Yellowstone. And USU wildland resources assistant professor Dan MacNulty says the reintroduced predators will go out of their way to find their favorite food — and it may not be a matter of taste, but rather their own safety.

But when a pack of wolves is large enough and the conditions are right, the canines will turn their attention to bison.

"Elk are smaller and they aren't as aggressive as bison," MacNulty said. "The odds of a successful elk kill are three times higher than with an encounter with bison."

An earlier study MacNulty worked on noted that wolves in groups of more than four tend to hold back when pursuing elk and let others take the risk of injury during the hunt.

"Given a choice, wolves will stay out of harm's way until it's safe to enjoy the spoils of the hunt," he said.

But when wolf packs hunt Yellowstone bison, the group typically involves nine to 13 canines cooperating in the effort. Even then, a kill is not always the result.

MacNulty says some of the largest Yellowstone wolves are about 140 pounds. Elk run up to 700 pounds and a bull bison can easily weigh more than twice that — up to a ton.

"The data we're collecting on wolf hunts is helping us understand how wolf pack size, bison herd size and environmental conditions affect wolves' ability to successfully hunt bison," said Aimee Tallian, a USU doctoral student working on the study.

MacNulty was camped in the Pelican Valley on St. Patrick's Day 1999 when the group he was with watched what was the first recorded observation of wolves successfully hunting adult bison in Yellowstone after their reintroduction to the ecosystem, perhaps for the first time in 60 years.

At dawn that March morning. the researchers were posted at an observation point within sight of a group of about 35 bison staying warm in a large geothermal area. Ten or 12 wolves from the Mollie's Pack were spotted on the fringe of the herd.

"It started kind of calmly as the wolves harassed a few individuals standing on the outskirts of the bare ground," MacNulty said. "As time wore on, the bison were getting agitated and antsy to move on."

In the winter months, bison seek places without snow. On open ground, bison are quite capable of defending themselves and will even fight as a group to stave off predators. That all changes in the deep snow of Yellowstone winters.

MacNulty noted there were a series of bare ground patches in the valley, all linked with single track snow trails. Pressured by the presence of the wolves, the bison eventually headed for the trail and made their move to the next bare island.

Marching single file, the bison at the end of the line had no opportunity to defend its backside and other bison could not turn to help.

"The wolves would grab the last individual in line and hold on. The bison would pull the wolves through the snow until they arrived on an open patch where it was assisted by the herd," he said. "In the snow, the wolves have the advantage. Out of the snow, the bison have the advantage."

The island hopping continued throughout the day. With sunset approaching, MacNulty watched as the determined wolves latched onto not one but two bison.

"Eventually one group of wolves gave up and went to join the others and the pack was on one bison," he said.

Still, the bison got away. The animal rested on the bare spot as MacNulty watched the wolves eating blood-covered snow.

When the bison started to leave again, the cow that had barely made it to safety was too tired to move along. The wolves moved in for a feast, but after all that work and the long wait, dinner was cut short: A grizzly moved in soon after the kill and took over the bison — a frequent frustration for the wolves of Yellowstone.

Elk numbers have declined in Yellowstone since the reintroduction of wolves, but the numbers of bison are climbing.

Studies like those MacNulty and Tallian are producing will help biologists in the park and across the West understand the complexities of wolf and prey ecosystems.

"This research is especially helpful in Yellowstone, as it's the only national park in the contiguous United States where free-ranging wolves and bison co-exist," said Doug Smith, director of the Yellowstone Wolf Project. "Further, the wolf-elk relationship is changing and insight into why wolves sometimes choose bison over elk has great value for understanding ecological dynamics in Yellowstone."

Eventually, research on wolves and bison in the park might help with wolf management outside the park.

"Management that takes advantage of wolves' risk-averse behavior may be an effective way to reduce wolf predation on livestock," MacNulty said.

Twitter: @BrettPrettyman