In a move that is raising the ire of wildlife advocates, one of the Bay Area’s largest open space agencies is drawing up plans that could allow the killing of mountain lions and coyotes to protect cattle owned by ranchers who lease its lands.

The Midpeninsula Regional Open Space District, a government agency based in Los Altos and funded by property taxes, owns 65,000 acres — an area twice the size of San Francisco — across San Mateo and Santa Clara counties.

A decade ago, the district, created by voters in 1972 to preserve wildlife, protect open space and provide public recreation, began leasing some of its property to cattle ranchers.

Now many of the ranchers and their supporters say that mountain lions and coyotes are killing their livestock. They want the district to reduce the number of predators.

“If something isn’t done, the population of the lions is going to increase more and more. And we’re going to have more and more problems,” said B.J. Burns, president of the San Mateo County Farm Bureau.

The district has drawn up a draft policy that would allow coyotes to be killed after they kill two calves or other livestock, and mountain lions to be killed after they kill three calves or other livestock. The “lethal take” could happen only after the rancher had tried other methods to deter the predators, such as fencing, guard dogs or lights.

District officials say the “three strikes” approach is one that will remove the most relentless predators. They note that private landowners already can apply to the state Department of Fish and Wildlife to get a permit to kill a mountain lion after it kills domestic livestock just once.

“We have taken a very careful and measured approach,” said Ana Ruiz, general manager of the district, at a meeting late last month.

But wildlife advocates say the proposed policy, which would be the first of its kind among any local parks or open space district in the Bay Area, is misguided.

“Mountain lions should take precedence over livestock,” said J.P. Rose, an attorney with the nonprofit Center for Biological Diversity. “These lands were bought for conservation, and killing lions to benefit private livestock operators is antithetical to that purpose.”

Taxpayers didn’t preserve some of the Bay Area’s most scenic forests, meadows and wild areas from development so that the wildlife living there could be shot to help commercial businesses, critics of the plan say.

“The people who voted for open space were buying those lands to protect the resources out there,” said Henry Coletto, who served as game warden with the Santa Clara County Sheriff’s office from 1988 to 2004.

“Shooting mountain lions or coyotes is ludicrous,” he said. “We’re paying millions and millions of dollars for this land. I think if you took a poll about shooting coyotes and lions out there, you wouldn’t have anybody agree with that other than cattlemen. People on private property can manage the land how they want, but on public lands, they should be managed for the protection of the wildlife, the water and the natural resources.”

According to the district’s statistics, seven ranchers lease about 11,000 acres from the district. Last year the ranchers grazed 594 cattle in five district preserves, all of them in rural San Mateo County: Russian Ridge, Skyline, Purisima Creek, La Honda Creek and Tunitas Creek open space preserve.

Last year, seven calves were killed by predators, a rate of 1.2%. Since 2013 when it first began keeping statistics, 22 calves, cattle and steer have been killed on district lands.

The ranchers pay $16.20 per month in rent for each cow and calf pair that they run on the district’s open space preserves. That’s among the lowest rate of any local parks or open space agency in the Bay Area. The Santa Clara County Parks and Recreation Department charges $19.40 per month, for example, and the East Bay Regional Park District charges $20.75.

For the last six years, the Midpeninsula open space district also has had a policy of paying ranchers fair market value for their cattle, per pound, when the livestock is killed by predators. Over the last six years, the district has paid $19,319, or $2,760 a year on average.

Many parks agencies don’t allow commercial cattle grazing. It’s not allowed on California’s state parks or on most national parks, such as Yosemite or Yellowstone.

But officials at the Midpeninsula district say grazing is an important tool to reduce fire risk by keeping grass and vegetation in check. They also say it helps support agriculture — a politically influential constituency in rural Santa Clara and San Mateo counties.

Ranchers said they like the reimbursement policy. But they are requesting that they be paid more and that the lease rates be reduced. They say the policy now doesn’t take into account all of the income that the dead livestock could have generated had it lived to grow to full weight. And, they add, cattle are stressed when predators come out, even when the livestock aren’t attacked, and the stress can limit their growth.

“I’m not looking for charity, but our hands are tied,” said Vince Fontana, a rancher who leases 2,000 acres of district land.

Fontana noted that profit margins for cattle ranching are low. And, he said, many of the nonlethal approaches can be expensive and often don’t work.

The environmental groups mostly say that they are in favor of paying the ranchers more for their losses — something that has been done over the past two decades as wolves have been reintroduced in Montana and other Western states.

That approach may work best, said Chris Wilmers, one of the state’s leading mountain lion biologists. Wilmers, director of the UC Santa Cruz Puma Project, said that the population of mountains lions in the Santa Cruz Mountains is unknown but they are regularly killed in collisions with cars and by landowners with depredation permits on private land, which has led to concerns about their viability.

Identifying which individual lion killed more than one calf would be difficult, he said. And if some are killed on Midpeninsula lands, others will take their place.

“To really reduce the predation pressure, you’d have to go on a massive killing campaign,” he said.

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What’s causing so many hummingbirds to visit Los Gatos feeder? Wilmers and other scientists have put tracking collars on 80 mountain lions in the last 11 years in the Santa Cruz Mountains, he said. From 2008 to 2014, the researchers found 439 kills: 348 deer, 31 raccoons, 18 domestic cats, 10 opossums, 9 wild boars, 7 domestic goats and just four cows.

“I have a lot of compassion for ranchers. It’s a tough business,” Wilmers said. “They make very little profit, so when cows get killed it is a financial and emotional issue for them, which is very real. But I also have a lot of compassion for the mountain lions. Their population has become increasingly devoid of genetic diversity, and the built environment is increasingly impinging on their habitat.”

The Midpeninsula district had planned to have its board vote in March on the proposal. But because of the growing controversy, late last month, Ruiz recommended a slower approach with more public meetings. The next public meeting is expected to be in January. Members of the public interested in following the issue can go to www.openspace.org/grazing-management-policy-amendment.