vast majority of voters do not want symbols of their heritage turned into cuts of meat.

Enter the Adoption Incentive Program, which is built on the idea that paying adopters $1,000 a head is far cheaper than the $24,000 average lifetime cost of keeping a horse in government hands.

The program nearly doubled the number of horses leaving the holding system, and the bureau called it “a win for all involved” that was helping “animals find homes with families who will care for and enjoy them for years to come.”

The bureau’s once-sleepy adoption events were transformed. “It became a feeding frenzy — I have never seen anything like it,” said Carol Walker, a photographer who documents the wild herds of Wyoming.

In February, she arrived at an event in Rock Springs, Wyo., and found a line of trailers a half-mile long. When the gates opened, people rushed to sign up for adoptions without even inspecting the mustangs.

world champion in dressage.

But the adoption program has hardly been selective. One man in Oklahoma was paid to take horses even though he had previously gone to prison for kidnapping and beating two men during a horse-slaughter deal gone bad.

The program has rules meant to discourage quick-buck seekers. Adopters are limited to four animals a year and do not get full payment or title papers for 12 months.

Even so, records show several instances where families like the Kidds banded together to get more than four horses. And numerous mustangs bearing the distinctive government brand began showing up at slaughter auctions after the one-year wait was up.

“We used to see one or two mustangs occasionally, usually old ones that someone had owned for years, but suddenly the floodgates opened,” said Clare Staples, who founded a wild horse sanctuary in Oregon called Skydog Ranch.

Managers warn that the growing herds could graze public lands down to dirt, which would devastate cattle ranchers who compete for grass, and harm delicate desert landscapes and native species.

For decades government auditors and scientific advisers have warned the bureau to move away from roundups and instead control populations on the range through fertility control drugs delivered by dart and other management tools that don’t add horses to the holding system, but the bureau has never changed course, in part because the cost of storing horses has crippled its ability to do anything else.

“We are at a make-or-break point,” said Celeste Carlisle, a member of the wild horse program’s citizen advisory board and a biologist for a wild horse sanctuary called Return to Freedom, which has pushed for alternatives to roundups. “We have to turn things around, or it will result in disaster.”

At the kill-buyer auctions, people who love wild horses are scrambling to respond.

One night last fall, Candace Ray, who lives near Dallas, was clicking through photos on the website of a nearby auction when she spotted 24 young, untamed mustangs. Within hours she was rallying hundreds of donors on Facebook.

Ms. Ray cajoled a young couple who give riding lessons on their nearby farm, Cody and Shawnee Barham, to drive to the auction and do the bidding.

The mustangs were all small and skittish. None had apparently ever been handled. Serial numbers branded on their necks showed they had been born free in Nevada, Utah or New Mexico.

The Barhams kept bidding for hours. By midnight they had spent $16,000 in donations and owned 24 horses. When they got the title papers, the names of the adopters who sold the horses had been blacked out with marker. But holding the papers up to a light revealed the names and addresses of the Kidd family.

The Barhams brought the mustangs to their farm, opened the trailer doors and let them run. The couple plans to train them to accept a halter and then find people who will give them “forever homes.”

Cody Barham stood one recent morning watching the herd nibble in one of his fields, a grease-stained John Deere hat on his head and a 9-millimeter pistol on his hip (for snakes). He watched his wife walk quietly into the pasture with her outstretched hand holding a horse cookie. One of the braver mustangs, a little black stallion, approached to sniff.

“Our goal is to get them to the point where you can just love up on ’em,” he said. “But after all they’ve been through, it might take them a while to trust people.”

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