Nicknamed “the surge,” it was modeled after the military’s Iraq war strategy, circa 2007, which helped change the course of the conflict. Hundreds of officers from the National Park Service and other federal agencies swarmed the reservations, and crime was reduced at three of the four reservations — including a 68 percent decline at Mescalero Apache in New Mexico, officials said. Wind River, as has been true for much of its turbulent history, bucked the trend: violent crime there increased by 7 percent during the surge, according to the Department of Justice.

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Despite its bucolic name, the reservation, nestled among snowcapped peaks and rivers filled with trout, is a place where brutal acts have become banal. A rambling stretch of scrub in central Wyoming the size of Rhode Island and Delaware combined, Wind River has a crime rate five to seven times the national average and a long history of ghastly homicides.

During the initiative, which increased the number of officers on the reservation to 37 from 6, crimes included the murder of a 13-year-old girl who had been missing for four days and whose partly clothed body was found under a tree, and the killing of a 25-year-old man, who the police say had been beaten with a child’s car seat and a dumbbell by two friends after a sexual encounter.

“This place has always had the gloom here,” Kim Lambert, a tribal advocate on the reservation, said as she drove by a line of small houses people refer to as “murderers’ row.” “There has always been the horrendous murder. There has always been the white-Indian tension. It’s always been something.”

Crime may be Wind River’s most pressing problem, but it has plenty of company. Life, even by the grim standards of the typical American Indian reservation, is as bleak and punishing as that of any developing country. On average, residents can expect to live 49 years, 20 years fewer than in Iraq. Unemployment, estimated to be higher than 80 percent, is on a par with Zimbabwe’s, and is approaching the proportionate inverse of Wyoming’s 6 percent jobless rate.