Let them dig their own darn holes.
The Humane Society of the United States condemned Trump’s hunting plans, saying prairie dogs are an important species for the Great Plains because more than 100 other animals depend on the prairie dog either as food or move into the burrows they dig, said Lindsey Sterling Krank, the organization’s director for its Prairie Dog Coalition.
And let the weepy tree-huggers cry for the cattle who break their legs in prairie dog holes, and suffer in agony until the rancher finds a lamed heifer and has to put her down .. often leaving a orphan calf ("Dogie") to die because no other heifer will adopt him.
Ranchers ... who grow the hamburgers that the Humane Society probably eats at their fund-raising BBQ's ... have two ways of minimizing the Prairie Dog Menace: Poison, or shooting. Trapping is not an effective means of killing of Prairie Dogs (who are the victims of Coyotes ... who will gleefully take down a calf or a nursing cow).
Poisoning either Prairie Dogs or Coyotes is not a good alternative, because the carcass will end up being eaten by scavenger, such as the Bald Eagle (our national symbol) and they die from the effects of "secondary poisoning".
And then some other scavenger eats their body, and the strychnine moves on.
There is a good reason why Prairie Dogs are also called "Prairie Rats".
Hunting them is the most humane method of keeping the rodent population down to manageable levels. When coyotes find a dead prairie dog, their pack feeds for a day.
And the ecological benefit of the coyote?
They eat lamed cows. If the rancher doesn't find the cow first, coyotes don't bother to kill the cows, they just start on the hind legs and keep eating until they get to the vital parts. They particularly enjoy eating the intestines of cattle before they are dead. I've seen parts of cattle spread over a half-acre when a pack of coyotes finds one that can't keep up with the herd. The cow just drags herself along on three legs while the dogs snarl and bite and rips raw flesh from the living animal. THAT is pitiful, and cruel.
Cattle are a lot easier to catch than Prairie Dogs, and there's enough there for a pack to feed for three days.
If you don't know the ecology of the prairie, you probably aren't qualified to opine about the poor prairie dog.