For a quick estimate, convert the AUMs in the Buckeye and Pine Nut allotments to wild horses. The Allotment Master report has the data.
Add the active AUMs and divide by 12:
Horses displaced from HA = (481 + 1,471 + 1,150) ÷ 12 = 258
Given that a small part of Buckeye overlaps the HMA, the number of horses displaced from the HA by privately owned livestock is probably around 250, maybe a bit less.
The AML in this area is zero and the advocates have supplanted the government as resource enforcers, at least for now.
They recently acquired a Jeep to make sure that none of the mares can escape their darting rifles and the fundraising effort has been dropped from their web site.
You might be able to read about it on socialist media.