There are documented studies that show mountain lions hurting bighorn sheep populations, that is fact.
They are only a one of many factors hurting Mule Deer.
I also believe them to be a large factor on dwindling deer herds here in California where lions are protected.
I've seen five lions in recent years, which used to be a very rare occurance indeed.
Another phenomenon is the numbers of deer grouping near rural subdivisions presumably to present less of a target to the more secretive and shy lions.
I believe the blossomed elk population throught the west is a also a major factor for mule deer decline.
Elk recovery programs were virtually too successful.
Elk are at record numbers in many areas now.
The muleys cannot compete with the elk for feed.
Most of the time the elk are grazers and do not compete with the deer that are browsers, but in the most critical period, that being the dead of winter when snow is deep, that is when the elk hurt the deer.
The elk reach higher, and dig deeper for the sparse feed at that time of the year.
Today, record book bulls are being recorded like never before, primarily from Utah and Arizona, which are not highly populated with wolves (yet).
The heyday of muledeer were the sixties and seventies.
Numbers were at an all time highs and record book bucks were falling like Jennifer Flowers' panties.
Elk were tough to find with big bulls being very rare indeed.
During that time lions were shot for bounties and coyotes were poisoned and trapped relentlessly.
Muleys thrived.
Perhaps unnaturally.
It is a complex web of habitat, predators, (both human & animal) and other hooved competitors.
In the grand scheme of things I think we need predators, but we cannot "manage" one part of the ecosystem, we need to look at the entire thing.
The biggest obstacle being habitat loss and creatures that were listed on the ESL that truly needed protection at one time, primarily wolves & Grizzly bears that according to recent population numbers are in a very stable if not flourishing state.
The public dictates policy and we live in times that do not favor big game hunter's desires.