I for one love to see the wolf dispersing, such a wise and intelligent animal, it's great to see nature healing herself. It's easy for humans to rush to conclusions, especially with such an emotionally charged issue as wolves, but it is also important to step back and observe what is best for the ecosystem as a whole. As someone who has studied with a couple of the researchers who have been working on the wolf reintroduction in Yellowstone I would love to share some of what they have observed.
First off roughly 80% of wolf depredations in the Greater Yellowstone Ecosystem (GYE) are compensatory, less than 20% are additive. This means that roughly 80% of the elk that wolves kill would have died anyway, less than 20% would have otherwise survived. This is due to a wide variety of factors, be it harsh winter conditions, lack of forage (due to overpopulation), broken limbs, etc. Wolves don't kill healthy elk, they are cursorial predators that depend on the weak portions of the population for their survival. The biggest effect that the wolves had on the elk was modifying their behavior, not their numbers. It is also important to note that before the wolf reintroduction elk were universally considered to be overpopulated in the GYE, which includes more area outside of the park than in it. Their degradation of the ecosystem was clearly visible, as they were well outside of their natural balance. Even though the USFS was doing everything they could think of to increase the number of hunters in the ecosystem it was not enough.
There is a high degree of communication that happens between predator and prey. This is part of an evolutionary arms race where the prey always has an advantage. In each interaction the predator only has dinner to loose, where as the prey has it's life at stake. Healthy herding animals exhibit a wide variety of postures and behaviors to show that they are healthy (stotting for example). This communicates to the predator that it is not worth their
energy, as the animal is healthy. When the predator sees a weakness in the animal this is when they chose to pursue their advantage.
I believe that the reason the video calls the elk deer is because the narration is from a TED talk given by a Brit. In the UK elk have been hunted to extinction by humans. This is something that wolves cannot do, as has been demonstrated thoroughly over a long term study of Isle Royal (most notably by L. David Mech). Even in a small nearly isolated ecosystem on an island in the middle of lake superior wolves have never been able to hunt the moose to extinction. When the moose numbers fall low enough the wolf numbers self regulate, such beauty and wisdom is the way nature works.
Hunting wolves is an extremely ineffective strategy for their population control, as wolves breed to their food supply. This has been demonstrated with the aerial gunning of wolves in Alaska. Because the wolves are breeding to the available food supply even when a large portion of the population is killed they compensate for this in their breeding behavior. Usually a pack only has one breeding pair, but when the food supply is bountiful and the wolf numbers have been anthropomorphically lowered (via aerial gunning and poisoning) then the pack will have two or even three breeding pairs. These are behaviors that have naturally adapted over thousands of years, so the wolves are best able to support their ecosystem.
The wolves that were re-introduced are indeed larger than the last subspecies known in the United States (before humans killed the last of them) but are actually still smaller than some of the subspecies that used to roam the US. There were something like 7 or 8 (I can't remember exactly) different subspecies of wolves in North America, some of which were MUCH larger than the Canadian wolves, as they had evolved to primarily hunt Buffalo. The wolves that were introduced are the closest living genetic relative to the wolves that were once widespread throughout the US.