Just setting up nature reserves will not be enough...
 

Ongoing global biodiversity loss unstoppable with protected areas alone

Read the full article for more - also take a look at the graph.
BAsically the reason this is not working is, that the protected areas are only local, migrations are impossible, adaptation is impossible, the percentage overall is way not large enough and so on. Sadly, people still stick to this as a primary approach, giving the public a good feeling about this ("oh we destroyed that landscape, but we set up part of it as a nature reserve") which eliminates the need for them to think larger...

Huh, this actually brings up a good point.

How is a population of any organism supposed to sustain itself if it can't sustain genetic diversity?

Just more reason that the answer is not to parcel nature off, it's to let it run wild! A lot of people have been saying this for a while (including me), now there's proof. The whole world is an interconnected system, and we as a species must recognize this fact.

TBH it seems a little strange that genetic diversity was not factored in when reserves were first created.

It was probably because they neglected to think of the larger animals.

For example, there could be seven distinct populations of Northern Alligator Lizards in Yellowstone, which would provide enough genetic diversity for them to thrive and survive, but there would be far less room for Black Bears, which are much larger, breed more slowly, and intermingle as they roam different areas.

The alligator lizards are small compared to the bears, and so they can sustain genetic diversity, but the bears might not be able to do that, since they are larger and breed more slowly.

Well, that's always a possibility, but that's still a helluva'n oversight. Seems kinda counterintuative, as well. Usually the largest/most visible animals are the first considered, it would seem. Or their migratory patterns.

Yeah, I go so excited about population genetics (one of my favorite subjects) that I forgot about the problem at hand. :P

Indeed, it seems almost to be as simple as an oversight of what they needed outside of things like space, food and water.

I think one has to think back to when that concept was developed and what the original intentions are. AFAIK, Nature parks were primarily intended to be kind of like zoos - especially beautiful places with wilderness for people to go to for recreation. The original concept did not so much include the functions we now ascribe to these parks. People also thought that keeping animals in a zoo would allow for the continued existence of the species - which works maybe in some instances bur not in the long run. At the time the nature reserve idea was born, I would assume that these patches were also not really isolated, there was a lot of semi-wilderness between them, so the species could actually travel.
Two major points are flawed and are now being recognized. One is the need for "wildlife corridors", basically stretches of (semi-)wilderness that connect these spots, another is that changing climate will change the biodiversity of these places and if there is not way for the animals to migrate, these spots will become dead, as species that would wander off cannot do so and then die off and species that would replace them have no way to get there.
Overall I would say that the diversity of ecosystems is vital, so it makes no sense to make wildlife parks that are all forested, when there are animals that need vast stretches of plains or undammed rivers. One defining property of wilderness is freedom and wild animals travel long ways, migrate vast distances. In a fragmented landscape, they cannot really be wild and free anymore, so in a way they are broken.
The white settlers in the US did the very exact same thing with the native americans, the Australian colonizers do the same with the aboriginal people there - take the land, put the original inhabitants that roamed in freedom and wildness about these lands into confined reservations or zoos/towns and claim that this alleviates them from the guilt of actually destroying these inhabitants way of life and maybe their essence. And one has just to look at what humans do in that situation, how these communities that have been ripped open and displaced often react - by violence and abuse. Now think again why bears or wolves attack people or even fight among themselves. In the end the colonized solution to that is "management" - in wildlife it is shooting animals to maintain an artificial balance, in human displacement it is police and military. A real solution would be to return the land.
Creating wide wildlife corridors, extending nature reserves by many times more than what is done now would be a good start.