What it will come down to is a very large lack of connecting wilds for animals to migrate in order to escape the changes to each unique environment. What we have now are islands with pockets of interesting animals that simply cant survive going through a hundred miles of city or highway in order to get to a home. Its a little different in boreal forests where it stretches pretty far with connecting pathways for large scale movement, but in areas where the habitat is already fairly small unique and protected theres no room to move.

We then get in to the debate where these changes to the climate will make some animals explode replacing the large number of dieing out species and completely dominating an ecosystem. It wont be diverse but it could be even more lush. Biodiversity is a very interesting topic if you ever feel like looking at a few papers about fast changing climate papers you start seeing a larger picture of what happens to these quick changing areas with no natural bridges to the next.

Also what happens to that one dominating special after the climate change comes, when a specialized fungus that decimates it comes along? Biodiversity is one of natures only real defenses to some of these changes, without it everything is vulnerable.

All of this is Imho :P