Many plant and animal species are doing just that to escape global warming in the Northern hemisphere. They march the other way in the Southern hemisphere. This is an interesting review of some of the pertinent issues.
The only people who are still unpersuaded on the question of global warming are American wingnuts. Really. I'm not exaggerating. Everybody else on this earth is on the other side of the issue. This is yet another very good reason to get the wingnuts out of power.
I've kept a garden diary for roughly ten years. There is a clear trend in the flowering times of many plants towards earlier times, and a clear trend for some species to start thriving when at first they didn't do well at all. These would be species that the books tell me should like it hotter than my Zone 6a garden. On the other end of plant preferences, I no longer can grow lupines. They need a cooler summer.
This is not a scientific study and I have not controlled for other variables that might be changing (like my neighbors' trees growing and giving me more shade). But I'm not alone among gardeners to spot similar changes in a very short period of time.