1. Which does this "adjust" mean? "make change to regulate" or "get accustomed to"?
2. What does this "from under it" mean?
h21)...Earth's habitable climatic zones will start moving too, generally away from the Equator and toward the poles. That means many species of plants and animals will also have to move in order to survive. Whether or not they do will depend on how fast a species can adjust its habitat range, and how quickly that range moves out from under it.
Have you copied it correctly? The last sentence sounds all wrong to me, as if there might be missing prepositions or something. I think I can guess what the writer is generally trying to say (that species' survival will depend on how quickly they can adapt to new habitats) but it doesn't really make any sense to me. Is the writer a native speaker?
1. Yes, as you said, to make the meaning of "adapt to", "adjust" needs "to" and "adjust something" is just making change like "adjusting the height of a chair by its lever", so it sounds wrong. I think this was written either by a non-native speaker or rewritten wrong.
2. "that range moves out from under it" doesn't seem to make sense, either. "it" might mean the original environment, but I can't get it.
Whether or not they do will depend on how fast a species can adjust toits habitat range, and how quickly that range moves out from under it.