New research sheds light on this possibility.
ScienceDaily (Oct. 7, 2010) — New research suggests that climate change following massive volcanic eruptions drove Neanderthals to extinction and cleared the way for modern humans to thrive in Europe and Asia...
"[W]e offer the hypothesis that the Neanderthal demise occurred abruptly (on a geological time-scale) … after the most powerful volcanic activity in western Eurasia during the period of Neanderthal evolutionary history," the researchers write. "[T]his catastrophe not only drastically destroyed the ecological niches of Neanderthal populations but also caused their mass physical depopulation."