To further pursue the logical line that Dave started above, imagine that humans and Neandertals live in the same general area at the same time. They are reproductively isolated - no interbreeding takes place. They are separate species, each at the top of the food chain. At some point, humans and Neandertals wage war. As it happens, the humans win and drive the Neandertals to extinction. Later on, the humans look back and wonder why there are no creatures similar to them in intelligence.
See how this scenario could play out? This is an excercise - I do not know if the actual reason for Neandertal exinction is known - but I think it should illustrate the concepts.
SNG