How did we become the surviving species? Why advantage did we have? What caused the death of Homo Erectus and the Neanderthals?
Also how long have we been the only genus of the Homo species?
unless we have almost perfect knowledge of the environment, there is almlost no way to know. it could have been disease tolerance, food preferences, sexual selection, etc...
Neanderthals were superbly adapted to the cold. Even though full modern humans began migrating out of Africa around 60,000 years ago, Neanderthals managed to hold on to their territories until about 30,000 years ago. It turns out that Europeans are descended from Central Asians, and the Central Asians were able to finally colonize Europe, which was then in the middle of an ice age, because they were adapted to the cool climates of the Central Asian Steppes.
Just exactly how the Central Asians were able to replace the Neanderthals remains a mystery. It is possible that Homo sapiens were able to communicate better. Neanderthals lack the gene that enables humans to communicate verbally and abstractly.