I’m sure killing a mammoth with a spear works, and trying to kill it with a bow and arrow wouldn’t.
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True. But if a group of humans encountered a group of neanderthals—the group with the bow and arrows would be dominant. Because at first the neanderthals would not even know what hit them.
That would cause the kind of fear that would cause the Neanderthals to shink from contact with humans.
That would also explain why for the first time neanderthal ranges shrank into ever smaller pockets.
Morphologically, Neandertals can't be seen (apart from some occasional behemoth athlete). The modern human population carries a varied about of DNA from them, which is because they are among our ancestors. The percentage is roughly the same as each of us carry from each of 46 of our great-great-great-great-grandcestors.