Ummm, just thinking here.
If ‘Evolution’ is true, then we are the decendants of Neanderthals, right? Thus, Homo Sapiens was a mutation that was ‘successful’ and from a single mutation, Homo Sapiens emerged as the dominant species - eventually wiping Neanderthal out.
So, if we had a single mutation - for the mutation to propogate wouldn’t it be impossible for that mutation NOT to spread without interaction with Neanderthal? Further, if Homo Sapiens is a mutation, how could our DNA not contain Neanderthal code - as that would be the logical progenator.
This is about as amazing as saying that a child has DNA similar to that found in his parents.
The thought it that for the most part modern humans and Neaderthals were separate branches of the humanoid family. There was some mixing, apparently, but it would be more correct to say that Neanderthals and modern humans each evolved from a common ancester, and not too far back in each line, or they could not have interbred. A donkey and a zebra can interbreed, as can a wolf and a coyote. Doesn't happen much, but it can.
Dental analysis for a long time has indicated that there was Neanderthal descent among European populations.
DNA analysis, now that it has found this evidence, can give a quantifiable figure, like 4%. So out of every 100 great to the n-th power grandparents that a typical European person has, it is likely that 4 of them were Neanderthals.