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From WIKI:
Modern humans and Neanderthals share 99.7% of their DNA
and
1–4% of the DNA of living non-African humans are found by the Max Planck Institute to likely come from Neanderthals, a result confirmed in 2012, and refined to 1.5–2.1% in 2014
What do they mean? If it is similar for 99.7, how it could be that 1.5%-2% is unique genes from Neanderthals? The Africans do not have them, so African different from European in 1.5-2% ? But that's not true.
Q. “What do they mean?”
A. Two different things
This means that if you compare, base for base, the total DNA sequences of a group of Neanderthals with a group of humans — doing appropriate statistics — you will find, on average, 99.7% identity.
This is because that 1–4% (generally thought nearer 2%) that is thought to come from Neanderthals could still be 99.7% identical to the human DNA it is thought to have replaced.
How can that be?
First let us assume that there are no genes unique to either humans or Neanderthals. (This may not be true, but the assumption emphasizes that we are considering the same genes.) Now suppose that after the divergence of Neanderthals and humans from their common ancestor the Neanderthals acquired a mutation that produced a new haplotype for a particular gene that spread to all Neanderthals. The percentage difference in DNA would be small, but the haplotype and hence the gene counts as Neanderthal. If it enters the European human population by interbreeding after emergence from Africa, then that gene is regarded to have come from Neanderthals. So the idea is that this is true for approx. 2% of non-African genes, even though the originating Neanderthal DNA may be 99%+ similar in sequence. Likewise, differences are observed between Africans and non-Africans in these gene haplotypes, even though the DNA sequence otherwise is very similar.
I have not discussed the evidence for this 2% gene haplotype difference here as I recently covered it in an answer to another question, specifically on that topic. (Hence my somewhat late interest in this question when it re-emerged.)
start by checking to see if they are comparing the same thing, are they comparing base pair sequence, functional genes, non-functional genes, whole sequence or only the variable portions, one could even be comparing nuclear or mitochondrial DNA or both. I could not determine whether mitochondrial DNA latter was used in the listed estimate for last study.
the first is comparing exact nucleotide sequence while the second is comparing functional gene differences (for the listed numbers, they compare them several ways) so of course the numbers do not match. Note both are also comparing different reconstructed genomes, and with different methods no less.
imagine comparing two dictionaries, one person checks to see if definitions match letter for letter exactly and ignores missing definitions, the other checks to see if they cover all the same words and give the same definitions considering them the same even if the exact wording and punctuation are different, of course the two people will get different percent differences.
