What explains the presence in living humans of DNA sections which are identical to DNA found in Neanderthals who lived 40 000 years ago?

It can be explained by hybridization among human and neanderthal ancestral populations.

Explanation:

Next-generation sequencing (NGS) technologies coupled with bioinformatics tools have enabled to confirm admixture between Neanderthals and humans. The technique to identify admixture events consists in discovering nucleotide regions from neanderthal genomes that could be inserted in human genomes, thereby the observed sequence homology must be statistically significant (e-value). This emergent research field is known as paleogenomics.

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