The understanding of the relationships between modern humans and Neanderthals has been elegantly resolved by the incredible sequencing of the entire genome of 6 Neanderthal genomes. The sequencing is so detailed that it even includes the Histocompatibility loci. Through this analysis it was found that the particular locus that humans share with Neanderthals was picked up by humans, through cross-breeding, (for you bears huggers out there), and retained it as it provided a selective advantage for survival in colder Europe. It provides immune reactivity against such viruses as EBV, that was absent in the previous humans.
And here is a little fun trivia for those genomical and histocompatabiliphiles out there. You know who you are!
DNA sequence of Neanderthals
It has been found that HLA-A*02, A*26/*66, B*07, B*51, C*07:02, and C*16:02 of the immune system were contributed from Neanderthals to modern humans. After migrating out of Africa, modern humans encountered and interbred with archaic humans, which was advantageous for modern humans in rapidly restoring HLA diversity and acquiring new HLA variants that are better adapted to local pathogens.
It has been found that introgressed Neanderthal genes exhibit cis-regulatory effects in modern humans, contributing to the genomic complexity and phenotype variation of modern humans.
This sort of DNA genomic analysis will fit this recent skull into the framework of human evolution. This will likely be possible as the skull has teeth, that provide the most stability for ancient DNA with less contamination.