Crossing paths in the Near East 120–60 TYA there was repeated interbreeding between Neanderthals and the proto-humans emerging from Africa. Though Cro-Magnon and Neanderthal largely kept to themselves in Europe, with separate communities, interbreeding occurred there as well. Upper Paleolithic skull fossils show a mosaic of Neanderthal and Cro-Magnon features.
When Neandertals and modern humans mixed, they were at the edge of biological compatibility. ~ American geneticist David Reich
Though most Neanderthal genetic input was adaptively removed from modern humans, 2–4% of the DNA in Eurasians today descends from Neanderthals. This genetic influence is equivalent to that of a great-great-great-grandparent. The conferred benefit for descendants of the interbreeding was an improved immune system. Native Africans have no Neanderthal DNA.
Around 55 TYA, Eurasia began to swing wildly between frigid and temperate in short cycles lasting mere decades. The cold snaps brought ice sheets to what had been forests.
Animal populations upon which Neanderthal preyed were devastated. Nonetheless, Neanderthals, though diminished in numbers, adapted to the early rounds of climatic calamity.
The weather got worse: oscillations between warm and frigid becoming increasingly wrenching. The fluxes brought profound ecological shifts in both flora and fauna, as evolution worked double time to keep up. In the course of a single individual’s lifetime, many of the plants and animals were replaced by new species.
Climate problems may have been compounded by resource competition between Neanderthals and Cro-Magnon. That withstanding, it is unlikely that early humans were determinative in the demise of Neanderthals.
The climatic see-saw became too much of a challenge for Neanderthals. Already splintered into small groups, they dwindled and died out ~40 TYA. The timing coincides with a cataclysmic volcanic eruption in Italy, which provoked an abrupt cold spell throughout Europe.