For about ten years now there have been debates and discussions about the nature of Neanderthal admixture across Eurasia. How many admixture pulses were there? What is the relationship between admixture and selection? The fact is that West Eurasians have less Neanderthal admixture than East Eurasians. One explanation is that there was further admixture in East Eurasians. Another is dilution of Neanderthal admixture in West Eurasians due to later migration from Africans or Basal Eurasians (both of which lack Neanderthal admixture). But it could also be that the power of selection varies across Eurasia, with the lower population size of East Eurasians over the long-term resulting in less removal of Neanderthal ancestry from their genomes.

I think the main answer to the variation has to do with dilution. In particular, gene-flow from a very Basal Eurasian group into West Eurasians.

But, that doesn’t mean I don’t think selection has had an impact. A new preprint gets at this, Quantifying the contribution of Neanderthal introgression to the heritability of complex traits:

…We integrate recent maps of Neanderthal ancestry with well-powered association studies for more than 400 diverse traits to estimate heritability enrichment patterns in regions of the human genome tolerant of Neanderthal ancestry and in introgressed Neanderthal variants themselves. First, we find that variants in regions tolerant of Neanderthal ancestry are depleted of heritability for all traits considered, except skin and hair-related traits. Second, the introgressed variants remaining in modern Europeans are depleted of heritability for most traits; however, we discover that they are enriched for heritability of several traits with potential relevance to human adaptation to non-African environments, including hair and skin traits, autoimmunity, chronotype, bone density, lung capacity, and menopause age. To better understand the phenotypic consequences of these enrichments, we adapt recent methods to test for consistent directional effects of introgressed alleles, and we find directionality for several traits. Finally, we use a direction-of-effect-aware approach to highlight novel candidate introgressed variants that influence risk for disease…

The basic result seems to be that outside of a few characteristics, a lot of the Neanderthal variation is just not retained in the human genome. Traits like height, BMI, and EDU, are highly polygenic. So the genome-wide selection against Neanderthal alleles would be important.