What were Neanderthal genes good for?

Many years ago, Gregory Cochran began pushing the idea that modern humans have some small percentage of Neanderthal inheritance, and that humanity as it exists today acquired by interbreeding with Neanderthals certain useful gene variants that had been evolving separately in cold Europe. Both predictions appear to be true, and now studies are looking at which fitness-enhancing gene versions were picked up wholesale from Neanderthals.

At West Hunter, Cochran reviews some new data:
Exactly which kinds of Neanderthal alleles would give advantage was less obvious.  I suspected that Neanderthals would be resistant to local pathogens, and that such genetic defenses could easily pay off in modern humans moving into Eurasia.  It looks as if some of that happened – there is a good chance that some common HLA alleles in Eurasians originated in Neanderthals, and some Neanderthal variants involved with defense against viruses have become common. 
I thought that anatomically modern humans might have picked up alleles that dealt better with the big swings in day length characteristic of northern latitudes.  In an earlier talk, Sakararaman  mentioned a common Neanderthal version of the CLOCK gene in Europeans, but that doesn’t show up in the paper, so maybe that turned out to be a mistake. 
It looks as if both Europeans and East Asians have picked up Neanderthal versions of  several keratin filament genes, involved in hair and skin formation. Not fixed, but pretty common.  This might have something to do with the non-kinky hair found in most Eurasians. 
Some of these common Neanderthal alleles may have some effect on the central nervous system, but as usual, we have such a poor understanding of gene function that it’s hard to tell. A Neanderthal variant of TANC1 is common in Europeans, and that gene is thought to regulate dendritic spines and excitatory synapses.  Looking at the broader question, an unusual number of selected Neanderthal alleles were found that are associated with major depression. So maybe those alleles affected mood regulation. Perhaps depression is part of a strategy for dealing with long winters. 
There are gene deserts in which you find very few Neanderthal alleles, presumably because those alleles didn’t work well in modern humans. There is a dearth of testes-associated gene,  not too surprising because they evolve particularly rapidly and are therefore more likely than average to be incompatible with a sister group that diverged some time ago.  The area around FOXP2 is such a desert:  Neanderthals were perhaps worse at speech, or any rate different in some way that didn’t mesh. 
There are some signs of reproductive incompatibility with modern humans, but obviously not enough to prevent adaptive introgression. David Reich suggests that Neanderthals were “at the very edge of being biologically incompatible”.  I doubt that, for two reasons.  First, the known cases of species intersterility in primates all took longer to develop. Bonobos and chimps manage, and they’ve been separated something like 800,000 years. In addition, there is evidence that African hunter-gatherers (Bushmen and Pygmies)  picked up some genetic material from an unknown archaic group, one that split off considerably earlier than Neanderthals, something like 900,000 years. ...
In our book, we suggested that the big bang of the Upper Paleolithic,  the dramatic increase in cultural complexity seen in Europe some 40,000 years ago, might have been triggered, at least in part, by an influx of adaptive Neanderthal alleles. Right now, from the evidence in these papers, I’m not seeing a strong case for that. Of course we only understand what half these genes are doing,  so the fat lady hasn’t finished singing, but  we may well be wrong.  Of course that dramatic increase in cultural complexity did happen, and for that matter, it is still true that average IQ scores are quite low in sub-Saharan Africa and its diaspora.  But IQ scores are also low in populations such as Australian Aborigines that have about the same amount of Neanderthal admixture as other people outside of Africa – so at minimum the story is  more complicated.