23andme, a company that sells genetic tests to individuals, has developped a Neanderthal heritage estimator: http://spittoon.23andme.com/2011/12/15/find-your-inner-neanderthal/. This estimator uses factor analysis on all the single nucleotide polymorphisms (SNPs, currently almost 1 million) that are part of their genetic test. This means we would expect the estimator to give a good indication of the SNPs that were introduced from Neanderthal after they met modern humans some 30,000 to 40,000 years ago. They use native Africans as a control group, so any SNPs that have spread to the whole world would be discarded. Any SNPs that were introduced earlier would also be discarded.
So how does this estimator correlate to neurodiversity (Aspie) score in Aspie Quiz? We would expect a large correlation if recently introduced SNPs from Neanderthal could explain most of today’s human diversity, but this is not the case. With a material of 167 people of European descent (out of totally 94,000) that did both Aspie Quiz and 23andme, there is a correlation of 0.12. That means that p < 0.07 that there is no relation between 23andme Neanderthal heritage percentage and Aspie Quiz scores (and that there is 93% probability that they are related).
So it does seem like 23andme Neanderthal heritage estimator does support the Neanderthal theory, but the correlation is much smaller than what we would expect. There could be many reasons for this low correlation, but the major reason is probably that science has not found any single SNP that could explain more than 1% of ASD. Since ASDs have no large relation to SNPs, we would not expect it to have a large correlation to any SNP-based genetic data. The largest genetic correlation is with Copy Number Variation (CNVs), but the Neanderthal genome does not include CNVs, and is composed of many small fragments that could prove hard to analyse in the context of CNVs.
Some further break-down of the data reveal other interesting insights. It seems like some questions in Aspie Quiz have larger correlation to 23andme than others. It is especially notable that questions related to Neurotypical compulsions and Aspie hunting seem to have considerably higher correlations to 23andme than others. These issues are atypical in the analysis of Aspie Quiz since they have too low diversity in relation to the number of different issues they cover. They seem to be recent evolution in modern humans (Neurotypical compulsion) and Neanderthal (Aspie hunting). This can explain why the correlation is lower than expected. What the 23andme estimator calculate is recent evolution in modern humans and Neanderthal, but most of the diversity in Aspie Quiz is much older than the 250,000 years that Neanderthal existed. In fact, Aspie Quiz suggests that neurodiversity is close to 2 million years old, meaning that only 10-15% of neurodiversity would be anticipated to have evolved in Neanderthal, while the other traits evolved in their ancestors in Eurasia.
But why then do 23andme mainly detect recent human evolution, and not the more ancient evolution of neurodiversity in Eurasia? Most likely because some of this diversity has spread one way or another back to Africa during the last two million years, and when the SNPs already exist in some (possibly low) proportion among Africans, 23andme would discard them as not of Neanderthal origin.