BBC has more on one unfortunate modern human inheritance from our ancestors interbreeding with Neanderthals:
The gene variant was detected in a large genome-wide association study (GWAS) of more than 8,000 Mexicans and other Latin Americans. The GWAS approach looks at many genes in different individuals, to see whether they are linked with a particular trait.
People who carry the higher risk version of the gene are 25% more likely to have diabetes than those who do not, and people who inherited copies from both parents are 50% more likely to have diabetes.
The higher risk form of the gene – named SLC16A11 – has been found in up to half of people with recent Native American ancestry, including Latin Americans.
They discovered that the SLC16A11 sequence associated with risk of type 2 diabetes is found in a newly sequenced Neanderthal genome from Denisova Cave in Siberia.
Analyses indicate that the higher risk version of SLC16A11 was introduced into modern humans through interbreeding between early modern humans and Neanderthals.