I’ve posted on this before. So I will post again just to reiterate something: in terms of genes, Jon Snow and Daenerys Targaryen are much closer to being full-siblings than they are to being aunt and nephew.

You get different numbers depending on how deeply you look at the pedigree of the two. But their relatedness is probably above 40% and below 50%. Others have confirmed:

Yes, calculating the inbreeding coefficient from the pedigree, I calculate the coefficient of relationship between Jon and Daenerys as 43.75%. — Jonathan Pettitt (@genotripe) April 16, 2019

The verbal reason without math and genealogies is simple: Daenerys Targaryen comes from an inbred lineage, and more importantly, two generations of brother-sister marriages. This means that Daenerys Targaryen and Rhaegar Targaryen were genetically much more similar than typical full-siblings. Because of this, Jon Snow and Daenerys Targaryen are much more genetically similar than typical aunts and nephews, because Jon Snow’s father was to a first approximation genetically a male and older version of Daenerys Targaryen.

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