Felarof
New Member
While catching up on Exploring LotR, I came across a part of ep 82 Where prof. Olsen says: "[quoting from Discord chat] If Strider took the Ancestry DNA test, what percentage of elf heritage would he see? [laughs] I'm not sure; you'd have to do the math; you could totally do the math on that. You know going back to Beren and Luthien, right and back through to Elros, figure out the genetic percentage of Elros Tar-Minyatur, and then do the math as it goes through generations. You can count the generations, as we're given the number of generations directly, so you could totally do the math. It would be small though. A quite small percentage. Trifle thinks it's sixty-four generations between Elros and Aragorn; that sounds about right; in the ballpark, anyhow." If you just want to know the percentage, the best estimate I came got to is 0.000000003638%. Here is the math behind that estimate. Elros Tar-Minyatur is 5/8 elvish (as Eärendil was half elvish and Elwing was 3/4 elvish) Elendil's line only breaks off until the 5th king of Numenor. So, as first I will do an estimation in which no spouses have elvish bood, before doing a more practical estimation, the denominator will rise from 8 (2^3) to 256 (2^8) at Valandil, son of Silmariën and 1st lord of Andúnië. This would then rise to 67,108,864 (2^26) for Elendil, 19th lord of Andunie (or rather the son of Amandil, 18th lord of Andunie). Now following Appendix A, one can count down to Earendur at 2^35, Arvedui at 2^50, and eventually come to Aragorn II (aka Strider) at 2^66. 2^66 is 73,786,976,294,838,206,464, so in this estimation Aragorn is 5/73,786,976,294,838,206,464 elvish. A better estimation would be include the elvish blood of the all of the wives (and Silmarien's husband Elatan). Here I estimated that Elatan and Silmarien were 5th cousins (or an equivalent situation) as marriages of closer relatives would likely have been illegal and it would have been improbable that inbreeding would have started much later in Numenor. One also has to guess the dates at which the Numenorean population in Middle-Earth would have grown small enough for the elvish blood to be mixed with more pure human blood. For the latter estimate I picked the fall of Arnor (so Beleg of Fornost would be the first to be born of an intermarriage with pure (or close to pure) humans. This would put Amlaith of Fornost at 5/256 (2^8); Arvedui at 2^21, and Aragorn at 2^37, which is 137,438,953,472. 5/137,438,953,472 calculates to 0.0000000000363797880709171295166015625 or 0.00000000363797880709171295166015625%, which can be rounded to 0.000000003638%. Finally the estimate of 64 generations between Elros and Aragorn is very accurate, as the actual measure is 63. Please comment if you find any miscalculations or you do not think my estimates for the amount of inbreeding are correct.
