I know Aragorn is descended from Elros the half-Elf, and from what I've been able to find, there are somewhere between 64 and 99 generations separating Elros from Aragorn. I can't do the math, I don't know how many generations actually separate them, and I don't know if Aragorn had any other Elves in his family tree.
So how much Elven blood flows through Aragorn's veins? What percentage of his total DNA comes from Elves?
It rounds up to none, but getting there is fun.
A note before I get started: I'm going to use the word "blood" a lot, and very imprecisely. I don't literally mean blood, or genetic markers, or anything like that. I just mean ancestry, the way I would call myself 1/4 Irish, because my grandmother was ethnically Irish. "Blood" is just a slightly simpler way to express that idea.
Aragorn's parentage diverges from the Elves with Elros, brother of Elrond, who made the choice of the Edain at the end of the First Age. There is no other intermarriage with Elves along Aragorn's line until we get to Aragorn himself, so we can simply count the Kings (and Queens) of Númenor, Gondor, and Arnor, and the Chieftains of the Dúnedain, until we get down to Aragorn. We start with part i of Appendix A.I, the kings of Númenor.
"The Thain's Book" (note: defunct and not archived) helpfully provided a family tree of the Kings of Númenor, which goes down as far as Isildur before skipping to Aragorn, so you can see how these different people relate to one another:
For the sake of accessibility, and also citing some of the more surprising statements, let's go through the chain:
At this point Aragorn's line diverges from the Kings. The next King is Tar-Elendil's son Tar-Meneldur, but Appendix A tells us that Aragorn is descended from Tar-Elendil's daughter Silmariën:
In the days of Tar-Elendil the first ships of Númenóreans came to Middle-earth. His elder child was a daughter, Silmariën. Her son was Valandil, first of the Lords of the Andúnië in the west of the land, renowned for their friendship with the Eldar. From him were descended Amandil, the last lord, and his son Elendil the Tall.
Return of the King Appendix A "Annals of the Kings and Rulers" (i) "Númenor"
So let's continue the list
Unfortunately here we don't know any more until Eärendur, but he's identified in Unfinished Tales as the Fifteenth Lord of the Andúnië, so there are 13 unaccounted for names.
From here we turn to Part ii of Appendix A, "The Realms in Exile". "The Thain's Book" again compiled a helpful family tree of the Rulers of Arnor, and the Chieftains of the Dúnedain, all the way from Elendil to Aragorn:
For accessibility purposes:
So, what we have is that Aragorn is the 64th descendant of Elros. The Elven-blood gets a little more diluted with every generation. Unfortunately we can't nail down an exact percentage, because we don't know the lineage of these 64 wives; when you get a tree this deep, it's almost inevitable that you're going to end up marrying your 30th cousin or something (Arvedui married his 23rd cousin 6 times removed)2.
But we can put a lower bound on things by assuming that the spouses were all 100% human, so the bloodline dilutes by half each generation. Believe it or not, there's a formula for calculating this: for generation i, the amount of Elven blood is n/(2^i), where n is the amount of blood in generation 0 (which, in this case, is Elros).
Now, Elros was not a full Elf. His parents were both half-Elven, and his grandmother was even more half-Elven.
1/2 Elven1/4 Elven, making Elwing 5/8 Elven.This means that Elros, genetically, was 9/16 Elvish.
Finally, we can arrive at an answer, using the formula from earlier4:
That tiny number is the smallest quantity of Elven blood that can be in Aragorn's veins. Absent his complete family tree, rather than just the line of Kings and Queens, this is the best we can do. However, considering how tiny that number is, I highly doubt that there was enough Elven blood in all of Númenor to bring that up significantly higher; you might gain a couple of decimal places, but in the end it's still going to be effectively nil.
To give you an idea of how miniscule of an amount this is, if I mixed a single drop of my blood, a volume of 0.0357 mL, into Lake Erie, with a water volume of 4.8x10^14 L, Lake Erie would have about as much "me" in it as Aragorn has "Elf" in him.
1 That Amandil was the son of Númendil is repeated frequently throughout History of Middle-earth XII.
2 It's nearly impossible that there wasn't some marriage between (distant) cousins in Aragorn's family tree. A 2004 paper estimated that the most recent common ancestor of all humans lived about 3000 years ago, and Aragorn and Elros are separated by much, much more than that5 In fact, we know this happened at least twice: Arvedui's wife was a princess of Gondor descended from Elendil, and Aragorn's mother Gilraen was said to be related to the Chieftains of the Dúnedain.
3 Since Lúthien's mother Melian was a Maia, we can use this same formula to determine that Aragorn is 1/(2^66)=1.355x10^-20=0.000000000000000001355% Maia
4 Because my formula assumes Elros is generation 0, but my list counts from 1, I'm going to use the exponent 63 instead of the 64 I gave earlier for Aragorn's generation number.
5 From Appendix B, Elros died in S.A. 442, and Aragorn was born in T.A. 2931; so Aragorn was born nearly 6000 years after Elros' death.
0's. Honestly, with numbers that small, an order of magnitude doesn't really matter
Commented
May 30, 2015 at 2:41
The answer to this question should be primarily determined not by how many generations passed between Elros and Aragorn, but rather by how many Edain populated Númenor originally. If there were only between five and ten thousand Edain (cited here: How many Edain were left at the end of the First Age?), then after less than twenty generations, almost all the original settlers would fall into one of two categories. There would be those with no living descendants and those who are ancestors to essentially all the living Númenóreans.
By the time of the fall of Númenor, just about everyone on the island would have had roughly equal Elven ancestry. Since the initial population of less than ten thousand had one member who was approximately half Elvish, each member of the population would have had Elven ancestry at the level of about a part in ten thousand.
If Aragorn is a pure-blooded Dúnadan, this level of Elven blood would not have been further diminished. On the other hand, if his ancestors intermarried with the common folk of Arnor, his fraction of non-human ancestry would be correspondingly diminished. However, the total amount could never be as low as the numbers cited in the other answers to this question.
I made this a while ago, using spreadsheets. The exact number of generations from Elros to Aragorn is unknown, but somewhere in the range of 65. I've calculated that this gives Aragorn 0.000000000000000003049318610115481% of elven "genes", and 0.00000000000000000033881317890172013562732900027186% of Maia "genes".
The table shows some interesting things: although Elrond is often called Half-Elven, he's more of an elf than he is a man. Only Eärendil was truly half-elven, 50/50.
With Arwen having some human "genes" from her grand-dad Eärendil, her and Aragorn's son Eldarion is more Human than Elven.
All of the answers assume there was no inbreeding amongst Aragorn's ancestors, which is impossible considering the assumed size of the Númenórean population and the number of generations involved. Buzz's answer touched on this.
You cannot simply do the math and say (for example) "One half-elf 50 generations ago means the amount of Elven blood is 2-51." It's very unlikely that the human population of Arda 50 generations ago was 2.252 quadrillion, which would be necessary if all of Aragorn's ancestors at that time were completely unrelated. According to this answer (which cites The Peoples of Middle Earth), the actual number of Edain at the start of the Second Age was 15 thousand at most.
Somewhere along the way, some cousins married; in fact, this happened many times. We know from Akallabêth that the Númenóreans disapproved of marriage between first cousins, but marriage between more distant cousins was permitted (and would have been necessary).
Bottom line: without more detailed knowledge about the size of the Númenórean population and the amount of inbreeding in the royal family, it's impossible to know. Too bad Aragorn never had his DNA tested!
This is a fascinating questions, but I think that some of the very well-researched answers, above, erred by not calculating the inbreeding that must necessarily have occurred. The problem is that there's no simple formula that can be applied, but there are some general arguments which apply. But there are some simple arguments which let us estimate an answer, and that dramatically increases Aragorn's elven ancestry.
Start with the facts as we know them: Elros was the only Half-Elven person who contributed to Aragon's ancestry. Elros was the first king of Númenor, and as @Buzz noted, Númenor was settled by between 5,000 and 10,000 Edain and the population grew from there. I don't believe that we have any population figures for later than that, though.
So we have a population of 10,000 founders, one of whom was 50% elven. (I know it's not exactly that, but that's close enough.) In our own history, kings, being rich, tended to have more than the average number of descendants. It's true that their heirs tended to have a high mortality, but they also left more bastards than the average person. So the genes of kings tend to spread through the population more efficiently than those of ordinary folk.
Until the Númenóreans started living back on the mainland of Middle-earth, they probably married almost exclusively among themselves. In about 13 generations, each Númenórean would have around 10,000 13th-great-grandparents and major league ancestry collapse would have occurred. This is true for everyone and is inescapable, since no Númenórean could possibly have had more than 10,000 distinct ancestors at the time of the founding. Which means that the average Númenórean had about 1/20,000th elvish ancestry (some had more, some had less, but that's a lower bound to the average assuming that Elros' descendants had average or better reproductive success.)
As time goes on, as long as the Númenóreans breed only among themselves, the percentage of elvish ancestry cannot decrease further! It can only be much higher if Elros' descendants tended to have more surviving children that other peoples' children. (Note: I'm not talking about the line of kings, but about all the people many generations removed from the kingship who nonetheless were descended from Elros.) Given the beliefs about the Kings of Men, I think a plausible argument could be made that this is so, but I won't try here.
(Of course, the line of Kings may have been more inbred than the average Númenórean, and this would have had some impact on Aragorn's percentage, also.)
Once Númenor foundered and the Númenóreans were the lords of Gondor and Arnor, the percentage of Elvish blood would decrease further, depending on the fraction of outcrosses. It's very hard to say how frequent they were, but still by the time of LotR, there's still a serious cachet to having Númenórean blood and people are spoken of as being true or pure Númenóreans. This suggests that some of the main families made a point of marrying within the Númenórean clan, so to speak, and that in some families the fraction of non-Númenórean ancestry would be much less than pure chance would suggest.
Bottom line: Aragorn's fraction of Elvish ancestry was much higher than 10-20 and if he was a pure Númenórean blood, it was most likely about 1/20,000, but could have been higher.
(Note also that this assumes that Elvish blood follows human blood's rules. This is a reasonable assumption, but it is only an assumption, and a plausible argument can be made that it doesn't. Note also that it seems unlikely that in Middle-earth "Elvishness" is carried in some set genetic loci which differ from Humans'. Elvishness seems to more a matter of their spirit or soul than of their DNA.)
We know that it's too far back in his lineage to actually claim him to be an elf. However, what if elf genes are dominant to human genes and those genes usually get passed down? It's not a question of blood as much as it's a question of DNA, chromosomes, and dominant and non dominant genes.
I won't pretend to be an expert in this subject as I clearly am not and know just a little more than the average Joe (I'm a computer programmer), but from my understanding, if I said that elves have dominant traits that would have a higher chance to pass through each generation instead of the human ones, then technically Aragon would still be more elf. Now obviously this is speculation, but as I see it, elves are to me like more evolved humans. I say this because they obviously share a common ancestor, meaning they are of the exact same species but are more advanced in every way, they live longer, hold more wisdom, better eyesight, quicker reflexes, not sure if they're stronger but they probably have the potential to be.
A good real world example of this is the relationship between early humans, neanderthals, and the homo sapiens of today. I differentiated between homo sapiens and humans only because most of the world today, especially in the Eurasia area, have some percentage of Neanderthal genes, as opposed to our pure human ancestors who came from Africa that were pure whatever they were (I forget name), before they interbred with neanderthals, to create us.
Since elves and humans can breed together with no genetic deformity or complications, then science proves that they come from a direct common ancestor, where that ancestor for one reason evolved to human and the same ancestor for another reason evolved to elf. The main reason for evolution is the need for survival, a species gets either wiped out or is forced to take on a change that will allow it to survive.
Imagine 2 sets of boars, one with a thick outer coat and one with a lesser coat in a cold climate, the thicker boar would retain heat better and in turn need less energy to keep its temperature and would probably be stockier opposed to the boar with a lesser coat, that would have to eat more, because so much of its energy would be spent on maintaining temperature. The result of this would be no need for further evolution for the thick skinned boar but the lesser coat boar would need to evolve to be smaller and skinnier to require less food to maintain body and muscle so that all of its energy goes to temperature regulation. If this didn't happen it would most likely not be able to maintain its temperature and die unless another advantageous evolutionary trait occurred.
So most likely the ancestor that turned human must've had it easier and didn't need to evolve as drastic as the ancestor that evolved to elf. A good example to give would be eleven eyes and how precise they are.
Imagine a world with plenty of food and no real top predator besides humans. Humans would thrive and there would be no need for a change. Then imagine that same species in an area that, for example, food is scarce and there are many predators trying to eat. That species would in the beginning suffer and start to die off. The strongest and fastest would survive and breed and this process would repeat until those traits became refined to almost perfection to allow for a better chance at survival. Eyesight speed and strength are good examples.
In conclusion, elf genes are more than likely dominant since they allow better chances for survival and probably carry over again and again through generations. So he more than likely is, for all technical purposes, a good part elf, even if his appearance doesn't look it since the genes that deal with that can go one way or the other since they don't really have an advantage one way or the other, or else they're very minute advantages or disadvantages.
