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I would appreciate insight into the average, median, RMS or any similar measure of relatedness among the current world population - and perhaps something about how rapidly this may be changing. A similar question is how un-related any two humans can be: i.e., what is the lowest degree of consanguinity between the two most distantly related people. The context is an exploration of how humans have evolved tendencies toward racism and other in/outgroup distinctions, when all humans share such a large fraction of DNA with each other, very nearly as much with non-human primates, and about half even with fruit flies. Might be some helpful lessons in there!

Apologies if the question is ill-formed, or answer readily available someplace - I've browsed the Web for several years on this topic, and found nothing I could understand..

Accessible material about most recent common ancestor and identical ancestor point seems to indicate a wide range of both methodologies and results, based mainly on statistical simulations since "hard" genetic structures apparently do not persist. MRCA datings based on mitochondrial and other genetics seem to line up with human behavioral modernity, ca. 200 kya. But there seem to be extreme estimates as recent as 2.3 kya, which implies a lot of mobility and high fertility by some not-so-distant forebears (like Genghis Khan). In any case, IAP may be a better starting point for this shared-anncestry question.

I'm guessing that no human is further than about a 10th~12th cousin to any other. Can't be more that 32nd, since 2^33 is more than the number of living humans!

All thoughts, including guesses more informed than mine, will be appreciated.

~ ~ ~ ~ ~

Addendum - tried to post this as an answer, but it was deleted:

MANY thanks to Zo-Bro-23 for the time, effort and creativity to create his response. I hope it is well-indexed for future explorers to find!

In case useful or interesting to anyone,or sparks further contributions, here were/are my main motivations for this inquiry:

  1. Though having working knowledge of physical and natural sciences, and having minored in anthropology at Uni, I have never really grasped current estimations of "most recent common ancestor" and "identical ancestors point." This is probably due to my poor understanding of populations statistics, but may also reflect the huge uncertainty in and conflict between various MRCA and IAP methodologies. So I'm always seeking a simpler, if less precise, way to understand these propositions. Time-dependent mean/max degree of consanguinity seems like such a heuristic.

  2. The ancestor cone, as mentioned in the Quartz article linked by Zo-Bro-23: I've been using the same term for decades, so I suppose it's a natural way to describe something that isn't precisely conic or biconic. For me, the description follows naturally from the notion of the light (bi-)cone in Minkowski diagrams, extending the idea of a photon's world-line to that of a genomic cluster.

  3. I've long wondered about both genetic and memetic (e.g. religion, language, cuisine, art, toolmaking) contingency as they result from and induce changes in the topology of the ancestor cone. There are numerous groups that for geographic, religious or other reasons have been largely independent since we all left the Great Rift Valley (or wherever humanity arose). Having studied a bit of cultural diffusion, I've wondered if genetics, linguistics or anything else might give insight into how often and effectively the occasional Marco Polo or Squanto voluntarily or involuntarily acts as emissary between cultures. Many of these exchanges have apparently had significant cultural influence, and in some cases perhaps genetic as well. It might take very few such, over hundreds or thousands of generations, to lower substantially the degree of consanguinity of all humans.

  4. This does not even count the much larger migrations, both voluntary (e.g. Bering Strait crossings that peopled the Americas), semi-voluntary (the Irish famine that so strongly influenced US culture) or entirely unwillingly (the African slave trade). Another question concerns the influence of sex-linked characteristics in Africans on the general American population, where for several centuries, the great majority of interbreeding appears to have been between White males and (usually unwilling, one imagines) Black females. Perhaps too hot a topic for research?

  5. Pedigree collapse is a conflating factor of special interest to me, as most of my known ancestors belonged to a relatively small ethnic group that favored in-marriage, and (due to low social standing) was not attractive for outsiders to join. So other than couplings of necessity (rape, isolated populations), our cone is probably pretty narrow down to the bottom of the historic timeline. Not directly related by mechanism but probably relevant is the Galton–Watson process, the extinction of family names when a named lineage runs out of (usually male now; perhaps less so in "primitive" matriarchal societies) descendants.

  6. Not long ago, it was popularly believed that explosive population growth since the industrial revolution resulted in the number of living humans exceeding the number deceased. Current credible estimates seem to place the latter at slightly more than 100 bn, - a dozen ghosts standing behind each living soul. Theme for an SF movie?

There is also the question of speciation. It is widely accepted that Homo sapiens and Homo neanderthalensis interbred to a considerable degree. This would, of course, violate pre-cladistic notions of what constitutes a species. (The cited Quartz article could have been titled "Everyone on Earth is actually your cousin - including some non-humans." And if all humans are at least 15th cousins, how far are we from other living families, even phyla?) I believe that barring "lost world" scenarios, we have been alone on the planet for all of historic time, hence for the lives of most H. sapiens. But if we date humanity to behavioral modernity, and plot the ancestor cone with a logarithmic or horizontal axis (or even force it into a cylinder of constant width), the influence of some of these factors on present-day consanguinity might be seen as comparable to those of posited bottlenecks like the Toba catastrophe, climate change, pandemics etc.; and on a smaller scale, founder effects like the peopling of the Pacific islands and Australia.

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    $\begingroup$ It's interesting that you say you've been searching/browsing the internet and haven't seen anything (I believe you.) I wasn't even looking for this when I came across an article (a scientific paper) on genetic differences between populations based on geographical distance. I wish I could remember where I saw it, I'd post a link. I don't know just how much literature there is on the subject, but there's definitely some out there. $\endgroup$ Feb 4 at 21:02
  • $\begingroup$ @cTen, sorry that I took so long to answer. Although I found an article that states the final answer of "15th cousin", I didn't understand the equation that author used, so I just derived my own equation from start. I hope my answer is correct 😀 Please feel free to edit or comment if you think that anything is wrong or if you didn't understand something I went over. $\endgroup$
    – Zo-Bro-23
    Feb 9 at 7:17

2 Answers 2

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TL;DR: Most humans would be around your 13th cousin to your 15th cousin

Please feel free to edit the formatting of my equations to make them look better.

Deriving an equation

For simplicity's sake, we are assuming that only "blood relations" count. What I mean by this is, your mother's sister's son will count as your cousin, but your father's sister-in-law's daughter will not count as your cousin. Marriage relations will not be counted, and only birth relations will be.

Let's tackle this step by step. We are trying to find the degree of kinship when the number of relatives you have in that degree exceeds 8 billion. However, let's start by simply deriving an equation to find the number of cousins you have in a certain degree. For example, your siblings would be degree 0, first cousins would be degree 1, and so on. Let's denote this by the variable n. Now, given a person in any degree of kinship with you, you would share an ancestor with them. That is the definition of kinship. Given a person in degree n with you, your closest common ancestor will be n + 1 generations from you. That means that with your siblings (degree 0), your closest common ancestor is 1 generation from you (your parents). That is simple. Now, we want to find out how many common ancestors you have in that generation. Again, this is fairly simple. That would be 2n + 1. This can be understood by the fact that you have 2 parents, each of them have 2 parents, each of them have 2 parents, etc. The number of ancestors is getting multiplied by 2 each time. However, the number of ancestral couples you have in that generation would be 2n + 1/2 or simply 2n.

Now, let's assume that everyone has x number of children. This means that each of those 2n people would have x number of children. The number of children in the next generation would then be 2n * x. Each of those children will have x children, and so the number of children in the next generation would be 2n * x * x or 2n * x2. Hence, the formula for the number of people in your generation with whom you share this common ancestor would be 2n * xn + 1 (since the original ancestors are n + 1 generations above you).

However, we are not done yet. Of these children, some of them might be duplicates. What I mean is, you have 4 grandparents. We have assumed that each of them have x children and that each of those children have x children. So the total should be x2 children in the end. However, you count as both your father's child and your mother's child. This means that there will actually be less than x2 children. However, we only care about you, so we can just subtract the places where you are duplicated. This is essentially xn duplicates. Logically, that's because each of your ancestral generation (except the last one) are having only x children instead of 2x, which is value that we get when we count the two parents. So, the final equation is as follows:

c = (2n * xn + 1) - (xn + 1) where c is the number of cousins you would have below a certain degree, given that x is the average number of children per person, and n is the degree.

A couple of notes on the equation

  • We are subtracting 1 to account for you - You are not your own cousin
  • This will not work for siblings - You will get one less than the actual number

Testing the equation

If everyone has 3 children, you would have 14 first cousins. Your mother will have 2 siblings, and each of them will have three children. This is a total of 6 cousins from your mother's side. You will also have 6 cousins from your father's side. Added to your 2 siblings, that is a total of 14 (6 + 6 + 2). From the equation we get:

c = (2n * xn + 1) - (xn + 1)
Since everyone has 3 children, x = 3.
Since we are looking at first cousins, n = 1.
So the equation is:

c = (2n * xn + 1) - (xn + 1)
c = (21 * 31 + 1) - (31 + 1)
c = (2 * 32) - (3 + 1)
c = (2 * 9) - (4)
c = 18 - 4
c = 14

This means that we have 14 first cousins (if everyone has three children). Since this is what we arrived logically, the equation must be correct.

Although this is not a formal proof, I did go over this in my head for many hours, and it seems to work fine. Please comment if you have any revisions for the equation, and I am more than happy to make an edit.

Some caveats

Until now, we have assumed that everyone has exactly three children. However, this is not the case. Since we only need an approximate for our final answer, we will be using the average birth rate value. This means that most people will have x number of children. Some might have none, some might have many. However, using this value should give us a fairly good approximation.

Also, according to Rutgers anthropology professor Robin Fox, 80% of all marriages in history have been between second cousins or closer. This means that there you will have a lot less cousins than predicted by the equation, since even though we are assuming everyone to have x number of children, two people together are having x number of children, and so the total number of children in a generation will be much lower than predicted. Since inbreeding is so common, there's also a chance that you could be much further from someone than predicted by the equation.

Nevertheless, let's try to do some calculation. Before that, we need to think a bit more about population genetics. In India (where I am from), there is mostly only intermarriage (Indians marrying Indians). Although this is starting to change now, it was more or less like that for a long time. Because of this, there is a very low chance that I will be related to an American. We might have a common ancestor, but we might have to go as far as the first Homo Sapien for that. Because, of this, I might be much more related to a random Indian than a random human being. I have done some calculations for you below, but try experimenting on your own:

Rearranging the equation to find the degree of kinship

We will rearrange this equation to solve for n (the degree of kinship):

c = (2n * xn + 1) - (xn + 1)
c = (2n * xn * x) - (xn + 1)
c ≈ xn (2nx - 1) - We are ignoring the 1 because it is insignificant when xn is large enough
c ≈ (2x)nx - We are ignoring the 1 again because 2n is going to be very large for these problems
log c ≈ (n log 2x) + log x
log c - log x ≈ n log 2x
n ≈ $\frac{log c - log x}{log 2x}$

Since we are making some approximations in this rearrangements, we will need to do some trial-and-error work using the original equation in order to ensure that the answer is correct.

Calculation 1 - How many degrees is an Indian away from me?

Value of x: Average birth rate in India: 2.20 births per woman
Value of c: 1.38 billion
n ≈ $\frac{log c - log x}{log 2x}$
n ≈ $\frac{log (1.38 * 10^9) - log 2.20}{log 4.40}$
n ≈ $\frac{9.1398790864 - 0.34242268082}{0.64345267648}$
n ≈ $\frac{8.79745640558}{0.64345267648}$
n ≈ 13.6722663953

Verifying our answer

Value of n = 13
c = (213 * 2.2014) - (x13 + 1)
c = (8192 * 62218.2127343) - (28281.0057883 + 1)
c = (509691598.719) - (28282.0057883)
c = 509663316.713 ≈ 510 million

Value of n = 14
c = (214 * 2.2015) - (x14 + 1)
c = (16384 * 136880.068015) - (62218.2127343 + 1)
c = (2242643034.36) - (62219.2127343)
c = 2242580815.15 ≈ 2.2 billion

This means that I have roughly 510 million 13th cousins and roughly 2.2 billion 14th cousins.

Thus, the furthest an Indian can be is my 14th cousin.

Calculation 2 - How many degrees is another human being from me?

Value of x: Average birth rate across the world: 2.3 births per woman
Value of c: 7.9 billion
n ≈ $\frac{log c - log x}{log 2x}$
n ≈ $\frac{log (7.9 * 10^9) - log 2.3}{log 4.6}$
n ≈ $\frac{9.89762709129 - 0.36172783601}{0.66275783168}$
n ≈ $\frac{9.53589925528}{0.66275783168}$
n ≈ 14.3882105944

Verifying our answer

Value of n = 14
c = (214 * 2.2015) - (x14 + 1)
c = (16384 * 136880.068015) - (62218.2127343 + 1)
c = (2242643034.36) - (62219.2127343)
c = 2242580815.15 ≈ 2.2 billion

Value of n = 15
c = (215 * 2.2016) - (x15 + 1)
c = (32768 * 301136.149634) - (136880.068015 + 1)
c = (9867629351.21) - (136881.068015)
c = 9867492470.14 ≈ 9.9 billion

This means that I have roughly 2.2 billion 14th cousins and roughly 9.9 billion 15th cousins.

Thus, the furthest that any human can be is my 15th cousin.

Evaluation of results

Although these results show that we are all very close (depending on how you evaluate the results) in terms of kinship, there is another factor to consider. Through a phenomenon known as pedigree collapse, it is estimated that we share many common ancestors. That is, our great-great-grandfather from our mother's side might be the same as our great-great-grandfather from our father's side. This means that most people will be further than calculated by this equation. For example, if two cousins had a child, that child would only have six great-grandparents, not eight. Thus, that child will have less cousins than somebody else. We have also not considered marital relationships, and have only considered birth relations. Hence, the actual answer to your question might vary significantly from the values we calculated.

To learn more about this field, I would recommend checking out this article. It is very well-written in my opinion.

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One useful concept that you can use to do your estimations is "genetic distance" as is commonly measured using "fixation index".

Basically what you to is that you estimate/calculate the average number of pairwise differences if you compare chromosomes from people within one population (population A).

Then you compare the number you get with the average number of pairwise differences if you take one person from population A and another person from population B.

If the average number of pairwise differences within population A is 900 and the average number of pairwise differences between a person from population A and a person from population B is 1000 you get the genetic distance as measured with fixation index as "((1000-900)/1000)" = 0.1.

You are asking:

"what is the lowest degree of consanguinity between the two most distantly related people."

Here is a "Cavalli-Sforza" diagram showing how related different people are using the fixation index method: Genetic distance between different people using fixation index

I think the two most different peoples are some group of African pygmies and people on Papua New Guinea. (I can't find the link right now). One reason might be that Africans have no neanderthal admixture while people on Papua New Guinea have most of all, above 4 percent according to some estimate.

Note that as humans are "diploid", we have two copies of most chromosomes. Therefore you can in principle calculate how closely related you are to yourself using the same method.

Because of for instance "migration bottlenecks" African peoples tend to have the most variation among them.

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