Do I not understand genetics, or do I not understand math?

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Do I not understand genetics, or do I not understand math?

Postby King Author » Mon Apr 07, 2014 11:15 am UTC

Okay, regardless of whether you knew them or how you were raised, thus far in human history, every human being - now and arbitrarily far into the past - has had two biological parents, one male and one female.

You have two parents.
They each had two parents, so you have four grandparents.
They each had two parents, so you have eight great-grandparents.
And sixteen great-great-grandparents.
And thirty-two great-great-great grandparents.
etc.?

If you just keep doubling it like that, though, a mere 20 generations back you had over one million great-great-[...]-grandparents. 20 generations is only like, what, 400~600 years depending.

If you keep going back and keep doubling the numbers like that, your supposed number of great-[...]-grandparents will eventually outstrip the total number of human beings on the planet at that time.

Obviously, that can't be, so what am I doing wrong? (Aside from ignoring instances of incest, which would only lower the numbers modestly.)
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Re: Do I not understand genetics, or do I not understand mat

Postby speising » Mon Apr 07, 2014 11:18 am UTC

some of those can overlap.
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Re: Do I not understand genetics, or do I not understand mat

Postby King Author » Mon Apr 07, 2014 12:05 pm UTC

I know that. Everyone is distantly related. Hell, Obama and Dick Cheney are seventh cousins or something.

But is that it? Overlap? It's just overlap? A million ancestors in ~500 years is culled simply by overlap?
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Re: Do I not understand genetics, or do I not understand mat

Postby Flumble » Mon Apr 07, 2014 12:18 pm UTC

King Author wrote:But is that it? Overlap? It's just overlap? A million ancestors in ~500 years is culled simply by overlap?

Yes. It is one big pile of incest in the end. :P

Maybe it comforts your mind if you reason from "the first pair" of humans: their children had to reproduce with eachother and their children had to reproduce with their first cousins or with their siblings —and it's absurd to sleep with your first cousin, right?

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Re: Do I not understand genetics, or do I not understand mat

Postby brenok » Mon Apr 07, 2014 12:22 pm UTC

I think you're also ignoring the fact that usually people had more than two sons in the past, so each generation has actually more people than the previous.

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Re: Do I not understand genetics, or do I not understand mat

Postby speising » Mon Apr 07, 2014 12:43 pm UTC

brenok wrote:I think you're also ignoring the fact that usually people had more than two sons in the past, so each generation has actually more people than the previous.

and also some daughters :)

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Re: Do I not understand genetics, or do I not understand mat

Postby lalop » Mon Apr 07, 2014 2:51 pm UTC

King Author wrote:But is that it? Overlap? It's just overlap? A million ancestors in ~500 years is culled simply by overlap?

What else would it be culled by?

Keep in mind that the culling would also be exponential: a "same n-ancestor" (an ancestor that appears twice in the nth generation) would cut the number of n+1 ancestors by 2, n+2 ancestors by 4, etc.

Flumble wrote:Maybe it comforts your mind if you reason from "the first pair" of humans: their children had to reproduce with eachother and their children had to reproduce with their first cousins or with their siblings —and it's absurd to sleep with your first cousin, right?

IIRC the smallest human population was measured in thousands rather than ones.

But yeah, there are obvious implications when considering a starting population of thousands. You start off with at most 10000 families, and (assumng only inter-family reproduction), end up with at most half the families each generation. This can persist for at most log_2 10000 =13.29 generations. In practice, far less.

Incidentally, the same argument for a starting population of 10 billion yields log_2 10 billion = 33.22 generations.

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Re: Do I not understand genetics, or do I not understand mat

Postby Whizbang » Mon Apr 07, 2014 4:02 pm UTC

lalop wrote:
King Author wrote:But is that it? Overlap? It's just overlap? A million ancestors in ~500 years is culled simply by overlap?

What else would it be culled by?

Keep in mind that the culling would also be exponential: a "same n-ancestor" (an ancestor that appears twice in the nth generation) would cut the number of n+1 ancestors by 2, n+2 ancestors by 4, etc.

Flumble wrote:Maybe it comforts your mind if you reason from "the first pair" of humans: their children had to reproduce with eachother and their children had to reproduce with their first cousins or with their siblings —and it's absurd to sleep with your first cousin, right?

IIRC the smallest human population was measured in thousands rather than ones.

But yeah, there are obvious implications when considering a starting population of thousands. You start off with at most 10000 families, and (assumng only inter-family reproduction), end up with at most half the families each generation. This can persist for at most log_2 10000 =13.29 generations. In practice, far less.

Incidentally, the same argument for a starting population of 10 billion yields log_2 10 billion = 33.22 generations.



Do you mind clarifying this? I am afraid I don't follow. Thanks. :)

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Re: Do I not understand genetics, or do I not understand mat

Postby firechicago » Mon Apr 07, 2014 5:39 pm UTC

If a person occupies two different slots on your family tree, then their parents also occupy two different slots, and ther grandparents and their great grandparents and so on.

Suppose you only had one grandfather (your parents were half siblings). Therefore you only have three grandparents (2^2 minus one for the duplicated grandfather). Your grandfather only has one set of parents, so you can only have 6 great grandparents (2^3 minus the two duplicates). And those duplicated great grandparents can only have one set of parents so you can only have 12 great great grandparents (2^4 minus 2^2).

Overall a single duplication in generation n, means that all generations after n no longer have 2^g ancestors (where g is the number of generations counting your parents as 1), instead you have 2^g - 2^(g-n).

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Re: Do I not understand genetics, or do I not understand mat

Postby Izawwlgood » Mon Apr 07, 2014 5:44 pm UTC

Time travel. You're your own greatgrandfather.
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Re: Do I not understand genetics, or do I not understand mat

Postby firechicago » Mon Apr 07, 2014 5:54 pm UTC

Also, to respond to KA, your math is basically right: If your ancestors have stayed in one place for more than a couple generations, you're almost certain to find "incest" in the form of 3rd or 4th cousins marrying. And if you had perfect geneaological records you could probably find a common ancestor within the last 1,000-2,000 years for you and any other person now alive who isn't a member of a prehistorically isolated hunter-gatherer tribe.

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Re: Do I not understand genetics, or do I not understand mat

Postby Izawwlgood » Mon Apr 07, 2014 6:22 pm UTC

But yeah, humans are an incredibly inbred species, simply put. I don't think people understand how highly related we all are.
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Re: Do I not understand genetics, or do I not understand mat

Postby Derek » Mon Apr 07, 2014 7:36 pm UTC

Izawwlgood wrote:But yeah, humans are an incredibly inbred species, simply put. I don't think people understand how highly related we all are.

Not particularly more than other species, I think.

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Re: Do I not understand genetics, or do I not understand mat

Postby gmalivuk » Mon Apr 07, 2014 7:49 pm UTC

Current numbers may not suggest that at first glance, but the bottleneck down to a few thousands in our species's history means that yes, numbers or not, we are a pretty inbred bunch.
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Re: Do I not understand genetics, or do I not understand mat

Postby Izawwlgood » Mon Apr 07, 2014 7:56 pm UTC

Derek wrote:
Izawwlgood wrote:But yeah, humans are an incredibly inbred species, simply put. I don't think people understand how highly related we all are.

Not particularly more than other species, I think.

Extraordinarily more so. The human MRCA is ~2000-4000 years ago. There's a reason cousin or sibling pairing is so detrimental for humans, but not for... virtually every other species.

Remember hearing how Cheetahs are massively inbred because of a bottleneck of like, 20,000? The human bottleneck was supposedly ~half that.
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Re: Do I not understand genetics, or do I not understand mat

Postby Angua » Mon Apr 07, 2014 7:59 pm UTC

Could be worse, we could be Tasmanian devils. They're so inbred they have contagious cancer.
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Re: Do I not understand genetics, or do I not understand mat

Postby speising » Mon Apr 07, 2014 8:59 pm UTC

Izawwlgood wrote:
Derek wrote:
Izawwlgood wrote:But yeah, humans are an incredibly inbred species, simply put. I don't think people understand how highly related we all are.

Not particularly more than other species, I think.

Extraordinarily more so. The human MRCA is ~2000-4000 years ago. There's a reason cousin or sibling pairing is so detrimental for humans, but not for... virtually every other species.

Remember hearing how Cheetahs are massively inbred because of a bottleneck of like, 20,000? The human bottleneck was supposedly ~half that.


why is that? was there a catastrophe which reduced the human gene pool , or did just one tribe perform extraordinary well?

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Re: Do I not understand genetics, or do I not understand mat

Postby gmalivuk » Mon Apr 07, 2014 9:04 pm UTC

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Re: Do I not understand genetics, or do I not understand mat

Postby Bripirate » Mon Apr 07, 2014 11:37 pm UTC

Perhaps I'm being dense, but why would you assume that the total number of people that have ever lived on the Earth to be greater than the current population?

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Re: Do I not understand genetics, or do I not understand mat

Postby gmalivuk » Mon Apr 07, 2014 11:41 pm UTC

Fairly straightforward math leads to that conclusion. The total number who have ever lived is an order of magnitude greater than the current population.
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Re: Do I not understand genetics, or do I not understand mat

Postby brenok » Mon Apr 07, 2014 11:49 pm UTC

I don't think Mathematics are needed at all. Unless we are the first generation of humans, the total number of humans is larger than the present number.

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Re: Do I not understand genetics, or do I not understand mat

Postby gmalivuk » Mon Apr 07, 2014 11:54 pm UTC

It's not that simple. A population that doubled every generation would have as many alive at one time as dead in all previous times. (Yes, strictly speaking "all humans who ever lived" includes the ones alive now, but I don't think that was really the question.)
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Re: Do I not understand genetics, or do I not understand mat

Postby Izawwlgood » Tue Apr 08, 2014 12:16 pm UTC

Bripirate wrote:Perhaps I'm being dense, but why would you assume that the total number of people that have ever lived on the Earth to be greater than the current population?

Because it's easy to look at the doubling of previous generations and make the mistake that no one is related to anyone anywhere.

What actually happens is most people die instead of have babies, and most babies die, and throughout pretty much all of human history save the last... like... 200-300 years(ish?),the population was fairly stable, meaning most people were only replacing themselves. If you look at the pedigree from the link gmal provided, you'll quickly see how a single person from >4 generations ago is probably the ancestor of A LOT of people.

The take home should be that your chances of passing on your genetic material to the far future is actually pretty vanishingly small. But be glad; the average person on the street is probably as closely related to you as your second cousins, or so, so your genes probably will make it!

EDIT: Sorry, it's a few links off from what gmal provided, but this is the pedigree I meant. This is what happened in the human; notice the proliferation of the black mtDNA across all present day individuals, and notice how most previous generations aren't represented. The only inaccurate thing shown here is there'd be some lines between greatgrandkids and fifth cousins.
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Re: Do I not understand genetics, or do I not understand mat

Postby jestingrabbit » Tue Apr 08, 2014 12:52 pm UTC

Bripirate wrote:Perhaps I'm being dense, but why would you assume that the total number of people that have ever lived on the Earth to be greater than the current population?


fyi, the total number of humans lived tends to attract answers ranging from 50 to 200 billion. No matter which end of that spectrum you buy into, a hell of a lot more people are dead than alive.
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Re: Do I not understand genetics, or do I not understand mat

Postby mike-l » Tue Apr 08, 2014 4:40 pm UTC

Yeah. There's this persistent myth that there are more people alive now than are dead, which would be true if all of human history enjoyed the growth we were experiencing in the 60s and 70s, but of course that is nowhere near the case.

Incidentally, if that were the growth rate through all of history, then working backwards human population would only be about 1150 years old
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Re: Do I not understand genetics, or do I not understand mat

Postby King Author » Wed Apr 09, 2014 4:08 pm UTC

firechicago wrote:If a person occupies two different slots on your family tree, then their parents also occupy two different slots, and ther grandparents and their great grandparents and so on.

Suppose you only had one grandfather (your parents were half siblings). Therefore you only have three grandparents (2^2 minus one for the duplicated grandfather). Your grandfather only has one set of parents, so you can only have 6 great grandparents (2^3 minus the two duplicates). And those duplicated great grandparents can only have one set of parents so you can only have 12 great great grandparents (2^4 minus 2^2).

Overall a single duplication in generation n, means that all generations after n no longer have 2^g ancestors (where g is the number of generations counting your parents as 1), instead you have 2^g - 2^(g-n).


Ah, that's the explanation I wanted. Now it makes sense. Thanks.

mike-l wrote:Yeah. There's this persistent myth that there are more people alive now than are dead, which would be true if all of human history enjoyed the growth we were experiencing in the 60s and 70s, but of course that is nowhere near the case.

Incidentally, if that were the growth rate through all of history, then working backwards human population would only be about 1150 years old


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Re: Do I not understand genetics, or do I not understand mat

Postby mathmannix » Thu May 08, 2014 5:16 pm UTC

I don't think there's any serious (non-TIMECUBE-wackiness type) religion that suggests the human race is less than 5000 years old (or roughly 4300 years since the 8-bottleneck immediately post-flood). Your best bet for that would be a Matrix-style cover-up sci-fi theory.
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