Population Bottleneck

[Exial]

After debating with a YEC he has provided me with this equation that has me kind of stumped. He says this is a clear example showing that the human population bottlenecked around 6000 - 10000 years ago reducing the ENTIRE population to below a 1000. Now, I know this is a load of rubbish but do not possess the calculus skills to beat him at his own game.

Human DNA has a common essence of all but about 10%
Now, as you know, evolution expands this number as DNA code changes are what happens with evolution. So, the evolutionary rate for humans is about .01 or 1% a year. ( I think is is actually less, but its whatever.) That means that every year, 1% of the worlds population diversifies...
So the equation goes like this

Population of people * Diversification of Human DNA (the 10%) = Number of Humans (at Past Time) * Past Time (how far back your want to go) / Evolutionary Rate

which equals this:

Population of people * Diversification of Human DNA (the 10%) * Evolutionary Rate / Past Time (how far back you want to go) = Number of Humans (at Past Time)

6,000,000,000 * .1 * .01 / 10000 = 600

Now, you may doubt the equation, but this is a standard derivation problem. If you take a pre calc course, the formula should look very familiar. (or at least I think it was pre calc, it could have been something else)

 

[LifeToTheFullest!]

After debating with a YEC he has provided me with this equation that has me kind of stumped. He says this is a clear example showing that the human population bottlenecked around 6000 - 10000 years ago reducing the ENTIRE population to below a 1000. Now, I know this is a load of rubbish but do not possess the calculus skills to beat him at his own game.

Does the equation take into account selective pressures, population migration, disease, etc? I'm no math buff, but seems to me this equation ignores many variables.

 

[SithDoughnut]

That equation makes no sense. The maths works (I think) but the equation itself is nonsensical. There are a huge number of problems with it:

1) It assumes that the population has expanded in a linear fashion. Not true - population fluctuates, both in size and in rate of increase.

2) It assumes that evolution only diversifies a species. Not true - evolution can go both ways.

3) It assumes that the 'diversification rate' (how exactly that works, I'm not sure) is 1%. Where that figure came from, I don't know, it seems like your YEC friend just made it up. You don't make up statistics if you want a correct answer.

4) It wrongly assumes that there is a 10% genetic difference between humans - AFAIK it is a lot less (although feel free to correct me here). I believe the difference between humans and chimpanzees is about 2%, so it's less than that.

5) It doesn't follow the equation to its inevitable conclusion. If you increase the value of "past time" to 100,000 years - so we're now looking 100,000 years ago - there are now 60 humans. If you increase it to 1 million there are now 6 humans. If we assume that everything in this equation is correct, the human race is over 1 million years old, much too old to fit a YEC model.

6) It assumes that the human race was there at the start, without any evidence whatsoever to prove that.

7) The equation assumes that all humans are immortal - it does not take into account the fact that they die. For the equation to work, those 600 people who lived 10000 years ago have to still be alive today.

That's everything off of the top of my head for the moment. There's quite possibly more. Basically, the equation ignores all sorts of factors, and even if we ignore all the mistakes, it still proves that the human race is at least 1 - 6 million years old. You don't need to know much maths to know that it quite frankly does not work at all.

EDIT: I'm going to make the assumption that your YEC friend is a literalist Christian (YECs tend to be literalist Christians), at which point there is another issue - it totally ignores the flood, and so doesn't fit the Bible.

 

[sfs]

After debating with a YEC he has provided me with this equation that has me kind of stumped. He says this is a clear example showing that the human population bottlenecked around 6000 - 10000 years ago reducing the ENTIRE population to below a 1000. Now, I know this is a load of rubbish but do not possess the calculus skills to beat him at his own game.

I have no idea what this equation is supposed to represent, but it doesn't seem to have anything to do with human genetics. The DNA of two humans does not differ by anything like 10%; two copies of the genome actually differ by something like 0.3% (< 0.1% if you count only single-base differences and not larger insertions and deletions). In a constant-sized population, the genetic diversity remains constant over time (once the population has been around for a while). In a population that is rapidly expanding, like our population, the diversity will increase at a substantial fraction of the mutation rate; this would mean an increase of less than 0.000005% per generation. So the idea that our "divergence" should be rapidly increasing is nonsense.

If you do real modeling of human genetic diversity (which is something I've done professionally), you'll find that the human population looks like it's been around for at least many hundreds of thousands of years.

 

[Agonaces of Susa]

There are several known population bottlenecks in Earth's history.

The Bible says at one point there were only 2 people on the Earth: Adam and Eve.

Hopefully, everyone here has heard of them.

At another point in history there were only 14 human beings on the Earth.

"Far sighted Enki and and wise Mami
Went into the room of fate.
The womb-goddesses were assembled.
He trod the clay in her presence;
She kept reciting an incantation
For Enki, staying in her presence, made her recite it.
When she had finished her incantation,
She pinched off fourteen pieces (of clay)
(And set) seven pieces on the right,
Seven on the left. ...
Seven created males.
Seven created females."
-- The Atrahasis Epic, 18th century B.C.

Then after the Great Deluge of All there was only Noah and his kin.

Hopefully, you are familiar with the Great Deluge of All and the population bottleneck that caused.

Even fundamentalist Darwinists concede that the Toba supervolcano caused a population bottleneck 70,000 years ago.

 

[Exial]

The Bible says at one point there were only 2 people on the Earth: Adam and Eve.

What is the bible? who are adam and eve?

 

[LifeToTheFullest!]

What is the bible? who are adam and eve?

Peter Pan once said, "This won't do. What's the matter with you? All it takes is faith and trust. Oh! And something I forgot."

 

[sfs]

There are several known population bottlenecks in Earth's history.

The Bible says at one point there were only 2 people on the Earth: Adam and Eve.

Hopefully, everyone here has heard of them.

Heard of them. Didn't happen that way, though.

Then after the Great Deluge of All there was only Noah and his kin.

Hopefully, you are familiar with the Great Deluge of All and the population bottleneck that caused.

Yup. Didn't happen either.

Even fundamentalist Darwinists concede that the Toba supervolcano caused a population bottleneck 70,000 years ago.

That also didn't happen. (The bottleneck, that is, not the volcano.) There was no significant bottleneck in African populations, at least, 70,000 years ago. Early, extremely sketchy data suggested there might have been, but much more complete data rule it out.

 

[Agonaces of Susa]

Heard of them.

You're probably in the minority.

Didn't happen that way, though.

You have no scientific evidence of that.

That also didn't happen. (The bottleneck, that is, not the volcano.) There was no significant bottleneck in African populations, at least, 70,000 years ago. Early, extremely sketchy data suggested there might have been, but much more complete data rule it out.

The Archbishop of the Darwinist Church, namely Richard Dawkins, says otherwise.

 

[The4thrider]

I just noticed that your sig is the last lines from "the road" Ha, nice

 

[sfs]

You're probably in the minority.

I usually am.

You have no scientific evidence of that.

Do too.

The Archbishop of the Darwinist Church, namely Richard Dawkins, says otherwise.

I have no idea what Dawkins says about the subject. Since I know rather more about it than he does, I also don't care.

 

[The4thrider]

Do too.

I have no idea what Dawkins says about the subject. Since I know rather more about it than he does, I also don't care.

well... Can you show us your evidence?

 

[Agonaces of Susa]

I usually am.

I find that hard to believe.

Do too.

What evidence? A time machine, a crystal ball, or a scrying bowl?

I have no idea what Dawkins says about the subject.

I know for a fact he says the exact opposite of you.

Richard Dawkins claims in the Ancestors Tale that a population bottleneck came about as a result of the Toba supervolcano.

Since I know rather more about it than he does, I also don't care.

You claim to know more about so-called "evolutionary history" than Richard Dawkins?

 

[Agonaces of Susa]

I just noticed that your sig is the last lines from "the road" Ha, nice

Cormac is a demigod imo...

 

[The4thrider]

Cormac is a demigod imo...

Its a great book, its in the top ten for me. No country for old men is next.

 

[Agonaces of Susa]

Its a great book, its in the top ten for me. No country for old men is next.

I like those. But my two favorites are Blood Meridian and Outer Dark.

 

[The4thrider]

I know we are way off the OP.
My two favorite of all time are "The Art of War", and "The Book of 5 Rings"

 

[Agonaces of Susa]

I know we are way off the OP.
My two favorite of all time are "The Art of War", and "The Book of 5 Rings"

Those are rated G compared to my personal faves...

The Bible, The Mahabharata, and The Iliad ...

 

[The4thrider]

So we can continue our discussion
http://www.christianforums.com/t7475917/#post54990514

 

[sfs]

well... Can you show us your evidence?

Sure, or at least point you to the evidence.

The evidence is genetic. Changes in population size affect the frequency spectrum of genetic variation in that population in characteristic ways. Let's stick with variants that have only two alleles (e.g. single-nucleotide polymorphisms). If a population stays the same size for a long period of time, the distribution of allele frequencies is heavily weighted toward lower frequencies; specifically, the probability that a derived allele has frequency f is proportional to 1/f (or 1/(f(1-f)) if you don't know which is the derived and which is the ancestral allele).

A population that has expanded recently will have more low frequency variants than the constant-sized population, because the larger population can hold more variants, but the new variants haven't had time to drift to high frequency yet. (Note: "recently" here means any time in the last couple of hundred thousand years for humans.) A population that has been through a bottleneck, on the other hand, will show a deficit of low-frequency variants, since low frequency alleles often drift either to loss or to higher frequency during the bottleneck.

Non-African human populations show clear evidence for multiple bottlenecks. These include a bottleneck shared among all non-Africans, usually taken to reflect a small population migrating out of Africa, although there's nothing that says it couldn't include a contribution from Toba, since that's around the right time. It also includes additional modest bottlenecking in European population history, somewhat more in East Asia, and much more in native American populations.

African variation, on the other hand, shows modest evidence for a population expansion something more than 100,000 years, and no sign of a bottleneck around 70,000 years ago, or at any other time. For example, the first study to make a serious effort to fit human demographic models to variation data was published in 2005 (Genome Research 2005 Nov;15(11):1576-83.) It found bottlenecks in the history of European populations that amounted to an inbreeding coefficient of around 0.25, while for the African population studied the inbreeding coefficient was effectively zero (best estimate = 0.008). So the pattern really was inconsistent with there having been a population bottleneck in western Africa.

The next paper to do this kind of inference, by Alon Keinan and colleagues (Nat Genet. 2007 Oct;39(10):1251-5), found the same thing: clear evidence for expansion within the ancestral African population (by a factor of 1.8x, if I remember correctly), and no evidence for a bottleneck in the history of that population. Subsequent papers, using markedly better data sets as time has gone by, have been consistent in this regard. These include papers by Rasmus Nielsen, Carlos Bustamante and his group, and I think Gabor Marth. Probably others that I can't recall, too.

This is not to say that Toba could not have had any effect at all on the human population as a whole, but whatever effect it had was pretty small, and not a major determinant of our patterns of genetic variation.