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Author Topic:   Hello, cousin! (re: Recent common ancestors to all living humans)
RAZD
Member (Idle past 1404 days)
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Message 9 of 76 (328891)
07-05-2006 7:40 AM
Reply to: Message 4 by subbie
07-03-2006 2:12 PM


mathematic models again?
a range of migration rates, from a low level where almost nobody left their native home to a much higher one where up to 20 percent of the population reproduced in a town other than the one where they were born, and one person in 400 moved to a foreign country.
But to simply state they didn't account for regional separation when the article clearly says that they did seems disingenuous to me.
The point was the physical barriers between the different areas, North\South America and Australia are much much more difficult than moving from, say, France to Spain. Different country is not different continent.
The mathematics obviously did NOT account for any differences in ability to migrate to different places,
but then mathematical models are always limited in their reflection of the real world
From the article:
"It's a mathematical certainty that that person existed," said Steve Olson, whose 2002 book ...
Nope. The math is only as good as the assumptions and the model representing reality.
How can this be?
It's simple math. Every person has two parents, four grandparents and eight great-grandparents. Keep doubling back through the generations ” 16, 32, 64, 128 ” and within a few hundred years you have thousands of ancestors.
It's nothing more than exponential growth combined with the facts of life. By the 15th century you've got a million ancestors. By the 13th you've got a billion. Sometime around the 9th century ” just 40 generations ago ” the number tops a trillion.
But wait. How could anybody ” much less everybody ” alive today have had a trillion ancestors living during the 9th century?
The answer is, they didn't. Imagine there was a man living 1,200 years ago whose daughter was your mother's 36th great-grandmother, and whose son was your father's 36th great-grandfather. That would put him on two branches on your family tree, one on your mother's side and one on your father's.
And all you need to do is keep that on a regional basis mathematically to account for all the relationships necessary to double up the ancestors rather than have an expotential growth pattern on them.
This does NOT mean that people in africa, america, australia and asia HAD to interbreed to account for the numbers of ancestors.
Bad math, bad logic, bad conclusion.
Enjoy.

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 11 of 76 (329094)
07-05-2006 9:23 PM
Reply to: Message 10 by pink sasquatch
07-05-2006 3:04 PM


Re: mathematic models again?
Wrong. The majority of the report focuses on approximating regional differences in migration through history. ... As an example, the model assumes one-hundred individuals per generation migrate between northern Africa and Italy, while only one individual per generation migrates between New Zealand and Polynesia.
That still does not get you over the physical barriers between europe and the americas before columbus, for instance, which is then lumped in with the migration rate from New Zealand and Polynesia? Jazzns in Message 3 and Message 5 addresses some of this issue.
However, to simply dismiss it as a simple exponential model without, apparently, even examining the model (or even reading the abstract of the paper) is extremely problematic.
I look at the process as described in both the "sensational press" article and what is available in the abstract, and what I see is a model that essentially draws concentric circles around an idealized homogeneous population, and assigns different migration rates to the different radii of the circles in an inverse relationship. This basically says a LOT of close regional inter-breeding of nearby populations, and less and less interbreeding between distant populations.
Now you can cover the earth with these averaged migration circles but there are places where they just don't fit the geography. I don't see any correction for geography, and find that rather significant.
The abstract says:
These analyses suggest that the genealogies of all living humans overlap in remarkable ways in the recent past. In particular, the MRCA of all present-day humans lived just a few thousand years ago in these models.
That doesn't tell me how pre-christian egyptians could mix genes with inhabitants of Chilca Valley, for example.
It explains how populations on different continents can "overlap in remarkable ways in the recent past" but NOT that it in fact happened or that populations between different continents HAD to overlap at all.
The problem with this "MRCA" conclusion is that it just doesn't follow from the premises, for a number of reasons.
  1. One is that it assumes a homogeneous distribution in a homogeneous environment, with the only variable being rates of migration inversely proportional to distance by some averaged metric (whatever formula they used).
    This may be coming true with a global airtravel society, but it certainly did not exist pre-columbus. See (3).
  2. The idea of a single MRCA organism within a sexually reproducing population is bogus, therefore any conclusion based on it is bogus.
    You can take a population of say 200,000 individuals and every year for 1,000 years {protect\cull} the population so that there are always 200,000 individuals and at the end of that time genetically find out that they are all related in the recent past because of the shared genetic material, but at no time in the past was there a single individual with those shared genetics -- they have been combined from the resources of the whole population, picking the ones from different individuals that are "less costly" ... think of it as selecting gene Q from individual Q's offspring for environmental\sexual (E/S) factor Q, selecting gene R from individual R's offspring for (E/S) factor R, selecting gene S from individual S's offspring for (E/S) factor S, selecting gene T from individual T's offspring for (E/S) factor T, etcetera: the final population genetics will "find" a "MRCA" with Q, R, S, T, etc, genes when no single ancestor had them all. You can also have the same amount, more or less genetic diversity than when you started - there was no control on diversity along the way.
    I have the same problem with "genetic eve" and "genetic adam" btw, because there is no reason for all the genes to come from any single individual when so many ancestors have "participated" along the way and the population group is always intermixing the available genetic material in new combinations.
    You could keep this going for millions of years, and you would find, with continued evolution and natural selection, that you reach a point of equilibrium where you would always find a theoretical "MRCA" of the essentially the SAME age in each population no matter when you picked your sample, because you would only have so much material to work with.
    This is the essence of population mixing that results in new species when different populations are sufficiently isolated in space or time.
  3. Very recent (ie since columbus) migration and conquest\control and disease etc patterns have significantly shifted the genetic panorama, causing a level of genetic mixing much higher than previously and on more and more of a world wide level, this results in mixing the genetics of several previously isolated "MRCA" populations with some parts of some being selected over others and some not -- the result is NOT a "new" ancestor.
    Take the example above of a closed population of 200,000 individuals and repeat that with two or three others, after 1000 years mix them all together for what, 340 years or so? You can then derive a new theoretical "MRCA" that has even less basis in reality than the ones derived for each such population.

This study is not based on genetics, or geography, or even history (beyond 'cherrypicking' some historical parameters), but on what is possible mathematically given certain parameters and restrictive conditions and enabling assumptions. Claiming what is possible mathematically in an idealized structured {environment\population}, as something that then had to have occurred to all humans around the world is a logical leap that is totally unwarranted.
Enjoy.
Edited by RAZD, : clarified history

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 21 of 76 (329739)
07-08-2006 12:16 AM
Reply to: Message 12 by pink sasquatch
07-06-2006 11:00 AM


It just doesn't add up pink.
You would see that correction if you read the paper.
Is it on line anywhere? As you pointed out the Nature article requires a login - with full rights (I only have a guest account).
Pedigrees for all humanity | Nature
I've looked, and it seems all I can find are links to the Nature article with additional "abstracts" that don't add much information.
http://www.tiem.utk.edu/~gross/math151fall05/references.html
This paper uses a mathematical model and a simulation model to estimate how many generations in the past you would have to go to find an individual who was an ancestor to all human beings currently alive (the most recent common ancestor - MRCA). They compare results from a simple model that assumes random mating between all humans to a model that assumes the world is broken down into sub-regions with transfers of humans regularly occuring between these regions, in the same way a transfer matrix describes the movement of something between various components. Their results indicate that the MRCA lived in the relatively recent past (a few thousand years ago), and going back a few thousand more years (to about 7,000 years ago) we would get to the IA point where each present-day human has exactly the same set of ancestors.
It also does not surprise me that we already have a couple creaionist references to the paper (expect more eh?):
http://www.ldolphin.org/popul.html
In one set of estimates based on this model, the mean time back to the universal ancestor is 2,300 years (76 generations, assuming a generation time of a bit less than 30 years) and to the identical ancestors it is 5,000 years (169 generations) " the time of Aristotle and the first pyramids, respectively. The latter date is especially startling: had you entered any village on Earth in around 3,000 BC, the first person you would have met would probably have been your ancestor!
That looks suspiciously like the 'news' article ...
Page not found | Creation Safaris
Notice the model converges on a few thousand years ago, not millions. Such a date is closer to Noah than Lucy. Care should be exercised interpreting what this means, because it is somewhat of a counterintuitive artifact of a mathematical model that makes certain assumptions. Another counterintuitive result, Hein claims, is that "not many generations ago (about six), members of our pedigree existed that did not contribute to us genetically." The authors are not claiming that humankind popped into existence a few thousand years ago, but only that everyone alive today had the same ancestors. ... One question he asks is, "In the idealized models, how far back would one have to go to find a single couple who are the lone ancestors of everybody?" to which we might add, "and did their names start with A and E?"
We can’t judge how valid is Professor Rohdes’ computer model, but it is interesting that this was not published by Answers in Genesis, but by Nature and by researchers from MIT and Yale - not institutions particularly interested in validating Biblical chronology. It calls into question evolutionary assumptions about human pedigrees stretching back tens of thousands and hundreds of thousands of years. It also means that all those “racial” differences between people are superficial and must be of recent origin. Like AIG has emphasized in its Biblical creationist answer to racism, we truly are of "one blood," just as Paul told the Greek philosophers on Mars Hill (Acts 17).
Not too bad a take on their part (aside from the rather obvious inferences).
But this is exactly what my objections are about: the results do not correlate with evidence from other sources.
We have evidence from genetics where they in fact LOOKED for a common ancestor in female mtDNA and male yDNA and the results were on the order of 160,000 to 200,000 years. Either the model is flat out wrong or these several teams of geneticists working in different labs with different bits of evidence (male vs female), and all the groups that have replicated those results, were all in error in the same mysterious way. (let's see ... one suspect mathematical model wrong or lots of evidence wrong ... hmmmm ... hard to decide )
We also have evidence of cultural artifacts that such migrants would carry and which are used to judge how much "international" commerce was going on at any one time (like roman coins in England before the roman invasion). These (amazingly) do not show a mixture of artifacts from around the world at some 5000 years ago. They do not even show a small subset of universally common artifacts that could be attributed to a common "MCRA" propogating population infiltrating all other populations. I think I can safely say that there are NO artifacts from africa or europe in south america at cultural ages of 5000 years ago and vice versa.
The model takes this into account - no migration until it starts at a very low rate from Europe to North America via Iceland/Greenland in 1000 AD.
Migration across the Bering Strait region begins at 12000 BC in the model.
Some anthropologists argue even earlier dates for first colonizing the americas, based on some archaeological evidence in SA.
Indiana University Bloomington
http://www.embamex.co.uk/Update/2003/05/page_06.htm
http://allendale-expedition.net/pressreleases/1117pr.html
The first blush model had the "MCRA" some 800 years ago ... his name would have to be Cassanova eh? And it couldn't be a woman that recently ... the second model -- with "more realistic" factors -- pushes that to 5000 years: wow eh?
But 10 is also a "more realistic" approximation of a million than 1, and yet it is still totally inadequate as a real approximation. Going from 800 to 5000 is a small step towards 160,000 or 200,000 years.
I would be more than unimpressed if they set the parameters and the results were more in line with those 1000 AD and 12000 BC dates ... and maybe even (possibly) impressed if they ended up with a MCRA on the order of 160,000 to 200,000 years (to match the genetic evidence).
This is where I have trouble with the historical evidence they've used -- none of it appears to have been used to ground truth {ie - TEST} the model.
Of course this critical element could also be missing from the abstracts and tidbits available, but I don't see any reference in any of the available abstracts, news items and creationist papers to this kind of model checking.
One rather obvious benchmark would be just what the factors would need to be to result in a MCRA in agreement with genetics -- then they can argue how realistic those are compared to others. I don't see any references to this being done.
And this is still not addressing the problems with the "MCRA" concept noted in Message 11
Now I don't have any problem with grouping populations into regional groups that necessarily interact and are the source populations for the ancestors of the current populations -- this is all that is necessary to make the expotential growth of possible ancestors an erroneous concept.
Nor do I have a problem with super groups of regional populations interacting at a more casual rate.
But I still don't see how this gets to shared common ancestors the way the (available documents) claim. That just doesn't follow from the premises as presented. This alone makes the claim suspect.
You would see that correction if you read the paper.
I certainly don't see it in the results presented. The abstract must be lousy. What was used to ground truth the model? A mathematical model is only as good as the information used to tune it.
Read the paper before you criticize.
I can only read what is available to me. What I see so far -- from all the information available on line and from what you have portioned out -- leaves me underimpressed.
Enjoy.

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Replies to this message:
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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 25 of 76 (329828)
07-08-2006 10:17 AM
Reply to: Message 24 by nwr
07-08-2006 1:12 AM


The authors are not claiming that humankind popped into existence a few thousand years ago, but only that everyone alive today had the same ancestors.
No, that is not being claimed at all. What is claimed is that there was at least one common ancester.
From one of the "abstracts"
... and going back a few thousand more years (to about 7,000 years ago) we would get to the IA point where each present-day human has exactly the same set of ancestors.
That is one of the claims. One, btw, more credible than the MCRA conclusion.
Not having the paper in front of me, I cannot tell if that question was asked.
Looks like anglagard is going to get some email.
There could be an MRCA from 7000 years ago, yet it might be that none of my genes are inherited via that chain.
I'm pretty sure that contradicts the concept of "Most Recent Common Ancestor" - but then I think the concept is bogus, that it is never a single organism, but a population of a species that all contribute.

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 26 of 76 (329829)
07-08-2006 10:20 AM
Reply to: Message 23 by anglagard
07-08-2006 12:39 AM


email for paper
thanks.

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 30 of 76 (329852)
07-08-2006 11:58 AM
Reply to: Message 27 by nwr
07-08-2006 11:03 AM


I'm not sure why you are having problems with the MRCA conclusion. If there were common ancestors at one time, then there was a most recent common ancestor.
From an ancestor at, say, 200 generations ago, I could expect to inherit around 2-200 of my genes. That is far less than 1 gene.
I think you answered it. The fact is what you have is a mixture of all your ancestor genetics (plus mutations), but no one individual in a dominant source.
Some of my ancestors from 200 generations ago likely appear multiple times in my ancestral tree. That would increase the expected amount of DNA I would inherit from them. However, the MRCA probably appears relatively few times in my ancestral tree.
How do you know that all the "MRCA" genes come from one person? Put your answers together and you will end up with an MRCP (to use pinks acronym) without needing an MCRA concept. Sexual individuals do not breed alone.

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 31 of 76 (329855)
07-08-2006 12:02 PM
Reply to: Message 28 by anglagard
07-08-2006 11:08 AM


Re: Appendicies for Paper
thanks -- I now have my evening reading....

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 33 of 76 (329865)
07-08-2006 12:39 PM
Reply to: Message 29 by pink sasquatch
07-08-2006 11:31 AM


Re: genealogical, not genetic
An important point: The paper is solely modeling the genealogical MRCA, not a genetic MRCA. An ancestor in your genealogy need not contribute any genetic information to you as an individual, yet they were still in your family tree.
That's a different definition of MRCA than is used in genetics. Maybe we should call it most recent individual whose descendants have shaken hands with some ancestor or other of all other individuals. The 6 degrees of freedom thing.
You mention that you believe an MRCP (population) could exist, but not an MRCA. How small could an MRCP be for you to find it acceptable? Say, one-hundred individuals?
We are (were) talking about a time when the earth is covered with humans but even when we go back to the "founding" of species Homo sapiens there was a population that contributed to the next generation. These populations were always being mixed and remixed by sexual reproduction.
Could one-hundred individuals have a single ancestor in common?
They could have 100 individuals in common in different degrees in different (current) individuals.
Evaluating {most recent common ancestor}ship with my brothers and I get both my mother and my father - that is the closest you get to a single individual. When I include my cousins in the mix then I have also added a lot of ancestors, and this happens until the {ancestor population} starts to overlap. The overlap will be in different areas and in different degrees in different (current) individuals.
It is not a tree so much as a tapestry of interwoven threads. Some new threads are intorduced by mutations or migrants, and some are removed by death or infertility, but the number of interacting threads remains roughly the same. There never is a single parent of the group. This is what I was talking about above with a population in stasis where at any time you can measure the MRCP and come up with the same time difference for every generation.
The population evolves not the individual. The ancestors of Homo sapiens would appear no different to the first Homo sapiens than they do to us.
I see this paper has made it into the Wikipedia article
Most recent common ancestor - Wikipedia
And I find it disturbing how this is presented as an actual reality rather than a mathematical possibility, and in spite of the male\female evidence they cite that refutes it.
I'll read the paper tonight (I got it in email), and the appendices posted by anglagard, but I don't hold out much hope for it.

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 34 of 76 (329866)
07-08-2006 12:41 PM
Reply to: Message 32 by nwr
07-08-2006 12:26 PM


see the wikipedia article for even more confusion of gene\geneology.

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 36 of 76 (329943)
07-08-2006 8:39 PM
Reply to: Message 29 by pink sasquatch
07-08-2006 11:31 AM


Got the paper, but ...
Okay. Right at the start I have problems with the paper.
Just past the abstract it says:
In investigations of the common ancestors of all living humans, much attention has focused on descent through either exclusively maternal or exclusively paternal lines, as occurs with mitochondrial DNA and most of the Y chromosome4,5. But according to the more common genealogical usage of the term ”ancestor’, ancestry encompasses all lines of descent through both males and females, so that the ancestors of an individual include all of that person’s parents, grandparents, and so on.
For a population of size n, assuming random mating (and so ignoring population substructure), probabilistic analysis2 has proved that the number of generations back to the MRCA, Tn, has a distribution that is sharply concentrated around log2n. We express this using the notation Tn ~ log2n, meaning that the quotient Tn/llog2n converges in probability to 1 as n approaches infinity. In contrast, the mean time to the MRCA along exclusively matrilineal or patrilineal lines is approximately n generations6, and the distribution is not sharply concentrated. For example, in a panmictic population of one million people, the genealogical MRCA would have lived about 20 generations ago, or around the year AD 1400, assuming a generation time of 30 years. The MRCA along exclusively maternal lines would have lived something like 50,000 times earlier”in the order of one million generations ago.
(Source: NATURE | VOL 431 | 30 SEPTEMBER 2004 |http://www.nature.com/nature, "Modelling the recent common ancestry of all living humans" by Douglas L. T. Rohde, Steve Olson & Joseph T. Chang - pdf document)
First off lets take the age of that "MRCA along exclusively maternal lines" and see what we get:
2004 (time of article) - 1400 AD = 600 years in round numbers.
600 x 50,000 = 30,000,000 ... 30 million years ago?
That's several times the age of the earliest hominids to say nothing of the age of Homo sapiens (~160,000 years), so there is obviously something wrong with this calculation. {abe}Re comparison to genetic MRCAs {/abe}
Putting aside the issue I have with the "MRCA" concept, the other issue I have here at the start is the "probabilistic analysis2 has proved that the number of generations back to the MRCA, Tn, has a distribution that is sharply concentrated around log2n" while stating that "the mean time to the MRCA along exclusively matrilineal or patrilineal lines is approximately n generations6" with the result of a MRCA younger that either exclusively matrilineal or patrilineal line MRCA. Let me explain:
In the male part of the population the MRCA can be either male or female.
If male, then the MRCA cannot be younger than the exclusively patrilineal line MRCA.
If female, then the MRCA cannot be younger than the MRCA for the female part of the population (it could be older).
In the female part of the population the MRCA can be either male or female.
If female, then the MRCA cannot be younger than the exclusively matrilineal line MRCA.
If male, then the MRCA cannot be younger than the MRCA for the male part of the population (it could be older).
The youngest possible "MRCA" can not logically be younger than the younger of either exclusively matrilineal or patrilineal line MRCAs, and is most likely older (th best you can say is that it is somewhere between the two exclusive line MRCAs).
If this math generates a younger MRCA for a combined population than for an exclusive line, there is obviously something wrong with this math.
If the math model used here, inside each node or whatever, includes this erroneous math to calculate "when" the theoretical possible "MRCA" occured then it must also be in error.
Gravely.
Now the issue of modelling the migration patterns may or may not be accurate (and I still have some problems there), but the conclusions re "MCRA" are -- imh(ysa)o -- invalidated.
{abe}(see post 39 - I still have problems with taking Tn=log2n as fact rather than a possible lower bound){/abe}
Enjoy.
Edited by RAZD, : formating
Edited by RAZD, : strike out section

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RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 39 of 76 (330010)
07-09-2006 1:00 AM
Reply to: Message 38 by nwr
07-08-2006 9:39 PM


How many generations?
It's not all that obvious that it is wrong. It seems possible that the earliest common ancestor along female lines need not be a hominid. (Or don't you believe in evolution?)
Sorry, to clarify: in comparison to the mtDNA "MRCA" (150,000 years ago) it is obviously wrong.
Of course there were more ancient ancestors.
Would you care to explain that one? It seems obviously wrong.
msg38 writes:
For it to work, he has to have raped both of our maternal grandmothers.
The rapist wouldn't count, since the line of descent went through our mothers so was not patrilineal.
Yes, I''ve reconsidered that. Thanks.
I still have trouble with the MRCA concept necessarily occurring before the "IA" point:
Take say 10 couples that are arranged in a theoretical virtual circle, male\female\male\female\etc.
Each couple has a boy and a girl child that then mate with the children of adjacent couples, boys mate to the right and girls mate to the left.
Keep going until offspring of one couple meet at the far side of the circle and mate:

M--F M--F M--F M--F M--F M--F M--F M--F M--F M--F (0)
/\ /\ /\ /\ /\ /\ /\ /\ /\ /\
-F M--F M--F M--F M--F M--F M--F M--F M--F M--F M- (1)
\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /
M--F M--F M--F M--F M--F M--F M--F M--F M--F M--F (2)
/\ /\ /\ /\ /\ /\ /\ /\ /\ /\
-F M--F M--F M--F M--F M--F M--F M--F M--F M--F M- (3)
\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /
M--F M--F M--F M--F M--F M--F M--F M--F M--F M--F (4)
/\ /\ /\ /\ /\ /\ /\ /\ /\ /\
-F M--F M--F M--F M--F M--F M--F M--F M--F M--F M- (5)
\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /
M--F M--F M--F M--F M--F M--F M--F M--F M--F M--F (6)
/\ /\ /\ /\ /\ /\ /\ /\ /\ /\
-F M--F M--F M--F M--F M--F M--F M--F M--F M--F M- (7)
\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /
M--F M--F M--F M--F M--F M--F M--F M--F M--F M--F (8)
/\ /\ /\ /\ /\ /\ /\ /\ /\ /\
-F M--F M--F M--F M--F M--F M--F M--F M--F M--F M- (9)
\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /
M--F M--F M--F M--F M--F M--F M--F M--F M--F M--F (10)
(in this diagram each line is a circle so one end connects to the other end - think of it as rolled into a cylinder)
Every child in the final circle (#10) is now related to each of the original couples at the same time and to the same degree -- who was the "MRCA" in this setup?
Notice that this occurs at (n/2) generations, and that there is no MRCA Tn at log2n = 2.3 4.3 generations as the model used projects. {edited calculation}
Now this is idealized and limited, but it probably represents more mixing of genes than occurs on an average basis for a generalized population group. There is no reason there could not be several embedded (heh) cylinders of ancestry, especially when you consider different "classes" of individuals within a society where there are some breeding taboos.
Continue the pattern and each child is always related to the full circle of individuals 10 generations ago (and consider that each generation also introduces new mutations that take another 10 generations to share). Genetic drift will mean an introduction of new material into the mix at each generation, material that will not be carried by children of the immediate ancestors to the ones carrying the mutations. Lineages will be changing during the course of this interaction:
Each male will track his yDNA back to his original male parent in the circle, with each male tracking to a different male in the original circle (while showing genetic drift through mutations that have been introduced), and while sharing the original female partners genes (also showing genetic drift through mutations that have been introduced).
Each female will track her mtDNA back to the original female parent in the circle, with each female tracking to a different female in the original circle (while showing genetic drift through mutations that have been introduced), and while sharing all the original male partners genes (also showing genetic drift through mutations that have been introduced).
Using those mutations and the (current) rate of change to then project a genetic MRCA is obviously (to me) rather bogus - it will be confusing starting differences with mutation differences.
It's more of a tapestry weaving than a tree lineage in any reproductively interacting population.
I'm not sure where this leaves me with the migration issue, but the calculation of MRCA is still suspect as noted above. Using their the number generations (assuming the migration model is valid) = 76 generations and converting by the differences noted above and you get a value of e^76/2 = 5x10^32 generations to a "MRCP" .... at 30 years per generation, I'm willing to let the real answer be somewhere in between their low number and my high number.
{abe}
Now consider that social conventions and taboos act as a control on random mating to a certain level. If we assume this to holds for only 4 generations then the MCRA 'advances' 4/2=2 generations during those periods. If we then consider that the Tn=log2n formula applies to the {four generations} as a base unit this multiplies their Tn result by 4 to arrive at a time when this theoretical MCRA occurred. Combining these you get MCRA*4/2 - or a doubling of the theoretical timing.
The curious thing is that it doesn't matter how many generations you take this non-random control over, the date is doubled -- or am I missing something? It seems to me that this should affect the expotential function ...{abe}
Latter ...
Edited by RAZD, : mcra mrca ...
Edited by RAZD, : added info at end
Edited by RAZD, : corrected log base 2 calculation

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This message is a reply to:
 Message 38 by nwr, posted 07-08-2006 9:39 PM nwr has replied

Replies to this message:
 Message 40 by nwr, posted 07-09-2006 10:24 AM RAZD has replied

  
RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 41 of 76 (330089)
07-09-2006 1:36 PM
Reply to: Message 40 by nwr
07-09-2006 10:24 AM


Re: How many generations?
I haven't actually read the paper. I'm trying to manage on what I have read. Maybe I will have to read it, though I think it is unimportant enough to not warrant the time. I assume that the calculation of time to matrilineal MRCA is a crude back-of-the-envelope one, making lots of assumptions.
None of the math is in the {document\letter} -- we should also note that this is NOT a {presented peer reviewed paper} but a LETTER to the journal, and that there are different standards for peer review for letters compared to papers.
The math is all in the appendices that anglagard has kindly linked in Message 28.
The original 10 couples (20 people) are all MRCAs. There is no requirement that there be a unique MRCA.
Exactly. This is why I would rather talk about a MRCP as the genetics comes from the population rather than a specific individual. Using an individual in the concept makes people think there is one person who is the grand-whatever of all humans (with a typical tree type geneology image firmly in mind).
Talking about a {most recent common ancestor population} on the other hand is a much more realistic an image - and no, that population does not all have to be descendent from a single person or pair of individuals, they are descendent from their MCRP. The Homo sapiens in Ethiopia did not propogate from a singe individual Homo heidelbergensis but from a population of them. The Homo heidelbergensis did not propogate from a singe individual Homo ergaster but from a population of them. Etc. How big that population was we don't know.
To get to the point of a single individual organism you have to go back to before sexual reproduction.
The log2n is an asymptotic figure - what is approached for large n. You can't expect it to apply to small n.
It is presented in the letter as a proven mathematical fact, not as a lower limit.
Moreover, the asymptotic prediction is presumably based on random mating, not the constrained mating of your example.
No mating in sexual species is completely random. This is another problem with the concept. There are limitations in space, so even broadcast {seeds\eggs\sperm\pollen\whatever} can only randomly mate within select groups.
The constrained mating of my example is artificial -- to a point. I agree. That is why I think the reality falls somewhere in between. The question then is how to model the degree of {random\constraint} in the population.
I agree that is bogus. But does the paper actually attempt that? This isn't about genetics, as has been previously said.
Yes, they claim this is about geneology instead of genetics, so my "ancestors" include my great-aunt Matilda that died a "spinster" without having any children. But if you look at the geneology conclusions of MCRA and MCRP (= their IA concept) such a person becomes a non-player. Such a person is eliminated in the next generation from my grid as contributing to the "ancestry" of other descendents. Add a third child to any couple at any level that has no offspring and the woven tapestry closes around them without any propogation from them. Further:
an·ces·tor n.
1. A person from whom one is descended, especially if more remote than a grandparent; a forebear.
Great Aunt Matilda is not an ancestor. A relation yes, ancestor no.
If we are talking geneological ancestors we are talking genetic ancestors by definition of ancestor.
If I have calculated this correctly, then the generation 0 person directly above in your diagram occurs 252 times among those 1024 ancesters, so 252/1024 (around 25%) of the DNA comes from the generation 0 ancestor directly above. The generation 0 person 5 couples away appears only once, so only about .1% of the DNA comes from there. The 20 MRCA are all equivalent in the sense of ancestry (that they are ancestors), but they are not equivalent in genetic contribution.
I agree that it is not the same level from each couple in each descendent, but rather that the proportions in each descendent are apportioned the same from the original population.
btw you can model the distribution with the quadratic progression of (x + y)^m where m is the number of generations:
m=1 -- 1x + 1y
m=2 -- 1x^2 + 2xy + 1y^2
m=3 -- 1x^3 + 3x^2y + 3xy^2 + 1y^3
m=4 -- 1x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + 1y^4
etc
And this factoring can be determined easily from this graphic where you add the factors of the previous generation:
10                     1
/ \
9 1 1
/ \ / \
8 1 2 1
/ \ / \ / \
7 1 3 3 1
/ \ / \ / \ / \
6 1 4 6 4 1
/ \ / \ / \ / \ / \
5 1 5 10 10 5 1
/ \ / \ / \ / \ / \ / \
4 1 6 15 20 15 6 1
/ \ / \ / \ / \ / \ / \ / \
3 1 7 21 35 35 21 7 1
/ \ / \ / \ / \ / \ / \ / \ / \
2 1 8 28 56 70 56 28 8 1
/ \ / \ / \ / \ / \ / \ / \ / \ / \
1 1 9 36 84 126 126 84 36 9 1
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \
0 1 10 45 120 210 252 210 120 45 10 1
Each individual in generation 10 will have different couples contributing
252/(1+10+45+120+210+252+210+120+45+10+1)
= 252/1024 (note 1024 = 210)
= 24.6%
But also note that the 1's in generation 0 are the same couple -- so those should be replaced by a single 2. Wrap the diagram on a cylinder with these 1's overlapping and you can continue this pattern for more distant contributions, adding the overlapped portions for each couple's contribution. I suspect that in another 10 generations the contributions of each couple to each descedent become equal.
What this demonstrates is the power of a population in stasis to maintain a constant genetic base (except for allowing genetic drift and gradual introduction of neutral mutations). This is an argument for stasis in a constant population.
In all honesty, I think you are giving this paper far more importance than it is worth. It isn't about genetics, it is about combinatorics. It has very little relevance to evolution or biology.
It is presented as fact, and it has infiltrated Wikipedia as such. The importance is not to the relevance of the paper but to reducing the false information being promulgated.
It also has to do with the preponderance of belief that mathematical models can 'prove' elements of reality, both in the general public and in science. All math can do is model reality, it cannot become reality, and it can only make predictions -- it cannot "prove" any theory any more than the evidence can "prove" it (which is to say it can't). And the 'proof' is in the evidence and not in the math.
Enjoy.

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This message is a reply to:
 Message 40 by nwr, posted 07-09-2006 10:24 AM nwr has replied

Replies to this message:
 Message 42 by nwr, posted 07-09-2006 2:39 PM RAZD has replied
 Message 53 by pink sasquatch, posted 07-10-2006 2:45 PM RAZD has replied

  
RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 48 of 76 (330193)
07-10-2006 12:03 AM
Reply to: Message 42 by nwr
07-09-2006 2:39 PM


Re: How many generations?
The set of MRCAs might not constitute a population, but instead are scattered among many populations. The term "population" is imprecise enough that I am not convinced MRCP is meaningful. The ancestor relation, on the other hand, is precisely defined so that MRCA is well defined (even if unimportant).
An MCRA does not function without being in a population.
Only for people who misunderstand what this paper is describing. Admittedly, that might be most readers.
It's a letter to Nature, not a peer reviewed paper in the journal.
I'm talking about what the term is used for, whether it is in this document or other. If this document is making a special usage of a previously defined term that is not in compliance with that definition then there may be an additional problem with the document version.
If the term promotes misunderstanding then it is a bad term and should be replaced.
You are still discussing this as if the paper were about genetics. It isn't.
Well I thought that section was about the genealogy of the human family tree - what exactyly about this statement:
Talking about a {most recent common ancestor population} on the other hand is a much more realistic an image - and no, that population does not all have to be descendent from a single person or pair of individuals, they are descendent from their MCRP. The Homo sapiens in Ethiopia did not propogate from a singe individual Homo heidelbergensis but from a population of them. The Homo heidelbergensis did not propogate from a singe individual Homo ergaster but from a population of them. Etc. How big that population was we don't know.
Says genetics to you instead of genealogy?
If we are talking about genetic ancestors, we should be concerned about how much of our DNA was derived from a particular ancestor. But that genetic inheritance was never a concern of the paper. It was concerned only about the ancestral relation. Once again, it isn't about genetics, it is only about the combinatorial relationship of ancestry.
ge·ne·al·o·gy n. pl. ge·ne·al·o·gies
1. A record or table of the descent of a person, family, or group from an ancestor or ancestors; a family tree.
2. Direct descent from an ancestor; lineage or pedigree.
It seems to me that genetics is an inseperable part of the package of descent from biological parents.
Are we or are we not talking about the sexual reproduction of children from parents, and who inherit genes from them in the process? Why do we need to know how much of which from who to know that they are genetic ancestors as well as genealogical? Perhaps your usage of genetic is more restrictive than mine -- I don't need to quantify beyond "some" -- am I missing something?
I notice the Wikipedia article on "Mitochondrial Eve" uses genealogy to explain the genetics ...
Imagine a family tree of all humans living today. Now imagine a line from each individual to their mother, and continue those lines from each of those mothers to their mothers, and so on.
If I'm confused by some subtle difference I don't appear to be the only one.
In my estimation, you are one of those promulgating false information by virtue of your repeated treatment of the paper as if it were about genetics.
My argument is based on the genealogy given the diagrams and discussion to date, so if you have a problem with my using "genetics" loosly in this context then change it -- I don't see a big distinction unless you replace biological parents with adoptive parents.
Regardless of what you call it the model still does not model reality. That's the issue.
The appropriate response of a biologist to this paper should be
Ho hum!
In any case, this paper is mostly a curiosity of little or no importance to biology.
Is it any different than creationist nonsense?
In this case, the model involves the ancestral relationship, and this is pretty much straight out of biology. If you think there is a problem there, it isn't in the math. The model also involves assumption about the mixing of different populations, and I expect that is over-simplified and not completely realistic.
I have a problem with the assumption of random mating when mating, especially in human society is both currently and historically anything but random. Not only are there social traditions and taboos in effect but there is only so much population available at any one time, most especially when you have isolated populations.
I have a real problem with sketchy theoretical considerations being presented as proven truth and with it being promulgated in other discussions as if it were fact. They adjusted the model to go from 800 years to 5000 years -- how do we know that this is any more valid than the 800 number? What would another 'adjustment' end up at -- 30,000 years? How would we know if THAT was valid?

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This message is a reply to:
 Message 42 by nwr, posted 07-09-2006 2:39 PM nwr has seen this message but not replied

  
RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 49 of 76 (330194)
07-10-2006 12:04 AM
Reply to: Message 46 by randman
07-09-2006 10:13 PM


Re: Noah?
... and the facts appear to fit ...
What facts?

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This message is a reply to:
 Message 46 by randman, posted 07-09-2006 10:13 PM randman has replied

Replies to this message:
 Message 50 by randman, posted 07-10-2006 12:07 AM RAZD has replied

  
RAZD
Member (Idle past 1404 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 51 of 76 (330198)
07-10-2006 12:10 AM
Reply to: Message 44 by sfs
07-09-2006 5:07 PM


Re: Got the paper, but ...
No, there is nothing wrong with your calculation. If humans had had a panmictic population of size 1 million for their entire history, the most recent common ancestor in the maternal line would have occurred something like 1 million generations ago(*).
In other words the letter throws out figures without adjusting them for population nor mentioning that such should be done, meanwhile claiming to have solid proof of a theoretical result?
(*) There is one mistake, in fact, but it's not yours: the expected time to the MRCA for purely maternal inheritance is N/2 generations, not N generation. (Also, 20-25 years is a more realistic generation time for most of this period than 30 years.)
I had wondered about that with the result I had for my theoretical populations of 10 couples. Thanks.
On your other points, read nwr's responses. He or she understands the paper, and so far you don't.
Thanks for the kind comment. So far I don't see anything WORTH understanding, it's a flawed model.

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