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vineviz
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« Reply #100 on: August 03, 2012, 08:27:34 PM »

Also, the distribution of alleles for some haplogroups do look strongly non-normal for some STRs.

For example haplogroup I (n=5700) has the following allele distributions:

Again, this is incorrect reasoning.  That sample has a great deal of substructure, with differential reproductive success and uneven sampling.

We used to think that DYS393 was abnormally distributed in R-M269 until we discovered the substructure that explained it.
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JeanL
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« Reply #101 on: August 03, 2012, 08:31:59 PM »

Not sufficient proof, sorry.

How so? The modal values for G2a changed in at least 7 STRs in a time frame of 2000 years, if that isn't proof, then I don't know what it is.
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JeanL
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« Reply #102 on: August 03, 2012, 08:43:01 PM »

Again, this is incorrect reasoning.  That sample has a great deal of substructure, with differential reproductive success and uneven sampling.

We used to think that DYS393 was abnormally distributed in R-M269 until we discovered the substructure that explained it.

No the reasoning isn’t incorrect, there is definitely I1 and I2 subclades mixed in there, however that doesn’t stop some STRs from showing normal distributions, whereas other do not show anywhere near a normal distribution. Now, the main point on a more observable scale, is that when estimating the TMRCA of I1 and I2 one might choose a modal value of 23 for DYS390, however for all we know the allele value of their true ancestor could have been something else, for example 22 or 24. So in a sense what I am saying is that on a macro-scale this is more observable, but it does happen too on a micro-scale. The modal values of U106 and P312 differ by very little, however, that doesn’t mean that the ancestral value for those positions (STRs) that differ was either one of the modal values of either P312 or U106.  In fact it is possible for STRs that have the same modal allele values for both U106 and P312 to have a different ancestral allele value from the modal value. 
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vineviz
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« Reply #103 on: August 04, 2012, 06:13:21 AM »

No the reasoning isn’t incorrect, there is definitely I1 and I2 subclades mixed in there, however that doesn’t stop some STRs from showing normal distributions, whereas other do not show anywhere near a normal distribution.

It does stop you from being able to use that "mixed in there" data to infer whether or not the behavior of STRs is symmetrical or not.  Polluted pools of haplotype data like that are simply not useful for some purposes, like this one.

Now, the main point on a more observable scale, is that when estimating the TMRCA of I1 and I2 one might choose a modal value of 23 for DYS390, however for all we know the allele value of their true ancestor could have been something else, for example 22 or 24.

As a matter of procedure, when you use self-variance to estimate TMRCA you don't actually ever "choose a  modal value".
« Last Edit: August 04, 2012, 09:31:54 AM by vineviz » Logged
vineviz
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« Reply #104 on: August 04, 2012, 09:31:35 AM »

Not sufficient proof, sorry.

How so? The modal values for G2a changed in at least 7 STRs in a time frame of 2000 years, if that isn't proof, then I don't know what it is.
I wasn't asking for evidence that STRs mutate.  I was asking for evidence that they systematically mutate in one direction, evidence which is still lacking.
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JeanL
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« Reply #105 on: August 04, 2012, 09:51:16 AM »

I wasn't asking for evidence that STRs mutate.  I was asking for evidence that they systematically mutate in one direction, evidence which is still lacking.

That’s not what I said originally, I said that any given STR would likely attain one mutation in all its descendants in a mutational timeframe of 1/mu. I never said that it was one-directional, and I showed how in a time-frame of 2000 years the modal values of G2a changed by one mutation (either up or down) in at least 7 STR markers. So the evidence is there, and what is more, what I’m talking about, is actually a biological concept, which is called expected time for mutation. The only thing that would prevent it for happening would be total symmetry on mutation rates, however we know mutation rates are asymmetrical, because they are strongly dependant on the number of repeats, so there will always be a bias either forward or backward depending on the number of repeats of the STR. This bias is what makes the modal values change in a timeframe of 1/mu. This is what makes the STRs change, i.e.:

Avellanar Cave, Catalonia 5000 BC ==> Treilles Cave, SW France 3000 BC

DYS456:15==>14
DYS389II:29==>30
DYS385:14/14==>13/15
DYS393:13==>14
GATAH4: 12==>11
DYS448:22==>20

PS: Yeah one doesn’t choose the modal value, the modal value is the most frequent value on a distribution, hence the 50th percentile of the distribution of allele.
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vineviz
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« Reply #106 on: August 04, 2012, 10:12:24 AM »

I showed how in a time-frame of 2000 years the modal values of G2a changed by one mutation (either up or down) in at least 7 STR markers.

Actually, you showed that some G2a samples have different haploytpes than others.  Unless all modern G2a men are descended from the men buried in those caves, comparing the modal values for one ancient family to the modal values for all modern ones has no relevance to this discussion.

Anyway, even if the modal values for a population shift over time it doesn't complicate the TMRCA estimation process.
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JeanL
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« Reply #107 on: August 04, 2012, 11:50:02 AM »

Actually, you showed that some G2a samples have different haploytpes than others.  Unless all modern G2a men are descended from the men buried in those caves, comparing the modal values for one ancient family to the modal values for all modern ones has no relevance to this discussion.

What the two burials showed is not that some G2a samples have different haplotypes, but that the modal of G2a in Europe or at least SW Europe circa 5000 BC was different from the modal of G2a in SW Europe circa 3000 BC. We are taking about relatively close regions(i.e. Avellanar vs. Treilles) in space, yet their modal values changed at least in 7 STRs.  So the point wasn’t to compare those values to the values of modern day people, but to show how modals change with time. Moreover, even if modern day people aren’t descendants of those men buried on those caves, they would still share a common ancestor by the virtue of both being G2a, so here is a little experiment:
Modern modal values for European G2a+ derived clades from Rootsi.et.al.2012:

DYS456:15
GATAH4:12
DYS385:14/14
DYS393: 14
DYS448:21
DYS389II: 29

So the modal value of DYS456 went from being 15 as measured in the sample from 5000 BC, to 14 as measured in the sample from 3000 BC to 15 again in modern day European samples. Same thing happened to GATAH4, DYS385, DYS389. However it is not impossible to imagine that in between 3000 BC and present day the modal values of some of those STRs changed a couple of times. Which leads to the conclusion that modal values aren’t static with time, and that they might change due to different reasons, and bottlenecks aren’t the one reason that would change them, the expectation value is independent of demography. That is a locus with a mutation rate of mu, will attain a mutation in all its descendants in a timeframe of 1/mu regardless if the population was bottlenecking 50% of the time, or 80% of the time. So the mutational bias would manifest itself in the changes of modal throughout time. That is, if a bottleneck were to occur, the chances that the mutant would survive are small relative to the nonmutant under a model of nonmutational bias. This is mostly because the vast majority of the population at any given point in time would have the modal value whereas the offmodal values would be a minority, however the fact that the modal changes with time, which is evident in the case of G2a+ derived clades in Europe, means that the modal value is gradually shifting with time, so bottlenecks probably catalyze the shift, but unless there was a mutational bias, a bottleneck shouldn’t change the modal value of an STR, yet we see changes in modal values with time, so even if we were to attribute these changes to bottlenecks, it wouldn’t disprove that there is a directional bias in mutations which shifts the modal with time.

Anyway, even if the modal values for a population shift over time it doesn't complicate the TMRCA estimation process.


Well, it does complicate things, because for once the assumption that the modal value represents the ancestral value is one that is made. Hence why diversity is measured as a function of mutations from the so called modal value, if the modal value no longer represent the ancestral value, then the diversity measurements would lead to erroneous estimates for TMRCA. Of course, like I said before, this only happens when the MRCA of a haplogroup lived longer than the timeframe of 1/mu for any given STR. So hence why I mentioned earlier that for timeframes of 200 generations, STRs with mutation rates faster than 0.005 mut/gen could in fact have a modal value that is not the ancestral value any longer.
« Last Edit: August 04, 2012, 11:52:41 AM by JeanL » Logged
vineviz
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« Reply #108 on: August 04, 2012, 12:03:16 PM »

What the two burials showed is not that some G2a samples have different haplotypes, but that the modal of G2a in Europe or at least SW Europe circa 5000 BC was different from the modal of G2a in SW Europe circa 3000 BC.
It doesn't show this, no matter how often you repeat it.

That is a locus with a mutation rate of mu, will attain a mutation in all its descendants in a timeframe of 1/mu regardless if the population was bottlenecking 50% of the time, or 80% of the time.

No, after 1/mu only some descendants will exhibit a mutation.  On AVERAGE each will have 1 mutation:  some will have zero.  Some will have 1. Some will have 2.  And so on.
Actually, this is not quite the right way to express this.  After 1/mu about half of descendents will still have the ancestral value, either because their lineage never had a mutation or because they had multiple mutations that caused a reversion.

Well, it does complicate things, because for once the assumption that the modal value represents the ancestral value is one that is made. Hence why diversity is measured as a function of mutations from the so called modal value, if the modal value no longer represent the ancestral value, then the diversity measurements would lead to erroneous estimates for TMRCA.
This just isn't true:  it's not the way the math works.  

For one thing, there is no " assumption that the modal value represents the ancestral value." In fact, the fact that  such an assumption is NOT needed is one benefit of using variance to estimate TMRCA.

For another, directional drift in allele values (even if this happens, for which we have no evidence) would not have any impact on expressed variance.  In theory, a STR could have allele drift so strong that NO descendants have the ancestral value and STILL the TMRCA estimate would be accurate.
« Last Edit: August 04, 2012, 12:08:27 PM by vineviz » Logged
Maliclavelli
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« Reply #109 on: August 04, 2012, 12:06:17 PM »

So the modal value of DYS456 went from being 15 as measured in the sample from 5000 BC, to 14 as measured in the sample from 3000 BC to 15 again in modern day European samples.

Many thanks, JeanL. Hope that Mikewww has understood what I did mean with "mutations around the modal" and "convergence to the modal as time passes".
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Maliclavelli


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acekon
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« Reply #110 on: August 04, 2012, 12:12:13 PM »

@^^JeanL


Ditto, quite brilliant!
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Maliclavelli
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« Reply #111 on: August 04, 2012, 12:18:55 PM »

So the modal value of DYS456 went from being 15 as measured in the sample from 5000 BC, to 14 as measured in the sample from 3000 BC to 15 again in modern day European samples.

Many thanks, JeanL. Hope that Mikewww has understood what I did mean with "mutations around the modal" and "convergence to the modal as time passes".

But there is a 3rd possibility, that a mutation goes for the tangent. The actual differences amongst the haplogroups are due to this: sometimes a value is almost the same, sometimes is very different.
« Last Edit: August 04, 2012, 12:21:32 PM by Maliclavelli » Logged

Maliclavelli


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« Reply #112 on: August 04, 2012, 12:39:03 PM »

So the modal value of DYS456 went from being 15 as measured in the sample from 5000 BC, to 14 as measured in the sample from 3000 BC to 15 again in modern day European samples.

Many thanks, JeanL. Hope that Mikewww has understood what I did mean with "mutations around the modal" and "convergence to the modal as time passes".

I think we are getting the terminology for modal and ancestral values convoluted. We should keep in mind that modal values are related to a specific population measured. Naturally, the modal values may be different for different populations. Also, naturally, the TMRCAs for different populations will be different as their MRCAs were likely different people.

An SNP is just a signpost on a branch. We don't know how high or low on the branch unless we consider it context of other SNPs in the vicinity (on the tree.) The MRCA for a population with an SNP may not be the MRCA for everyone who ever had that SNP. The neat thing is all the new SNP discoveries which can help fence in how the tree grew through interclade analysis.

LOL, I've been criticized on this, but maybe there wasn't a lot of utility in what I just wrote. It's just definition based.
« Last Edit: August 04, 2012, 12:52:54 PM by Mikewww » Logged

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« Reply #113 on: August 04, 2012, 12:47:04 PM »

So the modal value of DYS456 went from being 15 as measured in the sample from 5000 BC, to 14 as measured in the sample from 3000 BC to 15 again in modern day European samples.

Many thanks, JeanL. Hope that Mikewww has understood what I did mean with "mutations around the modal" and "convergence to the modal as time passes".

But there is a 3rd possibility, that a mutation goes for the tangent. The actual differences amongst the haplogroups are due to this: sometimes a value is almost the same, sometimes is very different.

Maliclavelli, I welcome you to my place where utility is sometimes marginal. Please consider we have to laugh a bit from time to time.

@^^JeanL
Ditto, quite brilliant!

Acekon, I also welcome you to my place of marginal utility. Cheerleaders are important, too. LOL.
« Last Edit: August 04, 2012, 12:56:39 PM by Mikewww » Logged

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« Reply #114 on: August 04, 2012, 01:13:16 PM »

Maliclavelli, I welcome you to my place where utility is sometimes marginal. Please consider we have to laugh a bit from time to time.

I think that nobody may reproach me laugh, irony and even sarcasm, for what my knowledge of English permits me. “Marginal utility” is an economic theory. As to Genetics we could call “saturation”, but I prefer satisfaction.
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Maliclavelli


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JeanL
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« Reply #115 on: August 04, 2012, 01:14:03 PM »

It doesn't show this, no matter how often you repeat it.

Whatever, it does show it, but if you choose to ignore it, and go for the highly improbable alternative hypothesis, be my guest.

Actually, this is not quite the right way to express this.  After 1/mu about half of descendents will still have the ancestral value, either because their lineage never had a mutation or because they had multiple mutations that caused a reversion.

In theory that doesn’t happen, nor in practice, let me put it this way, assuming the most probable scenario, after a time of 1/mu the vast majority of the descendants would not have the ancestral value, and this is coming from actually doing computer simulations, not just talking about it. For example if a locus has a mutation of 1/10 or 0.01 mutations per generation, and an individual has 10 offsprings, then the expectation is that then at least one of them will have a mutation. Then on the next generation each one of the 10 offsprings have 10 offsprings, for the 9 nonmutant offsprings, there is an expectation that each would produce 1 mutant offsprings, so we will have 9 mutant offsprings in the second generation, now for the mutant offspring there is an expectation that he will produce 9 offspring which carry his mutation, and 1 which will carry a new mutation, which could be either back to the ancestral value or forward to a new value. So in the second generation instead of having 10 mutants offspring as would be expected for a population size of 100, we will have 18 offsprings which would carry at least one mutation. Now you carry this for 10 generations and one would see how the majority of the population after the 10 generations would no longer carry the ancestral value.

This just isn't true:  it's not the way the math works. 

Really!!! I would politely differ.


For one thing, there is no " assumption that the modal value represents the ancestral value." In fact, the fact that  such an assumption is NOT needed is one benefit of using variance to estimate TMRCA.

Then we must be talking about different methodologies, because for once, one of the things assumed when calculating TMRCA is that the modal value represents the ancestral value, so a measure of how many haplotypes are different from the modal on average times the mutation rate of the haplotypes would give us the TRMCA. Now if the reference frame is wrong, then the measurements are wrong, because what would count as 1 mutation could in fact be 2, and more over the vast majority of people that have the modal value would in fact count as 1 mutation or more, so there is a large amount of variance that is being ignored.

For another, directional drift in allele values (even if this happens, for which we have no evidence) would not have any impact on expressed variance.  In theory, a STR could have allele drift so strong that NO descendants have the ancestral value and STILL the TMRCA estimate would be accurate.

Well, let me put it this way, in your theory that could happen, in the theories I have studied that doesn’t happen, and expected mutation time is a very real concept, and in computer simulations (Using an expanding population under a Wright-Fisher model) that TMRCA does get undermined, so it is not drift, is about probabilities, and I feel we are going into a dead end, because you seem to be unfamiliar with the concepts I am talking about, so we are just going in circles. So it is not about drift, drift occurs mostly on autosomal DNA, on the SNPs, SRTs on Y-chromosomes behave like haploids, well they are haploids. So it’s not so much that they undergo drift, but that under a Gaussian probability model, each lineage under a tree is expected to attain a mutation in a time frame of 1/mu under a mutational bias model.
« Last Edit: August 04, 2012, 01:26:11 PM by JeanL » Logged
vineviz
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« Reply #116 on: August 04, 2012, 02:07:21 PM »

In theory that doesn’t happen, nor in practice, let me put it this way, assuming the most probable scenario, after a time of 1/mu the vast majority of the descendants would not have the ancestral value, and this is coming from actually doing computer simulations, not just talking about it.

Instead of playing word games, why don't you just make the computations instead?  You'd see where you are making your mistakes, I think, instead of relying on me to point them out.

In this case, the number of expected mutations per lineage in a pool of descendants  after time 1/mu is indeed 1.

It is also the case that roughly half of the descendants will still have the ancestral value. How can this be, you ask?  Why let me tell you: back mutations.

Some lineages will have experienced no mutations at all ( a little less than 40% fall in this category)

Some lineages will have experienced precisely one mutation (a little less than 40% fall in this category)

Some lineages will have experienced two or more mutations (about 25%, or so).  Among these, some lineages will have experienced reversing ("back" mutations).

The end result is that after time 1/mu the average number of mutations per descendant is 1, the percentage of descendants with the ancestral allele is a little less than 50%, and the percentage of lineages with at least one mutation is about 65%.

Then we must be talking about different methodologies, because for once, one of the things assumed when calculating TMRCA is that the modal value represents the ancestral value, so a measure of how many haplotypes are different from the modal on average times the mutation rate of the haplotypes would give us the TRMCA.

That's simply not an accurate description of how variance-based methods are performed. 

You take the variance of the alleles observed in the present, divide by mu, and get the TMRCA estimate.  That's it.  Done.  The mean allele is implicitly used in the variance calculation, but not because it is presumed to be the ancestral value, and the mode is never used implicitly or explicitly.
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acekon
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« Reply #117 on: August 04, 2012, 02:41:49 PM »

@Mikewww

LOL, for sure I'm not the sharpest tool in the shed.LOL.

Get out of JeanL's way- Timberrrrr, LOL

http://www.crowntreesurgeons.co.uk/enlarged/image1257264023.jpg

http://www.youtube.com/watch?v=WCgkEGeBNz0

All the calculations are in flux, including the anchors. Wrong 5000 year old anchor[or cherry picked to format preconceived ideas or bias] in str's, wrong conclusion[wrong input, wrong output].

You know I married an Irish girl. For example [membrane transport protein of uncertain specificity (CO2 or NH3) and unknown physiological role] the deletion or mutation p36.13-p34.3 [20k-30k?] would also change infant mortality rates, and by extension models of mutation. Fortunately I also carry the mutation and she did not have to take any mercury base shots.
« Last Edit: August 04, 2012, 02:55:20 PM by acekon » Logged

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JeanL
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« Reply #118 on: August 04, 2012, 02:46:17 PM »


Instead of playing word games, why don't you just make the computations instead?  You'd see where you are making your mistakes, I think, instead of relying on me to point them out.

I have done computer simulations, and plenty of them, and I’m not relying on you to point anything out, it’s become clear that you are ignorant of certain biological concepts, and like I said before we will just be going in circles.

In this case, the number of expected mutations per lineage in a pool of descendants  after time 1/mu is indeed 1.
It is also the case that roughly half of the descendants will still have the ancestral value. How can this be, you ask?  Why let me tell you: back mutations.

Not really, like I said before under a mutational bias model that would not hold true, however under a neutral model the modal value wouldn’t change with time, but that is not what is observed in aDNA, and that is not what is observed in computer simulations.

Some lineages will have experienced no mutations at all ( a little less than 40% fall in this category)

Some lineages will have experienced precisely one mutation (a little less than 40% fall in this category)

Some lineages will have experienced two or more mutations (about 25%, or so).  Among these, some lineages will have experienced reversing ("back" mutations).

Where are you pulling those numbers from? Did you miss the explanation I gave you, here let me reiterate it, one individual has 10 offsprings, and one of the locus has a mutation rate of 0.5 that is ½ chances of mutating per generations per offspring. So after one generation 5 offsprings are mutant, 5 are non mutant, then on the second generation the 5 offsprings that are mutant each have 5 offsprings that are mutant, and 5 offsprings that are nonmutant, the same thing happens to the offsprings that are nonmutant. Even if we assume that all mutations that happened to the offsprings of the mutant people are back mutations, then it would still give 50/100 mutants offsprings after two generations, hence why the vast majority of offsprings would not have the ancestral value. Of course that is under the unlikely scenario that all mutations on the mutant offsprings back mutate, when in reality some of them could back mutate while others would mutate forward.

The end result is that after time 1/mu the average number of mutations per descendant is 1, the percentage of descendants with the ancestral allele is a little less than 50%, and the percentage of lineages with at least one mutation is about 65%.


http://i1133.photobucket.com/albums/m582/jeanlohizun/Simulation-Fig1.jpg

What you are seeing is the allele distribution of a computer simulation. The demography is as follows, the  ancestral value is 8, the forward mutation rate is 0.5, that is 1 in 2 chances of mutating per generation per offsprings, the backward mutation rate is 0.4, thus producing a mutational bias of ~0.1 foward. The population expands for 10 generations, the expansion takes places for the first two generations (that is expected number of offsprings>1 for the first two generations), and then for the other 8 the population stabilizes to a constant population size (that is expected number of offsprings=1), all expectations are modeled as Poisson distributions. At the end of the experiment 200 individuals are randomly collected, and their allele values are analyzed in the histogram shown above. What it is observed is that the most frequent value, that is a 9, is actually 1 mutation away from the ancestral value, which was 8, only 40 individuals out of 200 individuals retained the ancestral value, so 20% of the population, that is nowhere near half.

That's simply not an accurate description of how variance-based methods are performed. 

You take the variance of the alleles observed in the present, divide by mu, and get the TMRCA estimate.  That's it.  Done.  The mean allele is implicitly used in the variance calculation, but not because it is presumed to be the ancestral value, and the mode is never used implicitly or explicitly.

Ok here is the problem, if you refer to most studies out there, you will see that when they say variance they refer to average number of mutations per marker or per haplotype, measured from the most frequent haplotype. So mutation rates are calibrated based upon that assumption, that the modal haplotype represents the ancestral haplotype, hence mutations away from the modal can be used as a measurement of time. Now if you mean variance as in the standard deviation of a set squared, again, the mean value is still being used to calculate the standard deviation, and you are assuming that the normal distribution describes the model, when in fact, if the modal value=/= ancestral value, then mutations do not occur as measured from the center value, so your mean (That is the ancestral value from which you would measure the number of mutations) would be different, and hence your standard deviation would be greater, and hence the variance would be greater. So in a nutshell what I am saying is that in order to use the calibrated mutation rates, the number of mutations that have occured with time should be measured from the ancestral value, if the values that are the 50th percentile aren't the ancestral, then the real mean value would be different, thus causing the distribution to be skewed relative to the ancestral value.
« Last Edit: August 04, 2012, 02:56:56 PM by JeanL » Logged
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« Reply #119 on: August 04, 2012, 02:52:29 PM »

@Mikewww
LOL, for sure I'm not the sharpest tool in the shed.LOL.
Get out of JeanL's way- Timberrrrr, LOL
http://www.youtube.com/watch?v=WCgkEGeBNz0

I tried your youtube link and got a blank screen with static. It said "An error occurred. Please try again later."  It is probably more appropriate than you imagined, but since our utility (as cited per B.S for me)  is limited, I agree, let's get out of the way. No need for cheerleading.
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vineviz
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« Reply #120 on: August 04, 2012, 03:34:10 PM »

Not really, like I said before under a mutational bias model that would not hold true, however under a neutral model the modal value wouldn’t change with time, but that is not what is observed in aDNA, and that is not what is observed in computer simulations.

Maybe if you program the simulations with a directional bias, as you described.

Where are you pulling those numbers from?

They are the only possible outcome of a normal (or Poisson) distribution for a single marker after time 1/mu.

If your simulations are giving you different outputs, they are either wrong or designed to produce a non-normal distribution.


What it is observed is that the most frequent value, that is a 9, is actually 1 mutation away from the ancestral value, which was 8, only 40 individuals out of 200 individuals retained the ancestral value, so 20% of the population, that is nowhere near half.
Because you rigged your simulations with a directional bias, of course.

And given the logical errors in your examples, I'm not willing to trust that you wrote the simulation correctly in other ways either.

Ok here is the problem, if you refer to most studies out there, you will see that when they say variance they refer to average number of mutations per marker or per haplotype, measured from the most frequent haplotype.

Strawman.  WHICH studies say that?  If you quote and cite one that does, I'll show you how it is wrong.

I'll give you a counter pre-emptively:  

Quote
Expansion times and their standard deviations (SDs) were calculated using 11 STRs (DYS19, DYS389I, DYS389II DYS390, DYS391, DYS392, DYS393, DYS437, DYS438, DYS439, and DYS460), whose mutation rates have been individually es- timated (Gusmao et al. 2005). The allelic variance of each STR was divided by the estimated mutation rate, and the mean of the variances was multiplied by 25 (intergeneration time in years).

Genetic and Demographic Implications of the Bantu Expansion: Insights from Human Paternal Lineages
Berniell-Lee et al.
http://mbe.oxfordjournals.org/content/26/7/1581.full.pdf+html

You'll find no shortage of authors who do it the same way.
« Last Edit: August 04, 2012, 03:35:21 PM by vineviz » Logged
vineviz
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« Reply #121 on: August 04, 2012, 04:28:27 PM »


Ok here is the problem, if you refer to most studies out there, you will see that when they say variance they refer to average number of mutations per marker or per haplotype, measured from the most frequent haplotype.

Strawman.  WHICH studies say that?  If you quote and cite one that does, I'll show you how it is wrong.

You may be thinking of the description sometimes provided by authors who cite Goldstein et al.

These folks are using ASD, which is a similar calculation but not necessarily the same as using self-variance (which has the advantage I mentioned earlier of not requiring an assumption about ancestral values).
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acekon
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« Reply #122 on: August 04, 2012, 05:46:07 PM »

Uncalled for on my part!
« Last Edit: August 05, 2012, 05:07:54 PM by acekon » Logged

YDNA: R-Z2105* Śląsk-Polska
MtDNA: U5b2a2*Königsberg-Ostpreussen
JeanL
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« Reply #123 on: August 04, 2012, 06:23:33 PM »

Maybe if you program the simulations with a directional bias, as you described.

But there is a directional bias, have you missed the discussion where I mentioned that under a neutral model, the modal values of a haplogroup wouldn’t change with time, yet they do. Also, the fact that mutation rates depend on repeat number, the higher the repeat number the higher the mutation rate for the most part, so yes, in essence there is a directional bias.

They are the only possible outcome of a normal (or Poisson) distribution for a single marker after time 1/mu.

If your simulations are giving you different outputs, they are either wrong or designed to produce a non-normal distribution.

Well for once a Normal or Gaussian distribution isn’t the same as a Poisson distribution for small values, but setting that aside, if we take into account a directional bias, which I have shown that exists, then there is an expectation for a mutation to occur in a timeframe of 1/mu, where this mu is the resulting directional bias, that is, mu=~0.1 for a set that has a forward mutation of 0.5 and a backwards mutation of 0.4. So my simulations are designed to produce realistic results based upon the known concepts of directional bias.  BTW the allele distribution produced at the end, was very clearly a normal distribution, centered around 9, in case you missed it.

Because you rigged your simulations with a directional bias, of course.

And given the logical errors in your examples, I'm not willing to trust that you wrote the simulation correctly in other ways either.

I couldn’t care less what you are willing to trust or not, I never hid that there was a directional bias, and when I said a 1/mu timeframe, I meant the resulting mutational bias.

Strawman.  WHICH studies say that?  If you quote and cite one that does, I'll show you how it is wrong.

I'll give you a counter pre-emptively: 

Quote
Expansion times and their standard deviations (SDs) were calculated using 11 STRs (DYS19, DYS389I, DYS389II DYS390, DYS391, DYS392, DYS393, DYS437, DYS438, DYS439, and DYS460), whose mutation rates have been individually es- timated (Gusmao et al. 2005). The allelic variance of each STR was divided by the estimated mutation rate, and the mean of the variances was multiplied by 25 (intergeneration time in years).

Genetic and Demographic Implications of the Bantu Expansion: Insights from Human Paternal Lineages
Berniell-Lee et al.
http://mbe.oxfordjournals.org/content/26/7/1581.full.pdf+html

You'll find no shortage of authors who do it the same way.

Myres.et.al.2010 study supplementary Table-2 , column F says “Avg Var”, yet if you calculate it, you see, average variance is calculated from the median haplotypes of each populations, hence the average variance is calculated as the average value mut/marker or mut/haplotype. Also, yes I am aware that the method is called the ASD(Average-Squared-Distance), here is what Busby.et.al.2011 says about ASD:

Quote from: Busby.et.al.2011
While acknowledging uncertainty, researchers usually report the age of Y chromosome lineages based on differences between individuals across multiple STRs, often using average squared distance (ASD) or related summary statistics [25,26] as unbiased estimators of coalescence time, T.

So there you have it, the ASD methodology, which does make use of the modal values is the most commonly used method. In fact when mutation rates are calibrated using pedigrees the ASD method is used, so those mutation rates couldn’t be used in a different method. Now measured mutations rates from father-son pairs have the issue that mutation rates depend on repeat number, and also that you are measuring a mutation across a generation, so once more, if the mean, median, modal, or whatever you want to call it, isn’t the ancestral value, then the variance would be undermined. Yes the median value is a mathematical concept, yes in this case under the assumption of a normal distribution that would be the correct value to use, but the point is, that when the modal changes with time the true distribution of mutations isn’t normal, because what you are counting as 0 mutations could in fact be -1 or 1, so it wouldn’t be a normal distribution centered around 0 mutations, but a normal distribution centered around -1 or 1 mutations.
« Last Edit: August 04, 2012, 06:23:59 PM by JeanL » Logged
vineviz
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« Reply #124 on: August 04, 2012, 09:34:50 PM »

But there is a directional bias, have you missed the discussion where I mentioned that under a neutral model, the modal values of a haplogroup wouldn’t change with time, yet they do. Also, the fact that mutation rates depend on repeat number, the higher the repeat number the higher the mutation rate for the most part, so yes, in essence there is a directional bias.

You've mentioned a lot of things that aren't true, and this is one.  Modal values of populations change for a host of reason, including genetic drift.


Myres.et.al.2010 study supplementary Table-2 , column F says “Avg Var”, yet if you calculate it, you see, average variance is calculated from the median haplotypes of each populations, hence the average variance is calculated as the average value mut/marker or mut/haplotype.
No, variance is not the same as counting mutations.  It is counting squared differences.  The distinction matters mathematically a great deal.

So there you have it, the ASD methodology, which does make use of the modal values is the most commonly used method.

You quoted one study which says it does NOT use the mode, then claim it uses the MEDIAN, all in support of a conclusion that MODE is the most commonly used method. You aren't making sense.

Besides, as I said before, it doesn't matter.  If Busby is calculating TMRCA wrong, then so what?  I'm not using his conclusions and neither are you.  My point originally was that TMRCA estimates using strict self-variance calculations are not influenced by any of this.  The variance provides a TMRCA estimate that is not affected in the least by any sort of directional bias, even if such a bias even existed.
« Last Edit: August 04, 2012, 09:35:37 PM by vineviz » Logged
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