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Author Topic:   Extent of Mutational Capability
PaulK
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 Message 256 of 279 (798861) 02-06-2017 1:52 AM Reply to: Message 255 by CRR02-06-2017 1:23 AM

Re: The Maths
Yes, I am sure.

Consider a timed race where the competitors start at fixed intervals. During the period in which the competitors are finishing the number that arrive within any particular sub-period has very little to do with the time taken to complete the course.

quote:

Say we are looking at a period of 100 generations with 100 mutations expected to be fixed from generation 1.
If the mean time to fixity is 100 generations then we would expect 50 of those mutations to be fixed in the time available.
If the mean time to fixity is 1000 generations then very few, possibly none, of those mutations will be fixed in the time time available.

The thing you are missing is that we are not restricted to those mutations. As I pointed out earlier there will be mutations from earlier generations moving to fixation. Ignoring them will obviously underestimate the number that are fixed.

quote:

The number of mutations that are expected to be fixed within the time period DEPENDS on the time to fixity

In fact it does not. You really shouldn't be accusing others of failing to understand the subject when you don't understand it yourself.

The more so, since the number expected to be fixed is clearly the right answer, while your argument is obviously wrong.

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Taq
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 Message 257 of 279 (798913) 02-06-2017 12:45 PM

Probabilities
The statistical models within population genetics "aren't my bag", so I thought I would pose a few questions to see if my limited understanding is correct.

Let's say that the mean probability of winning the Powerball lottery is about 1 in 150 million. We already know that the vast majority of winners did not buy 150 million tickets before they won. In fact, most winners probably bought less that 500 tickets in their life time, some much fewer. When you get enough people buying tickets you can have very rare or highly improbably things happen well away from the mean.

Would this also apply to the fixation of alleles? Each human is born 50 mutations. In a population of just 1 million, that is 50 million mutations in a single generation. With that many mutations isn't it possible for many of those mutations to reach fixation in a much shorter time frame than the mean fixation rate?

Edited by Taq, : No reason given.

Edited by Taq, : No reason given.

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 Message 258 of 279 (798928) 02-06-2017 3:44 PM Reply to: Message 255 by CRR02-06-2017 1:23 AM

Re: The Maths
 If the mean time to fixity is 100 generations then we would expect 50 of those mutations to be fixed in the time available.

I'm not sure that that can be right, even if it was relevant.

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 Message 259 of 279 (798993) 02-06-2017 7:50 PM Reply to: Message 258 by Dr Adequate02-06-2017 3:44 PM

Re: The Maths
I was right. The correct figure appears to be approximately 61%, independent of population size.
 This message is a reply to: Message 258 by Dr Adequate, posted 02-06-2017 3:44 PM Dr Adequate has not yet responded

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 Message 260 of 279 (799008) 02-06-2017 9:42 PM Reply to: Message 257 by Taq02-06-2017 12:45 PM

Re: Probabilities
 Would this also apply to the fixation of alleles? Each human is born 50 mutations. In a population of just 1 million, that is 50 million mutations in a single generation. With that many mutations isn't it possible for many of those mutations to reach fixation in a much shorter time frame than the mean fixation rate?

Well, ~61% do. This is because there is a lower limit on how long an allele can take to fixation, but no upper limit. Some of them are going to take a really long time. Because the time is large, they will contribute a lot to the mean time even though they are few in number.

Here's the results of a computer simulation of 10000 fixation events. The blue line shows where the mean time to fixation is.

CRR is making the not uncommon mistake of supposing that the mean must be the median.

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caffeine
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 Message 261 of 279 (799132) 02-07-2017 3:24 PM Reply to: Message 257 by Taq02-06-2017 12:45 PM

Re: Probabilities
 Would this also apply to the fixation of alleles? Each human is born 50 mutations. In a population of just 1 million, that is 50 million mutations in a single generation. With that many mutations isn't it possible for many of those mutations to reach fixation in a much shorter time frame than the mean fixation rate?

While some would go to fixation quicker than the mean, wouldn't a larger population mean it's harder for any mutation to go to fixation? A mutation is much more likely to be fixed (or lost) in a small population than a large one, isn't it? Am I missing something obvious?

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Taq
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 Message 262 of 279 (799142) 02-07-2017 5:38 PM Reply to: Message 261 by caffeine02-07-2017 3:24 PM

Re: Probabilities
 caffeine writes:While some would go to fixation quicker than the mean, wouldn't a larger population mean it's harder for any mutation to go to fixation? A mutation is much more likely to be fixed (or lost) in a small population than a large one, isn't it? Am I missing something obvious?

That's a good point as well. If the probability of an allele reaching fixation is 1/n, where n is the population size, then a large population would decrease the probability of any single allele reaching fixation. I believe this is why population bottlenecks can fix many neutral alleles in a short amount of time.

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 (1)
 Message 263 of 279 (799146) 02-07-2017 7:30 PM Reply to: Message 261 by caffeine02-07-2017 3:24 PM

Re: Probabilities
 While some would go to fixation quicker than the mean, wouldn't a larger population mean it's harder for any mutation to go to fixation?

Note that in the end every new mutation will either be lost or fixed.

Now the chances of it being lost are proportional to the population size.

But so is the number of new mutations in the population per generation.

Hence the rate is independent of population size: the rate at which mutations are fixed in the population is equal to the rate at which they occur in the individual.

(Of course, this only applies to neutral mutations, but quantitatively those are the important ones.)

Edited by Dr Adequate, : No reason given.

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CRR
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 Message 264 of 279 (799192) 02-07-2017 11:24 PM Reply to: Message 260 by Dr Adequate02-06-2017 9:42 PM

Re: Probabilities
You're right about mean vs median but apart from that there are no surprises. In round numbers you can say the minimum time to fixity is about Ne and the curve asymptotically approaches the x-axis.

There is a similar shaped curve for income distribution with the result that about 60% earn less than the average.

As an example then let's say we have a population of Ne=90,000 and a period of 360,000 (4Ne) generations. (About 7.2 million years at 20 years/generation)

If each member has ~100 new random mutations then the total number that will eventually reach fixation is 100*360,000=36,000,000.

But how many will actually be fixed in that period?

Essentially no mutations occurring in the last 90,000 generations will achieve fixation. Of the mutations in the first generation 60% of those that will eventually reach fixation will actually be fixed. A lower proportion will be fixed for each succeeding generation reaching 0% at 270,000 generations. Approximating this as a linear relationship we get
Number fixed=60% * 3/4 * 1/2 ≈ 23%. That is, of the 36 million mutations generated during this period, that are expected to eventually reach fixation, only 23% will actually be fixed by the end of the period.

This number will also fall if the population size is larger. For a population size Ne=360,000 almost none of the potentially fixed mutations will actually be fixed within the time period.

Immediately after separation of a parent population into two separate species there will of course be a pool of mutations common to both species. Some of these will be fixed in both, and some will be lost in both, so that they will not produce any genetic difference between the species. Some however will be fixed in one OR the other and will then contribute to the genetic difference. How much difference will this make? I don't know and so far none of the respondents has shown they know either. But it's not sufficient to simply assume it will supply any shortfall, or that it will be insignificant.

How many new mutations are there for each of us? According to https://en.wikipedia.org/wiki/Mutation_rate it is around 64 new mutations per generation, so the figure of 100 used above is an upper bounds estimate.

So the original question was whether genetic drift could account for the genetic difference between humans and chimps. I have shown that the simplistic calculation given back at #176 does not stack up.

The calculation would have to include realistic mutation rates, population sizes, times to fixation, and pre-loading of mutations from the common ancestral population. All these factors are relevant. Maybe there is a PhD in here for someone.

My basic calculations given above suggest to me strongly that genetic drift over ~7 million years would not explain the bulk of genetic differences. Some estimates suggest the last common ancestor was as far back as 13 million years but I don't think even that will salvage the situation. Now I could be wrong, but you'll have to do much better than so far to convince me.

However even this does not address the other question of non-homologous genes in each species. In the human Y chromosome 20% have no homologue anywhere in the chimp genome. Overall the figure is about 10%. Similarly chimps have about 10% of their genes that have no homologue in humans.

 This message is a reply to: Message 260 by Dr Adequate, posted 02-06-2017 9:42 PM Dr Adequate has responded

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 Message 265 of 279 (799193) 02-07-2017 11:52 PM Reply to: Message 264 by CRR02-07-2017 11:24 PM

Re: Probabilities
So, you can't find anything you even think is wrong with my second argument?
 This message is a reply to: Message 264 by CRR, posted 02-07-2017 11:24 PM CRR has not yet responded

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 Message 266 of 279 (799195) 02-08-2017 12:24 AM Reply to: Message 264 by CRR02-07-2017 11:24 PM

Re: Probabilities
Well, there are a number of problems with this.

Problem 1

You write:

 My basic calculations given above suggest to me strongly that genetic drift over ~7 million years would not explain the bulk of genetic differences.

But you also write:

 Immediately after separation of a parent population into two separate species there will of course be a pool of mutations common to both species. [...] How much difference will this make? I don't know.

So your calculations involve ignoring a number of unknown size --- unknown except that you treat it as though it's zero when it certainly isn't.

Problem 2

Your choice of population size is arbitrary. You make no attempt to take into account the bottlenecks evidenced in the human population. What effect would they have? You don't know.

Problem 3

Because of one line in a Wikipedia article, you take 100 mutations/generation to be an "upper limit". But in fact there are scientific methods that give higher figures. See the first method given here, for example. (Obviously we can make no use of the second.)

Problem 4

You treat the length of time from the split as though it was fixed. It could be millions of years bigger.

---

Can anyone do better? I don't know. But given these four uncertainties, what we can say is that the range of figures we could get in theory includes the number we measure in practice. We're in the right ballpark. And unless and until the uncertainties can be reduced in such a way that theory can be shown to differ from practice, this is sufficient to provisionally conclude that the genetic distance between humans and chimps was produced by known real processes and not unknown magical ones.

---

Now, can you find any faults with my second argument?

 This message is a reply to: Message 264 by CRR, posted 02-07-2017 11:24 PM CRR has responded

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CRR
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 Message 267 of 279 (800753) 02-27-2017 2:37 PM Reply to: Message 266 by Dr Adequate02-08-2017 12:24 AM

Re: Probabilities
1. I didn't ignore it and I acknowledged it was greater than zero, however it is unlikely to make up the deficit required. So far you have not shown otherwise.

2. There WAS was a bottleneck about 4500 year ago when the human population was reduced to 3 breeding pairs. I did acknowledge the effect on variations in population size, however from the literature you can pick and choose the extent and duration of the bottleneck.

3. Your Sandwalk reference makes interesting reading. He acknowledges that MEASURED rates are well below 100 but argues for the higher figure so that the evolutionary story will work.

4. Indeed, and I said as much. "... but I don't think even that will salvage the situation. Now I could be wrong, but you'll have to do much better than so far to convince me."

I have already responded to your 2nd argument which I have said supports the idea of genetic entropy better than common ancestry.

 This message is a reply to: Message 266 by Dr Adequate, posted 02-08-2017 12:24 AM Dr Adequate has responded

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PaulK
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 Message 268 of 279 (800755) 02-27-2017 2:57 PM Reply to: Message 267 by CRR02-27-2017 2:37 PM

Re: Probabilities
1) according to the estimate of mean time to fixation provided by you the vast majority of genes fixed by drift should be variations found in the ancestral population. Your claim that it would "probably" be insufficient lacks any real support and cannot stand. The fact that you chose to do the wrong calculation despite the explanations hardly stands in your favour either.

2) the figure you give is almost certainly far too low and too recent.

3) your assessment dishonestly leaves out the fact that the indirect measurements are more reliable and give the higher numbers. Did you really think you could get away with that ?

4) given that you have to intentionally underestimate the number of mutations that would be fixed it is pretty obvious that your opinion is worthless on this, too.

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CRR
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 Message 269 of 279 (800757) 02-27-2017 3:37 PM Reply to: Message 268 by PaulK02-27-2017 2:57 PM

Re: Probabilities
1. " the vast majority of genes fixed by drift should be variations found in the ancestral population."

True, but it doesn't solve the problem. Mutation fixed or lost in BOTH populations will not contribute to differences between the populations. A mutation that is at 50% probability of being fixed has a probability of 25% of being fixed in both, 25% of being lost in both, and 50% of being fixed in one and lost in the other; and this is as good as it gets.

A mutation that is at 90% probability of being fixed has a probability of 81% of being fixed in both, 1% of being lost in both, and 18% of being fixed in one and lost in the other, eventually.

Actually there is a good chance that many will be neither fixed nor lost within the time available.

3. Since when are indirect measurements (estimates) more reliable than direct measurements? Did you really think you could get away with that?

4. Since my figures are based on published measurements they are not an intentional underestimate.

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PaulK
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 Message 270 of 279 (800758) 02-27-2017 4:03 PM Reply to: Message 269 by CRR02-27-2017 3:37 PM

Re: Probabilities
1) just saying that it won't solve the problem without any valid argument is mere assertion. And your calculation is meaningless without knowing how many mutations are available.

3) when the direct measurement is only partial and has to be extrapolated - or you could actually try reading the article. And yes, I do think I can "get away" with accurately representing it.

4) your calculation of the number of mutations to be fixed is an intentional underestimate which doesn't even try to be correct.

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