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Author Topic:   On the proportion of Nucleotides in the Genome and what it can tell us about Evolutio
Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 10 of 61 (524322)
09-15-2009 8:35 PM
Reply to: Message 9 by Wounded King
09-15-2009 7:02 PM


Another important consideration is that a lot of the genome is made up of highly repetitive sequences, so the composition of those repeated elements could heavily influence the makeup of the whole genome.
I was thinking that, but I couldn't find anything that tells me what the repeated sequences are.

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 12 of 61 (524333)
09-15-2009 11:15 PM
Reply to: Message 1 by slevesque
09-15-2009 5:13 PM


2- Does anyone have more information on such proportions from other species ? The more information we have, the more interesting this will be.
I found something that might interest you. Here's a table of 899 bacterial species. The figures in the row on the far right of the table are the AT content of the bacteria given as a percentage. This ranges from 83.4% to 25.1%.
And here are 67 species of archaea. The AT content ranges from 72.4% to 34.1%.
They don't seem to have eukaryotes, which is a shame.
Edited by Dr Adequate, : No reason given.

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 13 of 61 (524341)
09-15-2009 11:50 PM
Reply to: Message 1 by slevesque
09-15-2009 5:13 PM


Statistics --- ur doin it rong
Anyhow, as I hope everyone that will join this discussion knows, statistics is a very interesting subject. One of the properties of a random sequence is that, given enough repetitions, it will always tend to go towards a certain %. I may not be clear, so here is an example:
_ If I flip a coin for a very long time, the amount of heads and tails I should register should be close to 50% each.
Now, if we start with a simplistic model of mutations where they are a totally random and apply this fact, then given enough time and mutations, the % of each nucleotides in the genome should tend towards 25%.
No, wait a moment.
Given your assumptions about mutation and selection (which, as WK and others have pointed out, might be incorrect) you're still doing the statistics wrong. Because what you're describing is a random walk.
Think about coin-tossing again. It is true that if you keep tossing the coin, the ratio of heads divided by tails will tend to 1. But it is not true that the difference of heads minus tails will tend to 0. It doesn't particularly tend to anything.
In your selectively-neutral model, then, the AT content will simply go on a random walk as time goes by. We expect its average value over time to be 50%, but we have no grounds for thinking that it will have this value at any particular time (such as now) still less that it will tend to this value, or indeed to any value.

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 16 of 61 (524363)
09-16-2009 8:03 AM
Reply to: Message 14 by Peepul
09-16-2009 6:06 AM


Re: Statistics --- ur doin it rong
I think it does Dr A - the expectation value of the excess of heads or tails is the square root of n, where n is the number of tosses
My emphasis.
Do we not expect any particular random walk to meet the heads = tails axis infinitely many times as n tends to infinity?
Especially bearing in mind that this particular random walk has a floor and a ceiling.
But thanks for telling me that, 'cos I'd been wondering what the function was. Do you have a reference? But I'm not sure that it's relevant to my point.
Edited by Dr Adequate, : No reason given.
Edited by Dr Adequate, : No reason given.

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Replies to this message:
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 Message 28 by Dr Jack, posted 09-16-2009 11:01 AM Dr Adequate has replied

  
Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 18 of 61 (524369)
09-16-2009 8:42 AM
Reply to: Message 17 by Dr Jack
09-16-2009 8:17 AM


Re: Statistics --- ur doin it rong
The median number of times for a sequence of heads and tails to cross the zero line is 0, with all higher numbers occur with decreasing probibility.
How can zero be the median?
The reason for this is quite obvious if you think about it: because all future flips occur independently of those flips that have already happened, the chances are that there will not be a trend reversing any initial discrepency from zero.
No trend, certainly.
What of it?
---
I think you're still confusing the average difference from zero as n tends to infinity with the path of a particular random walk.
---
In any case, we are here discussing a random walk with a floor and a ceiling.

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Replies to this message:
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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 21 of 61 (524393)
09-16-2009 10:37 AM
Reply to: Message 19 by jacortina
09-16-2009 9:21 AM


Re: Statistics --- ur doin it rong
Talking about the median in this context actually means (the way I see it) comparing multiple sequences of coin flipping.
One might call it the "mean median".
If, in each of five sequences, the number of times the zero-difference point is crossed are (0,0,0,2,5), the median is zero. With six sequences (0,0,0,0,3,4), the median is also zero.
Zero can certainly be the middle number of an ordered set with an odd number of members or the average of the two middle numbers of an ordered set with an even number of members.
Basically, claiming a zero median is claiming that more than half the time, a sequence will NOT cross the zero-difference line.
How can zero be the median?
Talking about the median in this context actually means (the way I see it) comparing multiple sequences of coin flipping. If, in each of five sequences, the number of times the zero-difference point is crossed are (0,0,0,2,5), the median is zero. With six sequences (0,0,0,0,3,4), the median is also zero.
Zero can certainly be the middle number of an ordered set with an odd number of members or the average of the two middle numbers of an ordered set with an even number of members.
Basically, claiming a zero median is claiming that more than half the time, a sequence will NOT cross the zero-difference line.
Right, that's exactly what is being claimed. Now let's think this through.
In the first two tosses of the coin, we will either get HH or TT, in which case we will not meet the h = t axis --- or we will get HT or TH, in which case we will meet the h = t axis.
So after just the first two flips of the coin, it's fifty-fifty that we shall have met the h = t axis once.
Now, further flips of the coin can only increase, not reduce, the probability that we meet the h = t axis at least once.
Therefore, for n > 2, the "mean median" cannot be zero.

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 24 of 61 (524396)
09-16-2009 10:44 AM
Reply to: Message 20 by Dr Jack
09-16-2009 9:59 AM


Re: Statistics --- ur doin it rong
Sorry, I meant mode. My bad.
Oh, now you're going to bring the mode into this?
Apart from wondering why, I'd like to see your reasoning.
No, I'm not. More paths will not ever cross the zero line than any other particular number of crosses; what is more as the number of crosses increases, the number of paths that have that number of crosses decreases.
I didn't follow that.
Let me talk about the mean. You remember that, the thing we use when doing statistics and talking about expected values?
Well, rather than figure it out from first principles, I just got my computer to toss lots of coins for me.
Each number in the right hand column is the mean of a thousand trials.
number of coin tosses    number of times heads - tails = 0

2:                         0.500
4:                         0.853
8:                         1.438
16:                        2.360
32:                        3.644
64:                        5.165
128:                       8.226
256:                      11.866
512:                      17.422
1024:                     23.681
2048:                     34.958
4096:                     52.290
8192:                     72.220
16384:                   101.483
32768:                   139.231
65536:                   201.394
131072:                  275.738
262144:                  420.173
524288:                  560.344
1048576:                 826.211
I therefore stand by my claim that the number of times we'll meet the h = t axis will indeed tend to infinity with the number of coin tosses.
If you would like to dispute that, perhaps you could try thinking for a few moments about where, in that case, the asymptote would be.
Edited by Dr Adequate, : No reason given.
Edited by Dr Adequate, : No reason given.
Edited by Dr Adequate, : No reason given.

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Replies to this message:
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 Message 49 by Richard Townsend, posted 09-17-2009 7:05 PM Dr Adequate has replied

  
Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 25 of 61 (524397)
09-16-2009 10:50 AM
Reply to: Message 22 by NosyNed
09-16-2009 10:42 AM


Re: Statistics --- ur doin it rong
Meeting is not crossing. In these examples the crossings are zero.
(presuming I understand what is being put forward)
Apparently not. If the number of heads minus the number of tails is zero, then we have indeed met the h = t axis.

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 29 of 61 (524403)
09-16-2009 11:01 AM
Reply to: Message 27 by Dr Jack
09-16-2009 10:53 AM


Re: Statistics --- ur doin it rong
But you've not crossed it unless the next toss is the same.
So, you are not merely wrong, you're also calculating the wrong thing. Wrongly.
* facepalm *
Edited by Dr Adequate, : No reason given.

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 30 of 61 (524405)
09-16-2009 11:04 AM
Reply to: Message 26 by Dr Jack
09-16-2009 10:51 AM


Re: Statistics --- ur doin it rong
Mean is an extremely poor choice for a situation such as this - especially when considering the infinite limit - because of the large value distortion effect, and the non-normal distribution of the probabilities.
The most probable number of crosses is 0, followed by 1, followed by 2, followed by 3, etc.
* jaw drops *
I'm going to guess that you're not a mathematician.

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 32 of 61 (524407)
09-16-2009 11:07 AM
Reply to: Message 28 by Dr Jack
09-16-2009 11:01 AM


Re: Statistics --- ur doin it rong
After looking it up, I realise I have erred. In fact, the result I stated holds for a finite random walk, but it does not hold for an infinite random walk.
I'm not sure that you realize quite how badly you have erred, but yes, you frickin' well have.
Now go in peace my child.

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 33 of 61 (524408)
09-16-2009 11:09 AM
Reply to: Message 31 by Dr Jack
09-16-2009 11:05 AM


Re: Statistics --- ur doin it rong
You're not humpty-dumpty, words don't mean what you choose them to mean. Touching and crossing are different concepts.
According to your definition, perhaps. And you were being wrong about the wrong one.
Edited by Dr Adequate, : No reason given.

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 35 of 61 (524421)
09-16-2009 12:14 PM
Reply to: Message 34 by Dr Jack
09-16-2009 11:15 AM


Re: Statistics --- ur doin it rong
I used a word conventional in mathematics which you failed to understand, and since you didn't read my posts you attributed a meaning to my words that was (a) contrary to what I said (b) contrary to mathematical usage (c) contrary to the context in which I used it (d) obviously stupid (e) not actually relevant to the truth of what I was saying even if you misinterpreted me.
Have you ever thought of becoming a creationist?

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 39 of 61 (524460)
09-16-2009 5:18 PM
Reply to: Message 38 by AdminModulous
09-16-2009 1:56 PM


Re: You're wrong, no you're wrong
For the sake of moving the debate forward, can someone support their claim that the other person is wrong and put this gainsaying to bed? Thanks.
Done that: I did the work; no-one's quoted me being wrong about anything; I did the work; I have a PhD in math and know what I'm talking about; I did the work; analyzing "crossing" the h = t axis in the weirdo sense would be incredibly dumb because it would just make more useless pointless work for whoever tried to do it; I did the work; my math is correct; I did the work; I did the work rather than standing on the sidelines being wrong about what the result would be if I did the wrong calculation; I did the work; I am right about every mathematical proposition I've actually put forward; I did the sodding work, cheers.
Now, back to slevesque's question about genetics ...

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Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 41 of 61 (524465)
09-16-2009 5:46 PM
Reply to: Message 40 by slevesque
09-16-2009 5:23 PM


Wow, two pages of statistics, that wasn't expected.
I can't help you guys unfortunately, since well I haven't done any statistics yet, and mathematican-physicians don't usually do any unless you take it as an optional course.
Anyways, can't we agree that the ratio of heads/tails will tend to one when the number of n repetition tends to infinity ?
The ratio, yes.
Consider the following two cases.
Case #1 : We have a genome. We keep tossing a coin, and every time it comes up heads we add an AT base-pair, and every time it comes up tails we add a CG base-pair.
Now, this is not what you're trying to model. But it's what you're modeling. When you appeal to the Law Of Large Numbers in the way that you do, that's what you're modeling.
Case #2 : We have a genome of a fixed length. We keep tossing a coin, and every time it comes up heads we change a CG base-pair into an AT base-pair, and every time it comes up tails we change an AT base-pair into a CG base pair.
You probably shouldn't be modeling that, either. But that would be a "random walk" and wouldn't tend to anything.
However, I feel that this effect should be rather small. Because, if I remember correctly, mutations happen during transcription and technically the double strand of DNa has already been seperated by the ADN-polymerase (by memory, probably wrong about the name) and so the actual strength of the bond between G and C doesn't really impact te mutations during transcription.
But what about mutations the rest of the time?
About the impact of natural selection, we must not forget that EVEN IF, for example, GC mutations had a higher probability of being favorable than AT, than it does not readily follow that NS will be able to favor GC mutations to a high degree. This is because natural selection does not act upon the genotype, but the phenotype. And even though some mutations do have an observable impact on the phenotype, the vast majority of them are nearly-neutral and so natural selection cannot act upon them. Thus these mutations become fixed in a population through genetic drift, which is a random process.
Yes, but consider a reductio ad absurdum. If natural selection didn't count, and neutral genetic drift was all we had to think about, then it would be perfectly possible for this process to result in 100% AT. Now count how many amino acids can be produced by nucleotides just going ATTTATATATTTTATTATTATTTATAAAT ...
This is without counting that, from an evolutionary point of view, the majority of the genome is composed of junk DNA, and so mutations inside this DNA are not affected whatsoever by NS.
This is true of eukaryotic genomes, but I hardly see how it applies to bacterial genomes.
If, as I have shown, one bacterium has only 25.1% AT, and another has 84.3% AT, then the difference between them is more than half of the genome --- none of which, apparently, can be easily written off as "junk".
Edited by Dr Adequate, : No reason given.

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Replies to this message:
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 Message 51 by sfs, posted 09-17-2009 10:32 PM Dr Adequate has replied

  
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