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How Much Is .1% Difference In Our Dna?


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#21 rbarclay

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Posted 13 January 2008 - 09:33 AM

I'm a little confused. Maybe a lot confused.

In reading all this about genomic similarities and differences I'm struck with the question: "So?"

Other than its usefulness in letting us use mice as guinea pigs for medical research, etc., what does genomic similarity have to do with evolution?

I know, I know. Common ancestors, and all that. But, isn't this really just another classic case of scientists with a particular worldview leaning on their presuppositions, and assuming common ancestry? Classic circular reasoning.

You'll find genomic similarities between humans, mice, bananas, and virtually everything else. Every living creature has some DNA similarities to every other living creature. In fact, isn't everything in the universe made up of a similar set of building blocks called chemical elements?

Personally, I have no problem with research finding out that all living creatures share genetic similarities. Proves a common designer, and common creator. In order to think otherwise, you have to assume the vastly unproven, and unprovable, hypothesis of evolution.

Dave

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Dave

I agree with you and you will find that Creationist agree with. It really boils down to what religion you want to believe. There is the religion that holds a materialistic faith, that is, evolution or you have the religion that believes God supernaturally created everything. I know there are many variations in between but it is basically one of these two worldviews.

Your interpret ion of the scientific data is based on what religion you believe in. The evolutionist claim that they stand on the data science provides, however; creationists does not agree with their interpretation so this is why you have such debates. Is it important? That depends on what you believe God has called you to do in this area of His work. I believe it is important and that is based on what I believe I have been led to do. Now this does not mean your in put is not important or relevant again it is based on what you are called to do.

I commend you on the stability of your faith. To be able to say you believe in a common designer is great and it is an encouragement to me to read it.

Bob Barclay

#22 deadlock

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Posted 13 January 2008 - 12:52 PM

Dear Trilobyte,
You seem to be making an error regarding the number of mutations. When that is fixed, the math seems to work just fine. As I mentioned in my previous post (links available if you want), each generation has on the order of 100 new mutations.
With 100 new mutations we have

461,538 x 100 = 46,153,800

Chimps have a 35 million base pair difference from humans so this seems on the right order. In fact, it gives plenty of mutations for this simple calculation since chimps presumably have about the same number of mutations away from the common ancestor. It should be noted, however, that a full account must include a discussion on how each mutation gets 'fixed' into the population.

Of these 35 million, we do not know how many are 'beneficial'. Certainly the vast majority are neutral since they either occur in the non-coding regions or do not change the protein. Negative mutations are removed either at birth (e.g., through miscarriages), susceptibility to disease or  simply result in reduced fertility - effectively removing them from the genome.

Hope that helps,
James

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I would like to see the source of this information.

#23 jamesf

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Posted 14 January 2008 - 08:27 PM

I would like to see the source of this information.

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Hi Deadlock,
If you would like to read the original source, the best is probably Nachman et al. If you go to the 4th link here you can get a PDF that I found accessible.
http://scholar.googl...011705268067414

That paper mentions 175 mutations. However, when that paper was published, it was thought there was a higher number of base pairs and genes, so you need to adjust for that.


In doing a search, I also just found this which says it very well and has citations to the original.
http://www.talkorigi.../mutations.html

To quote from that link
"What is the net result," you may ask. Some mutations are fatal or very bad. These mutations get eliminated immediately. Some are silent and don't count. Sometimes a mutation is definitely advantageous; this is rare but it does happen. Almost all mutations which aren't silent and which aren't eliminated immediately are neither completely advantageous nor deleterious. The mutation produces a slightly different protein, and the cell and the living organism work slightly differently. Whether the mutation is helpful or harmful depends on the environment; it could be either.

If you think about it, life has to work this way - mutations (changes in the genetic material) are happening all the time. The average human being has about 50-100 mutations, of which about 3 matter, i.e., they actually change a protein.


Hope that helps.
James

p.s. here is something I found surprising. I put in a google search for "100 mutations" to see if I could find any new papers or discussions. Look at the top result on Google.

http://www.google.co...:en-US:official

Very curious

#24 deadlock

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Posted 15 January 2008 - 10:52 AM

Hi Deadlock,
If you would like to read the original source, the best is probably Nachman et al. If you go to the 4th link here you can get a PDF that I found accessible.
http://scholar.googl...011705268067414

That paper mentions 175 mutations. However, when that paper was published, it was thought there was a higher number of base pairs and genes, so you need to adjust for that.
In doing a search, I also just found this which says it very well and has citations to the original.
http://www.talkorigi.../mutations.html

To quote from that link
"What is the net result," you may ask. Some mutations are fatal or very bad. These mutations get eliminated immediately. Some are silent and don't count. Sometimes a mutation is definitely advantageous; this is rare but it does happen. Almost all mutations which aren't silent and which aren't eliminated immediately are neither completely advantageous nor deleterious. The mutation produces a slightly different protein, and the cell and the living organism work slightly differently. Whether the mutation is helpful or harmful depends on the environment; it could be either.

If you think about it, life has to work this way - mutations (changes in the genetic material) are happening all the time. The average human being has about 50-100 mutations, of which about 3 matter, i.e., they actually change a protein.


Hope that helps.
  James

p.s. here is something I found surprising. I put in a google search for "100 mutations" to see if I could find any new papers or discussions. Look at the top result on Google.

http://www.google.co...:en-US:official

Very curious

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The Link you posted is based on the assumption that Homo Sapiens and Chimps have a common ancestor, so it´s not valid.

#25 jamesf

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Posted 15 January 2008 - 07:20 PM

The Link you posted is based on the assumption that Homo Sapiens and Chimps have a common ancestor, so it´s not valid.

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The Nachman paper got mutation rate of 2.5 x 10-8 for each nucleotide.

There are a number of ways one can calculate mutations. Kondrashov (2003) looked at the probability of a particular set of mutations that caused a human disease.

http://www.ncbi.nlm....pubmed/12497628

From this they get a quite similar estimate of 1.8 x 10-8 mutations per nucleotide. This is consistent with what most studies get for mutation rates in other vertebrates.

I still recommend that you look at the Nachman paper or the discussion on talkorigins if you want to see how the calculations are made regarding the conversion of mutation rate to total harmful mutations (my discussion was much too simplistic).

I hope that is the sort of paper you are looking for.
James

#26 deadlock

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Posted 16 January 2008 - 11:32 AM

The Nachman paper got mutation rate of 2.5 x 10-8 for each nucleotide.

There are a number of ways one can calculate mutations. Kondrashov (2003) looked at the probability of a particular set of mutations that caused a human disease.

http://www.ncbi.nlm....pubmed/12497628

From this they get a quite similar estimate of  1.8 x 10-8 mutations per nucleotide. This is consistent with what most studies get for mutation rates in other vertebrates.

I still recommend that you look at the Nachman paper or the discussion on talkorigins if you want to see how the calculations are made regarding the conversion of mutation rate to total harmful mutations (my discussion was much too simplistic).

I hope that is the sort of paper you are looking for.
James

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They only talk about estimates but nobody shows from where the numbers come.
I want to know how they make those calculations.

#27 jamesf

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Posted 17 January 2008 - 02:23 PM

They only talk about estimates but nobody shows from where the numbers come.
I want to know how they make those calculations.

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Should I assume you did not or could not read the paper? (I understand that it may be difficult to access).

The paper discusses 20 human diseases that are known to be caused be genetic mutations (mostly single nucleotide mutations). For each disease, the study cites previous work that has estimated the probability of that disease in the population. The study then looks at the length of the gene that is mutated (the longer the gene, the greater the chance for a mutation to create an error).

From this, the study calculates the relative probabiliy for a point mutation at any given nucleotide in these different genes.

The 20 different diseases give similar answers for the probability of mutation. The study concludes (in the equation on page 22) that the each generation produces approximately 100 mutations across the whole genome (including non-coding DNA and neutral / silent mutations).

I do not have a strong genetics background, but it seem fairly straightforward.

I do find it interesting that the answer is quite similar to the studies that estimate mutation probabilities from human chimpanzee divergence. I actually did not expect the answers would be as close as they are.

#28 deadlock

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Posted 17 January 2008 - 02:36 PM

Should I assume you did not or could not read the paper? (I understand that it may be difficult to access).


The link you gave goes to an abstract without any further information.If you have the link to the complete article, please post it.

#29 jamesf

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Posted 17 January 2008 - 02:55 PM

The link you gave goes to an abstract without any further information.If you have the link to the complete article, please post it.

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Afraid I can access that one only through my library account. Here is a related paper though that looks to be using the same method, that I can access from home.

www.journals.uchicago.edu/cgi-bin/resolve?AJHG990217PS

Mutation Rates in Humans. II. Sporadic Mutation-Specific Rates and Rate
of Detrimental Human Mutations Inferred from Hemophilia B

See if that one works.

#30 jamesf

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Posted 27 May 2008 - 03:11 PM

Since this got off track on the Gitt thread, I put it here where this was previously discussed back in January

The Nachman paper got mutation rate of 2.5 x 10-8 for each nucleotide.

There are a number of ways one can calculate mutations. Kondrashov (2003) looked at the probability of a particular set of mutations that caused a human disease.

http://www.ncbi.nlm....pubmed/12497628

From this they get a quite similar estimate of  1.8 x 10-8 mutations per nucleotide. This is consistent with what most studies get for mutation rates in other vertebrates.

I still recommend that you look at the Nachman paper or the discussion on talkorigins if you want to see how the calculations are made regarding the conversion of mutation rate to total harmful mutations (my discussion was much too simplistic).

I hope that is the sort of paper you are looking for.
James

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Now starting from the Gitt board

Are you suggesting that the probability of a specific mutation in a specific spot of the genome is 10^-8 ?

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yes. That is the conclusion of a number of studies. For example, the chance that your child will get hemophilia by a point mutation at a very specific location on the genome is about 1 in 10^8 or p=10^-8

Dont you know the difference between the probability of a mutation happens and the probability of a specific mutation happens in a specific spot ?

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response

Yes, I believe I do. The probability of a mutation in a specific spot is around p=10^-8

The probability that you have no mutation anywhere (relative to your parents)  would be about
p = (1-10^-8)^k

The probability that at least one mutation 'happens' anywhere in an individual would be
p = 1-(1-10^-8)^k

where k is the number of base pairs.

Well, as Percy says, some parts of the genome mutate at higher rates than others. Furthermore, most point mutations are neutral because they occur in non-coding DNA, do not change the protein or occur in genes that have duplicates (as we previously discussed)

http://www.evolution...ded&show=&st=0

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From Deadlock

1 - My calculations are based on the assumption that all bases and positions have the same probability of mutation.Hot Spots were not in discussion, but although it can change the calculation, it does not solve the problem.

2 -  10^-8 is the probability of happening hemophilia , it´s not the probability of a mutation happens. You cannot use the probability of hemophilia and assume that all bases in the genome has the same probability of homophilia.

3 - The human´s genome has 3 billion positions, if use 10^-8 as the probability of a mutation happens in a specific position then it means that 2.9 billions positions have probability zero, what is an absurd.So, if Hemophilia has 10^-8 then other mutations must have probability lower than 10^-8.

4 - independently from your flawed reasoning, your calculations have errors too.

    4.1 if 10^-8 is the probability of a mutation happens in a specific location and k is the number of locations then k * 10^-8 must be 1.look at this :

k * 10^-8 = 1; 10^-8 = 1/k ; 10^-8 = k.

But we know that k is greater than 10^-8.

4.2  p = (1-10^8)^k . I dont know if it was a typing error but 10^8 must be 10^-8 , because negative probability does not exist.

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Deadlock,
As requested by Terry, I have moved this discussion off the Gitt board to hear where we were discussing this previously.
Also, you will note, that I did fix a typo (the 8 to a -8) as you noted. However, you should note that probability summation requires that you take the the probability to the kth power (not multiply by k). For example, if you had 3 base pairs each with a mutation probability of 0.1, the probability that you have at least one mutation is
P(of at least one mutation) = 1-(1-p)^k = 1-(1-0.1)*(1-0.1)*(1-0.1) = 1-0.9*0.9*0.9=0.271

Also note at the top pf this post that a number of different diseases result in a similar estimate of the probability of a point mutation. I think this number is pretty widely accepted with some variation between species and places on the genome.

Hope you find that useful. Not sure how this bears on Gitt, but thought I would try to help with the math.
James

p.s., the following point does not make any sense to me.

From Deadlock
3 - The human´s genome has 3 billion positions, if use 10^-8 as the probability of a mutation happens in a specific position then it means that 2.9 billions positions have probability zero, what is an absurd.So, if Hemophilia has 10^-8 then other mutations must have probability lower than 10^-8.

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You can not calculate probabilities this way. Maybe if you explain what you are trying to calculate, I could help. If you flip a coin and it comes up heads (e.g., a mutation), it has no effect on the next time you flip the coin (no effect on the probability of another mutation).

#31 deadlock

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Posted 27 May 2008 - 04:14 PM

Since this got off track on the Gitt thread, I put it here where this was previously discussed back in January
Now starting from the Gitt board
yes. That is the conclusion of a number of studies. For example, the chance that your child will get hemophilia by a point mutation at a very specific location on the genome is about 1 in 10^8 or p=10^-8
response
Deadlock,
   As requested by Terry, I have moved this discussion off the Gitt board to hear where we were discussing this previously.
   Also, you will note, that I did fix a typo (the 8 to a -8) as you noted. However, you should note that probability summation requires that you take the the probability to the kth power (not multiply by k). For example, if you had 3 base pairs each with a mutation probability of 0.1, the probability that you have at least one mutation is
   P(of at least one mutation) = 1-(1-p)^k = 1-(1-0.1)*(1-0.1)*(1-0.1) = 1-0.9*0.9*0.9=0.271

   Also note at the top pf this post that a number of different diseases result in a similar estimate of the probability of a point mutation. I think this number is pretty widely accepted with some variation between species and places on the genome.

Hope you find that useful. Not sure how this bears on Gitt, but thought I would try to help with the math.
   James

p.s., the following point does not make any sense to me.
You can not calculate probabilities this way. Maybe if you explain what you are trying to calculate, I could help. If you flip a coin and it comes up heads (e.g., a mutation), it has no effect on the next time you flip the coin (no effect on the probability of another mutation).

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1 - It´s a basic concept in probability , the sum of the individuals probabilities must be equal 1.So, the sum of the probabilities of all positions in the genome must be 1.If the probability is equal in all positions and you have k positions then
k * p = 1.

the possible combinations of flipping two coins :

(k,c)(k,K)(c,k)(c,c) = 4 possible combinations. what is the probability of a specific combination ? 1/4.

1/4+1/4+1/4+1/4 = 1.

What is the probability of happening c in the fist coin ? 2/4
the probability of it doesnt happen ? 1 - 2/4

p + q = 1 -> 2/4 + 2/4 = 1

The sum will always be 1.

using your formula the probability of not happening a c in the first coin would be:

p = (1-1/2)^1 = 1/2. it´s the probability of a k flipping one coin how could it be flopping two ?

in the mutation case p = 10^-8, so you say that the probability of mutation does not happen in 3 positions would be :
p = ( 1 - 10^-8 )^3
p = ( ( 10^8 - 1 )/10^8) ^3
p = ( ( 100000000 - 1 )/10^8 )^3
p = ( ( 999999999/100000000)^3
p = 1.

In other words you are saying that is practically certain that 3 mutations will not happen.

Even me, a creationist, isn´t so pessimistic about evolution :lol:

#32 jamesf

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Posted 27 May 2008 - 06:48 PM

1 - It´s a basic concept in probability , the sum of the individuals probabilities must be equal 1.So, the sum of the probabilities of all positions in the genome must be 1.If the probability is equal in all positions and you have k positions then
k * p = 1.

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Sigh.... The above statement is false. Deadlock, I really don't mind helping you understand some issues in probability theory. However, when you make these errors and then attack those helping you by saying things like the quote below, you really create a lot of unnecessary hostility.

I suspect statements like the one below even go against forum rules.

It´s amazing your lack of knowledge about probability.But you dont need to believe me.Please, go to a university near your home and ask a teacher of statistics and after that tell me what is his answer.

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And when you make such statements and then make basic errors, you just look foolish. Could we tone down this rhetoric just a bit? Everyone makes mistakes. Certainly, I make mistakes (just ask my wife). However, if I make a basic error and it is pointed out, at least I hope I will have the courage to admit it.


1 - It´s a basic concept in probability , the sum of the individuals probabilities must be equal 1.So, the sum of the probabilities of all positions in the genome must be 1.If the probability is equal in all positions and you have k positions then
k * p = 1.

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So where is the error in the above statement? The sum of probabilities = 1 only when you consider all possible states that the system can be in (like you did in the coin flip example). It does not work when you apply it to the probability at each position. Consider an example where the probability of a mutation is 0.1 and you have three positions on the genome.

does k * p = 1?

does 3 * (0.1) = 1?

of course not

With a genome size of 3 billion and 4 kinds of base pairs, the number of possible states is
4^(3,000,000,000) which is a very very large number (my calculator says infinity but it should be something like 10^2,000,000,000). So if you could calculate the probability of each one of those states (whatever that would mean), it should sum to 1.



in the mutation case p = 10^-8, so you say that the probability of mutation does not happen in 3 positions would be :
p = ( 1 - 10^-8 )^3
p = ( ( 10^8 - 1 )/10^8) ^3
p = ( ( 100000000 - 1 )/10^8 )^3
p = ( ( 999999999/100000000)^3
p = 1.

  In other words you are saying that is practically certain that 3 mutations will not happen.

  Even me, a creationist, isn´t  so pessimistic about evolution  :lol:

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Ok, now apply that equation to the size of the genome

p(zero mutations) = (1-10^-8)^(3,000,000,000)
=(.99999999)^(3,000,000,000)
=9.3*10^-14 (if my little calculator got all those digits right)

So there is an extremely small chance of having no mutations

p(of at least 1 mutation) =1 - p(zero mutations)
= 0.99999999999999 (or something like that)

So the probability that your child will have at least one mutation is very very high.

On average a person has over 100 new mutations each generation. Luckily, most all of those are neutral. Some small fraction are harmful and if you have one of those you will have fewer offspring and the gene will vanish from the gene pool. Some smaller fraction are beneficial and if you have one of those, you will have more offspring (relative to your peers) and the gene can multiply through the gene pool.

Beneficial simply means that those with that new gene have a slightly higher chance of producing fertile offspring. What we can not calculate is how many different possible mutations would be beneficial.

After a few generations there will be more of the beneficial genes relative to the harmful ones. Since we do not know how many mutations might be beneficial (without trying out every possible combination of mutations with every possible combination of genome in the population), we can not calculate the probability that any particular mutation would be beneficial.

I guess a very very rough analogy would be the game of poker where you already hold a hand of cards with a few redundant cards (7 card stud). If you changed one of the cards at random, what would be the chance that it would give you a winning hand? To answer that, we would need to know the rest of your cards and know the cards of the other players. One does not want to calculate the probability of a particular set of cards. Rather, one wants to calculate the probability that the card you drew gave you a better hand - remembering that there are several different ways to build a winning hand.

James

#33 deadlock

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Posted 28 May 2008 - 02:22 AM

Sigh.... The above statement is false. Deadlock, I really don't mind helping you understand some issues in probability theory. However, when you make these errors and then attack those helping you by saying things like the quote below, you really create a lot of unnecessary hostility.
  I suspect statements like the one below even go against forum rules.
And when you make such statements and then make basic errors, you just look foolish. Could we tone down this rhetoric just a bit?  Everyone makes mistakes. Certainly, I make mistakes (just ask my wife). However, if I make a basic error and it is pointed out, at least I hope I will have the courage to admit it.
So where is the error in the above statement? The sum of probabilities = 1 only when you consider all possible states that the system can be in (like you did in the coin flip example). It does not work when you apply it to the probability at each position. Consider an example where the probability of a mutation is 0.1 and you have three positions on the genome.

does k * p = 1?

does 3 * (0.1) = 1?
 
    of course not


First, It´s not a personal attack , it´s only a conclusion based on the foolish things about probability you and he are saying.

Second, look at the absurdity you are saying in the above assertion. If the genome has only 3 positions , how coould the probability of a mutation happens in one of them be 0.1 ?

let´s use a coin as analogy : a coin has two possible answers : Head or Tail.

The sum of probabilities of any event must be 1.

if we assume that the probabilities of head and tail are equal then we devide 1 by 2.We give an equal part of the probability to each possible result.So, 1/2+1/2 = 1

Let´s imagine that the probability of Head is 1/3.Now , we have a problem because 1/3+1/2 <> 1.So, we have to re-calculate the probability of tail, what is obvious because if the probability of head decreased then probability of tail must increase.

Now, analizing your example. we have only 3 positions and you are saying that the probability of a mutation happens in one of them is 1/10.Of course, we have a problem here. 1/10+1/10+1/10 <> 1.what is the solution ? if the probability of each position was equal then it would be 1/3, because 1/3+1/3+1/3 = 1.But if you say that one of them has the probability of 1/10 then you must increase the probabilities of the other two in a way that the sum be 1.


With a genome size of 3 billion and 4 kinds of base pairs, the number of possible states is
4^(3,000,000,000) which is a very very large number (my calculator says infinity but it should be something like 10^2,000,000,000). So if you could calculate the probability of each one of those states (whatever that would mean), it should sum to 1.
Ok, now apply that equation to the size of the genome

p(zero mutations) = (1-10^-8)^(3,000,000,000)
                        =(.99999999)^(3,000,000,000)
                        =9.3*10^-14 (if my little calculator got all those digits right)

So there is an extremely small chance of having no mutations

p(of at least 1 mutation) =1 - p(zero mutations)
                                    = 0.99999999999999 (or something like that)


Explain me, how ( 0.99999999 )^(3,000,000,000 ) could be equal = 9.3*10^-14 ?

correct answer is (99999999/10^8)^(3*10^9) = ? , put it in the Excel and see the answer it ´ll give you.

The thing is worse than I thought.The problem begins in algebra.

What do you want me to say ? That you and Percy are brilliant mathematicians ?

#34 deadlock

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Posted 28 May 2008 - 05:30 AM

The reasons why you're wrong (hundreds of orders of magnitude wrong) exist on several levels. First, to make sure you understand just how small a number you're claiming the probability of a mutation at a pre-specified location is, I'll transform it into standard exponential notation, which I can only do approximately because normal calculators do not work with numbers this size:

(1/3)^(10^7) =~ 10^-470000

That's 10 raised to the power of negative four hundred and seventy thousand! That's 4700 times smaller than a goolgolth!

Second, if you're probability value is correct, then the probability value for a mutation in the necessary location for your RNA polymerase example would have been in roughly the same ballpark. This means the mutation would never occur in the lifetime of the universe. Yet the scientists were able to perform the experiment in a reasonable time, so obviously your figure cannot be anywhere near right.

Third, I think if you attempt to show how you arrived at your (1/3)^(10^7) figure you'll find that you're way, way off.


When someone calculates the probability of something, he must consider first the following assumption:

is The probability equally distributed throughout the possible results ?

There are 3^(10^7) possible mutations in our case.If we assume that the probability is equally distributed then the probability of a specific mutation in a specific spot is 1/3^(10^7).Remeber that the sum of all probabilities must be 1.So, (3^(10^7)) * (1/3^(10^7)) = 1.Let´s analyze the RNA polymerase case.If statistic data shows that the RNA polymerase mutation probability is greater than 1/3^(10^7), it means that the above assumption was wrong, in other words, the probability is not equally distributed throughout genome.But it does not change a basic probability law, the sum of all probabilities must be 1.So, the obvious conclusion is that there are other mutations which probability is lower than 1/3^(10^7) to compensate the increase in the RNA Polymerase probability.As evolution needs mutations happening throughout genome then the problem stands.

#35 jamesf

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Posted 28 May 2008 - 08:28 AM

First, It´s not a personal attack , it´s only a conclusion based on the foolish things about probability you and he are saying.

Second, look at the absurdity you are saying in the above assertion. If the genome has only 3 positions , how coould the probability of a mutation happens in one of them be 0.1 ?

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k (the size of the genome) and p (the probability of mutation at any point) are independent. You are assuming that they are tied together by
k*p=1

As mentioned before, you are incorrect. I see that you have difficulty admitting your error and prefer to ridicule the one trying to help. Despite your attitude, I will try to explain using two problems shown below.

Also, I can increase the probability of mutation at any point (p) by putting the animal into heavy radiation. This does not affect the size of the genome (k). k and p are independent. Also, it has been shown that the probability of a mutation (p = about 10^-8) at any given site is pretty constant for a range of animals despite changes in the size of their genome (k). k and p are independent

If you still don't understand this, you may wish to solve the basic problems I show below. If you still feel that I am making the error, you may wish to show the problem to some other creationist that you trust.

Explain me, how ( 0.99999999 )^(3,000,000,000 ) could be equal = 9.3*10^-14 ?

correct answer is (99999999/10^8)^(3*10^9) = ? , put it in the Excel and see the answer it ´ll give you.

The thing is worse than I thought.The problem begins in algebra.

What do you want me to say ? That you and Percy are brilliant mathematicians ?

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Using Excel
POWER(.99999999,3000000000) = 9.35762E-14

Does your excel work differently? What answer did you get?

When someone calculates the probability of something, he must consider first the following assumption:

is The probability  equally distributed throughout the possible results ?

There are 3^(10^7) possible mutations in our case.If we assume that the probability is equally distributed then the probability of a specific mutation in a specific spot is 1/3^(10^7).Remeber that the sum of all probabilities must be 1.

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I am going to resist all comments about your mathematical skills.

Since you prefer your own math to solve such problems and don't seem to believe in our math, let us just try two straightforward problems and you show me what your answer is. And show me how you calculate it with "your" math.

1. Three people each have a deck of cards (52 cards) and each person draws one card at random from their deck. What is the chance that at least one person will draw an ace of spades? (k=3, p=1/52)

2. Three genes each have a probability of 1/52 of mutating in a given generation. What is the probability that at least one of the genes mutates in a generation? (k=3, p=1/52)

hint: you should get the same answer

I showed you my math, and thought I could help. However, you seem to think my solution is either wrong, or impossible, and then felt it was necessary to make hostile statements. So let us just use these simple problems. I would like to see how you solve the problem using your math.

James

#36 Guest_92g_*

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Posted 28 May 2008 - 02:01 PM

IMO Statistics is mental torture... :lol:

I think the 2 sides here are arguing different aspects of the same point. Its true that if we assume a uniform distribution on point mutations, then the probability is the same for each point, and they have to sum to 1. So, its true that if we have 3 points, and a uniform distribution, then the chance is 1/3.

If you assume some sort of conditional probablility then the probabilities for a given place will change based on the new distribution, and you can have differing probabilities for the given locations.

Perhaps that's what led to this statement:

Sigh.... The above statement is false. Deadlock, I really don't mind helping you understand some issues in probability theory. However, when you make these errors and then attack those helping you by saying things like the quote below, you really create a lot of unnecessary hostility.

,

the object of which was not false. Maybe I'm missing something....

Terry

#37 Fred Williams

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Posted 28 May 2008 - 04:09 PM

Ok, now apply that equation to the size of the genome

p(zero mutations) = (1-10^-8)^(3,000,000,000)
=(.99999999)^(3,000,000,000)
=9.3*10^-14 (if my little calculator got all those digits right)

So there is an extremely small chance of having no mutations

p(of at least 1 mutation) =1 - p(zero mutations)
= 0.99999999999999 (or something like that)

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I haven’t had a chance to check everyone’s statistics (nor do I want to :o) but this approach is flawed. To calculate the probability of no events you should use a Poisson distribution. If the mutation rate is 100 per person, the proper calculation is:

P = e^100 = 2.66*10^43.

I agree with James the rhetoric needs to tone down in this thread, especially when talking about statistics since the odds everyone will take a turn at flubbing is p=.999982. It would be P=1, but since I've involved myself it can’t possibly be 1. :lol:

Fred

#38 deadlock

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Posted 28 May 2008 - 04:11 PM

1. Three people each have a deck of cards (52 cards) and each person draws one card at random from their deck. What is the chance that at least one person will draw an ace of spades? (k=3, p=1/52)

2. Three genes each have a probability of 1/52 of mutating in a given generation. What is the probability that at least one of the genes mutates in a generation? (k=3, p=1/52)

hint: you should get the same answer

I showed you my math, and thought I could help. However, you seem to think my solution is either wrong, or impossible, and then felt it was necessary to make hostile statements. So let us just use these simple problems. I would like to see how you solve the problem using your math.

James

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p = 7957/52^3 = 0,06

I think we are wasting our time. You wont agree with my calculations and I wont agree witn your calculations, so I think the only way to solve this is asking someone else with Graduation in statistics that both sides respect.I dont know if it can be done.

#39 deadlock

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Posted 28 May 2008 - 04:40 PM

k (the size of the genome) and p (the probability of mutation at any point) are independent. You are assuming that they are tied together by
k*p=1


of course they are tied together.

p = number of favorable postions / number of possible positions.

if the probability is uniform then p = 1/k. But if it is not then k*p <> 1, but the sum of all p must be 1.As I said about the coin.

if the probability of head is 1/3 then the probability of tail must be 2/3, because

1/3 + 2/3 = 1

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Posted 29 May 2008 - 03:01 AM

so much bad math!!!!!!!!!

;(

it makes my head hurt


http://mathworld.wol...Statistics.html




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