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  Topic: bFast's Allele Blender, Zachriel< Next Oldest | Next Newest >  
Zachriel



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(Permalink) Posted: Mar. 08 2008,21:55   

bFast proposes a simulation.
Quote
bFast: 1111111222 2212112211 1221212112 1112222121 1212221112 1112212112 1112122121 1122212212 1221122222 1121121121 2221122222 2221112122 1121121112 2221222212 1222211212 1221212121 1221111221 1122121111 1122212112 1212112222
SUM = 301

Bob O'H: you’re illustrating a well known problem, genetic drift. With a population size of 5, the relative fitness has to be very large to have a visible effect. Drift is a large factor in small populations, so even alleles which reduce fitness can become fixed.

Bob O'H makes an important point. Some alleles will become fixed even without selection.

Meanwhile, in a reasonable population of competitors, their overall fitness will tend to improve. That inevitably means more and more individual alleles will improve, even if particular alleles are gained or lost along the way.

This is an example of how global pressure can bring about local changes.


--
Update: The results are much as expected. In a recent run, I used a 100x100 grid for a population of 10000. Each genome is 100. When a replication occurs, there is a 10% chance of a mutation. Only 1's and 2's are allowed thus far. The child then displaces a weaker neighbor, if any. This creates a nice nested distribution of varieties across the grid. After 100 generations, the average fitness is about 1.8 per allele. The corners of the grid tend to have more primitive varieties. This is a typical genome:

1212112211 2122222212 2222212222 2222222221 2122222221
2212222122 2122122211 1222221212 1222222112 2122222222

Next step is to allow very rare 2-to-3 mutations. I'm also considering some sort of sexual recombination, but watching 1's doin' it doesn't strike me as particularly interesting.

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Zachriel



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(Permalink) Posted: Mar. 08 2008,21:58   

Quote (Zachriel @ Mar. 07 2008,06:47)
bFast proposes a simulation.
Quote
bFast: 1111111222 2212112211 1221212112 1112222121 1212221112 1112212112 1112122121 1122212212 1221122222 1121121121 2221122222 2221112122 1121121112 2221222212 1222211212 1221212121 1221111221 1122121111 1122212112 1212112222
SUM = 301

Allele Blender uses a typical selection criteria called The Early Bird Gets the Worm, also known as I only need to outrun you, Albert. In other words, strong positive selection. Lately, I've allowed very rare 2-to-3 mutations. Of course, while some are lost, once established they tend to quickly dominate the population.

I have tried to contact bFast to make sure I have represented his model correctly. The only contact I have found is at ISCID. Someone might want to give bFast a heads up.

* Niels Bohr and Albert Einstein were taking a walk in the woods, vigorously debating the philosophical underpinnings of quantum theory, when a gigantic bear suddenly burst out of the underbrush and raced toward them. Niels immediately whipped out his fine running shoes and began lacing them up.

Einstein, furrowing his brow at Bohr, said: "Niels, there's no way you can outrun that bear."

"That's true," Bohr calmly replied, "but I don't need to outrun the bear. I only need to outrun
you, Albert."


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Zachriel



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(Permalink) Posted: Mar. 08 2008,21:59   

Quote (Zachriel @ Mar. 07 2008,06:47)
bFast proposes a simulation.
Quote
bFast: 1111111222 2212112211 1221212112 1112222121 1212221112 1112212112 1112122121 1122212212 1221122222 1121121121 2221122222 2221112122 1121121112 2221222212 1222211212 1221212121 1221111221 1122121111 1122212112 1212112222
SUM = 301

These are all adjustable, of course:
* Alleles can now vary from 1 to 9.
* Mutations occur every 10% of replications.
* Only 10% of these 10% can cause an incremental improvement, most of the rest being detrimental.

Fitness rapidly improves.
Recombination with a random neighbor improves even faster.
Recombination with the fittest available neighbor is faster still.

But recombination with the most attractive neighbor still works very well, but has a peculiar effect. To simulate this, the Peahen chooses a mate from the immediate neighborhood—not based on fitness—but based on the one with the prettiest tail. The prettiest tail is defined as the longest length of trailing 1's—a trait which is actually detrimental to the overall fitness.

The Peacocks Tail



Notice the family resemblance among neighbors, and the small clan of uglies in the middle left column. This run has a genome of length twenty so you can more easily see the effect.



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Zachriel



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(Permalink) Posted: Mar. 08 2008,22:19   

Quote (bFast @ Mar. 08 2008,19:18)
I have written my own sim at this point, and it fails miserably!  So bad, in fact, that I think it must have a bug.

It isn't necessary to reinvent the wheel. I believe I have a working simulator. It's open source, and I'm more than willing to share. However, I want to make sure that the model correctly represents what you are trying to test.

We have a population, each member represented by a genome. Each allele is a numeral. A member spawns a Child which then competes in the population. Fitness is determined by the sum of genes.

In the Allele Blender, each member of the population is located on a grid. Each new Child will replace the weakest in the vicinity, assuming the Child is fitter. Is this correct?

(By the way, starting with your original organisms, and assuming strong positive selection, Organism 2 will quickly dominate the population. The 3-allele in Organism 4 will almost definitely be lost.)

Quote (bFast @ Mar. 08 2008,19:18)
- No new alleles are created during the simulation.  I suspect that the addition of new alleles would increase the noise, therefore increasing the problem.

I assume you mean more than two available versions at each locus. Using your concept, it was easy to have nine varieties, 1 through 9. If a given gene is a 2, then a standard mutation as described above would be either a 1 (detrimental) or a 2 (neutral). Very occasionally we might see a 2 increment to a 3. A novelty.

Quote (bFast @ Mar. 08 2008,19:18)
- The number of alleles per organism is small (initially 200).  I suspect that the more alleles, the worse the signal to noise problem.

I think you mean the number of genes (each allele being represented by a numeral). It's just a parameter. I can adjust that to any reasonable number. There are several relationships that we can discover that will help us extrapolate to larger numbers. I'll provide some details later.

Quote (bFast @ Mar. 08 2008,19:18)
Selection is, well "pure", the definition of "fit" never changes, every organism death is determined by its ideally measured fitness compared to another organism.  This is a very positivistic model.

That seemed to be your intent. But that can be easily adjusted. I have already added proximity, recombination, random mate selection, mate selection for fitness, and mate selection for an arbitrary trait (the peacock's tail). We could also add a random fudge factor. It doesn't really change the end result. Even with no selection, alleles become fixed. It's an important concept that I would be happy to discuss.

       ' Recombine
       For a = 1 To numAllele
           If Rnd < 0.5 Then
               Mid(Child, a, 1) = Mid(Mate, a, 1)
           Else
               Mid(Child, a, 1) = Mid(Parent, a, 1)
           End If
       Next a


Quote (bFast @ Mar. 08 2008,19:18)
I would love to hammer this challenge out with you to prove that in an ideal world a new mutation actually can catch on.  I would also love to see the sim prove that a mutation is more likely to fix in a large population.  So far my sim isn't doing any better with a large population (its a dog by about 50,000).

Not only can new mutations fix, but they can do so in the absence of selection.

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Zachriel



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(Permalink) Posted: Mar. 08 2008,22:19   

Quote (bFast @ Mar. 08 2008,19:18)
I would love to hammer this challenge out with you to prove that in an ideal world a new mutation actually can catch on.  

Hi bFast! I have several open source projects that demonstrate various aspects of evolution.

Nest of Letters shows how even neutral mutations can and will become fixated in populations.



Killer Rabbits started with a very cool simulation by Wonders for Oyarsa posted on Telic Thoughts. Ironically, he overlooked the process of fixation that was staring him in the face.



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Zachriel



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(Permalink) Posted: Mar. 09 2008,08:17   

Neutral Drift and the Law of Small Numbers

Consider a single locus in a population limited by circumstance to just two.

       A, B

Let them replicate.

       A1, A2, B1, B2

Now, we keep two at random. These are the possibilities.

       A1, A2
       A1, B1
       A1, B2
       A2, B1
       A2, B2
       B1, B2


There is a one in three chance of forever losing one of the two alleles. But let's assume that we end up with both alleles. But then, over each succeeding generation, we are again faced with a one in three chance of forever losing one of the two alleles. Sooner or later, we will have A, A or B, B. Fixation.

Now consider a population of three.

       A, B, C

Replicate.

       A1, A2, B1, B2, C1, C2

Now choose three. There are twenty possibilities. Some of them include all three alleles. But some don't. Even if all three alleles make it into the next generation, we are again faced with a significant possibility of losing one of the alleles forever. Eventually, we will lose one allele. Such as this.

       A, A, B

Now replicate

       A1, A2, A3, A4, B1, B2

Again, choose three. Notice that there is a finite chance of keeping both alleles. But there is also a finite chance of losing another allele forever. Eventually, this will happen. Fixation.

Which allele will become fixed? It's random. So in the first case, it is 1/2. In the second case, it is 1/3. But notice that it takes longer with the larger population. Indeed, Hardy-Weinberg proved that in an infinite (undisturbed) population, the rate of fixation is zero. But no population is infinite.

But we can make an even more powerful statement. Instead of a single allele, consider a genome of a 100 alleles. Assume, the rate of neutral mutation is 1 per 100 per allele per replication. That means each genome will have a single mutation. If it replicates a hundred children, then the average locus will have experienced one mutation (an average of one per child). What is the chance of a particular allele being fixed? One in a hundred. So what is the Expected Number of some mutation becoming fixed when we have a hundred mutations? 100*1/100 = 1. It's the same for any size genome, any size population. The rate of fixation of neutral mutations is equal to the rate of neutral mutations regardless of population size.

This is not an empirical result. It's arithmetic, and is based on the assumption of neutrality. From what I gather, you are attempting to understand the case of nearly neutral evolution.

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Zachriel



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(Permalink) Posted: Mar. 09 2008,08:43   

In any case, you haven't provided us enough information to be sure we are properly simulating your model.  If we consider these two genomes:

       1111111111111111111...

and

       1111121111111111111...

You've defined fitness as the sum of the alleles. Assuming strong positive selection and a low mutation rate, the 2-mutation should quickly dominate the population. With a high mutation rate, then various mutants will compete to dominate the population, but any pure-strain will be quickly overwhelmed.

Among your original organisms, Organism 2 will quickly dominate the population. The 3-allele in Organism 4 will almost definitely be lost. But then any future advantageous mutation to the dominant Organism 2 will then come to dominate the population:

       xxxxxxxxxxxxxxxxxxxxxx...

and

       xxxxxXxxxxxxxxxxxxxxxx...

Remember, Neils only has to outrun Albert.

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Zachriel



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(Permalink) Posted: Mar. 09 2008,09:41   

Quote (Zachriel @ Mar. 08 2008,22:19)
I have already added proximity, recombination, random mate selection, mate selection for fitness, and mate selection for an arbitrary trait (the peacock's tail).

I changed sexual selection for the tail to be a preference for a long tapering tail.

I am allowing the 'head', the two leading loci, to mutate faster. This results in faster evolution in that region. (I'll probably fiddle with that feature. Maybe allow the head region to expand.) Here's a typical organism.

      99544535322222111111

Notice the 'head' has hit the limit of 99. The tail is ...322222111111, but you can guess that some of its relatives probably have longer tails. (They do.) It's quite amazing how powerful sexual selection for an arbitrary trait can be at shaping the organism.


Update

Took out the 'head'. Too contrived.

Trying longer genomes. Works as before, with or without recombination, with or without mating selection for fitness, with or without mating selection for a beautiful tail.

  ' Beauty is in the eye of the beholder
  ' Long tapering tails preferred


  Public Function calcBeauty(Mate) As Integer
  Dim mv, mk As Integer
 
      mk = Val(Right(Mate, 1))
      calcBeauty = 0
 
      For a = numGenes To 1 Step -1
          mv = Val(Mid(Mate, a, 1))
          If mv = mk Or mv = mk + 1 Then
              calcBeauty = calcBeauty + 10 \ (mv + 1)
' Thinner the better
              mk = mv
          Else
              Exit For
          End If
      Next a

  End Function


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Zachriel



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(Permalink) Posted: Mar. 09 2008,10:14   

bFast emailed and said he has his simulator working. However, his email didn't reveal details sufficient to replicate his results. Unsurprisingly, he does say it confirms his suspicions.

bFast, when you get the chance, maybe you could provide some examples using small genomes and populations so we can see how it works. Then it should be easy to scale it up once we understand what you are modeling.

My first question has nothing with introducing the novel 3-allele mutation: Why doesn't Organism 2 quickly dominate the population? Why would you think that Organism 4 with the 3-allele would propogate? I would expect that line to die out and be replaced by Organism 2. Indeed, without new mutations being introduced, we would expect the entire population to be dominated by clones of Organism 2. Organism 4's only hope is to find a rock to hide under.

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Annyday



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(Permalink) Posted: Mar. 09 2008,14:54   

I am not in the least bit a programmer, but if you're actually getting funky results from a simulation, bFast, I'd like to see the simulator and the results. Mathematical modeling of changing populations is a mainstay of evolutionary theory, so funky results in simulations are pretty interesting.

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bFast



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(Permalink) Posted: Mar. 09 2008,18:06   

The question that I present is, how easy is it for natural selection to favor an advantageous point mutation (signal) in light of the various destractions (noise)?

I see noise in four areas:

1 - Allele populations.  Organisms, such as myself, consist of a mishmash of alleles that exist within the community of origin.  As such, any one individual will not have an ideal mix of alleles.  If an organism, such as myself, has the lucky slightly beneficial point mutation, will natural selection be able to favor it dispite all of the other alleles flying around in the population.

2 - New alleles.  Each individual organism will be hit with zero to a few mutations within the active DNA.  The fact that each organism is de-idealized by these mutations increases the noise, making it more difficult for natural selection to be able to favor a slightly beneficial point mutation.

3 - The fickleness of natural selection.  In two given contexts natural selection will favor different alleles.  For instance, I am more intelligent than most.  As such, I have a good allele set wrt intelligence.  I am decidedly less athletic than most.  As such, I don't have a good allele set wrt athletics.  If a given opportunity for selection involves me and a friend trying to outrun a hungry bear, in all likelihood my above average intelligence will do me no good, and I'll be lunch.  To make matters worse, I think that natural selection is probably best at ignoring allele mixes altogether, and causing one to be removed from the pool for no reason other than being in the wrong place at the wrong time.

4 - Bulk-editing.  Alleles come with an entire gene full of baggage.  Our dear lucky mutation has to happen within an existing allele.  This existing allele may not be a rising star.  Now a new allele exists which may be marginally better than its falling star cousin, but may not be sufficiently advantageous to beat out other alleles floating around in the population.  When organisms such as myself produce offspring, we generally exchange genetic data in bulk units called chromosomes.  So even if a gene is a particularly good one, I think that the fact that it is packaged up in a chromosome presents a challenge.

Now, I have produced a simulation that selects out issue number 1.  The question is, is noise source 1 in itself sufficient to disable natural selection for a slightly beneficial mutation?

My sim's algorithm is as follows:

Initialization accepts 3 parameters: gene count, population, mutant count.

- Per population, I create an organism
-   Per organism, I create an array of 'gene count' elements.
-   Each element is initialized with a random 0 or 1, representing allele #0 or allele #1 where we assume that the #1 allele is 'fitter' than #0.
-   Each element is given a 'fitness' number -- the total of 1's in its genes.
-   for 'mutant count', organisms are selected at random, and the first gene is boosted to allele #2.  The 'fitness' number is adjusted.

Processing accepts 1 parameter: cycles and returns the total number of active mutants.

- Per cycle:
-    two organisms are selected at random
-    the less fit of the two is decomissioned, and replaced by:
-       two organisms are selected at random
-       through the genes of these organisms, either the first or 2nd organism's allele will be selected.
- the 'fitness' of the new organism is measured.

One "generation" is considered to be Population cycles (on average, the death/replacement of each individual.)

The general results of my sim are as follows (I haven't run lots of simulations yet, nor have I done careful logging yet.):

- when there are 200 alleles per organism, the mutant dies very about 9 times out of 10.  If the mutant lives to get about 20 organisms to contain it, it rather quickly becomes fixed.  Dying or fixing doesn't seem to have much to do with population.

- when there are 2000 alleles per organism, the mutant dies rather often, often enought that I have skipped past early processing and seeded the system with multiple mutants.  If it has 50 mutants in a 1000 population, the mutant usually survives, and fixes rather quickly.

- when there are 20,000 alleles per organism, the population of the mutant seems to wander like it is influenced by the throwing of a dice -- genetic drift.  I have been seeding with 100 in a population of 1000, and have yet to be able to get it to fix.  

NOTE: As all allele 1s are motivated to increase in popularity, one may consider that a bunch of them have fixed within this process.  As they fix, the amount of noise, the number of alleles in the population decreases.  I have not yet measured the number of fixed alleles in the calculation, but I suspect that with the small counts, the reason NS grabs the beneficial mutation so solidly at some point is because the noise has significantly decreased.

Now, in real world organisms, there is (almost) always an abundance of available alleles.  In fact, when there are not, it is conserning.  This is caused, of course, by other organisms obtaining mutants that have infiltrated the population.  Populations always have many alleles, so the mutant of interest fixing because all of the nearby alleles fixing is an artificial situation.

A major question that I have as I present this sim is, how many alleles are there in a population.  I could envision that there are a whole lot.  I know that I contain 2 sets of genes, each set has 25,000 coding genes.  My wife also has 2 sets of genes.  So between the two of us, let alone our neighbors, we have 100,000 coding genes.  But, for how many of those genes is there only one allele within the population?  For how many of those genes are there literlally hundreds of alleles?  Bottom line, how many alleles are disguising my lucky beneficial mutation.  My sim suggests that somewhere less than 20,000 is too many, that it produces too much noise for natural selection to filter out, when selecting a beneficial point mutation -- and that, dispite the other sources of noise as described above.

  
bFast



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(Permalink) Posted: Mar. 09 2008,19:00   

Zachriel, "Indeed, without new mutations being introduced, we would expect the entire population to be dominated by clones of Organism 2. Organism 4's only hope is to find a rock to hide under."

In an asexual environment, this would obviously be so.  Which presents a problem.  It would seem that in an asexual environment, the signal to noise issue becomes very much stronger.  It is only in the most fit of organisms, that an advantageous mutation would stand a breath of a chance.   ???

  
Zachriel



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(Permalink) Posted: Mar. 09 2008,21:31   

Quote (bFast @ Mar. 09 2008,18:06)
- Per cycle:
-    two organisms are selected at random
-    the less fit of the two is decomissioned, and replaced by:
-       two organisms are selected at random
-       through the genes of these organisms, either the first or 2nd organism's allele will be selected.
- the 'fitness' of the new organism is measured.

That's a rather odd selection method. You pit organism 1 against organism 2, but it's not the victor that reproduces, but a recombination of two other organisms. I suppose it should result in evolution towards higher fitness, though. I'll test it to be sure.

Quote (bFast @ Mar. 09 2008,18:06)
- when there are 200 alleles per organism, the mutant dies very about 9 times out of 10.

Yes, of course.

That's what we would expect for a near neutral mutation (your mutation only increases fitness by a small percentage) in the midst of chaos (randomized genomes). So?

Quote (bFast @ Mar. 09 2008,18:06)
As all allele 1s are motivated to increase in popularity, one may consider that a bunch of them have fixed within this process.  As they fix, the amount of noise, the number of alleles in the population decreases.  I have not yet measured the number of fixed alleles in the calculation, but I suspect that with the small counts, the reason NS grabs the beneficial mutation so solidly at some point is because the noise has significantly decreased.

Again, of course.

Try this. Assume there are no mutations. Run your simulation starting with your randomized genomes. Your population should evolve rapidly and fitness should fix at a high level. Then when you introduce your beneficial mutation, it will then tend to dominate because it will be distinguishing. Neils only has to outrun Albert.

Quote (bFast @ Mar. 09 2008,18:06)
Now, in real world organisms, there is (almost) always an abundance of available alleles.

Quite the contrary, most organisms, including humans, share almost identical genomes. It's just that we happen to be most interested in the differences. Indeed, this is an important aspect of sexual selection. A seemingly minor difference (a bit better singing voice, an unusual coloration in plumage) can make the crucial difference between a successful mating or not.

Quote (bFast @ Mar. 09 2008,18:06)
This is caused, of course, by other organisms obtaining mutants that have infiltrated the population.

Which is what Allele Blender simulates. New mutations are constantly being introduced. The amount of genetic diversity depends on several factors, including the mutation rate.

Quote (bFast @ Mar. 09 2008,18:06)
My sim suggests that somewhere less than 20,000 is too many, that it produces too much noise for natural selection to filter out, when selecting a beneficial point mutation -- and that, dispite the other sources of noise as described above.

No. Rather, it demonstrates that a near neutral mutation may drift to extinction in a chaotic genomic population. This is what is expected.

Quote (bFast @ Mar. 09 2008,19:00)
In an asexual environment, this would obviously be so.  Which presents a problem.  It would seem that in an asexual environment, the signal to noise issue becomes very much stronger.

Even without recombination, the Allele Blender quickly evolves higher fitness. (And it's much easier to distinguish the lines of descent, being uncrossed lines.) Without mutation also, the population will settle on a high fitness. With mutation, individual mutations, even if beneficial, may be lost, but other mutations will be found.

Try your simulation again, without any mutation first. Take a look at how the  system evolves. Then add some fixed rate of mutation. You'll find that the population more closely resembles biological organisms, complete with families of varieties.

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bFast



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(Permalink) Posted: Mar. 09 2008,22:42   

Zachriel:
Quote
That's a rather odd selection method. You pit organism 1 against organism 2, but it's not the victor that reproduces, but a recombination of two other organisms. I suppose it should result in evolution towards higher fitness, though. I'll test it to be sure.

This is certainly not sexual selection.  But why should we assume that the victor should also get the privelage of reproduction.  Am I to assume that shortly after my handicapped friend I get chased by the bear, and he gets eaten, I get to reproduce?

You will note that when the allele count is 200, this sim works as expected, when it is 2000, it works as expected -- more slowly than the first, but it still evolves.   When the allele count gets to 20,000, genetic drift becomes the predominant paradyme.  This is what I would expect (exactly where the numbers lie is outside of my capacity to predict, but I expected that at some point genetic drift vastly dominates over selection.)  So, as expected, if there are too many alleles in a population, they act as noise, and the signal of the new mutation is drowned out by the noise of all the other alleles flying around everywhere.

Now, the real question is how many alleles are in the average human population?  So far the answer you provided is, "most organisms, including humans, share almost identical genomes."  When the possibility exists of there being 100,000 alleles in the coding DNA of myslef and my wife, in addition there's the active, but not coding DNA (introns, etc.)  When that kind of numbers are being talked about, if 90% of our genes are identical, and the other 10% have an average of 5 alleles, that's still a lot of alleles.  Therefore, within the scope of the numbers that we are dealing with "almost identical" is a pretty mushy term.

Is there a hard estimate of how many alleles are in the population of a typical human community?  (I assume that the alleles in my town are more important to me than additional alleles floating around darkest Africa somewhere.)

  
JAM



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(Permalink) Posted: Mar. 09 2008,23:36   

Quote (bFast @ Mar. 09 2008,22:42)
Now, the real question is how many alleles are in the average human population?

Not at all. The real question is, how many SELECTABLE alleles are there versus how many alleles that produce no change in fitness?
 
Quote
So far the answer you provided is, "most organisms, including humans, share almost identical genomes."  When the possibility exists of there being 100,000 alleles in the coding DNA of myslef and my wife,...

My training is in mammalian genetics, and I have never heard the term "alleles" used in that context. I think you're missing the point.
Quote
...in addition there's the active, but not coding DNA (introns, etc.)  When that kind of numbers are being talked about, if 90% of our genes are identical, and the other 10% have an average of 5 alleles, that's still a lot of alleles.

But not all of them affect fitness.

Moreover, there are genes for which selection drives polymorphism, such as those in the Major Histocompatibility Complex.
 
Quote
Is there a hard estimate of how many alleles are in the population of a typical human community?  (I assume that the alleles in my town are more important to me than additional alleles floating around darkest Africa somewhere.)

That's funny that you should put it in such disturbingly quasi-racist terms, as Africans, being from the cradle of mankind, tend to be much more polymorphic (they have lots more alleles/gene) than any of the human groups that left Africa.

  
bFast



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(Permalink) Posted: Mar. 09 2008,23:59   

JAM, "That's funny that you should put it in such disturbingly quasi-racist terms"

I didn't mean slight.  I only was reaching for a population that was physically the farthest away from me.  I am likely to mate within my community, not a distant community.  The calculations need only reference the assessible genepool, not the total conceivable genepool.

I am still not finding an answer to my question, however.  How many alleles are likely to exist within the human population in the average community.  I can accept that many alleles are "not selectable", "fully neutral".  Fine enough, how many "selectable" alleles are there in a typical community of humans?  

I've been trying to find the answer to the question.  So far I've found the following site: http://books.google.ca/books?i....U&hl=en

It says the following:  
Quote
Perhaps as many as half of the loci in the human population are polymorphic


Quote
the chances of two people who are both "Caucasoid" differing in genetic constitution at one site on a given chromosome are about 14.3 per cent.


If I read this correctly, there's LOTS of alleles!!

  
Bob O'H



Posts: 2153
Joined: Oct. 2005

(Permalink) Posted: Mar. 10 2008,01:21   

bFast - just a couple of observations.
1. It would help if you could clarify your terminology.  I think when you write "alleles" you mean "genes".  In Zachriel's notation, when he has a string of numbers (1112111), each number is a "gene", and each value that a gene can take is an allele.  I think you're describing the same thing, but you're using "allele" when you mean "gene".

Yeah, I know.  Terminology is a pain.  But it will help everyone understand what you're doing.

2. I agree with Zachriel that you have an odd selection scheme.  A "better" scheme might be to select an individual at random to die, and then select the replacement with a probability proportional to the individual's fitness (i.e. divide by the sum of the fitnesses).  Or have a discrete time model and at each generation pick N individuals with replacement with probabilities proportional to the individuals' fitnesses.

3. The reason the focal gene's frequency drifts when there are more genes is that it has a smaller effect on fitness.  If we just think of the binary case, the genetic variance for one gene is p_i(1-p_i) where p_i is the frequency of the 1 allele, and the total genetic variance is sum p_j(1-p_j).  The proportion of variance for one gene is then

p_i(1-p_i)/(sum p_j(1-p_j))

and obviously the sum increases as each new gene is added, so the proportional effect of the ith allele get smaller.  Hence, the effect on fitness is less (because it is the absolute numbers you are using for that), so drift becomes more important.

--------------
It is fun to dip into the various threads to watch cluelessness at work in the hands of the confident exponent. - Soapy Sam (so say we all)

   
JAM



Posts: 517
Joined: July 2007

(Permalink) Posted: Mar. 10 2008,02:09   

Quote (bFast @ Mar. 09 2008,23:59)
JAM, "That's funny that you should put it in such disturbingly quasi-racist terms"

I didn't mean slight.

It sure seemed that way. You're ignoring my point, which is highly relevant to your question.
Quote
I only was reaching for a population that was physically the farthest away from me.  I am likely to mate within my community, not a distant community.

Does your wife know about this? Seriously, do you not have any African-Americans in your community?
Quote
The calculations need only reference the assessible genepool, not the total conceivable genepool.

Why? You're not making any sense.
Quote
I am still not finding an answer to my question, however.

That's because, as Bob and I have noted, you are mangling the relevant terminology. Hint: geneticists don't use the term "genepool."
Quote
How many alleles are likely to exist within the human population in the average community.

In Africa, or in North Dakota? I can't see how there wouldn't be "average communities" in both places. Or are you hinting at racism again?
Quote
I can accept that many alleles are "not selectable", "fully neutral".

Those are generally described as polymorphisms. There are tens or hundreds of thousands.
Quote
Fine enough, how many "selectable" alleles are there in a typical community of humans?

I don't know, but I know that each of us is heterozygous for 5-10 recessive lethal alleles. Does that help?

The other place to look is in the huge study of Icelandic folks, which would only provide a lower bound, as they are very inbred.
Quote
If I read this correctly, there's LOTS of alleles!!

Is that a problem?

Google's not going to help if you use the wrong terminology.

  
Zachriel



Posts: 2709
Joined: Sep. 2006

(Permalink) Posted: Mar. 10 2008,09:53   

Quote (bFast @ Mar. 09 2008,22:42)
Zachriel:      
Quote
That's a rather odd selection method. You pit organism 1 against organism 2, but it's not the victor that reproduces, but a recombination of two other organisms. I suppose it should result in evolution towards higher fitness, though. I'll test it to be sure.

This is certainly not sexual selection.  But why should we assume that the victor should also get the privelage of reproduction.  Am I to assume that shortly after my handicapped friend I get chased by the bear, and he gets eaten, I get to reproduce?

Thanks for providing your algorithm. I have reproduced your results. As I had expected, your selection method does result in strong positive selection. Starting from randomized genomes of 0's and 1's, the population rapidly evolves to maximum fitness. With recombination turned on, that's all 1's; 1111111111111111....


   ' This one dies
   If pFit < rFit Then
       r = r1: c = c1
   Else
       r = r2: c = c2
   End If


--------------
Proudly banned three four five times by Uncommon Descent.
There is only one Tard. The Tard is One.

   
bFast



Posts: 44
Joined: Mar. 2008

(Permalink) Posted: Mar. 10 2008,09:53   

JAM, you bore me.  You don't at all answer my real question, but spend all your energy trying to twist what I am saying into something racist.

  
bFast



Posts: 44
Joined: Mar. 2008

(Permalink) Posted: Mar. 10 2008,09:59   

Zachriel, "Starting from randomized genomes of 0's and 1's, the population rapidly evolves to maximum fitness."

Yes. My algorithm works.  However, the greater the number of alleles, the more slowly any one evolves to maximum fitness.  By about 20,000 they all mostly just wander about aimlessly.

How many alleles that actually do something exist in the average human community?  What is the reasonable number that I should be using when running my sim?

  
Zachriel



Posts: 2709
Joined: Sep. 2006

(Permalink) Posted: Mar. 10 2008,11:39   

Quote (bFast @ Mar. 09 2008,22:42)
You will note that when the allele count is 200, this sim works as expected, when it is 2000, it works as expected -- more slowly than the first, but it still evolves.   When the allele count gets to 20,000, genetic drift becomes the predominant paradyme.  This is what I would expect (exactly where the numbers lie is outside of my capacity to predict, but I expected that at some point genetic drift vastly dominates over selection.)  So, as expected, if there are too many alleles in a population, they act as noise, and the signal of the new mutation is drowned out by the noise of all the other alleles flying around everywhere.

Of course. So? With a (nearly) neutral mutation, we expect that most will be lost. (With your randomized genome with a size of 2000, the average fitness of each organism is 1000 with a standard deviation of ~22, so a single allele change from a 1 to a 2 is insignificant.) Keep in mind the chance of fixation of a (nearly neutral) mutation is (nearly) equal to the proportion in the population. If at a given locus, 1% of the population has the 2-allele, then we would expect the chance of fixation to be about 1% (perhaps a bit better because there is weak selection).

However, if we introduce the occasional random mutation, the results are strikingly different. The population rapidly evolves by sorting through the randomized 0's and 1's of the genome. Once some order is imposed, the 2-allele then becomes a significant benefit and the selection becomes stronger.

As to your question about natural genetic variations, not only do mutations add variation, but we also have variation due to geographic separation. Your simulation assumes random mating across the population, which will tend to lead to a monomorphic population. However, the Allele Blender uses proximity for both environmental and mating selection. This results in geographic patterns of diversity.

It may be a few days, but I'll try to provide more specifics.

--------------
Proudly banned three four five times by Uncommon Descent.
There is only one Tard. The Tard is One.

   
bFast



Posts: 44
Joined: Mar. 2008

(Permalink) Posted: Mar. 10 2008,12:34   

It seems to me that there are three classes of alleles that are of interest:

- Primarily beneficial alleles, those that have not yet fixed, but eventually will.  Probably a small number.

- Alleles that cause differences between individuals, but are not easily rated as better or worse compared to their sibling alleles.  Like, who's to say that curly hair is better or worse than straight.  In some circomstances one will be favored over another, but hardly with universality.

- Alleles that are functionally identical to their sibs even though they are technically different.  Such as an alternate amino within the same family, causing the same net result.  I think these can be ignored.

So the two numbers of interest are: beneficial alleles, on the rise, and alleles that cause phenotypal differences, but not universal advantage.

As human populations have, until the last couple of centries, been predominantly located into communities, I would assume that numbers from the Icelandic study mentioned by JAM would make sense.

  
bFast



Posts: 44
Joined: Mar. 2008

(Permalink) Posted: Mar. 10 2008,13:14   

Let me just also say, in case it makes for easier numbers, that we don't by any means need human numbers.  We could take numbers from any other species of mammal as far as I am conserned.

  
Zachriel



Posts: 2709
Joined: Sep. 2006

(Permalink) Posted: Mar. 10 2008,13:22   

Quote (bFast @ Mar. 10 2008,09:59)
Zachriel, "Starting from randomized genomes of 0's and 1's, the population rapidly evolves to maximum fitness."

Yes. My algorithm works.  However, the greater the number of alleles, the more slowly any one evolves to maximum fitness. By about 20,000 they all mostly just wander about aimlessly.

That is not what my results show. With a randomized genome of 20,000 genes (0's and 1's), population of 100, no mutation, your selection algorithm, per generation,

        G        Avr. Fit
        0         10010
        1         10038
        2         10077
        3         10121
        4         10180
        5         10220
        10       10411
        20       10741
        30       10994
        40       11216
        50       11383


In other words, definitely not drift. It's easy to understand why you saw what you wanted to see within these long strings of numbers.

Which brings us to a broader point. Try to hold your own views skeptically. Instead of trying to merely confirm them, try to falsify them. Even if you think you have demonstrated your point, someone might vary the selection algorithm slightly and produce a different result. You have to be able to explain not only your own results, but everyone else's too.


        11326 11428 11409 11396 11408 11411 11333 11380 11334 11369
        11325 11318 11455 11374 11370 11359 11361 11406 11338 11371
        11373 11306 11412 11413 11382 11407 11414 11379 11373 11371
        11407 11370 11387 11398 11326 11365 11417 11397 11405 11420
        11376 11393 11421 11378 11389 11401 11371 11394 11437 11387
        11383 11377 11381 11356 11379 11386 11381 11397 11372 11395
        11339 11400 11383 11353 11351 11425 11411 11384 11408 11386
        11404 11377 11388 11420 11375 11394 11345 11371 11397 11398
        11426 11416 11368 11373 11414 11355 11385 11341 11377 11362
        11383 11358 11408 11363 11355 11396 11345 11448 11362 11372


--------------
Proudly banned three four five times by Uncommon Descent.
There is only one Tard. The Tard is One.

   
J-Dog



Posts: 4402
Joined: Dec. 2006

(Permalink) Posted: Mar. 10 2008,13:27   

Quote (bFast @ Mar. 10 2008,13:14)
Let me just also say, in case it makes for easier numbers, that we don't by any means need human numbers.  We could take numbers from any other species of mammal as far as I am conserned.

Welcome to open posting, bfast.  I once was Glarson and DRat so that I could post at UD.

And in honor of your attempt to break free of your brush with the Dark Side, I propose, as you suggested, a non-human mammal species to use with your sim.  

I suggest a mammal covered with blubber, not a lot of brain power, and constantly attempting to increase its breeding opportunities through loud, agressive, and to us here, non-sensical chest beating behaviour.  Of course I am talking about a Walrus (aka DaveScot) and an Innuit woman.

Please put this in your sim for me.  (Although I suspect this will not prove a very fruitful use of your time.)

Thanks,

J-Dog
Banned Twice - And loving it.

--------------
Come on Tough Guy, do the little dance of ID impotence you do so well. - Louis to Joe G 2/10

Gullibility is not a virtue - Quidam on Dembski's belief in the Bible Code Faith Healers & ID 7/08

UD is an Unnatural Douchemagnet. - richardthughes 7/11

  
JAM



Posts: 517
Joined: July 2007

(Permalink) Posted: Mar. 10 2008,15:25   

Quote (bFast @ Mar. 10 2008,09:53)
JAM, you bore me.  You don't at all answer my real question,


Really? How did you conclude that the three responses were not sincere efforts to answer your question at all?

1) There are tens or hundreds of thousands.

2) I don't know, but I know that each of us is heterozygous for 5-10 recessive lethal alleles. Does that help?

3) The other place to look is in the huge study of Icelandic folks, which would only provide a lower bound, as they are very inbred.
Quote
...but spend all your energy trying to twist what I am saying into something racist.

Then why not simply explain what you mean by "average community"? In the context of your question, I have no idea what you mean by that qualification.

I don't think that any twisting is involved in concluding that your trying to exclude "darkest Africa" from your analysis *seems* racist.

  
JAM



Posts: 517
Joined: July 2007

(Permalink) Posted: Mar. 10 2008,15:28   

Quote (bFast @ Mar. 10 2008,12:34)
As human populations have, until the last couple of centries, been predominantly located into communities, I would assume that numbers from the Icelandic study mentioned by JAM would make sense.

So have you changed your mind since you wrote, "You don't at all answer my real question,..."?

I still don't know what you mean by "communities," as average African communities would still be much more polymorphic than average European or Asian communities.

  
bFast



Posts: 44
Joined: Mar. 2008

(Permalink) Posted: Mar. 10 2008,15:29   

J-Dog:
Quote
Of course I am talking about a Walrus (aka DaveScot) and an Innuit woman.


I was actually quite seriously thinking that we may know more about alleles that do stuff in dogs, as dogs have been bread from wolves into so many varieties.  So maybe we have a better logging of the effect of various alleles in dogs/wolves than in other mammals, such as walruses.  Oh yea, we'll have to include your genes.

  
bFast



Posts: 44
Joined: Mar. 2008

(Permalink) Posted: Mar. 10 2008,15:32   

JAM, the numbers available for the Icelandics seems just ducky as I suggested two posts back.  Though we may see the Icelandic community as "ingrown" by modern standards, I suspect that 200 years ago, (most of human evolution happened before 200 years ago, yes?) or 500 years ago, small, relatively isolated communities were much more common than they did now.  Selecting for an isolated community should produce a smaller allele count than would a count of all alleles within humanity.

  
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