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Author Topic:   The End of Evolution By Means of Natural Selection
ZenMonkey
Member (Idle past 3529 days)
Posts: 428
From: Portland, OR USA
Joined: 09-25-2009


Message 361 of 851 (555988)
04-16-2010 4:09 PM


Restoration of diminished alleles.
Faith and I had the following exchange in Message 65 of the Reduction of Alleles by Natural Selection (Faith and ZenMonkey Only) thread.

Faith writes:

ZenMonkey writes:

So we should agree if fur color is a neutral trait that confers no reproductive advantage, then if some accident reduces the frequency of a given allele at some point, but doesn't eliminate it, then it's highly probable that eventually the allele will reestablish itself in the population and regain its former standing, so to speak.

I don't see why this is "highly probable." It COULD regain its former standing, but it doesn't seem to me to be "probable" that it would come back to that extent from its highly reduced position. I would think something would have to favor it, some sort of selection for that to happen -- yes, reproductive advantage of some sort.

As I understand it so far, in Faith's model every species has a set number of alleles for any given gene locus, and thus a finite set of possible traits arrising from those alleles. In the simple example I've been using I posit a situation in which a single gene controls fur color in rabbits, with a pool of alleles coding for black fur, grey fur, etc. It seems logical to me that if fur color is a genuinely neutral trait giving no reproductive advantage, then the prevelance of any given fur color in a population will be primarily determined by the dominance relationships among the various alleles. In other words, if the allele for black fur is dominant to all the others, that for brown fur is dominant to grey but recessive to black, and that tan is recessive to all the others, then under normal, essentially static conditions there should be relatively more black rabbits than all the others, more browns than greys, and that tan rabbits will be the rarest. That's what the standard Mendelian d/r chart leads me to think anyway. Here's how I work out all the possible combinations of four alleles.

Black + Black = Black
Black + Brown = Black
Black + Grey = Black
Black + Tan = Black

Brown + Black = Black
Brown + Brown = Brown
Brown + Grey = Brown
Brown + Tan = Brown

Grey + Black = Black
Grey + Brown = Brown
Grey + Grey = Grey
Grey + Tan = Grey

Tan + Black = Black
Tan + Brown = Brown
Tan + Grey = Grey
Tan + Tan = Tan

So all the possible pairings give us 7 Black rabbits, 5 Brown rabbits, 3 Grey rabbits, and 1 Tan rabbit. I believe that this would be the general statistical distribution of fur color in any group of rabbits with these four alleles. Again, in this model we have complete dominance, a single gene coding for a single trait, and a trait that is neutral in character, giving no reproductive advantage.

My assertion is this: if some accident temporarily reduced the numbers of a certain allele - say that there was a volcanic erruption that just happened to bury almost but not quite all of the black rabbits - then eventually that allele would re-establish itself in the general population in the same relative position it had before. To me, this simply follows out from the math, that with nothing else to stop it, the Black allele would simply by virtue of its being dominant to all the others, have to regain its position after a sufficient number of generations, even if you started with just one surviving black rabbit.

Given the limits I've described, am I right, or am I missing something here?

It now occurrs to me that a second, perhaps even more vital question arrises from this situation. Given all of the above, it is also inevitable that the Tan allele would have to manifest itself from time to time in every generation, even if it were recessive to all the others? Is there any way that we can have this Tan allele hiding in the gene pool but never actaully producing any tan rabbits?

For the sake of the argument, please stick with the given limits and don't drag in partial dominance, mutation, natural selection with regard to this trait, or other concepts that lie outside the realm of this hypothetical. I really believe that this should work out just by virtue of the math, but I'd like to be sure.


I have no time for lies and fantasy, and neither should you. Enjoy or die.
-John Lydon

What's the difference between a conspiracy theorist and a new puppy? The puppy eventually grows up and quits whining.
-Steven Dutch


Replies to this message:
 Message 362 by nwr, posted 04-16-2010 4:25 PM ZenMonkey has responded
 Message 364 by PaulK, posted 04-16-2010 5:11 PM ZenMonkey has not yet responded
 Message 365 by Dr Adequate, posted 04-16-2010 5:23 PM ZenMonkey has responded
 Message 371 by Faith, posted 04-16-2010 6:18 PM ZenMonkey has not yet responded

  
nwr
Member
Posts: 5804
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 4.6


Message 362 of 851 (555994)
04-16-2010 4:25 PM
Reply to: Message 361 by ZenMonkey
04-16-2010 4:09 PM


Re: Restoration of diminished alleles.
I disagree with your math.

ZenMonkey writes:
Again, in this model we have complete dominance, a single gene coding for a single trait, and a trait that is neutral in character, giving no reproductive advantage.

That's the key here.

With no reproductive advantage, the relative proportion of each gene in the next generation will be almost identical to the relative proportion in the current generation.

The black gene remains dominant in the genetic sense, that possession of that gene results in the black trait. However, the proportion of black creatures will forever remain insignificantly small unless there is some statistical freak event that causes a major change in the relative gene frequencies.


This message is a reply to:
 Message 361 by ZenMonkey, posted 04-16-2010 4:09 PM ZenMonkey has responded

Replies to this message:
 Message 363 by CosmicChimp, posted 04-16-2010 4:49 PM nwr has acknowledged this reply
 Message 366 by Faith, posted 04-16-2010 5:44 PM nwr has responded
 Message 382 by ZenMonkey, posted 04-16-2010 10:25 PM nwr has acknowledged this reply

  
CosmicChimp
Member
Posts: 310
From: Muenchen Bayern Deutschland
Joined: 06-15-2007


Message 363 of 851 (556002)
04-16-2010 4:49 PM
Reply to: Message 362 by nwr
04-16-2010 4:25 PM


Re: Restoration of diminished alleles.
Random mating is assumed to be occurring in such ideal situations.

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PaulK
Member
Posts: 17008
Joined: 01-10-2003
Member Rating: 2.6


Message 364 of 851 (556005)
04-16-2010 5:11 PM
Reply to: Message 361 by ZenMonkey
04-16-2010 4:09 PM


Re: Restoration of diminished alleles.
I think you are confusing the allele with the trait. Black fur is a trait. The form of the gene that causes black fur is the allele.

I think that the dominance of the gene is not even relevant for considering the incidence of black fur. There might be a small recovery in the next generation because rabbits homozygous for the black fur allele will have only black-furred offspring, but that's all I can think of. Without selection, it's down to drift.


This message is a reply to:
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Dr Adequate
Member (Idle past 70 days)
Posts: 16112
Joined: 07-20-2006


Message 365 of 851 (556009)
04-16-2010 5:23 PM
Reply to: Message 361 by ZenMonkey
04-16-2010 4:09 PM


No, You Lose
Given long enough, and without any mutations happening, then one allele will become fixed. That's just math.

In many cases there has not been enough time, and in no cases have there been no mutations.

To me, this simply follows out from the math, that with nothing else to stop it, the Black allele would simply by virtue of its being dominant to all the others ...

You haven't done the math, and you are misunderstanding the word "dominant".

Faith is, of course, talking complete rubbish. But unfortunately, so are you.

I really believe that this should work out just by virtue of the math, but I'd like to be sure.

You haven't done the math. Where is the math?

You need "Wounded King", an actual geneticist, to talk about this, or you need me, an actual mathematician. Or both of us working in concert.

The "Great Debate" concept of these forums is stupid and should be abolished.


This message is a reply to:
 Message 361 by ZenMonkey, posted 04-16-2010 4:09 PM ZenMonkey has responded

Replies to this message:
 Message 386 by ZenMonkey, posted 04-16-2010 11:57 PM Dr Adequate has responded

  
Faith 
Suspended Member (Idle past 463 days)
Posts: 35298
From: Nevada, USA
Joined: 10-06-2001


Message 366 of 851 (556015)
04-16-2010 5:44 PM
Reply to: Message 362 by nwr
04-16-2010 4:25 PM


dominance
Surely genetic dominance does confer some population dominance too.

If there is no reproductive advantage then all the rabbits will pass on their alleles equally, and that means that whenever the dominant allele for black fur combines with the alleles for any other color, black fur will show up in the majority of combinations possible.

parents --------------- offspring
BB + gg (grey) will get 4 Bg, all black
BB + tt (tan) = 4 Bt, all black
BB + bb (brown) = 4 Bb, all black

Next generation all the heterozygous B's also pass on their blackness, Bt + Bt = BB, Bt, Bt, tt = three blacks and a tan, though Bt with tt = Bt, Bt, tt, tt = two blacks and two tans for a standoff. Meanwhile the homozygous blacks, BB, are still mating with the homozygous tans, greys and browns and repeating the same distribution of the first generation. And of course all the other colors are combining and increasing their own number according to their relative dominance. But over time the black SHOULD come to dominate.

It would be quite a project to work it all through with the hierarchy of dominance specified, but since black is dominant over all the others it seems pretty clear that eventually black should come to dominate the whole population, all other things being equal.

If not, why not?

(I don't think this has anything to do with what I'm trying to prove, but it's interesting -- hm, correction, it's relevant since I've had to take this into account myself but it isn't going to defeat my model is what I really mean. A population could conceivably reach the point where it's all black with mostly BBs but a few Bt's, Bg's and Bb's, or even a complete lack of the alleles for any of them, so that in a migration it could happen that all the heterozygous ones get swept along leaving the parent population all BB. If some BB's also come along in the migration black may yet come to dominate there too but meanwhile the recessives will be liberated so that it will start getting the other colors as well as the black.

ABE: After the rest of the discussion here I realize the black won't come to dominate without reproductive advantage of some sort (and in fact that was my very first response to Zen Monkey on the other thread when he raised this question), but it is true that all the other colors will now show up in the new population that were suppressed by the dominant black in the parent population (by drift of course in that situation).

ABE: AND, it doesn't have to have been a dominant that had such a high frequency in the parent population. The genetically dominant black could have been the one suppressed that then could have been taken into the new population where it would probably already be of a higher frequency than in the first population.

Edited by Faith, : No reason given.

Edited by Faith, : No reason given.

Edited by Faith, : No reason given.

Edited by Faith, : No reason given.

Edited by Faith, : No reason given.

Edited by Faith, : No reason given.

Edited by Faith, : No reason given.


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Replies to this message:
 Message 367 by PaulK, posted 04-16-2010 6:01 PM Faith has responded
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PaulK
Member
Posts: 17008
Joined: 01-10-2003
Member Rating: 2.6


Message 367 of 851 (556018)
04-16-2010 6:01 PM
Reply to: Message 366 by Faith
04-16-2010 5:44 PM


Re: dominance
This is exactly the situation I presented in my post. You are starting with rabbits homozygous for the B allele and thus the incidence of the black-fur trait increases - but only for one generation (and it decreases in the next).

However the relative frequency of the B allele does not increase. The number of copies of it doubles with each generation but only because the size of the population doubles in each generation. And that is all that is happening. Therefore after the initial increase (due only to the assumption that the surviving black rabbits are homozygous for B) the proportion of black rabbits will not increase either.


This message is a reply to:
 Message 366 by Faith, posted 04-16-2010 5:44 PM Faith has responded

Replies to this message:
 Message 369 by Faith, posted 04-16-2010 6:11 PM PaulK has responded

  
Dr Adequate
Member (Idle past 70 days)
Posts: 16112
Joined: 07-20-2006


(1)
Message 368 of 851 (556020)
04-16-2010 6:04 PM
Reply to: Message 366 by Faith
04-16-2010 5:44 PM


Re: dominance
Surely genetic dominance does confer some population dominance too.

No. You are stupidly, pathetically, droolingly, hopelessly incompetent and stupid and ignorant about the very meaning of the technical terms used in genetics.

Once more, once again, once again for one more time --- go and read a textbook of genetics.


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Faith 
Suspended Member (Idle past 463 days)
Posts: 35298
From: Nevada, USA
Joined: 10-06-2001


Message 369 of 851 (556021)
04-16-2010 6:11 PM
Reply to: Message 367 by PaulK
04-16-2010 6:01 PM


Re: dominance
Unfortunately I can't stay around for this until later but please indicate which post of yours you are referring to. Thanks.

This message is a reply to:
 Message 367 by PaulK, posted 04-16-2010 6:01 PM PaulK has responded

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PaulK
Member
Posts: 17008
Joined: 01-10-2003
Member Rating: 2.6


Message 370 of 851 (556022)
04-16-2010 6:13 PM
Reply to: Message 369 by Faith
04-16-2010 6:11 PM


Re: dominance
The reply to ZenMonkey just above. Re: Restoration of diminished alleles. (Message 364) I thought that it was pretty obvious that it had to be a recent post.

Edited by PaulK, : No reason given.

Edited by PaulK, : No reason given.


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Faith 
Suspended Member (Idle past 463 days)
Posts: 35298
From: Nevada, USA
Joined: 10-06-2001


Message 371 of 851 (556025)
04-16-2010 6:18 PM
Reply to: Message 361 by ZenMonkey
04-16-2010 4:09 PM


Re: Restoration of diminished alleles.
Far as I can see, you are right. I did it with alleles instead of colors and now notice that it works out the same as what you did.

This message is a reply to:
 Message 361 by ZenMonkey, posted 04-16-2010 4:09 PM ZenMonkey has not yet responded

  
nwr
Member
Posts: 5804
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 4.6


Message 372 of 851 (556030)
04-16-2010 6:56 PM
Reply to: Message 366 by Faith
04-16-2010 5:44 PM


Re: dominance
Faith writes:
Surely genetic dominance does confer some population dominance too.

That depends on what you mean by "population dominance".

If 1% of the alleles present at that location are black (taken as a percentage over the entire population), then 1.75% of the population will have a black trait. That comes from the counting of instances shown by ZenMonkey, and assumes random distribution of pairings. Nevertheless, in the next generation the proportion of black genes will remain at 1%, again assuming random pairings. In practice there can be some drift, but it will be small unless there is a reproductive advantage for one of the alleles.

Faith writes:
Next generation all the heterozygous B's also pass on their blackness, ...

Actually, no, they don't. If two heterozygous Bs mate, then 1/4 of their offspring will have no B allele. That's the expected statistical outcome, though a particular mating pair might happen to have a different distribution.

Faith writes:
It would be quite a project to work it all through with the hierarchy of dominance specified, but since black is dominant over all the others it seems pretty clear that eventually black should come to dominate the whole population, all other things being equal.

You only have to count the alleles present in the next generation. For a particular mating pair, each of their two alleles has a 50% probability of being used in a particular reproductive event. List out the possibilities, much as ZenMonkey did, and then count. You will see that the proportion in the next generation is the same as in the current generation. The only way that changes, is if there is a selective advantage so that combinations don't all have the same probability of surviving into the next generation.

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 Message 366 by Faith, posted 04-16-2010 5:44 PM Faith has responded

Replies to this message:
 Message 374 by Faith, posted 04-16-2010 7:58 PM nwr has responded

  
Taq
Member
Posts: 8488
Joined: 03-06-2009
Member Rating: 7.4


Message 373 of 851 (556031)
04-16-2010 7:02 PM
Reply to: Message 366 by Faith
04-16-2010 5:44 PM


Re: dominance
It would be quite a project to work it all through with the hierarchy of dominance specified, but since black is dominant over all the others it seems pretty clear that eventually black should come to dominate the whole population, all other things being equal.

If not, why not?

All things being equal, the ratio of black to other colors within the population will stay the same in every generation. You will always have black heterozygous parents having not-black offspring.


This message is a reply to:
 Message 366 by Faith, posted 04-16-2010 5:44 PM Faith has not yet responded

  
Faith 
Suspended Member (Idle past 463 days)
Posts: 35298
From: Nevada, USA
Joined: 10-06-2001


Message 374 of 851 (556038)
04-16-2010 7:58 PM
Reply to: Message 372 by nwr
04-16-2010 6:56 PM


Re: dominance
Next generation all the heterozygous B's also pass on their blackness, ...

Actually, no, they don't. If two heterozygous Bs mate, then 1/4 of their offspring will have no B allele. That's the expected statistical outcome, though a particular mating pair might happen to have a different distribution.

That's exactly what I said in the rest of that sentence, here:

Next generation all the heterozygous B's also pass on their blackness, Bt + Bt = BB, Bt, Bt, tt = three blacks and a tan,

However, I've worked it through and I see that you are all right, the dominants will not change their proportion barring reproductive advantage, they will retain the same proportion through all generations, which is greater than the others, but always the same proportion greater. That is "some population dominance," as I said also -- meaning there will always be more black rabbits than the other three colors, and more browns than greys and tans, and more greys than tans, barring any kind of selecting factor -- but they will not increase in proportion.

But I just realized Zen Monkey is not starting with equal numbers as I am. He's starting with a population in which the dominant blacks have been sharply diminished in number. But the same principle must apply.

Edited by Faith, : No reason given.

Edited by Faith, : No reason given.

Edited by Faith, : No reason given.

Edited by Faith, : No reason given.


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 Message 375 by nwr, posted 04-16-2010 8:10 PM Faith has responded
 Message 376 by RAZD, posted 04-16-2010 8:18 PM Faith has responded

  
nwr
Member
Posts: 5804
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 4.6


Message 375 of 851 (556040)
04-16-2010 8:10 PM
Reply to: Message 374 by Faith
04-16-2010 7:58 PM


Re: dominance
Faith writes:
That is "some population dominance," as I said also -- meaning there will always be more black rabbits than the other three colors, and more browns than greys and tans, and more greys than tans, barring any kind of selecting factor -- but they will not increase in proportion.

That's almost right.

There can still be less blacks than the other colors. But, due to the dominance, the proportion of blacks in the population will be greater than the proportion of black alleles in the gene pool.


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 Message 374 by Faith, posted 04-16-2010 7:58 PM Faith has responded

Replies to this message:
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