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Author Topic:   Fred Williams' Mutation Rate Article Obsolete
Fedmahn Kassad
Inactive Member


Message 1 of 45 (58640)
09-29-2003 9:35 PM


I have been quite busy recently, and haven’t had much time for posting. But I want to return to a reply that I made to Fred Williams that he just left hanging. The post is at
http://EvC Forum: Evolution and Probability -->EvC Forum: Evolution and Probability
Let me briefly summarize. Fred has written an article claiming that estimated deleterious mutation rates are too high for man and chimpanzees to share a common ancestor. I will not go into all the details of his argument, as it can be found at 404 Not Found
This article is the source of Fred’s claims of 40 offspring or 60 offspring, or even more required per breeding couple in order maintain equilibrium (i.e., to avoid genetic deterioration). So many offspring for a hominid are clearly impossible, so Fred concludes that this falsifies common ancestry for humans and chimps.
Of course Fred did no original research on this matter. He has merely selectively used the results of real scientists and interpreted these results in such a way as to prop up his faith. He ignored possible explanations to the (then) dilemma in favor of his conclusion, which was High rate supports recent creation of man. He also brushed off the possibility that the estimates may have been too high. He said that this was doubtful.
Fred, your 15 minutes are up. Your article is based on so much outdated information, it is no longer remotely accurate. In addition, I have been in contact with three of the people whose results/comments Fred uses to build his argument. These people are Dr. Adam Eyre-Walker, Dr. James Crow, and Dr. Michael Nachman. In the case of Dr. Nachman, Fred did not use his work in the article, but frequently uses a Nachman paper to justify his continued use of the argument.
All three scientists told me the same thing. They said previous estimates of U, the deleterious mutation rate, were all based on gene estimates conducted prior to the Human Genome Project. These estimates were in the range of 60,000-100,000 genes. The actual count by the HGP is in the range of 30,000. All three scientists told me that this means their estimate of U was too high by about a factor of 2.
To quote Fred: What pray tell does this mean? What are the authors failing to make crystal clear? It means that the number of conceptions (not offspring as Fred writes) would be less than 10 in order to maintain genetic equilibrium. This reduces the required number of surviving offspring down to somewhere between 2 and 5 in order to maintain equilibrium. Of course that’s not quite as compelling as writing 40 births before we get one offspring that escapes a new defect!, but that’s what can happen when one jumps to conclusions.
So, Fred, when can we anticipate that you will correct or remove your article? I know that others have asked you the same thing. Of course you may feel free to contact the scientists you have quoted, but you know that they will tell you the same thing. Just know that the next time you make this claim, you will be making a claim that you can no longer defend. The only way to salvage your article is to come up with estimates that were based on the correct number of genes. (Note that the Fay, Wyckoff, and Wu article doesn't meet this criterion).
Let the hand waving begin.
FK

Replies to this message:
 Message 2 by Rei, posted 09-30-2003 12:43 AM Fedmahn Kassad has not replied
 Message 3 by sfs, posted 10-04-2003 11:35 PM Fedmahn Kassad has replied
 Message 9 by Fred Williams, posted 10-07-2003 8:29 PM Fedmahn Kassad has replied
 Message 40 by wehappyfew, posted 11-10-2003 7:23 PM Fedmahn Kassad has not replied

  
Rei
Member (Idle past 7031 days)
Posts: 1546
From: Iowa City, IA
Joined: 09-03-2003


Message 2 of 45 (58682)
09-30-2003 12:43 AM
Reply to: Message 1 by Fedmahn Kassad
09-29-2003 9:35 PM


What? Fred leave in the middle of a conversation when he has trouble defending his stance? Refuse to address issues when you point out where he is completely inaccurate?
That would never happen.
------------------
"Illuminant light,
illuminate me."
{Is a statement like the above needed? - Adminnemooseus}
[This message has been edited by Adminnemooseus, 09-29-2003]

This message is a reply to:
 Message 1 by Fedmahn Kassad, posted 09-29-2003 9:35 PM Fedmahn Kassad has not replied

Replies to this message:
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sfs
Member (Idle past 2552 days)
Posts: 464
From: Cambridge, MA USA
Joined: 08-27-2003


Message 3 of 45 (59446)
10-04-2003 11:35 PM
Reply to: Message 1 by Fedmahn Kassad
09-29-2003 9:35 PM


Re: Truncation Selection
Since Fred doesn't seem to be interested in defending his article, let me give it a try. It is true that studies estimating the rate of deleterious mutations in humans overestimated the number of genes by about a factor of two. It is therefore reasonable to conclude that deleterious mutations coding sequence are only half as common as previously estimated. On the other hand, recent estimates of the amount of functional noncoding sequence are much higher than they used to be; the latest estimate is that it's about twice as much as the coding sequence. Thus the reduction in the estimated number of genes may be more than compensated for by the increased estimate of noncoding sites for deleterious mutations.
The problem with Fred's analysis is not the deleterious mutation rate, which may be correct (or may not -- the uncertainty is large), but what he does with it. He assumes that the only way to maintain genetic equilibrium is to keep producing offspring that have no new defects, which requires an impossible birthrate. That's simply wrong. It's quite possible for virtually all offspring to have new defects without it suffering genetic deterioration. Mutations are lost as well as created every generation; the only requirement for equilibrium is that as many be lost as created. In a real, natural population, pretty much all of the members have some slightly deleterious traits. The ones who have the most deleterious alleles are the ones least likely to reproduce, reducing the average number of deleterious alleles in the next generation. When that reduction exactly balances the increase due to new mutations, the population is at equilibrium. For example, if the deleterious mutations rate is 1.6/birth, if the selection coefficient for each is 1% (i.e. each makes the individual 1% less likely to reproduce), and if each pair of parents has 6 offspring (of whom on average two survive to reproduce), then the equilibrium average number of deleterious alleles is about 42. (This assuming multiplicative fitness -- no truncation selection here.)
Whether this simple scheme is adequate to handle deleterious mutations is an interesting question, and the kind of question that exercises people like James Crow. Fred's cartoon version has nothing to do with reality, however.

This message is a reply to:
 Message 1 by Fedmahn Kassad, posted 09-29-2003 9:35 PM Fedmahn Kassad has replied

Replies to this message:
 Message 4 by Brad McFall, posted 10-04-2003 11:53 PM sfs has not replied
 Message 6 by Fedmahn Kassad, posted 10-05-2003 12:25 AM sfs has not replied

  
Brad McFall
Member (Idle past 5051 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 4 of 45 (59448)
10-04-2003 11:53 PM
Reply to: Message 3 by sfs
10-04-2003 11:35 PM


Re: Truncation Selection
So, does the "equilibrium" deteriorate with or without return points? I can imagine not using Euclid's ideas and yet THIS WOULD NOT differntiate Gould's "plateau" from Hilbert's incidence geometry thus the benfit taken advantge by the 'next' generation (Croizat) still remains uncommented. I know you might think of a "higher order catastrophe set" but as to which is nature and which is nurture even if returned short of a determinate new stat of form changes remains magic to me and unable to address BOTH positive and negative sheets relative to any mutation relative to any trait relative to any form relative mendels line... I couldnt really get much father with Crow but maybe I just havent had this chance.

This message is a reply to:
 Message 3 by sfs, posted 10-04-2003 11:35 PM sfs has not replied

  
Rei
Member (Idle past 7031 days)
Posts: 1546
From: Iowa City, IA
Joined: 09-03-2003


Message 5 of 45 (59451)
10-05-2003 12:10 AM
Reply to: Message 2 by Rei
09-30-2003 12:43 AM


My apologies; Fred has just been driving me crazy in another thread, by refusing to answer my posts while badmouthing me in discussions with other posters. It's very frustrating when someone is effectively calling you an idiot (actually, a lot worse) concerning your knowledge about how to use something that you actually use at work, and have read about and worked with since middle school, and they've never touched one.
------------------
"Illuminant light,
illuminate me."

This message is a reply to:
 Message 2 by Rei, posted 09-30-2003 12:43 AM Rei has not replied

Replies to this message:
 Message 7 by Fedmahn Kassad, posted 10-05-2003 12:28 AM Rei has not replied

  
Fedmahn Kassad
Inactive Member


Message 6 of 45 (59455)
10-05-2003 12:25 AM
Reply to: Message 3 by sfs
10-04-2003 11:35 PM


Re: Truncation Selection
sfs: Since Fred doesn't seem to be interested in defending his article, let me give it a try. It is true that studies estimating the rate of deleterious mutations in humans overestimated the number of genes by about a factor of two. It is therefore reasonable to conclude that deleterious mutations coding sequence are only half as common as previously estimated. On the other hand, recent estimates of the amount of functional noncoding sequence are much higher than they used to be; the latest estimate is that it's about twice as much as the coding sequence. Thus the reduction in the estimated number of genes may be more than compensated for by the increased estimate of noncoding sites for deleterious mutations.
FK: Hey, I know you. What you say was approximately stated by 2 of the 3 guys that I contacted. They said the genes were overestimated, but this would be partially compensated since the amount of functional noncoding DNA is higher than previously believed. However, they said that when both factors were accounted for, the overall deleterious mutation rate was certainly less than 3.
I didn't even address theoretical mechanisms for dealing with the problem if the deleterious mutation rate still seems too high. I just wanted to point out that Fred's article is obsolete, and see how long it takes him to correct it. My guess is that it will still be floating around 10 years from now.
Also, as Dr. Nachman pointed out, these estimates are gross approximations. He implied that it would be quite silly to develop an evolution bashing argument based on estimates of U.
FK

This message is a reply to:
 Message 3 by sfs, posted 10-04-2003 11:35 PM sfs has not replied

  
Fedmahn Kassad
Inactive Member


Message 7 of 45 (59456)
10-05-2003 12:28 AM
Reply to: Message 5 by Rei
10-05-2003 12:10 AM


Rei: It's very frustrating when someone is effectively calling you an idiot (actually, a lot worse) concerning your knowledge about how to use something that you actually use at work, and have read about and worked with since middle school, and they've never touched one.
You will get used to it. After all, Fred is an electrical engineer. Apparently that gives him the expertise to write genetics articles and call those who don't agree with him "boneheads" and such. This didn't start with you. He has been doing it for years.
FK

This message is a reply to:
 Message 5 by Rei, posted 10-05-2003 12:10 AM Rei has not replied

Replies to this message:
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Admin
Director
Posts: 13013
From: EvC Forum
Joined: 06-14-2002
Member Rating: 1.9


Message 8 of 45 (59525)
10-05-2003 3:14 PM
Reply to: Message 7 by Fedmahn Kassad
10-05-2003 12:28 AM


Fedmahn Kassad writes:
You will get used to it. After all, Fred is an electrical engineer. Apparently that gives him the expertise to write genetics articles and call those who don't agree with him "boneheads" and such. This didn't start with you. He has been doing it for years.
This is well worth commenting on. First, one of my degrees is in electrical engineering, so I hope people understand that not all electrical engineers are like Fred. Some electrical engineers *are* able to disagree without being disagreeable. You gotta admit, though, that Fred even at his most obstinate, abusive and closeminded, is highly entertaining.
Second, when I developed this site I had the naive idea that moderators could keep discussions on track, that merely pointing out guideline violations would send members into spasms of productive and insightful dialogue. Needless to say my perception of what is possible has suffered some dramatic revisions over the past few years. Many (not all, mind you, or even most, but many) of my moderating attempts have left threads worse off, not better.
So even though Fred is violating more guidelines than he's following, my inclination is to leave him alone for the most part as long as people are able to maintain a healthy perspective on it and seem able to handle him on their own, which seems to be the case so far. I wish Fred would actually discuss something instead of engaging in variations around the theme of the "all this has been discussed before, if you said that in a meeting everyone would laugh at you, and I can't believe you still hold your erroneous beliefs" pose, but history says moderator intervention is unlikely to improve the situation.
As far as I know, Fred's claims of being an electrical engineer working in the computer industry are true, but, at least as expressed here at EvC, he has a rather cartoonish view of how people in our industry behave and interact. Particularly strange is his belief, at least as he appears to express it here, that people in the computer industry hold to a Creationist view of topics like information and genetic algorithms. I see no evidence of this among my own coworkers, and the publications Fred would normally subscribe to as a member of the IEEE (Institute of Electrical and Electronic Engineers) and the ACM (Association of Computing Machinery) express strongly opposing views, and in fact often present papers that are at the forefront of developing these nascent sciences.
------------------
--Percy
EvC Forum Administrator

This message is a reply to:
 Message 7 by Fedmahn Kassad, posted 10-05-2003 12:28 AM Fedmahn Kassad has not replied

Replies to this message:
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Fred Williams
Member (Idle past 4874 days)
Posts: 310
From: Broomfield
Joined: 12-17-2001


Message 9 of 45 (60003)
10-07-2003 8:29 PM
Reply to: Message 1 by Fedmahn Kassad
09-29-2003 9:35 PM


Fedman's usual vapor
Fedmahn has stated nothing original from his usual tirade about my article (a new strawman has arisen though that my conclusion was a High rate supports recent creation of man. Hmm). Missing again is any new U rate (I happen to know Keightley's adjusted number, which still does not bode well for evolution). But that is beside the point. My time is limited here due to a new assignment at work, and I just don't have the time for vaporous posts from someone whose only apparent "evidence" is "this scientist told me this!". Huh? Serious inquires only need apply!
Sfs on the other hand made a few comments worth addressing:
quote:
He assumes that the only way to maintain genetic equilibrium is to keep producing offspring that have no new defects, which requires an impossible birthrate. That's simply wrong. He assumes that the only way to maintain genetic equilibrium is to keep producing offspring that have no new defects, which requires an impossible birthrate. That's simply wrong. It's quite possible for virtually all offspring to have new defects without it suffering genetic deterioration. Mutations are lost as well as created every generation; the only requirement for equilibrium is that as many be lost as created.
Great! Then provide *evidence* for your claim. Crow attempted to slow the process mathematically using assumed synergistic epistasis. First, there is little or no evidence for synergistic epistasis, second, he only slowed the deterioration process. Do you really think an accumulative rate of 3 per individual per generation can be brought to a net of 0 over the entire population through selection? That is some trick! Problem is, it’s a story, not science. See article for details...
(BTW updated, abridge one coming soon...)

This message is a reply to:
 Message 1 by Fedmahn Kassad, posted 09-29-2003 9:35 PM Fedmahn Kassad has replied

Replies to this message:
 Message 10 by Brad McFall, posted 10-07-2003 10:22 PM Fred Williams has not replied
 Message 11 by Fedmahn Kassad, posted 10-07-2003 10:32 PM Fred Williams has not replied
 Message 12 by sfs, posted 10-07-2003 11:08 PM Fred Williams has replied
 Message 13 by sfs, posted 10-08-2003 12:00 AM Fred Williams has replied

  
Brad McFall
Member (Idle past 5051 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 10 of 45 (60015)
10-07-2003 10:22 PM
Reply to: Message 9 by Fred Williams
10-07-2003 8:29 PM


Re: Fedman's usual vapor
I'm curious how Mammy is going to show the bacteria have the same equilibrated OFFSPRING as the genes for horns could antenna even mobile across the F2 in the espts. I rarely show my Irish Elk but then there is little interest probably on the alleomtery among all snake taxa as to the distance between the eyes compared to the size of the eyes caused or not by the continual growth rate. Gould's notion of homology could be seen as well in the mammals horns as the snakes' vertebrae properly undertood relative to sisters but let me get the time too. Looks like this is all we will learn this semester.

This message is a reply to:
 Message 9 by Fred Williams, posted 10-07-2003 8:29 PM Fred Williams has not replied

  
Fedmahn Kassad
Inactive Member


Message 11 of 45 (60018)
10-07-2003 10:32 PM
Reply to: Message 9 by Fred Williams
10-07-2003 8:29 PM


Fred's usual handwave
Fred: Fedmahn has stated nothing original from his usual tirade about my article (a new strawman has arisen though that my conclusion was a High rate supports recent creation of man. Hmm).
FK: Perhaps you should reread your article. You concluded that since U was so high, this supported a recent creation of man. You wrote an entire paragraph on it. Hmm.
Fred: Missing again is any new U rate (I happen to know Keightley's adjusted number, which still does not bode well for evolution).
FK: You didn’t think I would do your homework for you, did you? But I am interested to see how long it takes for the new article to show up, as well as your usual spin.
Fred: I just don't have the time for vaporous posts from someone whose only apparent "evidence" is "this scientist told me this!".
FK: That’s hilarious, considering that your article was just an exercise in data mining and contained no original research. Where did your initial estimates of U come from? Duh, a scientist told you.
FK

This message is a reply to:
 Message 9 by Fred Williams, posted 10-07-2003 8:29 PM Fred Williams has not replied

  
sfs
Member (Idle past 2552 days)
Posts: 464
From: Cambridge, MA USA
Joined: 08-27-2003


Message 12 of 45 (60023)
10-07-2003 11:08 PM
Reply to: Message 9 by Fred Williams
10-07-2003 8:29 PM


Fred's response (I'll give my own response in a while) got me looking at his article again. A couple of additional problems with it poked up their heads when I did. First, there's his treatment of the Nachman and Crowell paper. Here's what Fred says about it:
quote:
Their ultimate explanation is the same used by Eyre-Walker, Keightley, Crow, et al, truncation selection. Again, there is NO evidence to support that such strict truncation selection occurs in nature, and even if it did would not solve the problem. The Genetics authors admit that truncation selection "seems unrealistic", but submit this view simply because the alternative explanation is unacceptable to them - that men and apes do not share a common ancestor.
Here's what Nachman and Crowell actually wrote:
quote:
The problem can be mitigated somewhat by soft selection (WALLACE 1991 ) or by selection early in development (e.g., in utero). However, many mutations are unconditionally deleterious and it is improbable that the reproductive potential on average for human females can approach 40 zygotes. This problem can be overcome if most deleterious mutations exhibit synergistic epistasis; that is, if each additional mutation leads to a larger decrease in relative fitness (KONDRASHOV 1995 ; CROW 1997 ; EYRE-WALKER and KEIGHTLEY 1999 ). In the extreme, this gives rise to truncation selection in which all individuals carrying more than a threshold number of mutations are eliminated from the population. While extreme truncation selection seems unrealistic, the results presented here indicate that some form of positive epistasis among deleterious mutations is likely.
They do not propose truncation selection as the solution; they propose synergistic epistasis. Truncation is a form (an extreme form) of synergistic epistasis, but all synergistic epistasis is not truncation. Their statement is quite clear, and Fred's report of their conclusion is simply wrong.
And then there's this:
quote:
Crow concludes by stating that the high mutation rate helps explain the advantage of sex to evolution. Sure, sex will certainly slow the propagation of harmful mutations (a conservation property completely consistent with a creationist viewpoint). But Crow is forgetting the other side of the coin, that sex will also slow the propagation of beneficial mutations! Recombination has long been considered a paradox among evolutionists9, since it greatly hinders the spread of those crucial "beneficial" mutations needed to make a man out of a monkey. Right out of the gate the mutation must overcome the 50% recombination barrier.
Here Fred is completely confused. Recombination doesn't hinder the spread of beneficial alleles: recombination increases the effectiveness of natural selection, so recombination both increases the spread of beneficial alleles and increases the rate at which deleterious alleles are eliminated. This advantage is widely thought to be the reason that organisms put up with the twofold cost of sex, since sex is necessary for recombination. See, for example,
Curr Biol. 2003 Jan 21;13(2):R68-70.
Genome evolution: recombination speeds up adaptive evolution.
Marais G, Charlesworth B.

This message is a reply to:
 Message 9 by Fred Williams, posted 10-07-2003 8:29 PM Fred Williams has replied

Replies to this message:
 Message 14 by Fred Williams, posted 10-08-2003 6:21 PM sfs has replied

  
sfs
Member (Idle past 2552 days)
Posts: 464
From: Cambridge, MA USA
Joined: 08-27-2003


Message 13 of 45 (60031)
10-08-2003 12:00 AM
Reply to: Message 9 by Fred Williams
10-07-2003 8:29 PM


Fred, what I described was just soft selection. Under soft selection, the number of deleterious alleles increases until the population is in equilibrium. This is hardly novel, and the math is easy. I wrote a simulation to do it; the code is at Page not found | Whitehead Institute, results at No webpage found at provided URL: www-genome.wi.mit.edu/~sfs/del1.6.gif and No webpage found at provided URL: www-genome.wi.mit.edu/~sfs/del3.gif. (The first shows the average number of deleterious alleles, starting at zero, accumulating and leveling off for 1.6 deleterious mutations/generation, and the second shows the same for 3.0/generation, and also shows the effect of truncation selection. But our website appears to be down at the moment.) Slowing the process mathematically is easy; the question is how biologically plausible the solution is. How many mildly deleterious mutations can a population tolerate, and what is the real spectrum of deleterious mutations, and generally how common is soft selection?. Crow (and Nachman, following him) is inclined to think that soft selection isn't that common, while Wallace thinks (thought? is he still alive?) otherwise. As far as I know, there really aren't a lot of well-established facts to draw conclusions from. Some selection is undoubtedly hard (there are lethal mutations), and some selection is undoubtedly soft, and some deleterious alleles undoubtedly have epistatic interactions. No one knows at this point what an accurate model of the whole process really looks like. What you have done is take an extreme model (that all selection is hard) that's known to be wrong, combined it with an extreme value from the possible range for the key parameter, ignored a known effect (epistasis) that works in the opposite direction, and then concluded from the whole effort that an entire field of science is wrong. This is just not the way to produce a valid argument.
And where on earth do you get the claim that Crow "only slowed the deterioration"?

This message is a reply to:
 Message 9 by Fred Williams, posted 10-07-2003 8:29 PM Fred Williams has replied

Replies to this message:
 Message 15 by Fred Williams, posted 10-08-2003 7:23 PM sfs has replied

  
Fred Williams
Member (Idle past 4874 days)
Posts: 310
From: Broomfield
Joined: 12-17-2001


Message 14 of 45 (60162)
10-08-2003 6:21 PM
Reply to: Message 12 by sfs
10-07-2003 11:08 PM


sfs argument truncated...
quote:
They do not propose truncation selection as the solution;
Yes they do.
quote:
they propose synergistic epistasis.
Yes, they do!
quote:
Truncation is a form (an extreme form) of synergistic epistasis, but all synergistic epistasis is not truncation.
Not true. Synergistic epistasis promotes some level of truncation selection.
quote:
Their statement is quite clear, and Fred's report of their conclusion is simply wrong.
No, it is you who is wrong. I have a paper from Crow via personal correspondence to prove it. While it is at home, I recall the term he used was pseudo-truncation selection (Crow agrees that truncation selection in general is unrealistic). I don’t think the paper was ever published, but I’m not positive about that. If I remember I’ll dig it up at home tonight.
quote:
Recombination has long been considered a paradox among evolutionists9, since it greatly hinders the spread of those crucial "beneficial" mutations needed to make a man out of a monkey. Right out of the gate the mutation must overcome the 50% recombination barrier.
Here Fred is completely confused. Recombination doesn't hinder the spread of beneficial alleles: recombination increases the effectiveness of natural selection, so recombination both increases the spread of beneficial alleles and increases the rate at which deleterious alleles are eliminated. This advantage is widely thought to be the reason that organisms put up with the twofold cost of sex, since sex is necessary for recombination. See, for example,
Curr Biol. 2003 Jan 21;13(2):R68-70.
Genome evolution: recombination speeds up adaptive evolution.
Marais G, Charlesworth B.
To be kind this is an illusion, to be frank it is pure nonsense. I already refuted this in a debate with Scott Page:
404 Not Found
(scroll about half way down to " "Sexual Recombination and the Power of Natural Selection")
In a nutshell, recombination increases the effectiveness of natural selection only in a harmful mutation environment. That is, only at some level of harmful mutation rate does sexual recombination start to become an advantage over clonal lineages.

This message is a reply to:
 Message 12 by sfs, posted 10-07-2003 11:08 PM sfs has replied

Replies to this message:
 Message 16 by vik, posted 10-09-2003 8:46 AM Fred Williams has not replied
 Message 18 by sfs, posted 10-09-2003 11:26 AM Fred Williams has replied

  
Fred Williams
Member (Idle past 4874 days)
Posts: 310
From: Broomfield
Joined: 12-17-2001


Message 15 of 45 (60172)
10-08-2003 7:23 PM
Reply to: Message 13 by sfs
10-08-2003 12:00 AM


Sfs's auto-truncate program!
quote:
the second shows the same for 3.0/generation, and also shows the effect of truncation selection.
Sfs, even with ‘doTruncate = 0’ you are using SEVERE truncation selection!!!!
quote:
/* Sort the offspring by their survival probability; take the top N */
for (ioff = 0; ioff < totoff; ioff++) {sortInd[ioff] = ioff;}
Bzzzt! You cannot sort offspring by survival probability, then lop off the bottom! This is classic truncation selection!
No wonder your graph leveled out!
I am however enjoying this exchange and appreciate your approach, horribly flawed as it is.
Against my better judgment, I am going to post a partial piece of a program endeavor I began that will be a much more rigorous and accurate simulation of population genetics. I have deleted some of the routines, and some of it I haven’t written yet. I will only leave this up for a short time:
404 Not Found

This message is a reply to:
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