by Joe Felsenstein and Michael Lynch
The blogs of creationists and advocates of ID have been abuzz lately about exciting new work by William Basener and John Sanford. In a peer-reviewed paper at Journal of Mathematical Biology, they have presented a mathematical model of mutation and natural selection in a haploid population, and they find in one realistic case that natural selection is unable to prevent the continual decline of fitness. This is presented as correcting R.A. Fisher’s 1930 “Fundamental Theorem of Natural Selection”, which they argue is the basis for all subsequent theory in population genetics. The blog postings on that will be found here, here, here, here, here, here, and here.
One of us (JF) has argued at The Skeptical Zone that they have misread the literature on population genetics. The theory of mutation and natural selection developed during the 1920s, was relatively fully developed before Fisher’s 1930 book. Fisher’s FTNS has been difficult to understand, and subsequent work has not depended on it. But that still leaves us with the issue of whether the B and S simulations show some startling behavior, with deleterious mutations seemingly unable to be prevented from continually rising in frequency. Let’s take a closer look at their simulations.
Basener and Sanford show equations, mostly mostly taken from a paper by Claus Wilke, for changes in genotype frequencies in a haploid, asexual species experiencing mutation and natural selection. They keep track of the distribution of the values of fitness on a continuous scale time scale. Genotypes at different values of the fitness scale have different birth rates. There is a distribution of fitness effects of mutations, as displacements on the fitness scale. An important detail is that the genotypes are haploid and asexual — they have no recombination, so they do not mate.
After giving the equations for this model, they present runs of a simulation program. In some runs with distributions of mutations that show equal numbers of beneficial and deleterious mutations all goes as expected — the genetic variance in the population rises, and as it does the mean fitness rises more and more. But in their final case, which they argue is more realistic, there are mostly deleterious mutations. The startling outcome in the simulation in that case is there absence of an equilibrium between mutation and selection. Instead the deleterious mutations go to fixation in the population, and the mean fitness of the population steadily declines.
Why does that happen? For deleterious mutations in large populations, we typically see them come to a low equilibrium frequency reflecting a balance between mutation and selection. But they’re not doing that at high mutation rates!
The key is the absence of recombination in these clonally-reproducing haploid organisms. In effect each haploid organism is passed on whole, as if it were a copy of a single gene. So the frequencies of the mutant alleles should reflect the balance between the selection coefficient against the mutant (which is said to be near 0.001 in their simulation) versus the mutation rate. But they have one mutation per generation per haploid individual. Thus the mutation rate is, in effect, 1000 times the selection coefficient against the mutant allele. The selection coefficient of 0.001 means about a 0.1% decline in the frequency of a deleterious allele per generation, which is overwhelmed when one new mutant per individual comes in each generation.
In the usual calculations of the balance between mutation and selection, the mutation rate is smaller than the selection coefficient against the mutant. With (say) 20,000 loci (genes) the mutation rate per locus would be 1/20,000 = 0.00005. That would predict an equilibrium frequency near 0.00005/0.001, or 0.05, at each locus. But if the mutation rate were 1, we predict no equilibrium, but rather that the mutant allele is driven to fixation because the selection is too weak to counteract that large a rate of mutation. So there is really nothing new here. In fact 91 years ago J.B.S. Haldane, in his 1927 paper on the balance between selection and mutation, wrote that “To sum up, if selection acts against mutation, it is ineffective provided that the rate of mutation is greater than the coefficient of selection.”
If Basener and Sanford’s simulation allowed recombination between the genes, the outcome would be very different — there would be an equilibrium gene frequency at each locus, with no tendency of the mutant alleles at the individual loci to rise to fixation.
If selection acted individually at each locus, with growth rates for each haploid genotype being added across loci, a similar result would be expected, even without recombination. But in the Basener/Stanford simulation the fitnesses do not add — instead they generate linkage disequilibrium, in this case negative associations that leave us with selection at the different loci opposing each other. Add in recombination, and there would be a dramatically different, and much more conventional, result.
Most readers may want to stop there. We add this section for those more familiar with population genetics theory, simply to point out some mysteries connected with the Basener/Stanford simulations:
2. The behavior of their iterations in some cases is, well, weird. In the crucial final simulation, the genetic variance of fitness rises, reaches a limit, bounces sharply off it, and from then on decreases. We’re not sure why, and suspect a program bug, which we haven’t noticed. We have found that if we run the simulation for many more generations, such odd bouncings of the mean and variance off of upper and lower limits are ultimately seen. We don’t think that this has much to do with mutation overwhelming selection, though.
3. We note one mistake in the Basener and Sanford work. The organisms’ death rates are 0.1 per time step. That would suggest a generation time of about 10 time steps. But Basener and Stanford take there to be one generation per unit of time. That is incorrect. However the mutation rate and the selection coefficient are still 1 and 0.001 per generation, even if the generations are 10 units of time.
Joe Felsenstein, originally trained as a theoretical population geneticist, is an evolutionary biologist who is Professor Emeritus in the Department of Genome Sciences and the Department of Biology at the University of Washington, Seattle. He is the author of the books “Inferring Phylogenies” and “Theoretical Evolutionary Genetics”. He frequently posts and comments here.
Michael Lynch is the director of the Biodesign Center for Mechanisms of Evolution at Arizona State University, and author of “The Origins of Genome Architecture” and, with Bruce Walsh, of “Genetics and Analysis of Quantitative Traits”. Six of his papers are cited in the Basener/Stanford paper.
You do not seem to understand this. We are measuring mutations that the machinery failed to correctly repair. It doesn’t matter whether the machinery could or could not repair the lesion, only whether it did or did not. Any time that a scientist talks of a mutation rate (without some qualifier), they are referring to the observed rate, given whatever repair mechanisms are active.
Knock out one of the repair mechanisms, and you get a cell with a higher mutation rate. DNA lesions are still arising at the same rate, they just aren’t getting repaired so efficiently.
You got this almost exactly wrong. The thing about uracil is as follows:
Cytosine de-aminates to produce uracil. The cell can recognize who is the mistake in the resulting G:U base pair, i.e. the U, and uracil-DNA glycosylase (UDG) removes the uracil and base excision repair fixes the lesion, returning it to a G:C base pair. Since the U was correctly repaired, it doesn’t show up as a mutation. On the other hand, if the cytosine has been 5-methylated, then 5mC deaminates to T, and UDG doesn’t recognize the error. TDG isn’t anything like as effective.
Interestingly, organisms like humans who methylate CpG dinucleotides are observed to have far fewer CpG dinucleotides than GpC dinucleotides. Can you see why?
By sequencing both parents.
Can you give me an example of how this would isolate a recombination event.
That’s right! Thank you for all the pretty pictures. This one is on point:
You find one allele in one parent, another allele in the other parent, and both in the offspring.
Or, one allele present in one of the parents, is missing in the offspring.
In place of things dying?
What is the “creation” part of natural selection? Don’t we have to create something before it can be selected? Why do evolutionists like to skip that part?
Because they BELIEVE, that’s why!
Really, Bill, you googled “guanine to uracil mutation” and got a lot of images.
You didn’t bother to check (or understand) that none of them show guanine deaminating to produce uracil.
I’d love to see the chemical pathway for a G -> U mutation…
In diploids, you do this with the two gametes that create an individual, and a gamete that it transmits to its offspring, Such as finding that in the latter a portion of a chromosome consists of the first part from the maternally-derived genome and the last part from the paternally-derived genome.
Alan, this right here is why you should retire as a moderator, effective immediately.
Faizal posts nothing but noise, and then complains about the noise, and you apologize to him.
Just quit already Alan. Because an atheist says only atheist posts are valuable, that doesn’t make it so. You have never been able to shed your bias appropriately enough to be a moderator. You don’t need Lizzie’s approval, just quit.
Huh? You asked
“How do we know this difference is not caused by genetic recombination?”
I answered your question: Sequence both parents and show that the point mutation is de novo.
I am unsure what to “isolate a recombination event” means.
We can easily rule OUT a recombination event being the source (see above). To demonstrate that a recombination event HAS occurred, you need to access the grandparent’s DNA too. Hence the annoying need for three-generation families to map disease genes by old-fashioned linkage analysis.
I asked before but it was lost in the cloud of phoodoo doo doo.
Is this new paper by B&S just a continuation of his “Mendel’s Accountant” nonsense? The ideas sound very similar if not identical.
So, bottom line, meltdown is a non issue except for small populations, and we already knew that small populations are at risk for extinxtion.
Not really. Mendel’s Accountant simulates a finite population. It also has some sort of recombination (like many people I have been scared off of downloading it by warnings about viruses, so I’m not sure).
The Basener/Sanford paper discusses models of selection versus mutation in infinitely large populations, modeling them by deterministic iteration of the frequencies of classes of equally-fit haploid gametes.
Yes yes bla bla more opinion from you. But you completely skipped the part where you explain how designed organisms avoid deleterious mutations.
If there is much more going on, which creates organisms and novel systems, then I its not important to explain how organisms avoid deleterious mutations(who says they are), you still obviously don’t get it. YOU have to explain what is creating. Random mutations is a lark.
When did I mention deaminating thats your claim. I was talking about guanine mutating to uracil.
This is a reaction catalyzed by enzymes yet the discussion is about mutation rate. How you got here is beyond me.
We are not skipping that part. We are discussing purifying selection. The “creation” part is the introduction of a deleterious mutation. Are you going to deny the existence of deleterious mutations as well? Does the Designer need to create them?
No, no, I said the CREATING part, not the destroying part. What is the creating part?
Mutational meltdown is mostly of interest to conservation biologists, but naturally it pops up in discussions on the evolutionary consequences of mutation pressure, like this one. I wouldn’t be worrying too much that the human race is genetically deteriorating though.
Have it your way. We are only discussing the “destroying part”, OK?
So what prevents the accumulation of deleterious mutants in designed organisms, if not natural selection?
DNA repair is not performed by enzymes?
Tell us more, Bill. What mechanism is responsible for DNA repair?
Uhh, yes it is. You’re still going to have to explain how that “much more going on” counteracts the effect of deleterious mutations.
It is you who said organisms “strive to succeed” as some sort of get out of jail free-card. You have done zero work making it clear what that is even supposed to mean, or how it works, or counteracts the effect of deleterious mutations.
It is random mutation, and they’re not “a lark”. The genes affect the physiological properties of organisms, and mutations in those genes cause changes to those properties. So new properties emerge when mutations cause new functional combinations of, or new genetic material.
Now, the only thing you have to add, is to declare in a mocking tone how much you fail to believe this and how preposterous you find it. Good for you, have fun with that. I don’t know how to refute an incredulous stare. I can’t make you believe things you clearly don’t want to and you deeply despise.
Just know this, your ability to declare and assert your disbelief is not a rational argument that should cause anyone else to change their views.
Are you trying to claim that repair enzymes in the germ line can catalyze the removal of an amine group from cytosine? If so what support do you have?
Bill is seeming unusually confused today. Even pictures don’t seem to be helping.
You continue to get things almost exactly wrong.
Originally, you claimed
which, in my generosity, I took as a typo/minor misunderstanding, since 5mC –> T cannot be identified as the erroneous base, whereas for C –> U the repair machinery can spot that U does not belong. Why else would you mention Uracil?
Guanine to thymidine (or uracil, wtf?) is a transversion.
The totality of your response was to lmgtfy a set of images found by the search “guanine to uracil mutation”, as if that contradicted anyting I had written. None of them show any such thing. That’s the downside of Google, mate.
The weirdness continues
Again I say, huh?
Just because enzymes that catalyse deamination are called deaminases, does not mean that every deamination is so catalyzed.
Deamination (of cytosine in particular) occurs SPONTANEOUSLY and is a major cause of point mutations.
So your question to Rumraket
is incoherent. You are confusing the spontaneous deamination reaction with the enzyme-catalyzed repair that (often) fixes the error.
(I am glad that you specified the germ line, though; otherwise we’d be off on a B cell wild goose chase.)
If so please support the claim that this process happens in the germ line. Please keep your answers concise and to the point.
It’s easy with flightless birds if one doesn’t want to see the powerlessness of natural selection:
“The evolution of loss of flight is one the most recurrent limb modifications encountered in nature (1). In fact, Darwin used the occurrence of flightless birds as an argument in favor of his theory of natural selection (2). He proposed that loss of flight could evolve selection in favor of larger bodies and relaxed selection due to the absence of predators. Loss of flight has evolved repeatedly, and is found among 26 families of birds in 17 different orders (1). Moreover, recent studies strongly suggest that the ratites (ostriches, emus, rheas, cassowaries and kiwis), long thought to derive from a single flightless ancestor, may constitute a polyphyletic group characterized by multiple independent instances of loss of flight and convergent evolution (3–5). However, despite the ubiquity and evolutionary importance of loss of flight (6), the underlying genetic and molecular mechanisms remain unknown.
The lack of predators and birdies lose the major function and natural selection is impotent… Who can argue with that?
Stories like that has gotta be true…
The lower than expected frequency of CpG dinucleotides.
How’s that for concision?
I’m willing to accept it’s not true. What do you have to offer in its stead?
I guess you gonna have to learn to live with yourself…somehow…
And at a third grade reading level, with no
polysyllabic words words of more than two syllableslong words.
Have you figured out if the evolution of flight in bats was a gain of function / increase in information yet? Or is that question still too scary to address?
So you have nothing to offer. Just thought I’d double check.
Do you really want me to spell it out for you?
Everyone, in the right frame of mind, mind you, knows what I mean when I say
“A story like that has gotta be true”, maybe with one exception of keiths… Especially if the contents of my comment totally contradicts my very last statement…
Are you that dumb? Well, I’ll leave it up the public to decide… When I read your comments, I begin to believe that sheer dumb luck has something to do with evolution of stupidity…
A question about your OP. You said:
Joe, my math is a little shaky on this, you said “if the mutation rate were 1”, but what if the mutation rate were 0.001, then does this mean the equilibrium frequency is 0.001/0.001 = 1, and thus selection is too weak? In other words the mutation rate doesn’t have to be even as high as 1? Am I not reading this correctly????
Also your value of s=.001 seems to be taken from Basener’s paper which is taken by a suggestion form Kimura.
So some questions. This is the AVERAGE s coefficient, what about the deviation from the mean? We could have a LOT of mutations below .001, that is lot of mutants with S < .001. So does the mutation selection balance formula incorporate a distribution of s values rather than s = .001, but rather mean_of_s = 0.001?
Also, Basener's simulation is obviously modeling a finite population. The mutation selection balance formulas are generally based on Fisher's assumptions of infinite populations. Is that right?
What conditions will that mutation selection balance cease to hold for finite populations. I saw some papers with nightmarish derivations for mutation selection in finite populations like this one which I could hardly make heads or tails of:
So I presume, the answer to the question, "when does the assumption of infinite populations sizes become inappropriate" is not so clear cut. Is that right?
Please tell me you are not serious Sal…
“It is clear that population genetics models rely on assumptions known to be false, and are subject to the realism / tractability trade-off. The simplest population-genetic models assume random mating, non-overlapping generations, infinite population size, perfect Mendelian segregation, frequency-independent genotype fitnesses, and the absence of stochastic effects; it is very unlikely (and in the case of the infinite population assumption, impossible) that any of these assumptions hold true of any actual biological population. More realistic models, that relax one of more of the above assumptions, have been constructed, but they are invariably much harder to analyze. It is an interesting historical question whether these ‘standard’ population-genetic assumptions were originally made because they simplified the mathematics, or because they were believed to be a reasonable approximation to reality, or both. This question is taken up by Morrison (2004) in relation to Fisher’s early population-genetic work. “ Samir Okasha 2006/2012
Hey J-mac, you’re good, where’d you come up with that? I wasn’t aware of it.
I do my reading… I try to be as good as you… that’s my motivation… well … one of them… 😉
I’m glad I could help…
My my but there are some cowardly ID-Creationists out there. Too afraid to answer the simplest questions about their claims.
Do I what? I did not ask a question.
Please do so.
You might think that, but I’ve seen no evidence that it’s true. Communication is difficult. You assume that everybody knows what you mean when you say that. But I suspect at this point nobody is really listening to you.
There’s nothing unusual about that when dealing with IDCreationists. They typically contradict themselves multiple times in the same paragraph.
Likewise yourself. And the public seems to have decided.
According to you, I’m exactly as your deity intended me to be. So suck it up.
I’m sure if we did some analysis we’d find that the IDCreationists mention “evolution” 1000x more then they mention anything related to their own position. Their actions speak the words that they cannot speak themselves.
There would have to be some evidence other than Darwinists speculating about some similarities and avoiding the chasms of differences…
It’s funny how the great leaps in evolution were apparently accomplished by natural processes in the past but today, after 100 years of mutagenesis experiments of fruit flies, we can only see 3 results:
Same flies, defective flies and dead flies…
Obviously, Darwinists can keep their fingers crossed in hopes that one day it is going be their day… and the information will increase in some miracles and unknown today way…
Until that happens, I wouldn’t keep my hopes very high, if I were a Darwinist, especially considering how population genetics speculative assumptions are exposed to be not only totally unrealistic, in comparison to real life scientific facts, but simply just false…
I’ve always believed that hope is a good thing but not when it is based on unfounded, unrealistic and blind faith…
That’s what evolution is found on but the materialistic propaganda sells as science… It’s a neat trick…
“If you repeat a lie often enough, people will believe it, and you will even come to believe it yourself…” – Joseph Goebbels
Given that, could you explain how you have determined that a specific mutation causes a loss of information?
For example, in the LTEE, when the ability to consume citrate appeared in the population did the “information”:
A) Go up
B) Go down
C) Stay the same
If you answer A or B could you quantify the change of information? I.E. what was the specific change FROM and TO in the quantity of information.
Given that you won’t be able to do that, does that not give you pause regarding your general understanding of “information”?
Also, given that your claimed source of information is a miracle anyway, why is it a problem that Darwinists are hoping for a miracle? If it’s not a problem for you why is a problem for any one else?
Perhaps, but not by you. You’ve certainly done no such thing. Otherwise you’d have published a paper and had your name entered into the scientific annals of people who’ve actually done something to progress our understanding of the world. Unless of course you want to link to where you’ve destroyed population genetics?
Remind me what your explanation for extant biology is? A magic man in the sky wasn’t it?
Are bacteria in LTEE any closer to anything other than bacteria?
Maybe they should let the bacteria out in the wild to turn it to anything other than bacteria?
But then again, if the “evolved” bacteria didn’t survive in the wild, it would be devastating to all Darwin followers…
So, think it’s safer for the Darwin faithful to keep the bacteria in the lab and pretend that something has been accomplished; bacteria outperforming other bacteria over thousands of generations and be ecstatic about it…
Keep your fingers crossed! That’s what blind faith is all about … 😉
Evasive non-answer noted.
My my but there are some cowardly ID-Creationists out there. Too afraid to answer the simplest questions about their claims.
ID-Creationists make lots of stupid claims but “mutations can only decrease information” is one of the dumbest. The simple reason is what any one mutation can do, another can undo.
If AAC –> AAG is a loss of information then
AAG –> AAC must be a gain of information by definition
Such mutations are empirically observed in the real world. They are called back mutations or reverse mutations.
That was not my question. You made a claim regarding the “information change”. I’m simply asking a trivial follow up question that, if you really knew what you claim to know, you’d have no trouble answering.
No, there is an obvious reason why that would happen and would be fully expected. Seems you can’t think of it however.
Sure, I guess our definitions of “something accomplished” differ substantially.
Here is what the LTEE has accomplished: http://myxo.css.msu.edu/ecoli/
Here at TSZ we see what you have accomplished. Some risible OP’s.
Sure, characterise it however you like. The fact remains that your side has done literally nothing to elucidate your position and how “Intelligent Design” works.
You appear mistaken whose faith is blind. I have “faith” that a methodical scientific investigation into the mechanisms of evolution will illustrate those same mechanisms.
For example, here are 255 scientific papers related to the LTEE. If you call that “blind faith” I have to wonder if you even know what “faith” means.
And all that new knowledge despite the fact that “bacteria are still bacteria”. If the experement was trying to evolve non-bacteria you might have a point.
In summary, you said this:
And I asked you how you have determined that the information did not increase. You simply avoided that question and instead answered questions I did not answer. Presumably because that’s your defense mechanism when your core beliefs are challenged.