Intelligent Design

Academic cover-up: can neutral evolutionary processes rapidly generate complex adaptations?

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In 2010, Lynch and Abegg claimed in a widely cited journal article that neutral evolutionary processes could generate complex adaptations much more rapidly than was previously believed. Their article contained a mathematical flaw, which was pointed out by Dr. Douglas Axe, but Axe’s critique continues to be ignored by senior evolutionary biologists, including the article’s authors, Professor Joe Felsenstein and Professor Larry Moran. Want proof? Read on.

For those readers who don’t know him, Michael Lynch is an eminent scientist: he is Distinguished Professor of Evolution, Population Genetics and Genomics at Indiana University, Bloomington, Indiana. He has also written a two-volume textbook with Bruce Walsh, which is widely regarded as the “Bible” of quantitative genetics. In 2009, he was elected to the National Academy of Sciences. His co-author, Adam Abegg, was an undergraduate student at the time when the paper was published. He is now a Research Assistant at University of Southern California.

For his part, Dr. Douglas Axe is the director of the Biologic Institute. His research uses both experiments and computer simulations to examine the functional and structural constraints on the evolution of proteins and protein systems. After obtaining a Caltech Ph.D., he held postdoctoral and research scientist positions at the University of Cambridge, the Cambridge Medical Research Council Centre, and the Babraham Institute in Cambridge. He has also written two articles for the Journal of Molecular Biology (see here and here for abstracts). He has also co-authored an article published in the Proceedings of the National Academy of Sciences, an article in Biochemistry and an article published in PLoS ONE.

Academic cover-up? You decide

On October 8, 2015, I addressed the following comment to Professor Larry Moran, over on his Sandwalk blog:

Hi Professor Moran,

Frankly, I’d be a lot more impressed with the claims of evolutionists (of whatever stripe) of they were willing to take criticisms by Intelligent Design scientists seriously.

Case in point: consider the 2010 paper by Lynch and Abegg, titled, “The Rate of Establishment of Complex Adaptations” (Molecular Biology and Evolution 27:1404-1414. doi:10.1093/molbev/msq020, available online at http://mbe.oxfordjournals.org/content/27/6/1404.full ), purporting to show that under the neutral theory, complex adaptations could get established in a population a lot faster than previously assumed.

Dr. Doug Axe wrote a response to that paper (“The limits of complex adaptation: An analysis based on a simple model of structured bacterial populations,” BIO-Complexity 2010(4):1-10.doi:10.5048/BIO-C.2010.4, available online at http://bio-complexity.org/ojs/index.php/main/article/view/BIO-C.2010.4 ). Lynch did not reply.

I emailed Lynch a couple of months ago, inviting him to comment on Axe’s paper. To my surprise, he said he hadn’t seen it before. But when I asked him what was wrong with Axe’s criticisms, he declined to be drawn into the discussion.

I also invited you to point out what was wrong with Dr. Axe’s criticisms of Lynch, in an online post on Uncommon Descent at http://www.uncommondescent.com/intelligent-design/id-like-a-straight-yes-or-a-straight-no-professor-moran/ . I’m still waiting.

I also wrote several times to Professor Joe Felsenstein, inviting him to say what was wrong with the paper. At first he promised he would respond, but he hasn’t gotten back to me, after several weeks. I’ve given up sending him reminders.

Something very, very fishy is going on here. It sounds like the evolutionists have given up debating Intelligent Design advocates, and are preferring to either ignore them or lampoon their views, instead…

Professor Moran’s excuse: The math is over my head

In response, Professor Moran wrote a brief comment dated October 8, 2015 (1:51 p.m.), in which he excused himself on the grounds that he wasn’t qualified to assess the mathematical modeling (I’ve highlighted key sentences in bold type – VJT):

Vincent Torely (sic) says,

I also invited you to point out what was wrong with Dr. Axe’s criticisms of Lynch, in an online post on Uncommon Descent. I’m still waiting.

Unlike you and most of your creationist friends, I’m not an expert on everything. In this particular case it requires expertise in mathematical modeling of evolution and I know very little about that subject.

Presumably you don’t either yet you imply that Doug Axe has challenged one of the world’s leading experts on the subject. Why should I take you seriously?

Professor Moran’s disclaimer is very odd, considering that he was confident enough to answer my question (which I posed to him in a May 2015 post), “Are you claiming that Dr. Axe and Dr. Meyer have misconstrued the nature of random genetic drift?” with a simple, unqualified, “Yes.” How could he be so sure of that, if he didn’t understand the math in Dr. Axe’s paper?

Professor Felsenstein’s response: “I’m on it!” (That was three months ago.)

Professor Felsenstein (who is, I have to say, more civil than Larry Moran) then promised to review Axe’s paper, in a brief follow-up comment on the same thread, dated October 8, 2015 (11:36 p.m.):

Vincent Torley recently reminded me of his request (and my excessively optimistic promise) that I look over the math of Lynch and Abegg vs. Axe. I will get that done.

Three months have passed since he made that promise. I might add that I first contacted him about Dr. Axe’s critique of Lynch and Abegg (which is just nine pages long, excluding references), way back in August 2015. That’s five months ago. I realize that he is a busy man, but I have to say that the lack of a response appears rather suspicious to me. Could it be that Professor Felsenstein hasn’t managed to find any errors or gaps in Dr. Axe’s mathematical reasoning? It’s beginning to look that way.

In an email to me, Professor Felsenstein also mentioned that he did not understand why, in Lynch and Abegg’s paper, the rate of occurrence of alleles with multiple mutations would depend on a linear function of the mutation rate, rather than a higher order of the mutation rate. In regard to Dr. Axe’s paper (which he had yet to read), Professor Felsenstein noted that someone putting forward an “impossibility” argument has to close off all available options, and not just some. Otherwise, the argument fails.

Professor Lynch’s response: feigned interest, followed by brusque dismissal

When I first contacted Professor Lynch last year about Dr. Axe’s critique of his 2010 paper, he kindly thanked me for alerting him to it, but claimed he’d never heard of it before, and added it would take some time to get to it (which I took to mean: read and respond to it). When I contacted him subsequently, his reply this time was rather dismissive: he said he didn’t think it was a worthwhile use of his time. And what was his excuse? He said he doubted whether any serious biologist took Dr. Axe’s paper, let alone his journal (BIO-Complexity), seriously.

I have to ask my readers: doesn’t it sound a little suspicious when someone writes a detailed mathematical critique of a paper a scientist has written, and that scientist is initially thankful when his attention is drawn to the critique, but then later on, he refuses to respond to it, simply because he doesn’t think any other scientist would take the paper seriously?

I should add that I bent over backwards to make matters as easy as I could for Professor Lynch to review Dr. Axe’s paper, by cutting and pasting the relevant sections from the paper into my email, to save Professor Lynch the trouble of reading through the entire paper to locate them. I shall reproduce them below, and invite readers to form their own judgments.

What Lynch and Abegg claimed in their paper

In their 2010 paper, Lynch and Abegg argued for “the plausibility of the relatively rapid emergence of specific complex adaptations by conventional population genetic mechanisms.”

After some detailed calculations, Lynch and Abegg concluded (bolding below is mine – VJT):

Noting that realistic population sizes, mutation rates, and selection coefficients have been applied throughout, these results suggest that quite complex alleles, with multiple neutral or deleterious intermediate states, can readily emerge in populations on time scales of 10^3 – 10^8 generations. Thus, for microbes with generation lengths of hours to days and very large population sizes, the mean time to establishment can easily be on the order of a few weeks to several months depending on the complexity of the final allelic state. Even multicellular species, with effective population sizes in the vicinity of 10^6 (Lynch 2007), are capable of establishing fairly complex adaptations on time scales of a few tens of millions of generations, the exact time span depending on the magnitude of the selective (dis)advantages of the intermediate and end states.

A few tens of millions of generations would mean a few tens of millions of years, for most animals. If Lynch and Abegg are correct, then evolutionists all around the world can heave a huge sigh of relief. After all, even a span of 80 million years would represent a mere 2% of the 4-billion-year history of life on Earth, so the origin of complex adaptations within the allotted time-span no longer appears to be much of a problem.

The concluding paragraph of Lynch and Abegg’s paper reads as follows:

Ultimately, the paths most frequently taken in the origins of evolutionary novelties will also depend on the rates at which neutral versus deleterious intermediate mutations arise. However, assuming that the distributions of selection coefficients for de novo mutations are not radically different among organisms, the preceding observations strongly suggest that the paths to adaptation may deviate strongly among organisms from different domains of life. Relative to multicellular eukaryotes, prokaryotes are expected to acquire adaptive alleles by paths involving neutral intermediates several times more rapidly than eukaryotes on a per-generation basis. In contrast, when there are multiple deleterious intermediate steps, multicellular species have much greater expected rates of acquisition of adaptive alleles on a per-generation basis. Of course, because the generation lengths of multicellular species can easily be 10^3 – 10^5 times greater than those for microbes, on an absolute time scale, rates of microbial adaptation may be comparable to or even greater than those for multicellular species even when intermediate allelic states are deleterious. However, the message to be gained from the preceding results is that the elevated power of both random genetic drift and mutation may enable the acquisition of complex adaptations in multicellular species at rates that are not greatly different from those achievable in enormous microbial populations.

The meat of Dr. Axe’s criticisms

In the passages quoted below, I have used ^ for superscripts and _ for subscripts. All bolding is mine – VJT.

First of all, here’s the abstract of Dr. Axe’s paper:

Abstract

To explain life’s current level of complexity, we must first explain genetic innovation. Recognition of this fact has generated interest in the evolutionary feasibility of complex adaptations—adaptations requiring multiple mutations, with all intermediates being non-adaptive. Intuitively, one expects the waiting time for arrival and fixation of these adaptations to have exponential dependence on d, the number of specific base changes they require. Counter to this expectation, Lynch and Abegg have recently concluded that in the case of selectively neutral intermediates, the waiting time becomes independent of d as d becomes large. Here, I confirm the intuitive expectation by showing where the analysis of Lynch and Abegg erred and by developing new treatments of the two cases of complex adaptation — the case where intermediates are selectively maladaptive and the case where they are selectively neutral. In particular, I use an explicit model of a structured bacterial population, similar to the island model of Maruyama and Kimura, to examine the limits on complex adaptations during the evolution of paralogous genes—genes related by duplication of an ancestral gene. Although substantial functional innovation is thought to be possible within paralogous families, the tight limits on the value of d found here (d ≤ 2 for the maladaptive case, and d ≤ 6 for the neutral case) mean that the mutational jumps in this process cannot have been very large. Whether the functional divergence commonly attributed to paralogs is feasible within such tight limits is far from certain, judging by various experimental attempts to interconvert the functions of supposed paralogs. This study provides a mathematical framework for interpreting experiments of that kind, more of which will needed before the limits to functional divergence become clear.

Next, here’s a short passage which will help readers understand the background to Lynch and Abegg’s paper:

Three potential routes to the fixation of complex adaptations have been recognized. The simplest is the de novo appearance in one organism of all necessary changes, which for large innovations is tantamount to molecular saltation. This route has the advantage of avoiding non-adaptive intermediates but the disadvantage of requiring a very rare convergence of mutations. The second potential route is sequential fixation, whereby point mutations become fixed successively, ultimately producing the full set needed for the innovation. By this route, the rate of appearance of each successive intermediate en route to the complex adaptation is boosted by allowing the prior intermediate to become fixed. But because these fixation events have to occur without the assistance of natural selection (or, in the case of maladaptive intermediates, even against natural selection) they are in themselves improbable events. The third potential route is stochastic tunneling, which differs from sequential fixation only in that it depends on each successive point mutation appearing without the prior one having become fixed. Here fixation occurs only after all the mutations needed for the innovation are in place. This route therefore benefits from an absence of improbable fixation events, but it must instead rely on the necessary mutations appearing within much smaller subpopulations.

Molecular saltation seems incompatible with Darwinian evolution for the same reason all forms of saltation do — namely, the apparent inability of ordinary processes to accomplish extraordinary changes in one step. If specific nucleotide substitutions occur spontaneously at an average rate of u per nucleotide site per cell, and a particular innovation requires d specific substitutions, then the rate of appearance of the innovation by molecular saltation (i.e., construction de novo in a single cell) is simply u^d per cell. This means that the expected waiting time (in generations) for appearance and fixation of the innovation scales as u^-d. But since u has to be a very small fraction in order for a genome to be faithfully replicated (the upper bound being roughly the inverse of the working genome length in bases), u^-d becomes exceedingly large even for modest values of d, resulting in exceedingly long waiting times.

Because of this, sequential fixation and stochastic tunneling are thought to be the primary ways that complex adaptations become fixed.

Finally, here’s the meaty mathematical critique which I emailed to Professor Lynch:

Among the many treatments of complex adaptation by sequential fixation and/or stochastic tunneling (e.g., references 2–6), one recently offered by Lynch and Abegg [6] is of particular interest because it claims that the above limitation vanishes in situations where the genetic intermediates en route to a complex adaptation are selectively neutral. For this case, they report that “regardless of the complexity of the adaptation, the time to establishment is inversely proportional to the rate at which mutations arise at single sites.” In other words, they find the waiting time for appearance and fixation of a complex adaptation requiring d base changes to scale as u^(-1) rather than the commonly assumed u^(-d). Because this should apply not only in the case of strict neutrality (which may seldom exist) but also in the more realistic case of approximate neutrality, and because it represents a striking departure from common probabilistic intuitions, it is important for this result to be examined carefully.

ANALYSIS
Assessing Lynch and Abegg’s treatment of the neutral case

Sequential fixation. Innovation by sequential fixation has to work against natural selection if any of the genetic intermediates are maladaptive, which is apt to be the case in many evolutionary scenarios. In such cases, sequential fixation is conceivable only in small populations because the efficiency of natural selection in large populations makes maladaptive fixation nearly impossible [7]. Focusing therefore on small populations, and initially on the limiting case of selectively neutral intermediates, Lynch and Abegg calculate the mean waiting time for arrival of an allele carrying a particular complex adaptation that is destined to be fixed within a diploid population as (1):

w_seq = [d.u]^(-1) + [(d-1).u]^(-1) + [(d-2).u]^(-1) + … + [2u]^(-1) + [2u. N_e. phi_2]^(-1), (2)

where d is the number of specific base substitutions needed to produce the complex adaptation, N_e is the effective population size (2), u is the mean rate of specific base substitution (per site per gamete), and phi_2 is the probability that an instance of producing the adaptive allele will result in fixation (given by Equation 1 of reference 6).

When written in the above expanded form, we see that the waiting time is being equated with a sum of d terms, each of these terms being the inverse of a rate. As explained by Lynch and Abegg [6], the individual rates are simply the rates of appearance within the whole population (per generation) of instances of the successive genotypic stages that are destined to become fixed, given a population in which the prior stage is fixed. So, for example, in a case where the complex adaptation requires five specific base substitutions (d = 5) and the predominant genotype in the initial population lacks all five, there are five possible ways for an allele of the initial type (call it stage 0) to progress by mutation to the next stage (stage 1). The first term enclosed in square brackets is 5u in this case, which is the per-gamete rate of appearance of stage-1 alleles in a stage-0 population. Because each individual allele in a population of neutral variants is expected to become fixed with a probability equal to the inverse of the total allele count [8], the rate of appearance of stage-1 alleles that are destined to become fixed in a diploid population of N individuals is equal to the total rate of appearance (2N × 5u per generation) divided by 2N, which equals the per-gamete rate of mutation to stage 1, namely 5u per generation.

When a stage-1 allele is fixed, there are now four possible ways for mutation to produce a stage-2 allele. The second term in square brackets, 4u, is again the rate of appearance of stage-2 alleles that are destined to become fixed within a population where a stage-1 allele has become fixed, and so on for the third and fourth terms. The final term differs because the complete complex adaptation (stage 5) has an enhanced fixation probability resulting from its selective advantage.

Since the mean wait for a stochastic event to occur is just the inverse of its mean rate of occurrence, the right-hand side of Equation 2 is now seen to be the sum of waiting times, specifically the mean waiting times for appearance of destined-to-be-fixed alleles at each successive stage within populations in which the prior stage has become fixed. The actual process of fixation (after a destined-to-be-fixed allele appears) is relatively fast in small populations, taking an average of (4.N_e) generations for neutral alleles [8]. Assuming this to be negligible, Equation 2 may seem at first glance to represent precisely the intended quantity — the overall waiting time for fixation of the complete complex adaptation from a stage-0 starting point. But if the implications of this equation are as implausible as has been argued, then there must be a mistake in the calculation.

This indeed appears to be the case. Specifically, of all the possible evolutionary paths a population can take, the analysis of Lynch and Abegg considers only those special paths that lead directly to the desired end—the complex adaptation. This is best illustrated with an example. Suppose a population carries an allele that confers no selective benefit in its current state (e.g., a pseudogene or a gene duplicate) but which would confer a benefit if it were to acquire five specific nucleotide changes relative to that initial state, which we will again refer to as stage 0. Lynch and Abegg assign a waiting time of (5u)^(-1) for a stage-1 allele to become fixed in this situation, which is valid only if we can safely assume that the population remains at stage 0 during this wait.

But this cannot be assumed. A stage-0 allele of kilobase length, for example, would have about 200-fold more correct bases than incorrect ones (with respect to the complex adaptation), which means the rate of degradation (i.e., fixation of changes that make the complex adaptation more remote) would be about 600-fold higher(3) than the rate of progression to stage 1. It is therefore very unlikely in such a case that the population will wait at stage 0 long enough to reach stage 1, and the situation becomes progressively worse as we consider higher stages.

It is possible to adjust the problem to some extent in order to achieve a more favorable result. For example, if we suppose that all changes except the five desired ones are highly maladaptive, then fixation becomes restricted to changes at the five sites. But even under these artificial restrictions, Equation 2 is incorrect in that it ignores back mutations [6]. Since the aim is to acquire the correct bases at all d sites, and there are more incorrect possibilities than correct ones at each site, counterproductive changes must substantially outnumber productive changes as the number of correct bases increases. So even in this highly favorable case, the analysis suffers from neglect of counterproductive competing paths. Productive changes cannot be ‘banked’, whereas Equation 2 presupposes that they can.

Stochastic tunneling. Lynch and Abegg’s treatment of stochastic tunneling with neutral intermediates is also problematic. To derive an expression for the waiting time when the population is large enough to preclude fixation of intermediate stages (Equation 5b of reference 6), they approximate the frequency of stage-d alleles at t generations as (ut)^d. While they note that this approximation is valid only if ut << 1, they overlook the fact that this restricts their analysis to exceedingly small values [of] (ut)^d. Specifically, they equate this term with the substantial allele frequency at which fixation becomes likely(4), and then proceed to solve for t, taking the result to be valid for arbitrarily large values of d. This leads them to the unexpected conclusion that “in very large populations with neutral intermediates, as d→∞, the time to establishment converges on the reciprocal of the per-site mutation rate, becoming independent of the number of mutations required for the adaptation” [6]. But since they have in this way neglected the effect of d, it should be no surprise that they find d to have little effect.

Footnotes (parentheses)
1 See Equation 5a of reference 6, which uses t-bar_e, s to represent the same quantity.
2 Much of the genetic drift in real populations results from non-uniform population structure and dynamics. In essence, the effective size of a real population is the size of an ideal population lacking these non-uniformities that has the same level of genetic
drift. A detailed discussion of N_e is found in the results and Discussion section.
3 Of the three possible changes to an incorrect base in this example, only one corrects it.
4 This being (4N_e .s_2)^-1 where s_2 is the fractional advantage conferred by the stage-d allele.

References [square brackets]

2. Behe MJ, Snoke DW (2004) Simulating evolution by gene duplication of protein features that require multiple amino acid residues. Protein Sci 13: 2651-2664. doi:10.1110/ps.04802904
3. Lynch M (2005) Simple evolutionary pathways to complex proteins. Protein Sci 14: 2217-2225. doi:10.1110/ps.041171805
4. Durrett R, Schmidt D (2008) Waiting for two mutations: with applications to regulatory sequence evolution and the limits of Darwinian evolution. Genetics 180: 1501-1509. doi:10.1534/genetics.107.082610
5. Orr HA (2002) The population genetics of adaptation: The adaptation of DNA sequences. Evolution 56: 1317-1330. doi:10.1111/j.0014-3820.2002.tb01446.x
6. Lynch M, Abegg A (2010) The rate of establishment of complex adaptations.
7. Kimura M (1980) Average time until fixation of a mutant allele in a finite population under continued mutation pressure: Studies by analytical, numerical, and pseudo-sampling methods. P Natl Acad Sci USA 77: 522-526. doi:10.1073/pnas.77.1.522
8. Kimura M, Ohta T (1969) The average number of generations until fixation of a mutant gene in a finite population. Genetics 61: 763-771.

Conclusion

The passages above represent a very brief selection from Dr. Axe’s paper, but hopefully, they are sufficient to expose the faulty mathematical reasoning in Lynch and Abegg’s 2010 paper.

I shall now throw the discussion open to readers. Am I the only one who thinks there’s something very funny going on here, when leading evolutionary biologists refuse to respond to the trenchant criticisms put forward by Dr. Axe in his paper?

What do readers think?

54 Replies to “Academic cover-up: can neutral evolutionary processes rapidly generate complex adaptations?

  1. 1
    Eric Anderson says:

    vjtorley:

    Thanks for bringing forward this interesting case.

    I’m not sure I would read too much into the fact that someone has had 5 months to address an issue and hasn’t yet done so. Personally, I have dozens of books and papers that I have been meaning to “get to” and haven’t yet done so, even in some cases in which I’ve told someone who brought a book or paper to my attention, “Thank you. Interesting. When I get some time I’ll check into it.”

    Much more telling in Lynch’s case is the fact that he was initially interested and then became dismissive when he checked into the source of the critique. It smacks of two possibilities: either he has a preexisting philosophical bias against those who aren’t “in the club,” or someone got to him in the interim. Either way, it doesn’t provide much confidence in his ability to be objective.

    You mentioned that there is a “mathematical flaw.” I’ve only just skimmed for now, but am I right in understanding that there is not a “mathematical flaw” in the sense of an actual, incorrect numerical calculation, but rather in the sense that they didn’t correctly model reality?

    In other words, it seems this might be another case (like so many of the evolutionary models and algorithms) in which the math purports to demonstrate some wonderful result supportive of the evolutionary storyline, but it is ultimately an irrelevant exercise in self-deception because the formula (however correct the math may be) doesn’t accurately model biological reality.

  2. 2
    vjtorley says:

    Hi Eric Anderson,

    Thank you for your comments. You are right. It’s the model used by Lynch and Abegg that Dr. Axe is attacking, and in particular its underlying assumption that productive changes can be banked.

  3. 3
    Mung says:

    If you’re a blind conductor, you wave your hands. It’s what you do.

  4. 4
    bFast says:

    I do wish that Dr. Moran would defend his favorite theory on this topic.

    I for one am sooo not buying the “neutral theory can generate complexity” hypothesis. It is sooo off in space logically. In fact, neutral theory, in my opinion is the death knell to naturalistic evolution.

  5. 5
    Eric Anderson says:

    bFast, agreed.

    It seems that neutral theory doesn’t have so much going for it in a demonstrably positive sense. Rather, it primarily seeks to avoid the problem of deleterious changes until, one fine day, Poof! Something advantageous comes along that can be selected.

    But, hey, if you refuse to accept the possibility of design. And if the only meaningful avenue open to you to account for biological innovation is happenstance changes. And if it is known that the vast majority of non-neutral changes are deleterious. Then, what are you left with?

    Well, let’s pretend that lots of neutral mutations can build up until that magical, inexplicable moment when the neutral mutations decide to come together to produce advantageous biological innovation.

    Perfectly logical! 🙂

  6. 6
    bill cole says:

    Hi vjtorley
    Dr Moran posted Lynch’s 2005 response to Behe and Snoke recently. This model was fixed with 2 adaptive mutations where the Behe Snoke model was variable. The 2005 paper claimed that 2 adaptive mutations could be achieved with 10^8 generations and 10^6 population sizes. Since multicellular evolution especially vertebrate would seem to require thousands of adaptive mutations I am struggling to see how these models do anything but make neutral theory very unlikely. Lynch’s 2010 model appears to improve the numbers but doesnot not seem to even scratch the surface of the number of mutations required for a new specie to evolve.

  7. 7
    Zachriel says:

    vjtorley: I emailed Lynch a couple of months ago, inviting him to comment on Axe’s paper. To my surprise, he said he hadn’t seen it before.

    That’s funny!

  8. 8
    Jonas Crump says:

    When someone writes a criticism of an article, is it not customary to submit it for publication in the journal where the original article appeared? It certainly was when I was a young pup. But even if that was not possible, I think that I would seek publication in a journal for which I was not Managing Editor. I am not suggesting that there was any conflict of interest, but I can certainly see that it could be perceived as such.

  9. 9
    PaV says:

    Let’s take the last critical error of Lynch and Abegg: what Axe is saying is this: if ut is very much smaller than 1—-the assumption that L&A make, then [ut]^d is a very small number. For example 1 over twenty, much smaller than ONE, raised to the fifth power is 1/3,200,000. L&A then “equate this term with the substantial allele frequency at which fixation becomes likely(4), and then proceed to solve for t, taking the result to be valid for arbitrarily large values of d.”

    IOW, when the equate the one to the other, they are orders of magnitude off.

    So, Axe says:
    But since they have in this way neglected the effect of d, it should be no surprise that they find d to have little effect.

    There’s a word for this: “blunder.”

    As to L&A’s equation, Axe rightly points out that they don’t take into account ‘backwards’ mutations. The mutations that occur are not set forever. They can revert.

    In fact, a little mental exercise I did makes me wonder about the very basic equations of neutral drift.

    Think about a diploid population of 100 individuals in which the ‘mutant’ individuals are equal to the ‘wild type.’ So, there are 200 genomes, half mutant, half wild type. Now think of them randomly mutating. Then you have, on average, 100 wild type genomes that can ‘mutate’ to the mutant type genome, and you have 100 mutant genomes that can only ‘mutate’ backwards. The wild type can only mutate forward. Let’s say one of the wild type genomes mutates forward while none of the mutant genomes mutates backwards. Now there are 199 wild type genomes and 201 mutant genomes.

    Terrific. We’re on our way to fixation! Or are we.

    During the next random mating, there are 199 wild type that can mutate forward, while there are 201 mutant genomes that can only mutate backwards. The mutation rate is the same for both type genomes. Hence, the odds of a “backwards” mutation are greater than a “forwards” mutation. I think it’s easy to see that unless some kinds of stochastic forces are present, the genomes would simply oscillate around 50% wild and 50% mutant. I would think this is exactly what “neutral” drift ought to look like.

    The population geneticists may point out that there could be some kind of ‘isolation’ that takes place which ‘shifts’ the ‘frequencies’ in favor of the ‘mutant’ genome. Yet, even so, it seems to me that if you have—using the above example—50 wild type genomes that can only mutate forwards, and 350 mutant genomes that can only mutate ‘backwards’, then we know which way the population will shift.

    And, it seems, the situation here might even be worse than it appears at first.

    If a wild type genome mutates, we know that not just any mutation will do. It has to mutate to some specific nucleotide base; not just any will do.

    However, a mutant genome has the choice of THREE nucleotide bases that shifts it back to the wild type, since, after all, the nucleotide site is ‘neutral.’ Hence, if my view is correct, it is therefore three times more likely for a mutant genome to revert to wild type, than a wild type to mutate forwards to a specific nucleotide.

    There seems to be real problems here.

  10. 10
    PaV says:

    Jonas:

    This is from the top of my head.

    Michael Behe had an article published by Elsevier (they published for the periodical involved). Then a storm erupted because, after all, Behe was publishing in a peer-reviewed journal, something completely unacceptable to the crowd who use, as a criticism of ID, the excuse that IDists don’t publish in peer-reviewed journals.

    So, Elsevier published the criticism, said that they were dropping the article, and left it at that.

    Behe said to them that he had a right to rebut the criticism. Elsevier refused to publish his rebuttal.

    When you were young, things were more rational. The idealogues have taken over.

    P.S. Please correct any errors. This is all from recollection.

  11. 11
    Jonas Crump says:

    PaV: “There seems to be real problems here.”

    I’m not saying that there is not. I honestly don’t know enough math to judge one way or another. All I am saying is that I will be more likely to believe a criticism of the paper if it is published in the same journal. Or at least in a journal where the critique is not written by the Managing Editor. Am I the only one who sees this as a possible problem? I hope not.

  12. 12
    Jonas Crump says:

    When you were young, things were more rational. The idealogues have taken over.”

    I don’t accept that portrayal. If there is a valid criticism of the math used, I don’t know any journal that wouldn’t accept it for publication. If published, the criticism would be open to further rebuttal.

    Did Dr. Axe make any attempt to respond in the original journal? Or any other journal? That is information that we don’t have. Conversely, how many dissenting opinions has Bio-Complexity published? Do they accept dissenting opinions for publications? (Most other journals do).

  13. 13
    PaV says:

    Jonas:

    Deny reality all you want; but it doesn’t make it go away.

    It’s not what you “see” that’s the problem; it’ what you don’t “see.” The deck is stacked against ID. Go watch “Expelled.” It will give you a taste of what happens in the vaunted “academy.”

  14. 14
    Mung says:

    Yes, let’s blame Douglas Axe for not getting his paper published in the “approved” place. LoL.

  15. 15
    Jonas Crump says:

    PaV: “Jonas: Deny reality all you want; but it doesn’t make it go away.”

    Did I say it would? All I asked is if Dr. Axe made any attempt to publish his response in any “traditional” venue? Or did he go directly to a venue that has no chance of being seen, or responded to? My earlier question still stands. How many dissenting opinions have been published by Bio-Complexity? All other legitimate journals have published them.

  16. 16
    PaV says:

    Jonas: Why don’t you ask him?

  17. 17
    PaV says:

    I believe we can disprove Lynch and Abegg in a very simple and straightforward fashion.

    According to their numbers, malarial parasites and bacteria should easily develop “resistance.” (See their Figure 5) They don’t. Hence, their numbers are wrong. QED.

  18. 18
    Jonas Crump says:

    PaV: “Jonas: Why don’t you ask him?”

    If he was really serious about his criticism, I would never have to ask him. He is smart enough (presumably) to know how best to rebut the claims made.

  19. 19
    PaV says:

    Jonas:

    If he was really serious about his criticism, I would never have to ask him.

    If you’re really serious about wanting to know, then you’ll ask him yourself. I’m sure there is an email address for him somewhere, or via Bio-COMPLEXITY.

  20. 20
    drc466 says:

    The reason that Lynch, et. al., publish so many mathematical models and computer simulations that purportedly show how “easy” it is for neutral processes to rapidly generate complex adaptations is that reality stubbornly refuses to do so for them.
    In the real world (i.e. the lab or the field), organisms show either 1) stasis, or 2) built in adaptability/variation (e.g. dog breeds). If you dig up a mummy, for example, and examine the bacteria thereon, you will find (surprise!) bacteria that look the same as modern bacteria.
    Mathematical models are so much more…pliable.
    My first response to these types of papers is always “fabulous, demonstrate that in a lab please!”

  21. 21
    Mung says:

    The reason that Lynch, et. al., publish so many mathematical models and computer simulations that purportedly show how “easy” it is for neutral processes to rapidly generate complex adaptations is…

    Lynch is the author of The Origins of Genome Architecture.

    My bet is that the answer is non-Darwinian. And if it’s non-Darwinian then … well, you do the math.

    They need something that isn’t magic-did-it.

  22. 22
    jerry says:

    If in fact the Lynch model is correct, there should be real life examples in various genomes illustrating the rise of these complex adaptations. The complex adaptations would be visible in a species but not in a related species where the adaptation did not take place. A failed version of the genomic sequence would be in this second species, one that did not mutate into the complex adaptation.

    There should be a forensic trail of how this happened. If there is none then Lynch’s thesis is not even speculation and a falsified hypothesis.

  23. 23
    JDH says:

    To recall other incorrect mathematical models — does the appearance that Lynch assumes you can bank on the fixation of the intermediated mutations make him a WEASEL?

  24. 24
    Jonas Crump says:

    PaV: “If you’re really serious about wanting to know, then you’ll ask him yourself.”

    I already know the answer. I looked through all of the articles in Bio-Complexity and there is not a single dissenting opinion.

  25. 25
    tjguy says:

    He(Lynch) said he doubted whether any serious biologist took Dr. Axe’s paper, let alone his journal (BIO-Complexity), seriously.

    Typical response. This is often used as an excuse to simply dismiss the argument without even engaging it.

    It’s put out by an ID journal or a Creationist website so it’s not even worth the time to address.

    This is not how science is supposed to work! Rather than seeking to protect one’s own beliefs and gain notoriety for one’s own papers – whether right or wrong – science is supposed to be about finding the truth no matter where the evidence leads – even if that means admitting your idea might not hold water.

    +
    I have a question about this statement:

    “A few tens of millions of generations would mean a few tens of millions of years, for most animals. If Lynch and Abegg are correct, then evolutionists all around the world can heave a huge sigh of relief. After all, even a span of 80 million years would represent a mere 2% of the 4-billion-year history of life on Earth, so the origin of complex adaptations within the allotted time-span no longer appears to be much of a problem.”

    OK, I’m showing my ignorance here, but this still doesn’t seem to add up to me. If it can take a span of 80 million years – a full 2% of the claimed history of life on earth – just for one type of complex adaptation to occur (sure – various adaptations are accumulating in different species/families/genuses all that the same time – but still…), can we really still say that there no longer appears to be much of a problem as far as time goes for evolution?

    Wouldn’t there be many many different adaptations necessary over the course of the evolution of life into a human for instance? How many different adaptations would have been necessary for that change to occur? Perhaps the ones early on in the process would not have taken as long. It seems that is what the article is claiming. But the larger and more complex the organism, the longer it would take, right? So if one adaptation takes a full 2% of history, that’s a really really long time because it means that at the most, there could only be another 48 of that type of difficult adaptation that takes place over the whole history of the evolution of a human being! And even 48 would be too many because also needs to be time for all the complex adaptations among simpler organisms as well.

    What am I missing? Maybe I don’t understand what is meant by an “adaptation”?

  26. 26
    John S says:

    You are all smarter than me. However common sense based in reality indicates neutrals don’t produce complexity in any context (perhaps in lifeless, controlled chemistry environments?). Especially random, unguided neutrals (is that redundant?). Especially not the nearly infinite complexities of life as we know it. At best you get some complexity along with some simplicity. Neutral begets neutral. Yet somehow entropy plus time is considered a help rather than a hindrance.

  27. 27
    Mung says:

    I don’t understand why the ID “critics” are not outraged at this cover-up.

  28. 28
    PaV says:

    Jonas:

    I already know the answer.

    Then why do you ask the question? Gamesmanship?

  29. 29
    PaV says:

    tjguy:

    Just something to add to the mix:

    Consider the “dog that didn’t bark.” In this context it means this: if it is so easy to “mutate” from one species to a new species, or from one protein to another, then, guess what, you now have a problem of fixity of species. If a chicken can easily mutate so that it can fly, then birds that fly can easily become chickens. Or, a mouse can become a bat, and a bat a mouse.

    We should be SURROUNDED by all kinds of change, and by all kinds of INTERMEDIATE FORMS.

    But we’re not. Their math is obviously wrong.

  30. 30
    Eric Anderson says:

    tjguy @25:

    Good catch on the timeframes and what would be required for significant organismal change.

    Note also the pea under the thimble:

    Lynch et al. refer to “complex alleles” (which is what they have actually tried to demonstrate with their math), and then in the very same paragraph transition to talking about “complex adaptations”.

    The latter is conveniently undefined and, conveniently, gives the reader the false impression that significant organismal changes can occur within the timeframes suggested. All the while with Lynch et al. conveniently and quietly failing to state that a new allele isn’t going to get you very far along the road to any meaningful morphological change.

  31. 31
    Eric Anderson says:

    Picking up on PaV’s point:

    If the broader claims are correct, it would mean that species are constantly in a significant state of flux — organisms throughout the entire biosphere ebbing and flowing from one change to the next. Or as David Berlinski stated more poetically, “like colors merging imperceptibly on a color chart.”

    But we don’t see anything of the kind. Stasis is everywhere. And in the few cases where do see some change it is only temporary oscillation around a norm.

  32. 32
    Virgil Cain says:

    Larry Moran had this post- Constructive Neutral Evolution (CNE)

    It is contingent serendipity all the way down.

  33. 33
    jerry says:

    Eric,

    If the broader claims are correct, it would mean that species are constantly in a significant state of flux — organisms throughout the entire biosphere ebbing and flowing from one change to the next.

    No, the basic assumption by the pro naturalistic evolution people is that there is a tree that constantly branches over long periods of time which leaves two separate lines that then digress. This branching has supposedly happened millions of times in the last 500 million years. If this is true, then a particular genomic sequence (or several) would be in both branches but in one branch for one of the populations the sequence changed/mutated and created new capabilities in this branch but not the other.

    This must be true for their position. But if there are not corresponding sequences in both branches, then how did the sequences arise in the one branch which led to unique capabilities but not in the other. There isn’t enough time. These changes take millions of years (or at least hundreds of thousands of years) so the sequences should be in both branches but in one it mutated further to produce a significant change while in the other it is still non coding or just not useful.

    So proof of Lynch’s ideas would be in genomes. Since they have not found too many, my guess is that not enough exist to make a meaningful difference. Else they would be barking very loud.

    The other person who is much further along on this than Lynch is Jurgen Brosius and his colleagues in Germany. His thesis is that the origin of new proteins is the non coding regions of the genome that slowly mutate over time till one day they are coded for something useful. He has examples but not too many so my guess is that this process operates but only ends up in small differences and certainly not complex adaptations.

  34. 34
    computerist says:

    His thesis is that the origin of new proteins is the non coding regions of the genome that slowly mutate over time till one day they are coded for something useful.

    It would seem that there should more probably be thousands if not millions of traces of useless “usefulness”.
    Just because something is functional, doesn’t mean it’s useful in any integrated sense.
    I don’t understand how the jump is made from these non-coding regions overtime into an automatic state of “usefulness”. Certain key flags may indicate whether instructions are to be coded, but for them to propagate to a state of usefulness, seems a bit of a stretch, unless they “knew” ahead of time, which is why ID makes more sense than the blind watchmaker. The combinations are far too great for this thesis to be realistic.

  35. 35
    Eric Anderson says:

    jerry, I was referring to the broader evolutionary claims of widespread change giving rise to adaptations ultimately leading to all the tremendous diversity and variety we see today in the biosphere. In order for these kinds of changes to produce what we see today, the rate of change must be prodigious indeed and, if Darwin was right, small and widespread.

    Changes that lie silent the genome — dormant and invisible to the hand of natural selection — are largely irrelevant to the vast morphological changes witnessed in the history of life. By definition, only when they become visible (by some hypothetical and unexplainable dint of cosmic luck) do they have any impact on the organism and any realistic chance of spreading throughout a population of any decent size.

    That we don’t see this widespread change happening all around us is prima facie evidence that it doesn’t occur. That could be rebutted, perhaps, by someone arguing that it takes too long to observe. Fine. But then what the neutralist is admitting is that he has a theory in search of evidence.

    Even if there are many neutral mutations, for which I am willing to acknowledge there may be some interesting evidence, there is no solid observational evidence that those neutral changes can (i) suddenly come together to form functional “complex adaptations”, or (ii) that such processes constitute a meaningful contribution to the history of life on Earth.

    It is all in the realm of theory and speculation — primarily in an effort to overcome the one issue that has been observed: the vast majority of non-neutral mutations are deleterious.

  36. 36
    jerry says:

    Eric,

    But then what the neutralist is admitting is that he has a theory in search of evidence.

    I am saying that if the evidence is there, it is discernible and the neutralist should be able to design the study to find this evidence. Because they don’t have the evidence when it is available to find, means that the evidence is not there and Lynch’s ideas are of no consequence.

    One of the virulent atheists in evolutionary biology is Jurgen Brosius and he thinks naturalistic evolution is a slam dunk through this process of mutations in the non coding regions. He and his colleagues have substantial publication record and I assume it is interesting but irrelevant to the actual evolution debate which as the headline says “complex adaptations.”

    I don’t think we disagree, just that the people here are not familiar with everything out there and they should be. There is nothing to worry about since if there was, all the trolls here would have heard of it ages ago.

  37. 37
    PaV says:

    jerry:

    The other person who is much further along on this than Lynch is Jurgen Brosius and his colleagues in Germany. His thesis is that the origin of new proteins is the non coding regions of the genome that slowly mutate over time till one day they are coded for something useful. He has examples but not too many so my guess is that this process operates but only ends up in small differences and certainly not complex adaptations.

    I recently posted somewhere—can’t remember where, here somewhere—in which I made the point that Larry Moran, and others like him, are very much concerned that there is evidence for ‘function’ in “junk-DNA” because the ‘absence’ of “junk-DNA” is doubly a problem: first, because it undermines the notion of ‘randonmness’ at the heart of Darwnism, but, also, secondly, because then there is less and less non-coding DNA that can “drift.” This use of non-coding DNA is what they believe gives rise to de novo genes, evidence for which is rising.

    Let’s not fail to notice this second problem.

  38. 38
    PaV says:

    Jonas Crump:

    This is from Lee Spetner’s article over at Evolutionary News. You can link to it from the blogpost right beneath this one on the home page.

    Here’s what he writes:

    Recently the group’s bimonthly publication, Reports of the National Center for Science Education, reviewed my book The Evolution Revolution. I was not surprised that the review by David E. Levin, who teaches in Boston University dental school’s Department of Molecular & Cell Biology, was negative. I requested the opportunity to reply in the journal, but received no answer. So I will offer a response here.

    So you think I make these things up, huh?

  39. 39
    Jonas Crump says:

    PaV, I hardly think that this is an example of censorship. He requested the opportunity to reply, late in December, and hadn’t received a response by early January. Given the holiday break, I don’t think that this delay would be unexpected.

  40. 40
    PaV says:

    Jonas:

    How in the world do you know when the request was made?

  41. 41
    bpragmatic says:

    “can neutral evolutionary processes rapidly generate complex adaptations?”

    How can this be shown to be plausible?

    What if the question was “can neutral evolutionary processes generate complex adaptations? (rapidly or not)

    Cut out the self serving esoteric BS from those getting paid to promote the tripe or with some philosophical agenda and the answer, most likely is HELL NO.

  42. 42
    Mung says:

    Remember when creationists were excoriated for not understanding that evolution was not random?

  43. 43
    Zachriel says:

    bpragmatic: How can this be shown to be plausible?

    In the context of the paper, complexity just refers to adaptations requiring more than one mutation.

    Mung: Remember when creationists were excoriated for not understanding that evolution was not random?

    It’s not, but mutation is generally random with respect to fitness.

  44. 44
    Mung says:

    Zachriel, neutral evolutionary processes are not stochastic?

  45. 45
    Zachriel says:

    Mung: neutral evolutionary processes are not stochastic?

    Evolution includes both stochastic and deterministic aspects. If two mutations result in a selectable adaptation, then the paper considers that a complex adaptation. Not sure your point beyond that.

  46. 46
    Zachriel says:

    It’s also worth pointing out saturation effects. If an adaptation takes three mutations, there are only 64 possible configurations of the three bases. Very broadly, if we assume a mutation rate of about 10^-8, then it would take about 10^9 replications to reach saturation. That would be equivalent to a population of a thousand for a million years, or a population of a million for a thousand years.

  47. 47
    Mung says:

    Zachriel: Evolution includes both stochastic and deterministic aspects.

    I didn’t ask about evolution. I asked about neutral evolutionary processes. If you don’t want to answer then please just keep silent rather than pretending to answer without actually answering. That’s just being intellectually dishonest.

  48. 48
    Zachriel says:

    Mung: I didn’t ask about evolution.

    Mung: Remember when creationists were excoriated for not understanding that evolution was not random?

    Mung: neutral evolutionary processes are not stochastic?

    Conflation. First, you ask about general evolution, which includes historical adaptation; then you ask about neutral evolution. Evolution includes both stochastic and deterministic aspects.

  49. 49
    Mung says:

    Zachriel, I’m not interested in playing your games.

  50. 50
    Zachriel says:

    Mung: I’m not interested in playing your games.

    Actually, you were the one who was playing word-games. You might acknowledge the point raised @48.

  51. 51
    Virgil Cain says:

    It’s not, but mutation is generally random with respect to fitness.

    The claim of “evolution” is that mutations are happenstance occurrences. The claim of “random with respect to fitness” is just meaningless in that regard.

  52. 52
    Virgil Cain says:

    You might acknowledge the point raised @48.

    Unfortunately there wasn’t any point raised in 48- equivocation is not a point.

  53. 53
    Mung says:

    Zachriel, do you mean to affirm that neutral evolutionary processes are not stochastic?

  54. 54
    Zachriel says:

    Mung: do you mean to affirm that neutral evolutionary processes are not stochastic?

    Neutral evolution is stochastic, by definition.

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