There’s plenty of time for evolution

December 29, 2010 • 8:41 am

One of the most common problems that laypeople have with evolution is that there doesn’t seem to have been enough time for it.  Given the idea that evolution is relatively slow, and yet there’s been an enormous amount of change since the first species a few billion years ago, how could natural selection (and other processes like genetic drift) have built all these exquisite, functioning organisms?

Part of the answer, of course, is that people fail to appreciate “deep time,” since we’re evolved to regard life over years and decades, not millions and billions of years.  Evolutionists often demonstrate this by compressing all of evolution into a calendar year, showing how much evolution has occurred in a short segment of that time.  Using this analogy in WEIT, for example, I show that the divergence between the ancestors of humans and chimps would have occurred only at 6 a.m. on December 31.

Another difficulty is that people assume that if one species evolves into another by changing many traits, it seems highly unlikely that they can all change at the same time by simultaneous fixation of adaptive mutations.  If evolutionary change of a species involves gene substitution at L genes (with L being a number), and the proportion of all genes in each generation that are more favored than the “primitive” type is 1/K (this number is low because most mutations are deleterious), then the number of “trials” it takes to get adaptive mutations at all the genes is on the order of KL .  In other words, each generation new mutations arise, and if adaptive ones aren’t there for every gene required to make a descendant from an ancestor, then that whole trial is discarded and the process starts the next generation.  Finally, after about KL generations have passed, you’ll get the right type.

But that can take a huge amount of time.  If you want to change 20,000 genes, for example, with only 1/40 of all segregating mutational variants being advantageous, then it would take 1034,040 “trials” (roughly the time it takes for a new adaptive mutation to become fixed) to effect this change.  This could never occur, since even with an organism having 100 generations per year and with a “trial” equivalent to one generation, this would take a number of years equal to 10 followed by 34,038 zeroes. (Since life began there’s only been about 3 followed by nine zeroes years.)  That’s not long enough!

As you’ve probably already guessed, evolution doesn’t work this way.  As evolutionary change is occurring at one gene, it’s simultaneously occurring at other genes, affecting other traits, if there are adaptive mutations in the populations for those traits too. A “trial” doesn’t involve producing variants at every gene, with evolution occurring only if all of the genes have adaptive variants.  Rather, in each trial the new adaptive mutations arise and begin their march toward fixation in some genes, leaving the rest to change during subsequent trials.  In other words, evolution occurs in parallel rather than in series.

How does that change the speed of evolution? This is the topic of a new paper in PNAS by Herbert Wilf and Warren Ewens, a paper with the endearing title given above, “There’s plenty of time for evolution.” (I don’t know of another scientific paper whose title contains a contraction.)   The point of Wilf and Ewens’s paper is to show mathematically that simultaneous substitution is much much faster than “serial” substitution, so that substantial evolutionary change can take place relatively quickly.  This isn’t a new point, but the equations are new, and they show, as the title says, that there has been plenty of time for lots of evolution to have taken place.

Wilf and Ewens simply invoke the fact that at each gene, the substitution process takes place independently, with new adaptive mutations retained at each.  If letters represent adaption mutations at each position in a word, with a “word” representing the number of genes differentiating an descendant from its ancestor, they propose the correct model:

But a more appropriate model is the following: After guessing each of the letters, we are told which (if any) of the guessed letters are correct, and then those letters are retained. [JAC: you don’t start the process over each generation, since if the right adaptive mutation is around for some genes, you needn’t consider those genes any longer.] The second round of guessing is applied only for the incorrect letters that remain after this first round, and so forth. This procedure mimics the “in parallel” evolutionary process. The question concerns the statistics of the number of rounds needed to guess all of the letters of the word successfully.

Here’s their complicated equation for the number of rounds of “guessing”, that is the number of rounds it takes to achieve adaptive evolution at every one of L genes:

The mean number of rounds that are necessary to guess all of the letters of an L letter word, the letters coming from an alphabet of K letters, is


with β(L) being the periodic function of log L that is given by Eq. 7 below. The function β(L) oscillates within a range which for K≥2, is never larger than .000002 about the first two terms on the right-hand side of Eq. 7.

Let’s put some biological numbers to this.  Let’s assume that we have to change 20,000 genes to get from an ancestor to a descendant. (That’s a LOT of genes, since the whole human genome is only a tad bigger than this.) And let’s assume that at each gene only 1/40 of all gene variants are adaptive.  (We’re assuming that if the population has as few as one “adaptive” variant, that one will sweep through the population.  That’s not strictly correct since some of these will get lost by genetic drift and never contribute to evolution.)  The 1/40 figure comes from assuming a population has a million births each generation, that there are 20,000 genes, that each generation of new births carries about 5 million new mutations in the genome—about 250 per gene—and that only one new mutation in 10,000 will be favored over the “resident gene type” (The mutation data are taken from humans, and assume that only a small percentage of new mutations arise in regions of the genome that actually do something.)

Using the formula, Wilf and Ewens calculate that complete gene substitution at all 20,000 genes would take about 390 “rounds” of guessing.

That compares to 1034,040 rounds of guessing if you ask for all the genes to change in a single “round”.

The difference occurs because under parallel evolution the number of trials (or mutational rounds that must occur to cause evolution) enters as K(log L) rather than KL.  The first number is much smaller when L is large.

Of course we already knew that evolution works in parallel, but what impresses me is the huge shortening of time that occurs under realistic assumptions.  This is one step towards dispelling the idea that Darwinian evolution works too slowly to account for the diversity of life on Earth today, even given the 3.5-billion-year history of life.

We need more models like this, for the idea that things are too complex to have evolved during Earth’s history is surprisingly common.  For another useful example, see the model by Nilsson and Pelger (1994) on how rapidly a complex eye can evolve from a primitive eyespot, given reasonable assumptions about mutation rate and adaptiveness. (Dawkins also has a piece in the 1994 Nature highlighting this result.)


Wilf, H. S., and W. J. Ewens. 2010. There’s plenty of time for evolution. Proc Natl Acad Sci USA 107:22454-22456.

Nilsson, D.-E., and S. Pelger. 1994. A pessimistic estimate of the time required for an eye to evolve. Proc. Roy. Soc. Lond. B 256:53-58.

Dawkins, R. 1994. The eye in a twinkling. Nature 368:690-691.

74 thoughts on “There’s plenty of time for evolution

    1. As I said, what’s new about this paper is the math that explicitly shows how much shorter the time is with sequential evolution.

      1. It’s also a simplification from the WEASEL model. The Wilf-Ewens model used in the paper “pins” successful guesses, which makes for a more mathematically tractable but less empirically accurate model than Dawkins WEASEL example, where successful guesses are subject to further mutation. However, showing the math (even for a simplified case) is at least trivial progress.

        Playing with a java based implementation for a bit seems to suggest that the WEASEL model itself may use a O(KL LOG L) probabilistic runtime – still an qualitative improvement to polynomial time from the naive exponential conception, but unsurprisingly slower than the O(K LOG L) result of Wilf-Ewens paper.

  1. This brings up a point that I’ve wanted explained to me for many years. (Let me say here that I am an ardent Darwinian, and have read Dawkins, Coyne, Ridley, Mayr, and of course Darwin.) But one thing that never seems addressed is how selection can act on multiple alleles at the same time. Particular genes obviously can become more or less frequent in the gene pool, but they don’t exist in isolation. Some macro-adaptations that determine life or death in pray animals (longer legs, say) work this way, but the “tiny advangages” one or another gene gives are likely canceled out by tiny disadvantages of other genes. I’m bigger than average, but I’m also asthmatic and nearsighted, but also resistant to tooth decay (no cavities ever.) There are a million other genes, each with multiple phenotypic effects, and few of them likely to be the determining factor in reproduction in and of themselves.

    How can minor variations emerge when so many things are going on in one organism? Even thirty thousand zeroes doesn’t seem like it would be enough. Though obviously it all happened in just the last few hundred million years.

    Will someone please help me with this question? I’ve written to Dawkins and asked various biologists but no one seems to understand the question.

    To restate: how can multiple minor phenotypic variations be acted upon in a statistically meaningful way when there are so many of them, and none likely to be decisive in an organism’s lifetime?

    1. “Statistically” is the key word. Natural selection doesn’t operate on single organisms. It operates on competing alleles in populations of organisms. A given allele’s tiny advantage doesn’t have to be decisive in any particular case. All that’s required for natural selection to get a grip is that individuals possessing that allele be slightly more successful on average than those with a different allele — even if that allele is just a tiny part of the reason for any given individual’s success.

    2. no one seems to understand the question.

      Well, I’m no biologist, and I don’t understand the question. 😀

      What do you mean by “determining factor” and “decisive”? AFAIU, as Gregory says all what is needed for positive selection is a *relative advantage* in differential reproduction (fitness). Eventually that advantage will make an allele go to fixation (which may be called a decisive state) in most cases.

      What do you mean by “canceled out”? The posted numbers means that most *new* mutations will be alone in being noticeable in an individual. (At a 250/10 000 probability to happen once.) In fact, I read on John Hawks’ blog of selective sweeps, where as I understand it selection of an allele sweeps with (on the chromosome) nearby genes alleles towards fixation whether they are slightly advantageous, neutral, or slightly disadvantageous. I don’t see the conspiracy in numbers that you seem to find.

  2. P.S. I really am not very good at math, which is why I couldn’t read Fisher. If you could put it lay language I would appreciate it. I’m a food writer by trade.

  3. Yet another ignorant claim based upon the demonstrably false notion that evolution is some kind of targeted search algorithm?!

    C’mon, Jerry. You know better.

      1. Umm, didn’t Lederberg demonstrate that mutations are random with respect to fitness…like 60 freakin’ years ago?

        But hey, if you want to argue that evolution works more like Vanna White turning letters on Wheel of Fortune, well, be my guest.

        1. This is irrelevant reasoning. Nobody implied that selection is a *targeted* algorithm. Therefore your argument is a non sequitur.

          The beauty of selection is that an algorithm without a target can result in the appearance of directedness. In pointing out the obvious about mutation, you merely emphasize that aspect.

          1. Wrongo, J.J.E.

            Wilf and Ewans’ model “guesses” at a letter, then is told if the guess is “correct”, and if the guess is “correct” the letter is “retained”.

            The only thing missing is Pat Sajek.

          2. Chunkdz–

            If the population is not at a local fitness maximum, there will be at least one route to a fitter sequence ( often more than one). So this “vanna white” model is a special case where the number of ways uphill is one. Correctly you state that in reality this won’t hold. But more uphill routes won’t alter the length of the evolutionary trajectory because it has been shown that in a walk on a fitness landscape, if multiple uphill paths exist to a single local optimum then the number of different base pairs between the current sequence and the optimum must be the same for each alternative trajectory. I can provide a citation when I return to my pc.

            So the model’s idealization should, to my understanding, not interfere with it’s accuracy.

          3. And seeing the complexity of the model equations, it is well they choose a simplifying idealization that nevertheless capture selection hill climbing. It is obvious that a model that would lie closer to the actual process would likely not contribute but detract from that capture.

            Or to turn it around, this is sufficient to capture the computational complexity of selection. No one would bother to put in more detail since it wouldn’t contribute to the estimate.

          4. Here is the citation:

            Weinreich, D. M., Watson, R. A. & Chao, L. Perspective:
            sign epistasis and genetic constraint on evolutionary
            trajectories. Evolution 59, 1165–1174 (2005).

          5. The problem is not the length of the path, or the number of paths.

            The problem is that genes don’t stop mutating when they reach some predetermined goal.

            If the researchers wanted to demonstrate the power of teleology they did a fabulous job.

          6. Chunkdz, you are verging on incoherence. There is no “predetermined goal” in evolution; and although the Wilf and Ewens model makes that assumption I have already demonstrated that this will not effect their conclusions in the slightest. Now you are shifting your focus by talking about other, irrelevant things. Unless you can offer something more substantive this case is closed.

          7. No, you claimed that somebody was making the claim that evolution is a targeted search algorithm. Nobody makes that claim except for perhaps certain brands of theistic evolutionists and certain brands of IDers.

            Ewens and Coyne don’t claim that natural selection is guided or otherwise targeted. The environment in which survival and reproduction occurs in part governs which variants survive well and which don’t. But make no mistake, that’s not “targeted” or “directed”. In the simple letter substitution model, the “goal” is a proxy for how the environment mediates survival. The same as happens in genetic algorithms.

            Let’s review, shall we?

            Yet another ignorant claim based upon the demonstrably false notion that evolution is some kind of targeted search algorithm?!

            People here make no claim that evolution is aimed at a target or is otherwise directed. Hence my first comment.

          8. People here make no claim that evolution is aimed at a target or is otherwise directed.

            Then they shouldn’t model evolution as a targeted process. It gives ammunition to the fundies.

          9. Who cares about the fundies? The simplification in the model was appropriate and has no effect on results so deal with it instead of making bizarre complaints.

          10. Ummm, you are the one who sees this as a targeted process. It is undeniable that certain genetic combinations are more favorable than others. Full stop.

            So, given that a recently originated genetic combination appears to be more fit than ancestral combinations, it is more than fair to ask what are the statistical properties of a process that could lead from one to the other. (High altitude tolerance in Tibetan populations, for example). So, in order to model the result of an undirected process, one need only posit that one combination survives better than its progenitor. This is what is being modeled. Still undirected, no matter which way you slice it. The misapprehension (and I agree, it is a deep one and very common among creationists) comes not from here or Ewens.

          11. “So, in order to model the result of an undirected process, one need only posit that one combination survives better than its progenitor.”

            Then model it correctly. If the target is survival, then sometimes losing a trait (letter) is the advantageous adaption. But this model doesn’t allow that, does it?. That’s because this model is a teleologists wet dream. It has absolutely nothing to do with evolution as it really happens.

            It basically answers Behe’s hedgehog allegory by saying “Well of course hedgehogs can cross a 1000 lane freeway! They simply walk from one end to the other without ever getting squashed and…Taa Daa!”

            Way to give aid and comfort to the enemy, Jerry. As a leading biologist you should know better.

          12. No, your assertions aren’t backed with sound logic. It isn’t teleological and I JUST gave you a non-directed, non-teleological grounding for the model. What more do you want?

            a: If the target is survival, then sometimes losing a trait (letter) is the advantageous adaption. b: But this model doesn’t allow that, does it?. c: That’s because this model is a teleologists wet dream. It has absolutely nothing to do with evolution as it really happens.

            Regarding a: What is your point? Seriously, not rhetorically. Your point is incoherent. Do you want to model indels? Do you want to model expression silencing? Do you want to model point mutations? What? It isn’t even clear you know what you’re talking about.

            Regarding b: Nor does it allow multiple demes with varying population size and migration. Again, what’s your point?

            Regarding c: This is a non sequitur. It doesn’t follow from a & b. And that word “teleological”? You keep using that word. I do not think it means what you think it means. (If it doesn’t allow loss of function mutations, that doesn’t imply it is teleological.) As I pointed out above, it is possible to observe in natura a genotype, which is different than its progenitor by a series of adaptive differences. It happens. Deal with it. Next, if such is the case, then there is no problem with modeling the process that leads to it. So, even on this trivial level, you don’t have a position. There is no teleology, unless you think modeling an adaptive walk is necessarily teleological. (If a mathematician or computer scientist specifies the environment how a system interacts with the environment, then whatever emerges will of course be adapted to the “purpose” of fitting the environment supplied in the model. If that’s what you’re thinking, then you miss the whole point for every kind of model.)

            But, I don’t think you fully comprehend how modeling works or else are being intentionally obtuse. The whole point of this exercise was to examine multi-locus adaptations. Demography, purifying selection, dominance, dominance, epistasis, etc. were not modeled. Nor were they intended to be. Surely they could be. But the small nugget of insight gained in this paper is that, in real genomes, parallel adaptation can happen, and it makes adaptation a lot faster than the naive serial models.

            And as for your melodramatic and sanctimonious disapprobation, that’s unnecessary and condescending as well as premature. Dude, you’re making a big deal out of your own misunderstanding.

          13. Then model it correctly.

            That is precisely what is done, see my previous comment.

            Simplifications is a good thing. This is why we use Newtons gravity theory to approximate general relativity (GR), and the known to be effective theory of GR instead of the unknown quantized theory that should underlie it.

            If you don’t understand the scientific (and technological) use of toy models, you have no business complaining those who use them to achieve understanding.

  4. What a load of codswallop!! It seems *any* nonsense can be published in the Proceeding of the National Atheist Society as long as it is seen as supporting atheism-evolutionism.

    It is *ridiculous* to assume that the conserved information sequences found in genes – such as the 60 residue homeobox motif – were formed by incremental natural selection. These domains comprise holistic biochemical entities, and the probability of a random search reaching them is practically zero.

    1. What is “ridiculous” is not the incremental evolution of genes, but your cocksure assertions in the face of your profound ignorance. Every gene or genetic element looks holistic after it’s evolved. Why are you so sure that these could not have evolved incrementally?

      I’ll let the others take you apart.

      1. You are getting a bunch of actual live IDists on this thread, I think because the IDist critique of Dawkins’ “methinks” illustration is one of the areas where they think they’ve really got the evolutionists, even though Dawkins himself noted that the targetting part is artificial, and he was just trying to demonstrate the difference between cumulative selection and all-at-once assembly.

        I believe “Atheistoclast” is this guy:

        Joseph Esfandiar Hannon Bozorgmehr

        …an antogonist on many skeptics-type forums, and recent author of:

        Joseph Esfandiar Hannon Bozorgmehr (2010). “Is gene duplication a viable explanation for the origination of biological information and complexity?” Complexity. Published online: 22 DEC 2010

        DOI: 10.1002/cplx.20365

        …and just mentioned here:

        There is some kind of weird pattern emerging where infobabble creationist (crypto, but barely) review articles are getting published in obscure new journals where the number of volumes is in the single digits. Has anyone else noticed this?

        1. Nick,

          Thanks. I finally banned the guy after he’d had his say and then started calling me names in his posts. What is weird is that, among nastier things, he called me a dupe for creationists, playing into their hands. Very clever if he was one of them.

          I have a copy of his complexity paper but decided not to read it.

          cheers, Jerry

    2. You really don’t even try do you? You aren’t even going to attempt to engage in the thinking of evolutionary genetics. You just make an assertion and run ahead, ignoring millions of man hours of research, experimentation, and modeling. And the best you can do is proclaim “codswallop” and “nuh uh!”?

      That is not only pathetic. It is disrespectful. An unreasoned dissent doesn’t merit a reasoned response. Get back to us when you’re actually engaging with the evidence and models actually used in evolution rather than trivial strawmen.

    3. Seeing the later posting, this comment seems like trolling.

      However, since it is so obviously wrong:

      the conserved information

      It is trivial in information theory that information, whatever measure you use, is a relative measure. For example, Shannon information is measured relative the messages employed, ideal Kolmogorov complexity is measured relative the language employed, and practical Kolmogorov complexity is measured relative the compression employed.

      Hence there can not be any “conservation” of information, under any circumstances. Say that your conserved homeobox regulates a patterning of legs, which is successful on (some places of) Earth. Now take land animals like a creationist and his or hers unlucky mate, and plunk them down on an ocean planet where they are sure their “information” is “conserved”.

      The creationists will flounder and drown (not unlike what they do elsewhere). And that particular homeobox will go extinct with them; it will be “non-conserved” information.

      This non-conservation is of course exactly what evolution is about. Shannon information of what is successful in past generations is channeled into the genome. (And is converted to some Kolmogorov complexity of DNA sequences, unrelated to the environment. Junk DNA is an excellent information provider.) But as the environment changes, what is successful does too.

  5. What an interesting result, and it seems to me it could form the core of an expanded equation that includes terms for Effective Population Size, reversions and drift induced allele extinctions. (This is a speculation from a non-professional mind you).
    So I’ll rephrase as a question: Could the equation be built into a Selection Model for small enough, but still interesting values for L – perhaps to simulate time to evolve a novel metabolic pathway?

    1. Warren Ewens (one of the two authors) is indeed a great mathematician and population geneticist. However, his considerable work on the subject of epistasis in the genome should have led to a more nuanced understanding.

      As chunkdz wisely comments, a random search is guaranteed to be successful in a short period of time if it is guided by a target.

      1. “As chunkdz wisely comments, a random search is guaranteed to be successful in a short period of time if it is guided by a target.”

        It’s not a random search, then. Neither is evolution, which is not a targeted search, but nevertheless moves in a direction, namely in the direction of increased fitness. It’s rather like water flowing downhill, actually.

  6. There is no credible way to explain the origination of the conserved protein domains by invoking adaptive incrementalism .The amino acid sequences that make up these motifs are *highly specific* and have experienced relatively little variation between taxa.

    Why am I so sure something like the homeodomain did not evolve from a simpler entity? I can’t be. Maybe there is some exaptive origin behind it. Forgive my inability to speculate to the nth degree, but I don’t dabble is unfalsifiable claims. That is not what science is supposed to be about.

    The precise folding ,resulting in a helix-turn-helix structure, of the 60 residue homeodomain is not something which could have been built up gradually – amino acid by amino acid. At some point even you have to admit that reductionism has its limits. The function of DNA-binding domains is due to the epistatic, holistic and synergistic interaction of many residues.

    I will be writing yet another letter of complaint to Randy Schekman (editor-in-chief of PNAS).

    1. The precise folding ,resulting in a helix-turn-helix structure, of the 60 residue homeodomain is not something which could have been built up gradually – amino acid by amino acid.

      You mean like the blood clotting cascade couldn’t have been built up gradually? The vaunted “argument from incredulity”. Care to back that with evidence?

      1. You’re basically arguing from complete and utter ignorance. Protein domains like the homeobox, are not reducible to their individual amino acids. They function and fold due to the synergistic operation of all of the residues acting as one unit.

        The authors of the paper make a fatally flawed assumption:

        “After guessing each of the letters, we are told which (if any) of the guessed letters are correct, and then those letters are retained.The second round of guessing is applied only for the incorrect letters that remain after this first round, and so forth.”

        This is the same nonsense that Dawkins come up with in the WEASEL program. It assumes that individual letters (in the right place in the final sequence) will be retained by selection irrespective of the wider of the other characters in the string.

        1. There are decades of work on the effects of epistasis on the statistics of evolutionary walks that you are ignoring. Adaptation can still occur in the presence of epistasis. All epistasis does is shorten walk lengths and lower fitness (unless it is beneficial epistasis).

        2. You’re basically arguing from complete and utter ignorance.

          Really? You wound me! I thought at worst I was arguing only from utter igorance. Utter ignorance I can bear proudly, but complete ignorance, egads! You cut me to the quick my dear!

          Protein domains like the homeobox, are not reducible to their individual amino acids.

          Very good. You have recently picked up a copy of Campbell’s Biology. Can we skip amatuer hour and actually get to a substantive argument? In any event, you’re projecting. I made no such argument. Besides, your assertion doesn’t become more accurate simply with repetition.

          I’ll humor you and follow this creationist chestnut to its logical conclusion. Let’s take for granted that indeed, there is no plausible path that could lead to what we observe today from essentially random sequence (and I will grant that only for the sake of argument). Then obtaining such a sequence of 60 letters need only start from a sequence that is not random. For example through duplication of existing sequences. Perhaps an exon shuffling event brought together sequences that were “close enough”. And since I give you the benefit of the doubt, I expect you’ll accept that at least SOME sequences can indeed be assembled piecewise. If not, then you yourself are making a very sweeping (and yet unsubstantiated) claim about the nature of epistasis. It is completely plausible to predict that not every potential trajectory involve the complext coadaptation that you assert would hinder the evolution of the homeodomain.

          In any event, if small motifs can be assembled through the simple piecewise hill climber, then these smaller units can be mixed and matched with one another through errors in replication (or even transcription, in the case of retrogenes). Now, it is entirely possible for properties of combined smaller units to emerge that would be impossible to obtain in a piecewise manner.

          This hypothesis relies on actual error inducing “mechanisms” observed in actual cells. And if (in a grand sweep of time) a “good enough” mutation ever does arise, it can then be fine tuned into an even better version.

          And indeed, there are many examples in the new gene literature of origination of novel sequences that would indeed be hard to assemble in a piecewise manner without starting from pre-existing constituents.

          Is this how ancient conserved domains originated? We don’t know. In fact, we may never know. This is a tough tough problem. But to suggest there is no credible way of building up larger coadapted units in an incremental fashio belies either an a priori commitment to that proposition or an ignorance of actual biology. If you were merely questioning whether biology actually proceeded along those actual directions, that would be acceptable, but to deny the plausibility of such pathways is ignoring what we know about molecular biology.

          1. You started your argument at point A and end up at the same place.
            Talk about circular reasoning.

            Would you instead kindly tell me how the paper solves the riddle of the homeodomain’s origin. The authors are assuming that the 60 letter motif could have been assembled character by character – this is complete nonsense to anyone with even the most basic knowledge of biochemistry.

            The paper is just a rehash of the stupid WEASEL program by Dawkins. I offers no new insights whatsoever.

          2. I offers no new insights whatsoever.

            No, no you does not.

            Sorry, couldn’t resist.

            But seriously, no, my argument was not circular. You can’t deny that some arbitrarily small motifs cannot be built in a piecewise fashion. Moreover, you can’t deny that combinations of small piecewise originated chunks could, when broght together, can sometimes exhibit properties that are more difficult to arrive at through piecewise evolution. Thus, there is no problem. But since this is a MODELING paper, something more tractable and simpler is examined. No doubt making it more realistic by modeling the mutation process more faithfully would only open additional avenues to explore adaptive substitution.

            And anyway, so what if this paper doesn’t detail a solution of every problem? Neither does Kimura’s famous 1962 paper. Neither does Sawyer and Hartl’s famous 1992 paper. What is your point? That a given paper doesn’t address the minutiae of what get your undies in a twist? Even if everything you said is assumed to be right (only for the sake of argument) your pissing all over the paper is equivalent to rejecting a cancer genetics paper because its insight can’t cure people in the hospital tomorrow.

    2. Ouch, this is obviously wrong too, and my SWOTI syndrome tingles:

      The precise folding ,resulting in a helix-turn-helix structure, of the 60 residue homeodomain is not something which could have been built up gradually – amino acid by amino acid. At some point even you have to admit that reductionism has its limits.

      Nothing says reductionism leads to theories with piecewise pathways.

      The post describes parallel processing, which is also ongoing in my reductionistically invented and produced laptop.

      Other wholesale reductionist processes are emergent properties like chemistry from elementary particles, or phase changes. (Did you know that your kettle doesn’t boil away water molecule by water molecule, but that the whole liquid volume can eventually boil? It is true! But perhaps you haven’t observed too closely, since a watched pot never boils…)

      “Holism” has been soundly rejected, since reductionism works and no one has presented even one case of “holistic” theory.

      1. You can’t understand protein folding except by an holistic understanding of how the various residues interact with each other rather than as individual parts.

        I suggest you start thinking in functioning systems and not constituent elements.

      2. Torbjorn: ““Holism” has been soundly rejected, since reductionism works and no one has presented even one case of “holistic” theory.”

        Lol! I guess systems biology should just pack it’s bags, close down the journals, defund the endowments and go home because Torbjorn said so!

        1. Exactly. Add to that much of cellular biology as well.

          A word conveys meaningful information because of the way its letters are arranged together – and not merely as the sum of the individual characters.

        2. That isn’t what I claim, I claim that they aren’t using holism to get results. If you have any example of successful holism methods, please provide them.

          Meanwhile, not surprisingly, neither Atheistoclast nor you get to grips with the discussion elaborating the actual science in the post. To nick from a previous commenter, let’s review, shall we?

          At some point even you have to admit that reductionism has its limits.

          I have described how reductionist methods don’t lead to piecewise pathways, exactly as the post illustrates.

          Protein folding is another excellent example to add to the previous ones, IIRC it is now understood that proteins folds along energy minimizing paths where different parts of the molecule folds in parallel. And this knowledge was gained by reductionist methods.

          Unless you can come up with a hitherto unseen and unexpected showstopper that makes science “irreducibly complex”, there is nothing further to argue here. Science is what it is, successful reductionism in all its glory.

          1. Reductionist methods do not adequately explain how functional and holistic systems come into being. They explain things like changes in the parts but not the operation of the whole.

          2. You fail to demonstrate that “holism” exist.

            Meanwhile, we have science, based on reductionism. One reductionist science predicting how function appears is evolution. Ever heard of it?

      3. I disagree, and while “holism”is a dicey word I am not a reductionist in philosophy (thought it works in certain situations.)

        However it isn’t necessary to rest our case on reductionism so we’re still waiting from a substantive, clear response from either Atheistoclast or chunkdz.

        1. I agree on both counts.

          First, what constitutes reductionism is (if I’m correct) essentially scientific method and possibly more, so there is no good definition and no hard and fast line to draw in the line. While I admit to a propensity to redefine such description to suit, I do think it is up to “holism” philosophy to show what it is and that it works. [Disclaimer: I’m also nowadays taking a very dim view of philosophy, to say the least. This likely makes it nigh impossible to have a reasonable discussion with on such matters.]

          Second, this is indeed beneath the matter at hand. I was among other things trying to point out that ““holism”is a dicey word”, and not a sound support for creationism. (Which of course we know none of today, all what was previously arguable (say, two hundred years ago) has fallen.)

          1. D’oh! “to draw in the line” – to draw in the sand. “discussion with on” – discussion with me on.

            [Returns to drink more coffee – it is sorely needed!]

          2. I believe that certain systems are “more than the sum of their parts” (to use a dried-up cliche) if that’s what is meant by “holism”. I also believe that simplification is an inherent part of the scientific enterprise and if that be reductionist, so be it (I don’t think it is, really).

            You are correct, this point is utterly irrelevant to whether creationism is true — it just isn’t.

    3. The amino acid sequences that make up these motifs are *highly specific* and have experienced relatively little variation between taxa.

      This sort of assertion is basically never true. Run a PSI-BLAST search. There is always variation. With most proteins, most of the time, you find homologs all the way out to the edges of statistically detectable sequence similarity.

      It might be possible to find a few exceptions, but if you do, they are exceptions that prove the rule. If thousands of protein domains exhibit massive ability to vary, and a few don’t (amongst the very limited sample of genomes we currently have), you don’t get to draw general conclusions from the exceptions and ignore the overwhelming overall pattern.

  7. Note: though this is a more complicated model, the way to explain what is going on in a simple way to technically literate students is to use the argument that Dr. Coyne used in his New Republic article “The Great Mutator”.

    For those who know about statistical distributions: the ID-Creationist types assume that the mutations must occur in some sort of binomial distribution (must occur in m out of n locations at once) whereas the appropriate distribution is a negative binomial one (occur in different locations, gets fixed by natural selection, etc.)
    We did the exercise in class; the students were able to see for themselves the increase in speed.

  8. There was a notorious headline in the New Scientist on 21st. Jan. 2009 which read “Darwin was wrong”. The article actually related to horizontal gene transfer (HGT) in the process of evolution. My twisted mind had speculated that the fiendish plan behind this spectacularly controversial title was to sell the magazine to creationists by the truckload. We would then just wait until some of them actually read it, understood it and had seen that it allowed evolution to proceed at such a fast pace that their theories would then disappear in a puff of logic – I am still waiting!

    Well, in spite of the article’s title which seems to have destroyed the credibility of the whole thesis, the tree of life which Darwin had envisioned to illustrate the evolutionary process could still be retained under HGT. All we need to do is assume a gardener, with too much time on his hands, had simply snipped twigs from one side of the tree and grafted them on to the other. The current discussion on genes evolving in parallel and thereby, if useful, being fixed in some way in the chromosome would be vastly speeded up by HGT. If whole sequences of genes that have proved useful elsewhere can be grabbed and tried out in different organisms rather than these sequences waiting to evolve in their new host, then this HGT would be more than useful. You could regard the current posting on parallel evolution as likening it to playing a fruit machine whereby any useful fruit sequence can be “held” and the other fruits spun again with the hope of a winning combination emerging. HGT would be similar to playing the fruit machine but with a further option of grabbing what could be a winning combination from the machine next door and inserting the sequence into your own machine before spinning the fruit – not an option in the real world but you get the point.

    The good news for all evolutionists is that the more complex and “messy” the progress or evolution seems to get the more options for evolutionary strategies to develop emerges. We can speculate that there may be more of these strategies yet to be found though whether they can be expressed in mathematical form is another matter.

    Robin Ducret

    1. I’m loath to inject references on biology among specialists, but since I’ve recently finished a course in astrobiology I do have some to spread around FWIW. 😀

      As I understand it, HGT is not a problem for phylogenetic methods provided a) you use genomes b) you use enough of them c) you complement with state transition analysis on where genes go.

      here is one recent (2010) example of how eubacteria, archaeabacteria and eukaryotes can be tree parsed. [Despite using a traditional rooting instead of trying several.]

      And here is one IMHO exciting paper using “gene birth, transfer, duplication and loss events”. The found robust signal of an Archean Expansion (AE; “Archaean genetic expansion”) is especially interesting here, considering creationists have dropped in. Note in fig 1 that actual AE genome changes in speed and diversity swamps the so called “Cambrian explosion”!

      And of course the explicit and robust signal of gene birth (!), duplication, loss (!) et cetera is another problem for creationists (and note that the paper explains why later times aren’t devoid of birth of new genes et cetera, if anything eukaryotes have probably increased the base rates considerably.)

      1. Hi Torbjörn,

        Thanks for the info. I have to confess that on looking at your suggested articles for further study I am now feeling a bit out of my depth. As an enthusiastic amateur my reading has not progressed much beyond the popular books on the subject of evolution, but no doubt you guessed that anyway. It’s that I just cannot help diving into any controversy that gets my inventive juices flowing. I suppose that your reply was also intended for the general populace of readers here so I hope that they find your comments helpful and stimulating.

        1. I’m sorry for the complications, as I’ve noted it is problematic for a layman to give references or pointers on an experts blog. Yes, as you surmised my comment was given with such a background.

          However, I hope my comment itself, if not all the references, explains some of the current HGT vs VGT results. (And I hope the biologists here will intrude if I’m wrong.)

          If nothing else, it is the figures that is the take home message of those references. At least the later paper has self-explaining figures, and the the first have phylogenetic trees, which should be googeable. (Phylogenetic trees is the one illustration that Darwin put into his basic evolutionary text, AFAIU.)

  9. That is a very interesting article. I’m not a biologist, so I’ll have to study a little on genes and mutations. (I am a physicist/programmer).

    Evolution is part of a bigger picture. You need time for Sun’s formation, you need time for our solar system’s formation, you need time for Earth’s formation, you need time for first form of life formation etc.

    The Big Bang theory offered a lot of time. 13.something billion years is more than anyone can conceive in human life-years.

    Still, to my surprise (I’ve been studying evolution and cosmology for the past 10 years or so) there are still lots of holes in this full A-Z process.

    It’s difficult for me as a physicist to grasp a theory that talks about steps from M to P, when N is simply missing. M is dependent on N, and if N proves impossible or fairly unlikely, than no matter how possible M-P is, things will never rich that point.

    What’s also surprising for me is just how much growth of information is in the difference between the simplest life form and the most complex. It’s not only change, but also evolution from complex (a simple life form is still complex) to more and more complex. Where does all that information come from? Can environmental change really drive that? Hair? Feathers? Nails? Bones? Eyes? Taste? Smell?

    I am trying to wrap my head around all this DNA thing and I learn about Gene mapping process which is something we’re still working on, it seems, as it’s a very complex task.

  10. In case you haven’t read the paper due to cost, here is the
    free arxiv version. I’m going to do some reading now–but I can vouch for Wilf without even looking. He is a great mathematician and even better educator. I’m looking forward to using his free textbook “generatingfunctionology” in my class this spring.

  11. Warren is right, as always.

    In thinking about reality,
    we reduce reality to models of reality so that we can do math on the models of reality to gauge which one is more plausible than the other.

    In this case, we are shown two EXTREMES, the “in series” extreme arrives at the result 10^34000, the “in parallel” extreme arrives at the result 390.

    Every evolutionary biologist would agree that 390 is not the right answer in reality, since this assumes a PERFECT “in parallel” substitution process. Even if the correct letter is guessed at a given position K in the word L, and even if it increases fitness, there is still a non-zero chance that it may be purged or replaced in subsequent rounds by a suboptimal letter, due to underlying stochasticity.

    However, there are way more “in parallel” events than “in series” events, so the correct answer in reality lies between 10^34000 and 390, but closer to 390 rather than 10^34000. I’d say about few thousand or tens of thousands, that number should vary between species. Only with ‘experimental evolution’ experiments (eg. growing E.coli over thousands of generations, sequencing, measuring fitness and computational modeling) we can guesstimate that number.

    Target: ABC Start: ZZZ
    Extreme 1 (in series, slot machine like):
    ZZZ -> … 10^(34000) … -> ABC
    Extreme 2 (in parallel):
    ZZZ -> AZZ -> AZC -> ABC (390 rounds)
    Reality (A may be lost at some point, and reappear again later on):
    ZZZ -> AZZ -> ZBZ -> ZBC -> ABC (~10,000 rounds?)

    I’d say in reality, we approach 390, rather than 10^(34000).

    Any thoughts? Correct me if I am wrong.

  12. 1- In order to say there is “plenty of time” you first have to know if any amount of genetic change can account for the anatomical and physiological changes required.

    And right now the best anyone can say is we have no idea if the changes required are even possible. The main problem being is there isn’t any evidence to suggest we are the sum of our genes/ genome.

    2- Throwing “deep time” at any issue is not scientific.

    1. 1. we do, you’re ignorant and misinformed.

      2. it’s irrelevant. you should read the statement not as “plenty of time” but “WAY WAY WAAAAAAYYYYYYY more than enough time”

      3. Go back to Dembski’s blog, you moron.

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