Want evolutionary change? Wait a million years.

September 22, 2011 • 4:12 am

The question of the pattern of stasis (no change) versus gradualism (persistent and continuous change) in the fossil record continues.  A new paper in the Proceedings of the National Academy of Sciences by Uyeda et al. comprises a huge survey and analysis of morphological change in animals (mammals, birds, squamate reptiles, and primates) over ten million years.  The purpose was to determine whether change between species in one trait—body size—accumulates gradually with the passage of time since species diverged, or whether that change is more episodic.  What they did was take a tremendous amount of data from three sources: current field studies of the rate of evolutionary change, fossil data showing change (again, this is all body size) through time, and estimates of rate of body-size divergence from living organisms whose divergence times can be estimated from molecular data.

Uyeda et al. then plotted the divergence in body size between related species (measured as proportional change, thus requiring a log scale) versus the divergence time. The graph below tells the tale: they see what they call a “blunderbuss” pattern, with not much change accumulating between species until they’ve diverged for about a million years, and then change occurring more rapidly and cumulatively after a million years.  I’ve put the caption at the bottom for those who want more information:

What we see here is that up to about a million years of divergence, there is some change between species, but it’s “bounded,” that is, it doesn’t tend to accumulate over time.  Then, after about a million years after divergence, body size starts changing without bounds, accumulating over time.  This pattern holds for the reptiles, primates, non-primate mammals, and birds.

There authors do all kinds of analyses, and test other explanations, but the pattern seems robust, and is not predicted by some models of morphological evolution, including models involving simple Brownian motion of body size (probably through genetic drift).  The best-fitting models involve a period of bounded evolution, in which body size is allowed to fluctuate, but between narrow limits, for a period, and then after that period multiple bursts of more extensive evolution can occur.

But what evolutionary process would keep a trait like body size fairly constant for a while and then, after a million years, allow rapid divergence?  The authors don’t have a firm explanation, but suggest this: for much of a species’ history, populations exchange genes, and each population might be drawn in different directions from others by natural selection. (Some populations may be selected to be large, others small.)  This genetic interchange among populations within a species keeps the species as a whole from undergoing wholesale change, although there are period of minor fluctuations such that the optimum body size of a species changes a bit for all populations, explaining the slight divergence over short time scales.  This optimum can reverse itself (sometimes it’s good to be big, perhaps when there is more food available; at other times, when there’s scarcity, it might be good to be small), but there’s no large directional change in selection pressures that would make all populations go in a single direction over a long period of time.

Why does big change happen after a million years, then?  The authors suggest that those big changes in natural selection that are persistent and affect all populations of a species, simply occur rarely. (Climate change is one factor that might obviously change body size in a directional way, but the author rule that out for several reasons.) As they say, “such significant, range-wide changes in selective optima may be sufficiently rare to explain the observed pattern of bounded evolution on time scales of <1 Myr [million years]”.  They also suggest that perhaps the range size of a species may also rarely contract to a small size—perhaps only a single population—that can respond to selective pressures without being held back by contervailing pressures in other populations, and then the (smaller) species can undergo rapid and unimpeded change.

I should add that the time scale for formation of a new species, though it varies greatly among groups, is typically on the order of 1-2 million years as well (Allen Orr and I give a table of this in the last chapter of our book, Speciation.) If speciation (which we consider to be the evolution of reproductive isolating barriers) is often a byproduct of changes in morphological traits like body size (themselves often driven by natural selection), then one might expect a similar “blunderbuss” plot of reproductive isolation versus divergence time.

We don’t have that information, and I’m not convinced that Uyeda et al. have the correct explanation for their data (to be fair, they offer only tentative explanations).  The “blunderbuss” pattern also needs to be tested for traits other than body size.  But if it holds, then we’ll have a new evolutionary phenomenon to explain.  We certainly haven’t run out of evolutionary problems!


Uyeda, J. C., T. F. Hansen, S. J. Arnold, and  J. Pienaar  2011.  The million-year wait for macroevolutionary bursts.  Proc. Nat. Acad. Sci. USA  108:15908-15913.

(Here’s the caption from the figure for you science geeks who want more info:

Fig. 1. The “blunderbuss pattern”, showing the relationship between evolutionary divergence and elapsed time. Divergence is measured as the difference between the means of log-transformed size in two populations (ln za and ln zb) standardized by the dimensionality, k. Intervals represent the total elapsed evolutionary time between samples. Microevolutionary data include longitudinal (allochronic) and cross-sectional (synchronic) field studies from extant populations. Paleontological divergence is measured from time series, including both stratigraphically adjacent (autonomous) populations and averaged longer-term trends (nonautonomous). We supplement these data with node-averaged divergence between species with intervals obtained from time-calibrated phylogenies. Pairwise comparisons between species (small points) are also presented to give a visual sense of the range of divergence values across taxonomic groups. Dotted lines indicate the expected 95% confidence interval for the multiple-burst model fitted tothe microevolutionary, fossil, and node-averaged phylogenetic data.)

73 thoughts on “Want evolutionary change? Wait a million years.

  1. Hmm… interesting… but isn’t the “blunderbuss” shape more an artefact of the logarithmic Interval axis? The delay would be far less marked and the subsequent growth more gradual over time.

    But I take it this would be common practice… ?


    1. I agree that the logarithmic time scale is driving the visual message here. I’d sure like to see it plotted on straight time instead, or as well.

      1. Yes, the pattern looks like this because it’s on the log scale, no that doesn’t make it an artifact. If it wasn’t on the log scale it would look like a standard brownian motion process, and you would only be able to see the phylogenetic comparative data. The point is to show how divergence scales from micro to macro; something that you simply can’t see on the raw time scale. Regardless, the models are fit to the raw timescale however; if that gives you any assurance that it is not an artifact.

    1. I love quote-mine opportunities like this because there is nothing that could more appropriately differentiate between those who love knowledge and those who are timidly small in the face of the mere prospect of knowledge.

      1. Very well put, but what always strikes me is the fundamental immorality of the practice. Quote-mining is lying, and religious opponents of evolution not only don’t hesitate to do it, they go considerably out of their way to do it.

        And btw, that’s the bad kind of lying, not the good kind, like lying to Nazis.

  2. Perhaps I’m misunderstanding, but isn’t a more familiar name for the “blunderbuss” pattern “punctuated equilibrium”? Given the prior recent discussion of Gould, I was very surprised not to see him mentioned here — am I mistaken in thinking that these data are precisely what he would have expected?

    1. I don’t see any reason why punctuated equilibrium would predict a stasis of one million years specifically. I think Gould would have expected it to be considerably longer in general, but I’m just guessing from reading his stuff. One million years is not a long time on a geological scale.

      1. Gould didn’t predict any particular length of stasis that I know of. And surely one would argue that any non-gradual change of stasis followed by rapid evolution is far closer to Gould’s notion than it is to the standard gradualist views of evolutionary change.

      2. Somewhere in one of his books he said – or at least I understood him to say – that stasis typically represented a large part of the lifetime of a species. So if 1-2 million years is a typical species lifetime, then to that extent the data would appear to be compatible.

        1. The average species life span is more like 10 million years, so one million is not enough to be the equilibrium part of punctuated equilibrium. Punk Eek is more long periods of stasis with short bursts of speciation, this looks more like long periods of change with short(ish) bursts of stasis.

          1. It depends on what taxa you’re working with. Mammals for example, are more like 1-5 million years, while marine inverts are closer to 10.

    2. From fig 3 in the paper a Brownian motion model seems at least viable as a first-order estimate of what the system does.

      I don’t think you get a “punctuation” out of the model behavior, but long-time variation dominating over short-time variation. That is gradualism, isn’t it?

      1. It’s somewhere between gradualism and punctuated equilibrium. Any time you get two camps of biologists arguing heatedly over a model like that, the answer will be somewhere in between (or variable between the two extremes in different systems/organisms). (TSEO’s law.)

    3. Punc-E with no claim to how long we go between ‘punctuations’ and no claim they are the same for different species would lead to a prediction of multi-modalism on charts like this; we should see many humps for a “generic punc-E” claim. We should not see just one.

      I think one hump is surprisingly uniform, and not predicted by either punc-e or gradualism. As Coyne says, next thing to do is see if it holds for other traits.

      1. Punc-E with no claim to how long we go between ‘punctuations’ and no claim they are the same for different species would lead to a prediction of multi-modalism
        That’s true — advocates of punctuated equilibrium generally have not specified time frames, and there is presumably no reason to presume that there would be a similar time frame across a wide variety of species.

    4. The blunderbuss pattern itself isn’t the product of punctuated equilibrium certainly. It is what you would see in either the case of a gradual Brownian motion or repeated punctuations (our Multiple-Burst model) on the log timescale (see Figure 3 in our paper). Consequently, it’s not surprising that it eventually looks like a blunderbuss, what was impressive to us was the consistency of pattern, timing and parameter estimates between independent data sources across a wide range of taxa. Furthermore, the interesting part is the amazing stasis (meaning substantial, but bounded change) below a million years. In fact, at coarse enough time scales Brownian motion and multiple-burst process models are indistinguishable (above maybe 50-100 my), which is why Brownian motion is often a pretty good fit to comparative data. We did support the multiple-burst model more than the Brownian model, and this supports many folks interpretation of punk-eek. However, we were cautious using this term because traditional punk-eek posits a specific relationship with phenotypic change and speciation, which we cannot see in our data, and consequently can’t say anything about. All we know is that burst-like evolution seems to be a better fit at present (though we caution in the paper against definitively throwing out Brownian motion). But I also like the model because the types of things that change phenotypes on the microevolutionary scale (new introduced species, new predators, new competitors, anthropogenic disturbance, being introduced to an island or new landmass etc.) are burst-like in the way that they change phenotypes (it sets a new optimum). I think the longer term process could have the same causes, just slowed down because it is played out over an entire geographic range.

  3. OB free pdf link.

    Very interesting. But I don’t get the statistical analysis. Fig 3 shows that the Brownian motion (BM) and multiple-burst model (MB) are virtually equally good. The supplement shows that BM assumes many fewer parameters (N degrees of freedom, where N is number of lineages) than MB (N*m degrees of freedoms, m increases with time). So BM whould be the best model in my naive statistical world. Also, it seems to be the usual default?

    However, instead of testing the models they use a bayesian measure of information for comparison only. That, as they note, assume independence, which MB is not. (The m degrees couple “bursts” over lineages – I think.) Say what!?

    If Brownian motion is the model, as a layman I am not sure what is learned. On short timescales there is an expected constant variation (set of current alleles, environmental effects), and on long time scales there is an expected increasing spread (say: drift, environmental change) that starts to dominate.

    1. You’re right about BM having fewer parameters, and the MB model is penalized accordingly by the AIC. Furthermore, you are right that the blunderbuss pattern appears in both. What you can’t see in Figure 3 is the distribution of the data. BM predicts a normal distribution at all timescales, MB predicts that at intermediate timescales (1-30 million years), you will start seeing lineages “hop out” as they get displaced, resulting in an overdispersed distribution. That is one of the aspects of the data driving the better fit for the MB model. Independence isn’t about the models, that doesn’t really make sense, it’s about whether or not the data you’re fitting the models to is independent, identically distributed (which it is not and is a major caveat we point out in our study). We mostly did the model fitting exercise to see what needs to be explained and to estimate parameters. Still, there are several aspects of the data that suggest punctuational change is a better description of the pattern.

  4. This would tie in nicely with the creationist complaint of like begetting like. Point to this study and tell ’em to wait a couple million years, then get back to you.

    (Or, less snarkily, point out that a recent analysis has shown that morphological changes remain minor for about a million years, and then divergence becomes much more readily apparent over the following million-year timespans.)



    1. Point to this study and tell ‘em to wait a couple million years

      Don’t be silly — Jesus will be coming back long before then.

    2. Point an old-earth creationist to this study and he/she will see a match for de novo creation of species to live within current environmental conditions or dearth in habitat after extinction event.

  5. It’s interesting to speculate on how much room is left for evolution of life on earth. Because the sun is heating up in it’s middle age, complex life “only” has a future remaining of the time separating us from the Cambrian:

    The Earth’s increasing surface temperature will accelerate the inorganic CO2 cycle, reducing its concentration to levels lethally low for plants (10 ppm for C4 photosynthesis) in approximately 500 million to 900 million years. The lack of vegetation will result in the loss of oxygen in the atmosphere, so animal life will become extinct within several million more years.

    We know that the sun’s evolution will kill all life relatively soon, but is there any credible speculation on what impact this inevitably hotter, drier earth will have on biological evolution, besides making everything extinct?

  6. I’m going to postulate that a million years is about the length of time it takes in “higher” animals to accumulate enough genetic variability for them to adapt sufficiently to a big environmental shift. If they don’t make it that far (or don’t accumulate enough mutations) they just die out in said shift.

    If no shift happens, maybe ecological divergence is inevitable once enough variability exists within the species. Or maybe I need some more coffee…

    1. I disagree. It’s basically a natural law that a trait like body size always has substantial genetic variance in natural populations. Take a dog or a pigeon and you can double body size far far faster than a million years.

      1. Yes the genetic variance is there to create a rapid response in dog body weight but look at the cost to dog fitness. Selection in the wild is not “for” a trait like body size. Maybe it takes a million years to resort (shake lose?) enough of the genetic and functional interdependencies to then allow the trait to take off.

        1. Yes, you’re right. The constraints hypothesis has not been ruled out. “Conditional evolvabilities” (how much a trait can evolve without changing other traits) are likely lower than standard evolvabilities, and might be low enough to slow down evolution substantially (although I have my doubts it could ever be low enough to explain a million years of stasis). Tom Kemp has a couple good papers where he talks about the concept of correlated progression, which I think is what you are describing. That may certainly play a role in slowing down evolution as well. I would think that would result in a gradual step-wise process though, and not punctuational changes. If body-size evolution is punctuational as we find, then it would seem we would need an explanation for why phenotypic integration suddenly decreases in boom-bust cycles that take a million years. Of course, all of these hypotheses do not have to be mutually exclusive.

  7. It is hard to grasp the meaning of this graph. Even with the explanation of the vertical axis it is difficult to determine what it really means. The logarithmic scale on the horizontal axis makes the pattern somewhat suspect. As you state, if it takes 1-2 million years to form a new species, the first three quarters of the graph is showing the divergence in body sizes of essentially the same set of species, while the last quarter of the graph shows all the species that developed during the next one billion years. My guess is that in general body size variance within a particular species is likely to be fairly limited, with really variances requiring new species. So in that light, this result doesn’t seem too surprising.

    1. Also, the blunderbuss seems largely due to points based on the last two methods, which seem nearly absent <1My. Is there any reason to worry that that may skew the outcome?

      1. The fossil data overlays the comparative data, which extends pretty far back and if you fit the models to only this data, you get the same estimate for the stasis distribution as you do from the other data sources (the variance of the bounded central band below a million years). There’s more overlap than you can see in the figure.

    2. genetic variance for body size is shockingly constant across species. Evolution acts only on genetic variation within species. A a general rule, the coefficient of variation for body size in all vertebrates, either in fossil populations or in extant populations, for linear size traits is ~6%, with a range of about 3-12%. However, as we see with artificial selection, it is easy to change body sizes much more than we ever observe on timescales far less than a million years. There’s no reason why natural selection couldn’t do this sometimes, but it doesn’t.

      1. How do you take into account sexual dimorphism? Does that follow the same rules, or does the dimorphism develop over a similar period?

  8. Thanks for posting this Jerry and giving a very good synopsis. The only quibble I have is where you say that it is “probably genetic drift” at longer timescales. To suppose that a trait like body size could be selectively neutral is entirely inconsistent with what we know. We always see selection on body size. Furthermore, we have models for genetic drift in quantitative traits and the parameters required to make a pattern like this are entirely unrealistic. Brownian motion doesn’t have to be genetic drift (although pure genetic drift is a BM process). More generally, BM is any process that is the sum of normally-distributed independent stochastic events. A better interpretation of Brownian motion in this case is “randomly walking adaptive zones”.

  9. Thanks for posting this, Jerry, interesting and useful, and the discussion is illuminating too – glad that Dr. Uyeda happened by.

    1. Yes. I do have questions though perhaps I should read the paper first, but one would be the initial size of animal – large mammals have a limit on the upward size, & a longer gestation & smaller population because of food source pressures. ‘Medium’ size animals can go up or down, but small animals also have a limit including life span & faster reproduction. What is my point? Not sure exactly, but all these things must have an effect on divergence of related species.

      1. The data set spans 357Myr which would date to the time of the first tetrapods. Acanthostega was one metre long. Best to check the data set though!

        For me the graph says that no dramatic change happens within and between related species over timescales less than 1-10 million years. Big changes can happen over timescales of 1-300 million years, however.

        This certainly provides a clearer picture for me, as a layman, of what is small and what is large in terms of evolutionary timescales. Puts numbers on what is micro and what is macro evolution.

  10. I never understood the “stasis” thing – it is utterly absurd to suppose that every gene change must somehow manifest as a morphological change. To call the occasional event in which a gene change or set of gene changes which cause a change in appearance “stasis” is just silly. Some morphological change may be gradual, some may be quicker (but imagine how long it takes to propagate a feature through a population), but the notion of stasis (that somehow nothing evolves for a period) is one which always gets me screaming.

    1. Nobody is assuming genic stasis, we’re talking about phenotypic stasis. The point of the plot is that the amount of phenotypic change you expect after 50 years is about the same as the amount of phenotypic 500,000 years. That’s simply an empirical pattern in need of explanation. Of course you can have a constant mean phenotype and still have continual turnover of alleles, we’re simply not talking about that. Stasis used in the paleontological sense is usually not no change, it is no accumulation of change.

      1. Thanks; I can agree 100% with your explanation about the meaning of stasis in paleontology. It gets confusing when terms are used differently (only a few years ago I was involved in a project where there were numerous arguments over the meaning of the words ‘plume’, ‘seep’, and ‘leak’).

  11. This is wrong. Something happend in the last 700 years in humans. We became science smart,went through an indusrtial revolution, started a technological revolution, explored space, and are curently going through a information revoloution. Humans are evolving rapidly. It is a soft tissue change, but it is a change. We need to acnoledge it! 100 years ago we couldn’t fly.


  12. looking at that plot, it seems like if they just plotted time on a linear scale they’d get a straight line/wedge.

    I mean, is it any wonder that as the time steps get bigger and bigger, the divergence gets bigger and bigger? I fail to see anything remarkable here.

  13. Every evolutionary event was instantaneous, occurring without gradual transformation. Natural selection had nothing to do with the ascending goal-directed sequence which the fossil record reveals. Natural selection has always been anti-evolutionary, serving to prevent change for as long as possible, a tactic which, with very few exceptions, ended with extinction. Without extinction evolution could never have occurred

    Furthermore, there is no convincing evidence that even speciation is still in progress. We observe rampant extinction without a single replacement.

    It is our position that the present biota is the climax of a planned scenario in which chance has played but a trivial role.

    In short –

    “A past evolution is undeniable, a present evolution undemonstrable.”
    John A. Davison


    1. Where to begin. The fossil records does not reveals any goal-directed sequence, where did you get that from? Species evolve from their predecessors, sometimes towards more complexity, sometimes towards less, whichever offers a greater possibility of survival. And just like in a Galton box, sometimes there is a series of changes that lead to greater complexity. The appearance of a goal-directed sequence is simply the result of the time it takes to reach higher levels of complexity.

      Natural selection does not at all serve to prevent change. Change is ongoing and continuous. Again, what made you think that?

      And of course speciation is still in progress. New species have been reported adapted to habitats that have only existed for a relatively short time. New species have formed under lab conditions. There is no reason to suppose that evolution has stopped. Do you have evidence to the contrary?

      Present evolution is only undemonstratable if you close your eyes to the demonstrations.

      1. blu28, whoever that is.

        I do not respond to pseudonymous adversaries nor do I allow them to comment on my weblog.

        Furthermore, I have countered all your claims in my peer reviewed papers, my essays and my book – “Unpublished Evolution Papers of John A. Davison,” Lulu Publishers.

        If some ‘real person’ is willing to engage me, here or anywhere else, I will respond.

        1. “blu28, whoever that is.” One mouse click would show you that blu28 is Brian Utterback and a lot more about him besides.

          If you make as little effort to review the evidence for evolution by natural selection, no wonder your criticisms command so little attention.

          So, in which journals were these peer-reviewed papers published?


          1. Ant Allan, another phony handle.

            I HAVE reviewed the evidence for natural selection and found it to have absolutely nothing to do with organic evolution except to delay it for as long as possible, a strategy which has, with very few exceptions, terminated in extinction.

            There is NO evidence for evolution through natural selection. That is my whole point. That was Leo S. Berg’s point as well in 1922.

            “The struggle for existence and natural selection are not progressive agencies, but being, on the contrary, conservative. maintain the standard.”
            Nomogenesis, page 406

            I recommend my essay – “Natural selection: The Achilles heel of Darwinism” avaialble under the new essays button at the top of my home page.


          2. I want to hear from Jerry Coyne what his opinion is concerning our science. I am betting he won’t say a word.


          3. Okay, I read it. Sorry I did. Alas, it provides no evidence at all for any of your propositions. No citations, reasons, thoughts, explanations at all. If you hadn’t listed them (in the last paragraph!) I wouldn’t have known what they were. Most of the essay is just whining about how the scientists of the past that have had their theories discredited really had the right idea and were great men unjustly treated. Again, no reasons given as to why you think that or any evidence to back up their claims.

            I have now spent much too much time on your writings. I still have not see a single suggestion of any evidence. All I have seen is a series of essays about how you have been persecuted along with those you admire. Too bad, I was willing to learn something new, but you did not deliver. I do not think I will be reading your writings again.

          4. “Ant Allan, another phony handle.”

            Actually, that is my real name, as I’ve mentioned several times on this website.

            Would you care to apologise?


    2. John has bee a persistent PITA on everyone’s websites for years and years now.

      he unfortunately lost his sanity in the 80s, was “retired” from his teaching position, and has since been one of the top science cranks out there.

      It’s quite said, really. When he was younger he actually published decent work in cell biology, even got a paper in Science IIRC.

      now, along with every science blog known to man, even UNCOMMON DESCENT has banned him from posting because he has become such a completely abusive crank.

      You’d actually be doing him a favor by banning him here too.

      wonder why it took him so long to find this place?

  14. I am wasting my time here. Coyne doesn’t even offer a contact email. He will pretend we do not exist just as Dawkins, Myers, Elsberry, Moran and every other Darwinian all do. They have always pretended that they had no adversaries. Darwinism is a hoax perpetrated and perpetuated by atheist inspired ideologues just as intolerant as the religious fundamentalists whom they openly ridicule. There is no place in science for either faction and there never will be.


    1. “Coyne doesn’t even offer a contact email.”

      Again, an amazing lack of not-much-effort. Have you not considered…

      Oh, wait. Jerry would probably be happier if you didn’t know his email address.


      1. Jerry Coyne is just as terrified of our science as are all the other Darwinian mystics which is why they all send out their minions to do battle with their adversaries. That has been the Darwinian way ever since 1859. It is the most persistent scandal in the history of science.

        Ask not for whom the bell tolls. It tolls for atheist inspired Darwinism, the most infantile proposal ever to find a receptive audience.

        “It is undesirable to believe a proposition when there is no ground whatsoever for supposing it to be true.”
        Bertrand Russell

        “Every great advance in natural knowledge has involved the absolute rejection of authority.”
        Thomas Henry Huxley

        “All great truths begin as blasphemies.”
        George Bernard Shaw



        1. I am not terrified of your “science”, which appears to me to consist solely of unpublished ravings; I am simply concerned for your sanity.

          My email is available publicly to anyone who cares to look for it, so you’re simply lazy in your assertion.

          And I join many other websites in inviting you to post elsewhere–perhaps on your own website,
          which nobody appears to read.

        2. Not every blasphemy becomes a great truth.

          Not every absolute rejection of authority has been a great advance in natural knowledge.

          … & Russell doesn’t apply: “Evolution as a process that has always gone on in the history of the earth can be doubted only by those who are ignorant of the evidence or are resistant to evidence, owing to emotional blocks or to plain bigotry. … There are no alternatives to evolution as history that can withstand critical examination.” — Theodosius Dobzhansky, “Nothing in Biology Makes Sense Except in the Light of Evolution”, American Biology Teacher vol. 35 (March 1973)”

          And you still owe me an apology for deriding my name.


          1. Not every blasphemy becomes a great truth.

            They laughed at Galileo — but they also laughed at Bozo the Clown…

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