Robert Sheldon on Mark Pagel

Mark Pagel’s letter in Nature seems to have caused extreme confusion among those who somehow want it to make a case for ID. The letter which is about the distribution of time between speciation events, has been compared to opinion polls and elections. Robert Sheldon’s article in TownHall.com compares it to random walks and the work of Neo-Darwinists showing how Mendelian inheritance can lead to natural selection. These three have almost nothing in common except the word “normal” or “Gaussian” turns up in all three.

A brief mention of the first two:

Random walks. It is true that under some conditions the distribution of some variables – such as displacement after n turns where n is large – can be modelled by a Gaussian distribution. This is nothing to do with the steps being small or large or random in size –  there is no meaning to small or large in this context because there is nothing to compare the step size to and a Gaussian distribution is achieved if the steps are all the same size – hardly random.

Neo-Darwinist statistics. Fisher and others, besides inventing the foundations of much of modern statistics, showed how the Mendelian inheritance mechanism could lead to natural selection – permanent changes in the gene pool under selection pressure. One result (I am not sure if they proved this or was already known) is to show how particulate inheritance at the gene level can lead to characteristics at the phenotype level such as height which are normally distributed. Seldon describes it this way:

Only hard work by the Neo-Darwinists of the 1930’s rehabilitated Darwin’s theory of evolution by incorporating Mendel’s digital information into a theory of the random spread of genes through a population. That is, finding Gaussians in the spatial distribution of Mendel’s genes would restore the “randomness” Darwin predicted.

This gives the impression that was in some way a desperate attempt to shore up a faulty edifice. In fact it simply solved the problem (and incidentally solved one of Darwin’s problems – the famous blending problem).

So what is Pagel’s letter all about? It is about the distribution of time between speciation events. One popular model of speciation is that other events (such as mutations) that happen frequently (that is frequently compared to the time between speciation events) and are small (in the sense of not causing a big change in the organism) accumulate under the pressure of different natural selection selections in different communities until the difference is so great the two communities become different species. This accumulation might be additive (each event adds to the difference between the communities) or multiplicative (each event multiples the existing difference between the communities). The stock example is something like the Galapagos finches – the beaks and other features gradually change under different selection pressures on different islands until the two types of finch are so different they are different species. This model should lead to an approximately normal distribution of time between speciation events.

There are other models. One of them is that speciation is typically caused by single event (which would by definition have the same frequency as speciation events) and must be a “large” event to cause speciation. If these events happen at a roughly constant rate and are independent of each other then the time between events and therefore between speciations will be exponentially distributed.

Pagel found for about 100 cases (phylogenies) that the large majority (78%) of distributions were exponential and only about 6% were normal (the others conformed to other alternative models).

To what extent does this refute “Darwinism” and support ID?

First – remember that this little study does not prove that 78% of speciations are caused by single events and that only 6% are the result of the accumulation of small events. It is only some evidence to support that hypothesis.

However, it is evidence. It looks like speciation caused by single events may be much more common that was previously realised. This is different from what Darwin originally proposed, but speciation as the result of one major event has been accepted as happening sometimes for many decades. The surprise is in its frequency.

However, both models have a lot in common.

Whatever the size of events both models treat them as random in two senses:
1) The events are independent of each other – in the large event case the events are exponentially distributed – in the small event case they may also be exponentially distributed or it may be some other distribution (the distribution of speciations will not be sensitive to the distribution of contributing events provided there are lots of them and they are independent of each other). It is just the size of them and the resulting effect on speciation that has to be different.

2) They are not directed towards any end. In the paper, Pagel describes some examples of “big” events that might cause speciation:

Factors apart from biotic interactions that can cause speciation include polyploidy , altered sex determination mechanisms, chromosomal rearrangements , accumulation of genetic incompatibilities, sensory drive, hybridization and the many physical factors included in the metaphor of mountain range uplift

So when Seldon writes:

Then looking at the distribution of “forks” in time, a random process should give us a Gaussian.

and later

The article goes on to explore the meaning of an exponential, which involves a lot of speculation, but the take-home point is that it means “forks” or “mutations” are decidedly _not_ random.

This is wrong.

It is also worth pointing out that this paper is no kind of evidence against the well established role of small events and natural selection in changing a species. It only discusses what causes a splitting of one species into two.

Pagel’s paper is evidence for a different model of speciation being much more common than previously supposed – but it is an entirely natural model.

What does this mean for ID? Actually it is bad news. The case for ID is primarily based on supposed evidence that small events plus natural selection cannot create the complexity of life. The viability of alternative natural models based on large events weakens this already weak argument.

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2 Responses to “Robert Sheldon on Mark Pagel”


  1. 1 Rob Sheldon March 18, 2010 at 6:03 pm

    A great post!

    One caveat–in my blog and in my comment, I said repeatedly that Gaussians imply randomness, whereas non-Gaussians usually imply non-randomness. Your point is that exponentials can be the result of a random process, so would be one of the “unusual” examples of random producing non-Gaussians.

    This may well be true. However, unlike a Gaussian, lots of other non-random things make exponentials. So since you produced a mechanism, lets pull it apart and see what it means that speciation events are NOT cumulative.

    1) species differ from each other by multiple mutations or variations. I don’t think this is a controversial point.

    2) Darwin suggested that species gradually mutate until something keeps the two sub-populations apart and we have a new species. Island populations were thought to do this, lots of population genetics solutions have been proposed. However, no matter which of the solutions you subscribe to, they all involve multiple, cumulative changes. This is not controversial.

    3) Multiple, cumulative changes that proceed randomly are also known as a “random walk”. Again, this is not controversial.

    4) “distance” traversed in a random walk, is described by a diffusion equation, df/dt = D dx2/dt2, which has solutions of f(x) that look like Gaussians. Not controversial.

    5) Then the expectation was that cumulative small mutations should be distributed (using some sort of linear mapping between the mutation time-differences and a spatial coordinate x) as a Gaussian.

    Let me say this again. In our random walk example, we take each mutation event as a “step”, where the initial position (lightpole) and the final position (new species) is the “distance” coordinate. Pagel didn’t have any information about steps that were reversed, so instead he looked at the “time between steps”. This is an added sophistication to our diffusion model, and has to do with “intermittency”. There’s a lot of literature on the topic which I am not that conversant in, but it is my general impression that this temporal measurement maps back into the spatial definition through the diffusion equation. (if you would like to direct me to the literature, I’d be happy to reconsider.)

    So that means a cumulative diffusive approach to a new species should demonstrate a Gaussian distribution in “speciation-space” and a concurrent Gaussian distribution in “delta-time” space.

    But Pagel found an exponential.

    What does this mean? One of our assumptions about speciation is wrong.

    6) Pagel, and apparently this blog, think that one-step speciation events are the answer. That is, there is no accumulation of small steps to produce speciation, but sudden, big steps, occurring at very infrequent intervals.

    Okay, let’s pull that apart.

    a) Does this require randomness? No. Lots of causes can have this effect. Does this require non-randomness? No, because the big jumps can be random too. But what it does require is that there NOT be a cumulative small step problem.

    b) I alluded to these “fat-tail” solutions in the original blog. And yes, exponentials are a “fat-tail” along with Cauchy, Levy and Poisson distributions. Fat-tail distributions have a number of disturbing properties:

    i) they do not exhibit maximum entropy. There are rearrangements of the members that are more probable than themselves. This means that they are inherently improbable, all other things being equal. In other words, some law other than random chance is producing this distribution, because random chance ought to produce the most probable (maximum entropy) distribution.

    ii) they do not exhibit minimum energy. There are rearrangements that minimize the “work” (which we arbitrarily claim is proportional to the “size” or “number of single codon replacements” of the mutation.)

    iii) they do not have a finite diffusion coefficient. This means they exhibit infinite diffusional velocity. In other words, they get places faster than chance. For example, bacteria when searching for food use a Levy-flight search pattern, since it is more efficient than diffusive-search. This is an example of purpose-driven search, which in our case would correspond to something law-like that is driving the mutation rate.

    c) All this non-Gaussian difficulty could be avoided if the delta-t distribution were Gaussian. But since Pagel and our blog host finds this otherwise, they claim that big steps can still be random. Perhaps, but it now becomes a “random-with-added-laws”, which is a bit disturbing.

    d) ID argues that large jumps are probabilistically forbidden. That is, 3 simultaneous mutations in the Plasmodium that causes malaria are required to convey quinine resistance. Mike Behe calculates this in his book “THe Edge of Evolution”. It took something like 10^20 generations of Plasmodium to acquire this mutation. Larger jumps, like those seen in Pagel’s data, would then be impossible by random chance.

    Thus Pagel’s data support the idea that speciation occurred by large jumps, which are not random, and indeed support Behe’s contention that speciation is NOT driven by Darwinian mechanisms.

    What drives it, neither Behe nor Pagel knows, but one thing we can be certain of, it isn’t Darwinian diffusion.

  2. 2 Milford April 10, 2010 at 6:17 pm

    I really like when people are expressing their opinion and thought. So I like the way you are writing


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