I recently published an article on Uncommon Descent on the value of probabilistic arguments in the evolution debate. Mathematician and ScienceBlogs contributor Jason Rosenhouse has since responded with a rebuttal on his blog. Here, I offer a brief response.
Jonathan M. is completely confused about what the issue is. Pigliucci certainly never claimed that biologists are not interested in evaluating probabilistic feasibility (whatever that even means). He said simply that evolutionary biologists do not assign probabilities to specific events in the way that ID folks would like.
For example, Jonathan M. points to a calculation in which biologist Sean Carroll estimated the probability of obtaining the same mutation four times independently in different orders of birds. In such a narrowly defined situation the problem has more to do with combinatorics than probability, and we can be confident that all of the relevant variables can be approximated with reasonable accuracy.
He also points to a paper by Durrett and Schmidt, in which they evaluated the probability of obtaining two particular mutations in at least one individual of a population. Once again, in such a narrowly defined situation it is possible to get a grip on all of the relevant variables. But notice that neither they, nor Carroll, were trying to calculate the probability of evolving a flagellum or anything remotely like that.
While it is true that the individuals in question do not attempt to calculate the probability of something of the complexity of a bacterial flagellum, to handwavingly assert that such calculations have no bearing whatsoever on questions such as this seems to me to be somewhat naive.
For example, let’s grant for purposes of our argument here that the conclusions reached in Douglas Axe’s bacterial population model are correct: That is, if a duplicated gene is neutral, then the maximum number of mutations that a novel innovation in a bacterial population can require is up to six, whereas if the duplicated gene has a slightly negative fitness cost, the maximum number drops to two or fewer. If one can demonstrate that the evolutionary steps to a functioning flagellum would likely require more co-ordinated mutations than this at the individual stages, then — even though the exact probability of the flagellum may not be directly calculable — it seems to be a plausible inference that the flagellum lies beyond the reach of the Darwinian mechanism.
But here’s the thing. According to Douglas Axe’s more recent research, done in collaboration with Ann Gauger, even a seemingly trivial switch from Kbl to BioF function requires at least seven co-ordinated mutations, putting the transition well beyond the reach of a Darwinian process within the time allowed by the age of the earth. Their paper studies the PLP-dependent transferases superfamily. They identified a pair within the superfamily with close structural similarity but no overlapping function. The enzymes chosen were Kbl (which is involved in threonine metabolism) and BioF (which is part of the biotin synthesis pathway). And they used a three-stage process (which you can read about here) to identify which sequences were most likely to confer a change in function.
And thus they estimated that seven or more mutations would be required to convert Kbl to BioF function.
Axe and Gauger’s paper is not an isolated result. For example, one fairly recent review in Nature reported that changing an enzyme’s chemistry may require multiple neutral or deleterious mutations.
When these results are taken into account in the context of the predictions of population genetics with regards the waiting time for multiple co-ordinated non-adaptive mutations which are required to facilitate a given transition, the situation for neo-Darwinism appears to be bleak.
In the case of the Durrett and Schmidt (2008) paper, evolutionary biologist Richard von Sternberg has applied the equations employed in that paper to whale evolution. The evolution of Dorudon and Basilosaurus (38 mya) may be compressed into a period of less than 15 million years. Such a transition is a fete of genetic rewiring and it is astonishing that it is presumed to have occurred by Darwinian processes in such a short span of time. This problem is accentuated when one considers that the majority of anatomical novelties unique to aquatic cetaceans (Pelagiceti) appeared during just a few million years – probably within 1-3 million years. The equations of population genetics predict that – assuming an effective population size of 100,000 individuals per generation, and a generation turnover time of 5 years – according to Richard Sternberg’s calculations and based on equations of population genetics applied in the Durrett and Schmidt paper, that one may reasonably expect two specific co-ordinated mutations to achieve fixation in the timeframe of around 43.3 million years. When one considers the magnitude of the engineering fete, such a scenario is found to be devoid of credibility. Whales require an intra-abdominal counter current heat exchange system (the testis are inside the body right next to the muscles that generate heat during swimming), they need to possess a ball vertebra because the tail has to move up and down instead of side-to-side, they require a re-organisation of kidney tissue to facilitate the intake of salt water, they require a re-orientation of the fetus for giving birth under water, they require a modification of the mammary glands for the nursing of young under water, the forelimbs have to be transformed into flippers, the hindlimbs need to be substantially reduced, they require a special lung surfactant (the lung has to re-expand very rapidly upon coming up to the surface), etc etc.
Moreover, Michael Behe has shown (see chapter seven of The Edge of Evolution) that the evolution of protein-protein binding sites by Darwinian means is immensely improbable. And Douglas Axe, Robert Sauer, Sean Taylor and others have shown that the preponderance of evolutionarily relevant (i.e. functional) protein folds is astronomically rare within sequence space. These types of problems are only accentuated a thousand fold when one considers systems which, by their very nature, require multiple inter-dependent protein interactions in order to perform their functions.
Jason Rosenhouse also mentions the well-known Wilf and Ewens PNAS paper:
This paper by Wilf and Ewens, also mentioned in the post, puts some mathematical meat on the bones of Dawkins’ suggestion. They are working with probabilities only indirectly, and certainly were not trying to assign precise numerical values to specific evolutionary events.
The abstract of this paper reported,
Objections to Darwinian evolution are often based on the time required to carry out the necessary mutations. Seemingly, exponential numbers of mutations are needed. We show that such estimates ignore the effects of natural selection, and that the numbers of necessary mutations are thereby reduced to about K log L, rather than KL, where L is the length of the genomic “word,” and K is the number of possible “letters” that can occupy any position in the word. The required theory makes contact with the theory of radix-exchange sorting in theoretical computer science, and the asymptotic analysis of certain sums that occur there.
This sounds awfully like an attempt to demonstrate the probabilistic plausibility of Darwinism to me. We ID proponents employ probabilistic logic as well, in order to ascertain the likelihood of evolutionarily relevant innovations emerging by Darwinian means. Only we reach the opposite conclusions from those reached by Wilf and Ewens. Darwinists are happy for probabilistic reasoning to be employed only when it suits their purposes in vindicating Darwinism. When ID proponents want to use probabilistic arguments to falsify Darwinism, they won’t be having any of it.
Douglas Axe humorously noted at the time,
If you search the current issues of professional science journals, I doubt you’ll find any papers titled “The Moon Orbits the Earth” or “Copper Conducts Electricity.” Assertions like these would work as section headings in an elementary science textbook, but no scientist would consider them newsworthy, for the simple reason that they aren’t.
Things are different in evolutionary biology, though. Here is a field that somehow never outgrew the need to reiterate its most basic tenets, as though its practitioners never had enough confidence in them to let them stand on their own two feet.
Lee Spetner points out the crippling problems with the paper:
Their model does not mimic natural selection at all. In one generation, according to the model, some number of potentially adaptive mutations may occur, each most likely in a different individual. W&E postulate that these mutations remain in the population and are not changed. Contrary to their intention, this event is not yet evolution, because the mutations have occurred only in single individuals and have not become characteristic of the population. Moreover, W&E have ignored the important fact that a single mutation, even if it has a large selection coefficient, has a high probability of disappearing through random effects [Fisher 1958]. They allow further mutations only in those loci that have not mutated into the “superior” form. It is not clear if they intended that mutations be forbidden in those mutated loci only in those individuals that have the mutation or in other individuals as well. They have ignored the fact that evolution does not occur until an adaptive mutation has taken over the population and thereby becomes a characteristic of the population. Their letter-guessing game is more a parody of the evolutionary process than a model of it. They have not achieved their second goal either.
If Darwinism can’t even handle the trivial, then what chance does it have when it comes to the bigger problems such as building flagella? And if we can’t even evaluate the probabilistic feasibility of the Darwinian mechanism, how can we ever learn whether it is up to the task at hand? Whether they realize it or not, Pigliucci and his ilk have, in effect, rendered Darwinism unfalsifiable.