Available here.

Axe’s analysis was motivated in part by the recent flurry of papers dealing with the problem of the waiting time for multiple independent mutations.

Here is Doug’s abstract:

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

This is definitely holiday down-time reading. Strong, large cup of tea or coffee — no alcohol for this one — a footrest, and maybe a nice cat purring nearby for those moments when you need to set the paper down and think about it for a while. Petting a cat while thinking (for a human) is a great symbiotic relationship.

quote of note: Be that as it may, the most significant implication comes not from how the two cases contrast but rather how they cohere—both showing severe limitations to complex adaptation. To appreciate this, consider the tremendous number of cells needed to achieve adaptations of such limited complexity. As a basis for calculation, we have assumed a bacterial population that maintained an effective size of 10^9 individuals through 10^3 generations each year for billions of years.

This amounts to well over a billion trillion opportunities (in the form of individuals whose lines were not destined to expire imminently) for evolutionary experimentation. Yet what these enormous resources are expected to have accomplished, in terms of combined base changes, can be counted on the fingers.a billion trillion = 10^19 is a number derived after ‘bending over backwards’ to be favorable to the Darwinian framework, And yet the ‘overly optimistic’ 10^19 number just so happens to line up extremely well with the 10^20 Dr. Behe found in ‘The Edge Of Evolution’ from the ‘real world’ results on malaria and HIV:

“The likelihood of developing two binding sites in a protein complex would be the square of the probability of developing one: a double CCC (chloroquine complexity cluster), 10^20 times 10^20, which is 10^40. There have likely been fewer than 10^40 cells in the entire world in the past 4 billion years, so the odds are against a single event of this variety (just 2 binding sites being generated by accident) in the history of life. It is biologically unreasonable.”

Michael J. Behe PhD. (from page 146 of his book “Edge of Evolution”)

Richard Dawkins’ The Greatest Show on Earth Shies Away from Intelligent Design but Unwittingly Vindicates Michael Behe – Oct. 2009

Excerpt: The rarity of chloroquine resistance is not in question. In fact, Behe’s statistic that it occurs only once in every 10^20 cases was derived from public health statistical data, published by an authority in the Journal of Clinical Investigation. The extreme rareness of chloroquine resistance is not a negotiable data point; it is an observed fact.

http://www.evolutionnews.org/2.....est_s.html

Waiting Longer for Two Mutations – Michael J. Behe

Excerpt: Citing malaria literature sources (White 2004) I had noted that the de novo appearance of chloroquine resistance in Plasmodium falciparum was an event of probability of 1 in 10^20. I then wrote that ‘‘for humans to achieve a mutation like this by chance, we would have to wait 100 million times 10 million years’’ (Behe 2007) (because that is the extrapolated time that it would take to produce 10^20 humans). Durrett and Schmidt (2008, p. 1507) retort that my number ‘‘is 5 million times larger than the calculation we have just given’’ using their model (which nonetheless “using their model” gives a prohibitively long waiting time of 216 million years). Their criticism compares apples to oranges. My figure of 10^20 is an empirical statistic from the literature; it is not, as their calculation is, a theoretical estimate from a population genetics model.

http://www.discovery.org/a/9461

————–

Again I would like to emphasize, I’m not arguing Darwinism cannot make complex functional systems, the data on malaria, and the other examples, are a observation that it does not. In science observation beats theory all the time. So Professor (Richard) Dawkins can speculate about what he thinks Darwinian processes could do, but in nature Darwinian processes have not been shown to do anything in particular.

Michael Behe – 46 minute mark of video lecture on ‘The Edge of Evolution’ for C-SPAN

http://www.uncommondescent.com.....ent-361037

“There are no detailed Darwinian accounts for the evolution of any fundamental biochemical or cellular system only a variety of wishful speculations. It is remarkable that Darwinism is accepted as a satisfactory explanation of such a vast subject.”

James Shapiro – Molecular Biologist

correction billionn trillion = 10^21 = 10^9 + 10^12

Hints that the odds of evolution of this to that is further complicated by needing co evolution of other biology to help the first biology.

All impossible if impossible exists in biology.

Behe’s number was actually over 10^20 and he rounded it down, IIRC.

Or rather Nicholas White’s number.

This thread is already on page 2. That’s a shame since this is an important paper.

Just a few brief comments.

Axe’s paper treats the paper by Lynch and Abegg first, and then he develops his own model based on the “island model” of Kimura and Marauyama.

In his treatment of L&A’s paper, Axe points out that their neutral model, based on an equation they derive, using an approximation for the presence of a cell with the complex adapted allele present that is independent of the number of bases (“d”) needed for this complex adapted trait, is counterintuitive and doesn’t make much sense.

L&A say that (ut)^d, when ut << 1, u being the mutation rate and t the time in generations, can basically be considered as u^-1. Axe remarks that if you ignore d is such a way, then it is no surprise that d has no effect on the time to fixation of the complex trait.

Briefly, let's assume ut is .01. Then (.01)^10 (that is, 10 base changes) is 10^-20, whereas u^-1 is, per L&A, 10^-6. Does it really make any sense at all that whether it is one base change needed, or 10 base changes needed, that the evolutionary process happens in roughly the same time frame?

Axe, having come up with his own model, compares his equations for the maladaptive and neutral cases to L&A's maladaptive and neutral cases. L&A's neutral case doesn't show a step-like increase in time to fixation per added base change needed, while Axe's and L&A's maladaptive equations do. Axe would conclude that L&A's neutral case equation gives odd results, ones that are not very believable.

I think it is fairly clear that L&A have made a mistake in their approximating procedure for the neutral case.

As to Axe's model, his model is very similar to Behe and Snoke's model, save for the fact that B&S's model has the maladaptive mutations crippling the organism, which Axe says, per studies conducted, doesn't really happen. Thus, Axe comes up with the possibility of more base changes for the maladaptive case. Nevertheless, he only end up with a high-end possibility of six base changes using his neutral model. This represents about 3-6 a.a. changes, substantially higher than Behe and Snoke's limit of about 2-3 a.a. Yet, as Axe oints out, this limitation on base change substitutions per Darwinian mechanisms, throws into question any Darwinian explanation for novel protein foldings, and, thus, Darwinism itself.

Axe's model seems quite realistic. So, once again, Darwinian capabilities for evolutionary change have been demonstrated to be remarkably limited.