This is correct. The probability of any single mutation occurring is equal to the mutation rare, which is about 10-10. The probability of an additional specific mutation occurring is also 10-10. The combined probability of any two specific mutations occurring is 10-20.
- If the development of some particular adaptive biochemical feature requires more than one specific mutation to an organism's genome, and if the intermediate mutations are deleterious (and to a lesser extent even if they are neutral), then the probability of the multiple mutations randomly arising in a population and co-existing in a single individual so as to confer the adaptation will be many orders of magnitude less than for cases in which a single mutation is required.
This is correct. It refers to the probability of the specific double mutation occurring and not to whether it becomes fixed in the population.
- The decreased probability means either that a much larger population size of organisms would be required on average to produce the multiple mutations in the same amount of time as needed for a single mutation, or that for the same population size a multiple-mutation feature would be expected to require many more generations to appear than a single mutation one.
This is a little bit misleading and possibly a little bit disingenuous. Everyone understood that chloroquine resistance was rare and that it almost certainly required multiple mutations. Behe developed an explanation based on the idea that two mutations were required and one of them, by itself, had to be very deleterious. This is because he used an incorrect value for the mutation rate that was several orders of magnitude too low. He based his calculations on the assumption that the two mutations had to arise in a single infected patient.
- In The Edge of Evolution I cited the development of chloroquine resistance in the malaria parasite Plasmodium falciparum as a very likely real-life example of this phenomenon. The recent paper by Summers et al. confirms that two specific mutations are required to confer upon the protein PfCRT the ability to pump chloroquine, which is necessary but may not be sufficient for resistance in the wild.
The recent paper by Summers et al. (2014) shows that seven of the chloroquine resistant strains that have been observed have at least four mutations and some of them are relatively neutral. This refutes and discredits the scenario that Michael Behe put forth in his book.
The reason why Behe's statement is disingenuous is because he uses the word "confirms" and because his sycophants are promoting the idea that Behe made "predictions" that have recently been confirmed [A Pretty Sharp Edge: Reflecting on Michael Behe's Vindication] [So, Michael Behe Was Right After All; What Will the Critics Say Now?].
As we all know by now, the "guesstimate" by Nicholas White refers to the possible frequency that a chloroquine resistant strain will be detected someplace in the world. This is a far cry from the probability that the correct mutations will actually occur. Behe's entire argument is based on the idea that 10-20 is the probability that two specific mutations will occur.
- The best estimate of the per-parasite occurrence of de novo resistance is Nicholas White's value of 1 in 1020. This number is surely made up of several components, including: 1) the probability of the two required mutations identified by Summers et al. coexisting in a single pfcrt gene; 2) the value of the selection coefficient (which can be thought of as the likelihood that the de novo mutant will successfully reproduce in a person treated by chloroquine and be transmitted to another person); and 3) the probability of any possible further PfCRT mutation needed to confer chloroquine resistance in the wild coexisting in the same gene with the other mutations.
As I explained in a previous post, the actual mutation rate in P. falciparum is 2.5 × 10-9. Thus, the probability of two specific mutations is 6.25 × 10-18 [Taking the Behe challenge!] [Flunking the Behe challenge! ]. Typical eukaryotic mutation rates are closer to 10-20. The probability of the two mutations occurring is getting close to Nicholas White's estimate of the frequency of the chloroquine resistant strain being detected.
- The known point mutation rate of P. falciparum, combined with the apparent deleterious effect of the required mutations occurring singly, suggests that component 1 from the previous bullet point will account for the lion's share of White's estimate, probably at least a factor of 1 in 1015-1016 of it. The other factors would then account for 1 in 104-105. These values are somewhat flexible, accommodating the uncertainty in our knowledge of the exact values in the wild. In other words, a decrease in our best estimate of the value of one factor can be conceptually offset relatively easily without affecting the argument by supposing another factor is larger, to arrive at 1 in 1020.
But, according to Michael Behe, there's a 10,000 (104) fold difference between the probability of the mutations occurring and their actual frequency. This is important because he attributes that difference to the fact that both of the two mutations are deleterious on their own. In other words, whichever mutation occurs first, that individual is likely to be eliminated by natural selection before the second mutation can occur. (Actually, he only says that one of the mutations has to be deleterious but that's a mistake.)
Summer et al. (2014) showed conclusively that this calculation is wrong. They showed that among the seven strains analyzed there were multiple pathways to resistance and that a minimum of four mutations were required for effective resistance. The showed that one mutation (K76T) was essential in all strains. All strains had one of two additional mutations that seemed to be required early on, N75E or N326D.
- Any particular adaptive biochemical feature requiring the same mutational complexity as that needed for chloroquine resistance in malaria is forbiddingly unlikely to have arisen by Darwinian processes and fixed in the population of any class of large animals (such as, say, mammals), because of the much lower population sizes and longer generation times compared to that of malaria. (By "the same mutational complexity" I mean requiring 2-3 point mutations where at least one step consists of intermediates that are deleterious, plus a modest selection coefficient of, say, 1 in 103 to 1 in 104. Those factors will get you in the neighborhood of 1 in 1020.)
There were at least four paths to resistance ....
The presumed evolutionary path to most of the resistant strains did NOT involve any intermediates that were less fit than the wild type. Strains carrying single mutations were detected in the wild.WT → K76T → K76T + N75E
WT → K76T → K76T + N326D
WT → N75E → N75E + K76T
WT → N326D → N326D + K76T
Recall that Behe's calculation of the mutation rate is too low by a factor of at least 100 in spite of the fact that he references the accepted mutation rate. The recent data by Summer et al. refutes three of Behe's assumptions: (a) that only two mutations are required to account for the appearance of resistant strains, (b) that a resistant parasite had to arise from wild type within a single infected individual, and (c) that one or more of the individual mutations are deleterious on their own.
Other than that, his calculations and his "predictions" are perfect!!!!
It is true that any specific set of 4-6 mutations is extremely unlikely. Nobody disputes that any more than they dispute the probability of a specific hand of bridge being dealt in the next deal. That's only going to happen once in 1028 tries. It's impossible that you will see it in your lifetime. But you still get to play bridge.
- Any adaptive biological feature requiring a mutational pathway of twice that complexity (that is, 4-6 mutations with the intermediate steps being deleterious) is unlikely to have arisen by Darwinian processes during the history of life on Earth.
When such a triple mutation arises we recognize that it was only one of millions and millions of possible evolutionary outcomes. There was no a priori requirement that Earth contain red pines and white pines just as there's no a priori requirement that you get a specific hand in the next deal.
This is hard for IDiots to understand since they begin with the assumption that humans are the designed outcome of the history of life on Earth and they assume that evolutionary theory has to explain why the tape of life will always play out in the same manner every time.
They can't conceive of an alternative history that didn't have Homo sapiens or white pine trees. If they are right, then Behe's argument makes sense. Evolution can't do that. But all the evidence we have indicates that they are wrong, and Gould is right1. Behe's argument makes no sense in the light of evidence of evolution.
There is an edge of evolution and it rules out design in favor of accident and contingency.
I call this experiment "replaying life's tape." You press the rewind button and, making sure you thoroughly erase everything that actually happened, go back to any time and place the past—say, to the seas of the Burgess Shale. Then let the tape run again and see if the repetition looks at all like the original. If each replay strongly resembles life's actual pathway, then we must conclude that what really happened pretty much had to occur. But suppose that the experimental versions all yield sensible results strikingly different from the actual history of life? What could we then say about the predictability of self-conscious intelligence? or of mammals? or of vertebrates? or of life on land? or simply multicellular persistence for 600 million years?
Stephen Jay Gould, "Wonderful Life" pp48-50
Summers, R. L., Dave, A., Dolstra, T. J., Bellanca, S., Marchetti, R. V., Nash, M. N., Richards, S. N., Goh, V., Schenk, R. L., Stein, W. D., Kirk, K., Sanchez, C. P., Lanzer, M. and Martin, R. (2014) Diverse mutational pathways converge on saturable chloroquine transport via the malaria parasite’s chloroquine resistance transporter. Proceedings of the National Academy of Sciences. [doi: 10.1073/pnas.1322965111]