An interesting paper appeared several months ago in an issue of the journal Genetics, “Waiting for Two Mutations: With Applications to Regulatory Sequence Evolution and the Limits of Darwinian Evolution” (Durrett, R & Schmidt, D. 2008. Genetics 180: 1501-1509). This is the second of five posts that discusses it. Cited references will appear in the last post.
Interesting as it is, there are some pretty serious problems in the way they applied their model to my arguments, some of which they owned up to in their reply, and some of which they didn’t. When the problems are fixed, however, the resulting number is remarkably close to the empirical value of 1 in 10^20. I will go through the difficulties in turn.
The first problem was a simple oversight. They were modeling the mutation of a ten-nucleotide-long binding site for a regulatory protein in DNA, so they used a value for the mutation rate that was ten-times larger than the point mutation rate. However, in the chloroquine-resistance protein discussed in The Edge of Evolution, since particular amino acids have to be changed, the correct rate to use is the point mutation rate. That leads to an underestimate of a factor of about 30 in applying their model to the protein. As they wrote in their reply, “Behe is right on this point.” I appreciate their agreement here.
The second problem has to do with their choice of model. In their original paper they actually developed models for two situations — for when the first mutation is neutral, and for when it is deleterious. When they applied it to the chloroquine-resistance protein, they unfortunately decided to use the neutral model. However, it is very likely that the first protein mutation is deleterious. As I wrote discussing a hypothetical case in Chapter 6 of The Edge:
“Suppose, however, that the first mutation wasn’t a net plus; it was harmful. Only when both mutations occurred together was it beneficial. Then on average a person born with the mutation would leave fewer offspring than otherwise. The mutation would not increase in the population, and evolution would have to skip a step for it to take hold, because nature would need both necessary mutations at once…. The Darwinian magic works well only when intermediate steps are each better (‘more fit’) than preceding steps, so that the mutant gene increases in number in the population as natural selection favors the offspring of people who have it. Yet its usefulness quickly declines when intermediate steps are worse than earlier steps, and is pretty much worthless if several required intervening steps aren’t improvements.”
If the first mutation is indeed deleterious, then the model that Durrett and Schmidt (2008) applied to the chloroquine-resistance protein is wrong. In fact, if the parasite with the first mutation is only 10% as fit as the unmutated parasite, then the population-spreading effect they calculate for neutral mutations is pretty much eliminated, as their own model for deleterious mutations shows. What do the authors say in their response about this possibility? “We leave it to biologists to debate whether the first PfCRT mutation is that strongly deleterious.” In other words, they don’t know; it is outside their interest as mathematicians. (Again, I appreciate their candor in saying so.) Assuming that the first mutation is seriously deleterious, then their calculation is off by a factor of 10^4. In conjunction with the first mistake of 30-fold, their calculation so far is off by five-and-a-half orders of magnitude.