The main thesis of the book is that there are some combinations of mutations that could theoretically be beyond the reach of evolution during the 3 billion years that life has evolved on Earth. Behe refers to this combination as a double CCC (1040). It's his estimate of the probability of a particular combination of four specific mutations arising by chance. Since we know that such combinations have arisen, Behe concludes that god(s) must have been involved.
There are many ways of exploring Behe's calculations in order to see if he has a point. The first problem is that the meaning of his conclusion is very unclear. Let's think about it this way ...
The probability of a particular bridge hand being dealt at a particular table is 5.36 × 1028 [52!/(13!)4] [see Bridge Probabilities (Wikipedia)]. The probability of two particular bridge hands being dealt in sequence at the same bridge table is about 1056 (actually closer to 3 × 1057). What this means is that every time you sit down and play a few hands of bridge you are experiencing probabilities that are lower than the double CCC that upsets Michale Behe. You don't act suprised when you see your bridge hand and you don't attribute it to any of the gods.1
This can't be what Michael Behe meant, can it? He describes a CCC as a "chloroquine-complexity cluster" and it's a cluster of two mutations—the ones that gave rise to chloroquine resistance in the malaria parasite. He says that the probability of this cluster arising is 10-20 (one in 1020). He thinks this is the probability of the double mutation but we've demonstrated already that his calculations and his logic are flawed [see Taking the Behe challenge! and Flunking the Behe challenge!].
Nevertheless, if the mutation rate is about 10-10 [see Why are the human and chimpanzee/bonobo genomes so similar?], then the probability of two particular mutations occurring is 10-10 × 10-10 = 10-20, which, by coincidence, happens to be the same number that Behe uses (even though his logic and calculations are wrong)2.
So let's go with CCC = 10-20 as the probability that a particular combination of two mutations will occur. For simplicity, we'll assume they occur in the same gene. Here's where this leads Michael Behe (pages 60-91) ....
What is the total number of creatures in the line leading to humans since it split from the line leading to modern chimps less that ten million years ago? If the average generation span of humanoids is rounded down, conservatively, to about ten years, then a generous estimate is that perhaps a trillion creatures have preceded us in the past ten million years. Although that's a lot, it's still much, much, less than the number of malarial parasites it takes to develop chloroquine resistance. The ratio of humanoid creatures in the past ten million years to the number or parasites needed for chloroquine resistance is one to a hundred million.Really? Does he really mean that there can't be any examples of two mutations occurring in the same gene since humans and chimps diverged?
If all of these huge numbers make your head spin, think of it this way. The likelihood that Homo sapines achieved any single mutation of the kind required for malaria to become resistant to chloroquine—not the easiest mutation, to be sure, but still only a shift of two amino acids—the likelihood that such a mutation could arise just once in the entire course of the human lineage in the past ten million years, is minuscule—of the same order as, say, the likelihood of you personally winning the Powerball lottery by buying a single ticket.
On average, for humans to achieve a mutation like this by chance, we would need to wait a hundred million times ten million years. Since that is many times the age of the universe, it's reasonable to conclude the following: No mutation that is of the same complexity as chloroquine resistance in malaria arise by Darwinian evolution in the line leading to humans in the past ten million years.
Let's think about this in two ways. First, the theory. The current population of humans consists of seven billion people. Every single one of them is certain to carry mutations (base pair substitution) that have arisen in the past few million years in every single gene [see Why are the human and chimpanzee/bonobo genomes so similar?]. Their children will have about 100 new mutations. If we assume that only one of these occurs in a gene, then in the upcoming generation every single human on Earth will have a CCC (two new mutations in a single gene). Behe says that this is impossible.
There are 25 amino acid substitutions. I don't know which ones occurred in the chimp lineage and which ones occurred in the human lineage but let's just assume that there were 12 mutations in the human lineage that caused an amino acid substitution. The probability of each one is 10-10 (one in 1010) because that's the approximate mutation rate. The probability of any two of these occurring is 10-20. In addition, there's a further low probability that these mutations would be fixed in the human genome.3
Michael Behe says that no mutation of the same complexity as the CCC could arise in the human lineage by Darwinian evolution and yet there they are. And that's just one gene out of 25,000 genes. It looks like CCCs are abundant.
We have a problem.
There are four possibilities that I can see.
- Behe was really talking about some other, unspecified, kind of mutation cluster.
- He means something special when he says "Darwinian" evolution that doesn't rule out the more common kinds of evolution. (The fibrinogen example is nearly-neutral alleles that have been fixed by random genetic drift.)
- The gods like to play around with fibrinogen genes.
- Behe has made a mistake.
1. This is not quite true. In my circle of friends, I frequently hear the name of one of the gods (Jesus Christ!).
2. Behe says that the mutation rate is 10-8 but gives a reference that says it should be 2.5 × 10-9.
3. The real probability is much less because after the first mutation occurs the second one can be at any other site in the gene. In the case of the fibrinogen gene, there are 866 codons. That means at least 866 × 10-10 or a probability of about 10-7 that a second mutation will occur in the same gene.