Meyer and Dawkins are in agreement on this point. In TBW Dawkins also argues that it is random mutation that produces the functional sequences. All natural selection can do is act like a ratchet, locking successful mutations in place, per his famous weasel example. Thus, it is mutation alone that is responsible for discovering functional sequences.
Further, both Meyer and Dawkins agree these successful random mutations must be very small in order for evolution to succeed. Dawkins explicitly argues in TBW against the possibility of evolution taking large jumps since the probability of landing in a region of higher fitness is much smaller than the probability of landing in a region of higher fitness after a small jump.
What they disagree on is whether there is empirical support for these small steps. So, there is no fallacy in this EN article by Meyer. They both agree on the argumentâs logical structure. What they disagree on is the evidence.
As for @T_aquaticus counter to Axeâs work, I think the two studies are apples and oranges. Axe was estimating how many possible arrangements of a set of amino acids can form functional proteins. @T_aquaticus paper is describing how quickly bacteria can evolve resistance to a new drug. It sounds like the drug itself aids the evolution:
Our results confirm the capability of the two βâlactamase inhibitor targets to efficiently promote the formation of catalytic antibodies endowed with this activity.
If I am understanding correctly, then it doesnât really sound like the articles are talking about the same problem. Axeâs study doesnât provide anything to encourage evolution towards a target, whereas the bacteria study does. It is also not clear how far away the bacteria are from the target, nor the targetâs size. If the bacteria start off close, or the target is big, then it is unsurprising fewer attempts are required to hit the target. Since the bacteria are evolving to avoid a drug, it seems like the target can be quite big, as it is easier to make a mismatch than a match.
And even if the 10^9 number is more accurate, and we assume this is the quantity to hit a single gene, then hitting the precise 20,000 genes in the human genome represent a probability of 10^180,000. Now maybe the space of possibilities is greater, so there is not only a single specific set of genes that have to be hit. But in order to make the 20,000 genes match the number of atoms in the solar system, 10^65, then we need a chance of x = 10^(-65/20,000) ~ 0.9925 of hitting a functional sequence by chance without the aid of natural selection to ratchet things into place. Which means we can pretty much just jam any DNA sequence together and get a functional protein out of the mix. And this is a lower bound on the probability.