Meyer Weighs In

It turns out the big Lawrence Krauss/Stephen Meyer debate is two and a half hours long. I've started watching it in installments. So far I've only gotten through Krauss' thirty minute opening presentation. I thought it was decent, though Krauss was overly nasty towards his sparring partner in his opening remarks. I sympathize with the sentiments, but I think he overdid it.

I haven't watched Meyer's presentation yet, but it looks like I may not have to, what with the internet all abuzz with people commenting on it. Stephen Meyer himself has now weighed in on the Richard Dawkins comment I highlighted in my previous post. That post was primarily about a poorly-argued comment left by Douglas Axe.

Meyer attempts to put some meat on the bones of Axe's comment. Here is a lengthy quote:

In any case, the need for random mutations to generate novel base or amino-acid sequences before natural selection can play a role means that precise quantitative measures of the rarity of genes and proteins within the sequence space of possibilities are highly relevant to assessing the alleged power of mutation-selection mechanism. Indeed, such empirically derived measures of rarity are highly relevant to assessing the alleged plausibility of the mutation-selection mechanism as a means of producing the genetic information necessary to generating a novel protein fold. Moreover, given the empirically based estimates of the rarity (conservatively estimated by Axe at 1 in 10^77 and within a similar range by others) the analysis that I presented in Toronto does pose a formidable challenge to those who claim the mutation-natural selection mechanism provides an adequate means for the generation of novel genetic information -- at least, again, in amounts sufficient to generate novel protein folds.

Why a formidable challenge? Because random mutations alone must produce (or “search for”) exceedingly rare functional sequences among a vast combinatorial sea of possible sequences before natural selection can play any significant role. Moreover, as I discussed in Toronto, and show in more detail in Darwin's Doubt, every replication event in the entire multi-billion year history of life on Earth would not generate or “search” but a miniscule fraction (one ten trillion, trillion trillionth, to be exact) of the total number of possible nucleotide base or amino-acid sequences corresponding to a single functional gene or protein fold. The number of trials available to the evolutionary process (corresponding to the total number of organisms -- 10^40 -- that have ever existed on earth), thus, turns out to be incredibly small in relation to the number of possible sequences that need to be searched. The threshold of selectable function exceeds what is reasonable to expect a random search to be able to accomplish given the number of trials available to the search even assuming evolutionary deep time.

Consult the original for relevant endnotes. Also, I have not preserved Meyer's rather extensive use of italicization here, so if you care about that follow the link to the original.

Now, our first, knee-jerk reaction to this should be skepticism about those numbers Meyer is throwing around. I do not know the details, but I can promise you that some mighty big assumptions went into the model underlying that 10^77 number. I suspect an expert in molecular evolution would have some choice words for those assumptions.

But that is beside the point, since Meyer's argument has two crass errors. For the sake of argument I am happy to accept his 10^77 number. In fact, you could double the exponent and I wouldn't care, since the specific number, contrary to what Meyer says, is irrelevant.

As it happens, Meyer's argument is essentially the same one presented by Murray Eden at the famous Wistar conference in 1966. I address this argument at some length in my recent paper on mathematical anti-evolutionism.

The first problem comes when Meyer writes this:

Why a formidable challenge? Because random mutations alone must produce (or “search for”) exceedingly rare functional sequences among a vast combinatorial sea of possible sequences before natural selection can play any significant role.

This is not correct. Random mutations do not have to search a “vast combinatorial sea.” In reality they only have to carry out a large number of highly localized searches. They are only searching the tiny portion of the sea in the neighborhood of their current location.

For this reason, what matters is not the relative rarity of functional gene sequences or proteins within the space of abstractly possible genes or proteins. Instead we need to investigate the topology of the space. Stepping stones in a large lake might be rare, but if they line up properly we can use them to get across. And so it is with evolution. If the functional sequences are near each other in the space, then evolution can move among them rather easily. That there might be vast swaths of unusable junk elsewhere in the space, very far from my current location, is neither here nor there.

We could imagine, for example, that the relative rarity of functional sequences in the space means that from any given functional starting point, there is only a small, but non-zero, number of mutational directions that preserve or improve functionality. If this is the case, then the selection pressure to stay on the few paths of functionality will be rather high. Meyer's argument would then backfire. The relative rarity of functional proteins in the space would actually make evolution simpler.

You might object that I am assuming a functional starting point. Evolution cannot begin those local searches until it has found something functional to begin with. And if that starting point has to be found by choosing at random from Meyer's vast combinatorial sea, then we face a serious problem after all.

This leads us to the second problem with Meyer's argument. If we are looking for the probability that evolution can find functional sequences, the ratio of functional to abstractly possible sequences is not the only issue. We must also consider the probability distribution. The ratio by itself would be relevant only if we assumed a uniform distribution, in which every sequence has the same probability. The reality, of course, is that the distribution is highly non-uniform. The space might be vast, but most of it comes with a probability so close to zero that it may as well not exist.

Presumably life originated from basic principles of physics and chemistry operating under the very unusual conditions of the early Earth. One particular starting point in the space had a very large probability of being found, since the physics of the early Earth basically guaranteed it. From there, the sequences near that starting point would suddenly have a very high probability of being found, allowing the process to get going.

This, then, is why Meyer's argument fails. The way he presents things, evolution is implausible because the ratio of functional gene sequences or protein sequences to abstractly possible sequences is very small. It is the smallness of the ratio that is doing all the work in his argument. In reality, though, you must also consider the topology of the space (are the functional sequences clustered together and joined by mutationally feasible paths) as well as the probability distribution (are certain sequences far more likely than others to arise in the course of evolution).

This is a further instance of what I mentioned at the end of my previous post. You cannot argue against evolution on the cheap. Asinine, back-of-the-envelope, combinatorial calculations will never get you anywhere. Instead you have to get your hands dirty doing the difficult research that is necessary to think clearly about these questions. Is protein space more like the way I describe it, with the rare, functional stepping stones conveniently lined up? Or is it more the way Meyer needs it to be, with tiny islands of functionality separated by uncrossable seas of non-functional junk?

I am not an expert in molecular evolution and neither is Meyer. However, the people who are experts routinely report back that things are not the way Meyer would like them to be. I trust their opinion more than Meyer's.