## How Many Ways Are There to Win at *Sandwalk*?

At University of Toronto professor Laurence Moran's blog *Sandwalk*, named for Darwin's famous "thinking path," I've followed a discussion of the evolution of de novo chloroquine resistance by malaria (which I wrote about here). The exchange has touched on a few issues that seem to confuse people easily.

One is how we should view the probability of winning something. In questioning my malaria numbers, a commenter remarked that it's misleading to focus retrospectively on a single event, such as winning a familiar game of cards, to calculate the odds of that exact arrangement of cards and declare it to be the likelihood of winning at the game. After all, there may be very many other ways to win, too. In order to correctly calculate the odds, he explained, one would have to take into account all of the ways to win, not just a single hand.

I agree completely. Fortunately, in the huge number of malaria cells exposed to chloroquine, all the proverbial hands have already been dealt many times over, so we can confidently calculate the odds from the statistics.

Here's an analogy. Suppose we observe a hall where around a thousand people are each dealt ten cards -- but not our normal playing cards. Instead there's a variety of strange symbols on the cards, in different colors and sizes, which we assume are distributed randomly to the players. We don't know the game they are playing or any of the rules, but we see that nobody in the group wins. That group shuffles out of the hall and a fresh group of a thousand people takes its place, is dealt ten cards, and again no one wins. This goes on until the 43rd group, where one person jumps up smiling and is declared to be a winner. Another 61 groups follow before there is another winner. After watching for a long time we record that on average the size of each crowd is a thousand people, and somebody wins once every 50 crowds.

So what are the odds of winning that game? Of course it's 1 in 50,000 -- the statistical average number of people it takes to get a winner. Since we don't know the rules, there may be just one way to win the game, or many different ways. There may be one rare card that is needed, or multiple different specific combinations of cards. When we eventually learn more about the game we might be able to figure out the rules and understand why the odds are what they are. But that doesn't matter for this. The odds of winning themselves won't change outside of our statistical uncertainty. They'll remain approximately 1 in 50,000.

We can deduce another pertinent lesson. There may be card combinations other than what have so far been dealt that win the game. But if there are, the probability of their occurrence is *less than or equal to *that of other ways to win that have already happened. The reason of course is that card combinations with significantly higher probabilities would already have been dealt in the large number of hands. The lesson, then, is that once we have good statistics, the probability of winning is fixed. It already implicitly includes any and all of the ways there are to win.

So, too, with chloroquine resistance in *Plasmodium falciparum*. The best current statistical estimate of the frequency of de novo resistance is Nicholas White's value of 1 in 10^{20} parasites. That number is now essentially fixed -- *no pathway to resistance will be found that is substantially more probable *than that. Although with more data the value may be refined up or down by even as much as one or two orders of magnitude (to between 1 in 10^{18}-10^{22}), it's not going very far on a log scale. Not nearly far enough to lift the shadow from Darwinism.

What's more, we can also conclude that the mutations that have already been found are the most effective available of any combination of mutations whose joint probability is greater than 1 in 10^{20}, since more effective alternatives would already have occurred and been selected if they were available. That's a point of great public health consequence.

Before investigating what it takes at the molecular level to confer chloroquine resistance, we might have conjectured that there was one exceedingly rare, necessary mutation, or a combination of several mutations, or a dozen different paths each with several required mutations. We would nonetheless expect that when we did uncover the pathway, we would be able to reconcile the likelihood of each of its steps with the statistical evidence. Although it was pretty easy to predict from the sequence evidence even as early as ten years ago, that is what Summers *et al.*'s recent work allows us to do now with great confidence. The fact that several point mutations are required before low chloroquine-pumping activity is observed for PfCRT, coupled with the known mutation rate, easily gets us very close on a log scale to Nicholas White's statistic, 1 in 10^{20}. There is no particular reason to grasp for other explanations.

Nor would it do any good. There is a lot of chatter at *Sandwalk *deriding the idea of "simultaneous" mutations (which was not intended in my book *The Edge of Evolution*in the sense it is being taken there, and which at this point I would gladly replace with other words simply to avoid the distraction). Yet it matters not a whit for the prospects of Darwinian theory whether the pathway consists of two required mutations that are individually lethal to a cell and must occur strictly simultaneously (that is, in the exact same replication cycle), or whether it consists of several mutations each with moderately negative selection coefficients, or consists of, say, five required mutations that are individually neutral and segregating at some appreciable frequency in the population, or some other scenario or combination thereof. The bottom line for all of them is that the acquisition of chloroquine resistance is an event of statistical probability 1 in 10^{20}.

It is the outlandish improbability of the pathway -- not its particular features -- that is the crux. It puts strong limits on what we can expect from Darwinian processes. And that is an important point for any biologist -- whether in a medical field or not -- to appreciate.

One other interesting point was raised in the comments at *Sandwalk*, a point that sounds in both science and philosophy of science. It is similar to, yet much broader than, the one dealt with above. Instead of asking merely whether we have counted all the ways to win a particular game, it essentially asks whether we have considered all the games that could have been played. The commenter writes:

[I]t is one thing to calculate the probability of a specific change ... from a specific, randomly chosen starting point ..., and it is a TOTALLY DIFFERENT THING to calculate the probability of SOMETHING interesting happening anywhere amongst thousands of genes and thousands of species over millions of years. When the modern scientist discovers that interesting evolutionary change, it is totally illegitimate to forget about all of the things that didn't happen.

I agree with this, too. Happily, the tacit hypothesis -- that very many possible-but-unrealized complex biochemical systems could have been made by random mutation/selection -- can actually be tested, but only to a degree. To the extent it can't be tested, it is unfalsifiable. To the extent that it can be tested, in my view, it has already been falsified.

Let's start with the untestable part. Could a plethora of very complex biological systems, other than the ones that in fact exist, have arisen by Darwinian processes over the course of life on Earth? That question strikes me as reminiscent of the multiverse hypothesis in physics -- the postulation of copious unseen and probably unknowable systems to account for the existence of apparently very improbable known ones. So, like the multiverse, to the extent that this proposal is untestable I regard it as not scientific.

How can the claim be at least partially tested? One way is to examine huge numbers of organisms under great selective pressure and see whether they do in fact evolve anything that looks like it might at least be on the way to becoming one of those postulated, frequent, hidden, new complex systems. Now, what data do we have that might be relevant?

Data on malaria, of course. And what we see there is that in a gargantuan number of organisms under relentless selective pressure from chloroquine, no new complex system evolved, only a few crummy point mutations in a pre-existing protein.

Let's consider the flip side of the malaria question. What mutations in more than ten thousand available genes have been selected over the past ten thousand years in billions upon billions of humans as a result of malaria exposure? A handful of point mutations and broken genes, none of which appears to be leading to anything like a new complex system. Other examples of Darwinian futility can be found in *The Edge of Evolution*. For the similarly very modest results of many laboratory evolution experiments, see my 2010 paper in *The Quarterly Review of Biology*.

If nature were thick with possible complex biochemical systems that could be found by Darwinian processes, we should expect to in fact find some when we go looking. We don't.

*Image: Darwin's "thinking path," Sandwalk/Wikipedia.*