Brown University biologist Kenneth R. Miller has posted a reply to my challenge to him to give a quantitative account for the extreme rarity of the origin of chloroquine resistance in malaria. I’m grateful to him for doing so. Although I strongly disagree with nearly everything he wrote, his essay gives the public a chance to see directly how one informed Darwinist reacts to a basic empirical challenge to the theory. This is the third in a series of four posts responding to it.

In my last two posts (here and here) I showed Miller’s claim that the K76T mutation in the chloroquine-resistance protein factor PfCRT had "no effect on transport activity" was simply incorrect, and that his argument that the mutation is selectively neutral strongly conflicts with the best relevant experimental evidence. Here I deal with his discussion that the existence of several pathways leading from partial to full chloroquine resistance somehow mitigates the improbability of its origin from zero resistance, and the baleful implications for Darwinism.

Miller writes:

Directly contradicting Behe’s central thesis, the PNAS study also showed that once the K76T mutation appears, there are multiple mutational pathways to drug resistance.

And once you have jumped over the Grand Canyon, there are multiple pretty trails you can explore. 

Here Miller’s mistake helps us to see the bad effects of the lack of quantitative rigor. He exclaims that there is not just one pathway from partial to full chloroquine resistance, there are "several mutational routes." His italics indicate that he thinks this is very important. But a moment’s quantitative thought shows that the number of pathways makes precious little practical difference. Suppose you were given a choice of a billion trillion roads to travel, but were told that only one of them led to safety; the others all led to certain death. You would likely feel pretty pessimistic about your chances. But suppose someone came along to tell you that there are actually several paths — in fact, five of them! So your odds of finding a safe path home have jumped from one in a billion trillion to five in a billion trillion. Feeling better? I didn’t think so.

If the odds of finding something by one path are an astronomically unlikely 1 in 10²⁰, then the odds of finding it by either of two equally probable ones are 2 in 10²⁰ — still astronomically unlikely. Even with a hundred paths the odds would be a profoundly prohibitive 1 in 10¹⁸. So it turns out that Miller’s strongly emphasized point has little practical importance. To avoid being misled by our imprecise intuitions, it is necessary to be as quantitative as the data allow.

The problem is actually somewhat worse than the above discussion indicates. Here’s how. Suppose there were an enormous number of routes a traveler could take. Almost all lead to oblivion, but one or more (it’s unknown how many) lead to a particular safe destination. After counting many, many travelers embarking and arriving by whatever route they happened upon, we reliably determined that approximately one in a billion trillion arrived at the safe port. That means the odds of finding any safe route to the destination is one in a billion trillion. It does not matter if in reality there are a thousand routes or just one, the odds of finding one of them remain one in a billion trillion. That’s because our numbers are derived from statistics, not from some pre-conceived, theoretical way of arriving at the destination.

The same goes for chloroquine resistance. The number of 1 in 10²⁰ against developing chloroquine resistance comes from estimating the number of malaria cells without resistance that it takes to produce and select one with resistance, no matter what genetic route is taken. So the number of routes that Miller emphasizes turns out to have no effect at all on the statistical likelihood of developing chloroquine resistance. Each route itself is actually less likely than the cumulative probability. All of the routes together add up to only 1 in 10²⁰.

Miller writes:

In most of these [pathways], each additional mutation is either neutral or beneficial to the parasite, allowing cumulative natural selection to gradually refine and improve the parasite’s ability to tolerate chloroquine. One of those routes involves a total of seven mutations, three neutral and four beneficial, to produce a high level of resistance to the drug. Figure 4, taken from the Summers et al. paper, makes this point in graphic fashion, showing the multiple mutational routes to high levels of transport, which confer resistance to chloroquine.

A chain is only as strong as its weakest link. And a Darwinian pathway is only as likely as its most improbable step. It matters not a whit whether later helpful mutations are easily acquired. It matters only that some steps are exceedingly unlikely. All of the pathways in Miller’s Figure 4 (which is Figure 3 from Summers et al.) require K76T — the most difficult, daunting change — as the first or second step. The pleasantly colored crisscrossing arrows of the figure might distract a person’s gaze, but they are not intended to quantitatively represent the improbabilities of the transitions.

Here’s an analogy. Suppose to win a prize you had to match seven numbers. The last five can be any number between one and three. The first two numbers, however, might be anything between one and a billion. Of course it doesn’t matter that the last five are pretty easy to guess, or that you might be permitted to guess them in any order. The steps that overwhelmingly control your odds of winning are the first two, the most improbable ones.

Here’s another one. Suppose there were a nice, pretty, level meadow where a person could easily walk around, smelling the flowers — but the meadow was situated on the top of a sheer-cliffed butte. If a travel agent told you how easy it was to walk around the pretty meadow without mentioning the brutal climb it would take to get there you would rightly conclude that, whatever other admirable qualities he may have, he was an unreliable guide.

Let me also emphasize, if any of the pathways or other factors Miller discusses made much difference, then the odds of malaria developing chloroquine resistance would be better than they are known to be. Miller’s argument has both a quantitative and a conceptual problem. He agrees that the development of chloroquine resistance is an extremely rare 1 in 10²⁰, but he doesn’t know why. He seems to really want one beneficial mutation to be available at a time, but the mutation rate in malaria is about a trillion times greater than the origin of chloroquine resistance. So why is the origin of resistance so rare? Resistance to another anti-malarial drug (atovaquone) arises de novo in nearly every infected person it’s given to. So why is de novo chloroquine resistance much, much, much less frequent?

That question is the bane of Miller’s perspective. Figure 3 of Summers et al. (Miller’s "Figure 4") shows that it takes a minimum of two mutations for chloroquine transport function to appear, that before both of them appear there is zero activity. That is the big problem for the evolution of resistance. That is the reason why de novo chloroquine resistance appears so much less frequently than resistance to other anti-malarial drugs that require only one mutation.

Miller:

There are indeed several mutational routes to drug resistance, and they are indeed the result of sequential, not simultaneous mutations.

"Sequential or simultaneous" is the wrong distinction. The only question relevant to Darwinian evolution is whether the helpful, selectable activity appears incrementally, with each additional mutation. Summers et al. shows that it doesn’t. There is zero chloroquine-transport activity until two mutations have occurred to the wild-type sequence. The relevant activity appears discontinuously, not incrementally.

Image credit: Alan Eng/Flickr.