Waiting Time Problem Redux

It appears the Discovery Institute is dipping their toes into the Waiting Time Problem (WTP) once again.

The gist of the argument is that if a beneficial adaptation requires two neutral mutations that are not beneficial by themselves then the amount of time to wait for those mutations is prohibitive.

It also appears that they are going to be publishing something in the near future on this subject, so I thought it was worth bringing to light.

There’s a LOT of material in that article, including responses to recent criticisms. With that said, here are a few of my initial reactions as a biologist non-expert in population genetics:

  1. They seem to waffle on the idea that 5-6 million years is enough time to account for the divergence seen between the human and chimp genomes. From my limited pop gen knowledge, the fixation rate of neutral mutations is equivalent to the mutation rate. One of the current estimates I have seen has a mutation rate of ~75 mutations per person per generation (here), so about 75 neutral mutations are fixed per generation across the human population. With a generation time of 25 years, that’s 200,000 generations. 75 mutations in 200,000 generations is 15 million fixed mutations. Do the same for the chimp lineage and that is 30 million fixed mutations in total. That’s pretty close to what is observed. Not sure what they are going on about with this one.

  2. I could be wrong, but they model each of the “coordinated mutations” as if they will both behave like neutral mutations. However, it would seem to me that the second mutation that appears would be treated as a beneficial mutation because of the interaction with the other coordinated mutation. Not sure if this is covered in their model, but it is something that sprang to mind.

  3. They assume the number of possible coordinated mutations are rare in any given genome. I see no reason why this would be so. They try to get a lot of mileage out of Behe’s example of chloroquine resistance in malarial parasites, but I see absolutely no reason why this one example can be generalized to all of genetics. If they can’t demonstrate the rarity of coordinated mutations then their argument seems to fall apart.

  4. They also can’t show us a single example of coordinated mutations in the species they want to talk about (e.g. cetaceans, humans).

  5. They ignore the massive number of neutral mutations already fixed in the human genome, some of which can be traced to the beginning of vertebrate evolution.

Those are my initial thoughts. I am wondering if others with actual expertise in population genetics find this article worth spending time on and responding to.


Thinking out loud . . .

I am also wondering if lactase persistence in humans could be a potential example to look at. There are several known mutations that confer this phenotype, and it is thought that these mutations supply a binding site for a transcription factor that drives lactase expression in adulthood. Could it be that these new transcription factor binding sites also include previously neutral mutations? Since the sequence motifs are known for these transcription factors, as are the sequences in other apes/primates, this seems to be a possible place to look.

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I’m sure there’ll be a Texan sharpshooter involved somewhere.

There is. I give them credit for at least acknowledging the problem, but their response is lacking.

They just proclaim that changes in function are rare. Period.

They go on to make even more egregious errors, but that first one is enough. In fact, they make this rather funny claim:

How is it any more unscientific to say that changes in function may be easy to find as it is to say that mutations causing changes in function are rare?

As others have noted, there are many examples of many different mutations resulting in the same human phenotype. The multiple (and recent) mutations conferring lactase persistence is a perfect example.

10.4: Lactase Persistence - Biology LibreTexts.


Interesting paper . . .

If I am reading it correctly, they are arguing that “coordinating mutations” (i.e. epistasis) actually speed up the evolution of new function. Instead of restricting the evolvability of a new function, neutral mutations actually open up a whole host of new mutations that can produce a new function.
The paper is pretty dense, so I think I will need some additional time to be confident that I am understanding it correctly, but at first glance it seems to directly argue against what the Discovery Institute is arguing for.

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Isn’t it more like they’re trying to claim that there is no ‘broad target wall’ for the bullets to hit just anywhere … but instead only tiny islands of beneficial mutation exist for any bullets to hit … so therefore the fact that a bullet hit one of them can therefore be considered significant? That’s how I’m interpreting the quote you included anyway. But I’m way out of my depth here - much farther out than you are.

And even if I’m understanding correctly - It seems to me that the sharpshooter fallacy would still apply; given that even with severely limited potential target surface - there is still a virtual machine-gun spray of mutations to work with.

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Why wouldn’t it be? Because it doesn’t support the views you bring with you? It certainly doesn’t look like low-level creationist gibberish. Some of that link seems peer reviewed and is based on mani stream ideas. I personally have no problem with accepting a God-guided evolution if the evidence rules out purely naturalistic views. Im certainly not going to rule this out going in.

Last but not least, some critics were puzzled by the fact that research papers on the waiting time problem authored by ID proponents could somehow even “sneak into” peer-reviewed journals like the prestigious Journal of Theoretical Biology . The reason is as simple as it should be obvious: because it is good peer-reviewed science and the common censorship of anti-ID activists sometimes fails to sabotage the publication of inconvenient research. It is the height of hypocrisy when the very same people, who pressure editors to reject manuscripts or issue disclaimers, then turn around and claim that ID proponents don’t publish their stuff in the peer-reviewed literature.



Makes sense. Kind of like playing poker: if I draw an eight, that’s a neutral sort of draw, but the moment I draw a second eight the combination is beneficial.

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how could this apply if the machine gun spray of bullets largely are not successful in that they do not result in mutually beneficial gains (in either direction) and that such gains would automatically limit the number to just one or two at a time? Wasnt that one of the earliest points made in the original article?

I’m not sure it does - and to be clear, unlike @T_aquaticus, I haven’t even read the article at all. So this is just my attempt to understand or seek clarification on what he’s been writing.

But as far as the analogy itself goes - even if a wall is patchy to the point where the targets on it were limited from the outset (only a small percentage of random mutations being beneficial), the shear volume of mutations (machine gun spray of bullets) may still ensure that even all the limited parts get hit, and one could still go in later and “draw in their target around” some of the successful bulletholes, thus committing the sharpshooter fallacy. That’s all I was trying to say.


This is the full text of the articles response to that. T has offered some pushback above.

2.) Most critics considered the most powerful objection to be the Texas sharpshooter fallacy (e.g., Moran 2016). They claimed that nature does not go for specific mutations as a target but is totally random and could have pursued many different ways to success. In short: this objection claims that you cannot assume a pre-specified target. This argument fails because it dubiously presupposes the existence of many targets, which is contradicted by the rarity of function in the search space for proteins and by the common phenomenon of convergence. The argument also fails to recognize that life cannot allow for periods of maladaptation only to descend a local peak of the rugged fitness landscape to explore other ones. Instead, life has to further adapt to its local fitness peak, which requires specific solutions for specific problems. It’s not like any beneficial mutation could do, or as if the fitness landscape would be flat and homogenous. A stem whale would have no use for a mutation that would be beneficial for a stem bird, such as improving skeletal pneumaticity. The targets were not arbitrarily imposed but are provided and constrained by nature. In the computer models applied in our publications on the waiting time problem we also allowed for alternative targets and fuzzy targets, so not just one pre-specified binding site, which prevents another possible critique. Generally, this objection seems to boil down to the unscientific claim “there could be x so that the problem disappears”, which is a non-sequitur that proves nothing and fails to be testable, because it does not make any specific empirical predictions.

By the way: In the context of this objection, Stern Cardinale (2022a, 2022b) also alluded to a study by Yona et al (2018) which showed that “random sequences rapidly evolve into de novo promoters”. This is interesting, but just refers to a very simple function, which was addressed by Miller (2022). But even more importantly this study is totally irrelevant for the problem of coordinated mutations and therefore is just a red herring. It does nothing to make the waiting time problem go away.

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First, let’s not forget how many bullets are being shot out.

Above, I cited a mutation rate of 75 substitutions per person per generation. That would be 7.5 million mutations per generation with a steady population of just 100,000. With a generation time of 25 years and 5 million years since splitting off from the chimp lineage, that’s 200,000 generations. 7.5 million mutations per generation for 200,000 generations is 1.5 trillion mutations.

The diploid human genome is 6 billion bases, so that gives us a total of 3x6 billion possible substitution mutations, or 18 billion in total. This means that during the proposed time that humans would have evolved there was enough time for every possible mutation to happen 83 times, assuming even distributions of mutations. Please note that this is with a rather small population of just 100,000. If there is a steady population of 1 million then each mutation happens 830 times.

Another way to put this is that it takes 240 million births to get all mutations (again, assuming even distribution).

I suspect that this is why the Discovery Institute is going in on coordinated mutations because if all it takes is a single mutation then evolution can easily find it.


I agree that there is a lot more depth than the usual creationist stuff, which is why I started a thread on the topic. There’s a lot of material in that article, so I can understand why someone with the expertise in population genetics may not have the time to get through all of it.

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The Birthday Problem is something I like to reference in threads like these.

How many people do you need to have a 50% chance of two people sharing a birthday (same month and day)?

Intuitively, you would probably think you need hundreds. You don’t. It only takes 23 people to have a 50% chance of two of them sharing a birthday. You only need 60 people to have over a 99% chance.

I strongly suspect that coordinating mutations can be modeled in exactly the same way.


A university friend made a bet based on this at a party; there were about seventy people there. Interestingly there were two pairs of people with matching birthdays!

I’d say that would match the problem where people are coming into a room and the question is how many people have to come into the room for one to have the same birthday as the first person to arrive – though the answer to that is large enough that there should be something like eight pairs of people with matching birthdays before someone has the same as the first person, which is interesting because if you’re looking at a single mutation and waiting for a useful mutation to “match” it you may actually be ignoring the real issue of whether any two people will have “matching” mutations.

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Quite true. It looks like high-level creationist gibberish.

Immediate problems in addition to those mentioned include

  • it spends a lot of time talking about the waiting time problem without ever showing how the waiting time is calculated;
  • it is indeed a giant Texas sharpshooter problem, because it talks about the probability of what has already happened;
  • the assumption that non-specialists can’t tell the difference between fir trees and cedar trees

and my favorite:

  • Bechly claims there were no responses to his 2nd article about his species pair ‘challenge’ (“crickets”), but AFAIK he has never addressed mine. That’s probably because doing so would require explaining why he misread “sea otters” (Enhydra) as “otters” (Lutra), why he misrepresented his sources, and how he can tell whether a creature has eyes from examining its footprints.
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Here is how I think the Birthday problem relates to coordinated mutations.

We have 70 people in a group, and it turns out that two of them have birthdays on May 15th. The Discovery Institute would look at the probability of 2 people in just 70 having a birthday on May 15th. This probability would be pretty low, far lower than you would expect to find in just 70 people. In fact, this would be the case in group after group of 70 people, where the specific date of the match is highly improbable. This is the Texas Sharpshooter fallacy.

What is happening in actuality is that there are many chances for two people’s birthdays to match. The chances of a specific day being that match is quite low, but the match is much more probable. In the same way, the interaction of two mutations resulting in a beneficial phenotype could be inevitable given the number of mutations in the human lineage, but the chances of a pre-specified set of two mutations occurring is quite low.


Also, they don’t show how the scenarios with very low probabilities apply to the actual species they are talking about. More importantly, the DI may be overselling how specific mutations have to be in order to be beneficial. This is from one of their references that they cite multiple times:

What the authors did was find situations where the probabilities were beyond what evolution could produce as a proof in concept of where the limits lay. However, in the real world the evolutionary pathways are far, far more probable. It is interesting to note that a time of 60,000 years for a new regulatory sequence seems to be reflected in the emergence of multiple beneficial mutations that regulate lactase in humans.


The probability of any two people out of 70 sharing a birthday on any date is ~0.999306058.

The probability of two specific people out of 70 sharing a birthday on a specific date is ~0.000007465. That’s 6 orders of magnitude different.

The DI use the probability of getting two specific mutations in a specific lineage instead of the probability of getting any two complementary mutations in any lineage (or any two lineages that then mate).

Incidentally, if you pick two specific point mutations possible in the human genome, the probability that someone already has them is ~0.00003[1]. That’s nearly as likely as two people sharing the same specific birthday.

  1. Treating all possible point mutations as equally likely to simplify the maths; this doesn’t affect the result as long as the distribution of mutations matches the distribution from which they’re picked. ↩︎


From the ENV article:

How in the world would they be able to model:

a) What would be beneficial for the ancestors of cetaceans.

b) Which mutations would be beneficial in any of the ancestral genomes.

c) The standing variation in those genomes.

There is also the issue of modeling these mutations as if neutral mutations have to reach fixation before epistatic interactions can be beneficial.

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