Kondrashov's Paradox: Why We Haven't Died 100 Times Over

[Nesslig20]

@talkpopgen

@UncensoredPilgrims

Saying “unselectable” is entirely accurate in the sense that drift overwhelms selection for effectively neutral mutations. It does not imply that there is a total lack of selection, or a selection coefficient of 0 (which would be strict neutrality, not near neutrality). All throughout his book, Sanford refers to these as near neutrals, not strict neutrals.

The prefix un- means “not” or “the opposite of.” Hence, unselectable literally means “not selectable,” which implies a total lack of selection. Again, Sanford’s own words were “…all such mutations can never be selected for.”

If we’re more generous, then “unselectable” is at best misleading. Consider the case in which Ns = 0.5 (beneficial, near neutral) and Ns = -0.5 (deleterious, near neutral). The former is 7.38 times more likely to fix than the latter, and 2.31 times more likely to fix than a strictly neutral mutation. This seems nothing like “unselectable”, in any sense of the word.

To bring up an analogy in physics.

Let’s imagine a small nano-scale particle suspended in an ideal fluid under a condition where no forces are subjected to the particle. The temperature is absolute zero. There is no motion whatsoever, even if the fluid does not become a solid.

Now let’s bring up the liquid to room temperature, then the particle starts to move in accordance with Brownian motion.

If you were to average out all the vectors of movements within all time intervals, it would equal to zero, but of course the particle does not sit still. The position it ends up in is entirely stochastic. (this is akin to evolutionary drift).

What happens if we add an additional force? A very weak force. Gravity for example. If gravity was the only factor, the particle would have a very simple, predictable, unidirectional movement. (This is akin to evolutionary selection). But in this situation, the gravitational force that is applied to the particle is very minor, in both absolute and relative terms. The forces that drive Brownian motion still dominates, such that the vast majority of the particle’s motion across time is dictated by Brownian motion (nearly neutral evolution). However, recall that the directions of all the major Brownian motions has a statistical average of zero, but the minor motions caused by gravity all have the same direction. This means that [at large time frames] there is a clear directional bias, in spite of the fact that Brownian motion dominates within every incremental time interval. This means that gravity still have an relevant effect on the average movements of small particles (They are not “un-selectable”)

Also, while we are on this subject, the physics that I just described actually applies to the (macro-)molecular processes that happens within cells. The vast majority of the motions of molecules, and even large protein-complexes, is also Brownian. However, this Brownian motion is made ever so slightly biased (average made non zero) via the conversion of energy. The last image above is from “On being the right size, revisited. The problem with engineering metaphors in molecular biology” which is a good read, and also discusses the implications of Brownian motion in biology.

[UncensoredPilgrims (Paul P)]

My debate opponent Dr. Hancock has done me the honor of giving a very comprehensive response, and so I believe I owe him the same respect. Out of respect to those who don’t want to delve into this quite so deeply, however, I will start with the most important points first in this post, and then from there I will proceed to do what I can to address his many other statements.

It would seem that for me to continue on this thread after this response would be to beat a dead horse, because Dr. Hancock has now made public statements that amount to concessions on every single point that was under debate. I will demonstrate each of these now.

In preparation for the debate, I took the time to catalog every statement I could find that Dr. Hancock had made re: Genetic Entropy over the several years he has been publicly commenting on it. I then boiled those down to what I considered the top three most serious attacks he had made. Here are his original claims.

1) Human effective population size is around 7 billion.

Hancock has now conceded that point:

I’m very happy to update to an estimate nearer Felsenstein’s, though to be precise we’d need to consult global life-tables.

For context, Felsenstein’s number is nowhere near 7 billion - it’s 2.7 billion. He referred to his previous statement as a “spitball”, which I do believe it was.

Probably more important than this, however, was my rebuttal to his use of recent Ne, rather than long-term Ne (as Kondrashov used) in the first place. His only response to this was to retort that I didn’t believe in equilibrium population size, which was a non sequitur since long-term Ne is based on many factors, none of which include any “equilibrium”. The population size component of long-term Ne is derived from the harmonic mean of the census size, which does not depend on there being an equilibrium at any point. Since the long-term plausibility of evolution is what is under debate, it is very clearly the long-term Ne that is relevant to that question.

2) Hancock claimed his simulation represented a defeater of Genetic Entropy.

Directly quoted from Hancock & Stern Cardinale’s Paper:

Our results act only to demonstrate that, in a stochastic
demographic model with a DFE inspired by empirical studies, populations will not be
driven to extinction due to the pressure from deleterious mutations, contrary to B&S

Not only does this represent a claim to refute Sanford, it also represents a claim to solve Kondrashov’s paradox, since this exact thing is the definition of the paradox. Kondrashov showed that realistic parameters for LMEs when applied to population genetics theory consistently demonstrate fitness decline (which would ultimately result in extinction). This is why Kondrashov considered this a paradox that “needs a resolution”.

Retroactively, Hancock is now attempting to create a false distinction between Sanford and Kondrashov that he should have known all along never existed. Sanford quoted liberally from Kondrashov in his book, and made it clear that Kondrashov’s Paradox was a big part of what he was calling “genetic entropy”.

Now, Hancock has conceded that his simulation did not solve the paradox (and that means it also didn’t refute Sanford, either).

If GE = Kondrashov’s paradox, as Paul plainly states, then these simulations are irrelevant.

To this, Hancock states that his simulation was only attempting to mimick the parameters Basener and Sanford used, but as I showed in the livestreamed debate, they bore little to no resemblance to one another.

3) Hancock stated that population geneticists don’t take their own models as gospel.

During our livestreamed debate, I quoted from Dr. Lynch who made it clear that not only does he take population genetics theory as gospel, he insists that if any claim about evolution cannot be shown to be feasable according to the established population genetics models, it should be held in doubt!

During the crossexam, at around timestamp 53:18, I asked Dr. Hancock if he agreed with Lynch’s statement. His response:

“Yes, of course.”

I’m unsure if he realized this contradicted his earlier statements, but in any case this was a concession on point number 3.

So that concludes all three of the points I brought up in the debate. But what about the topic of the debate as a whole? "Are mutational effects a problem for evolution?" Well it turns out that Dr. Hancock has conceded on that now as well! In the debate, he made the claim (again, during crossexam) that Kondrashov’s paradox had been solved. But now he has changed his mind on that:

Paul is correct that I said “we have resolved” in the debate – this is a incorrect and I appreciate Paul pointing it out. What I should have said is that we have resolutions to the paradox.

So, let’s try to make some sense of this doublespeak. In the debate, he gave a clear answer, yes, the paradox is resolved. Now he says that was a mistake. Apparently, there are “resolutions”, but the paradox is not actually resolved. I suppose what he means is that people have attempted to resolve the paradox, but there is no conclusive answer. To which I would not offer any disagreement. Certainly, there are attempts to resolve the paradox. Kondrashov offered several in his own paper as well.

Since both parties now agree that Kondrashov’s paradox is not solved, we can also readily agree that mutational effects are indeed a problem for evolution. With that, I will end this initial response (which should be the final chapter of this Price - Hancock debate of 2026).

[Rumraket (Mikkel R.)]

@UncensoredPilgrims

Your claim that rare mega-beneficial mutations can come in and compensate for the load is simply not supported by the evidence

It is in fact supported by the evidence, in exactly those experiments where Sanford and Rupe wrote GE must be happening anyway. It’s this inconvenient fact that has caused creationists such as yourself to subsequently change the idea of GE to suggest perhaps bacteria are immune to GE.

I should also note here with regards to your Sanford quote from his book:

@UncensoredPilgrims

On pg. 74 (3rd Ed), Sanford writes,

(…)This means that in bacteria, a much smaller proportion of the genome is near neutral and unselectable. This is why theorists [like Hancock!] typically prefer to use microbial samples.

That statement there doesn’t make logical sense.

First of all “theorists” like Hancock usually work on computers, doing modeling (not “microbial samples”). To be sure, they they do get data from experimentalists, and some times from doing their own field work.

But they don’t “prefer to use microbial samples” out of some nefarious plot to ignore populations with less effective population sizes (as Sanford suggests here), but because growing a billion bacteria takes a day, and you can measure their relative fitness over the course of a few hours.
Though the genetic manipulations required to engineer specific mutations so you can compare their relative effects across different environments and genetic contexts is definitely more complicated, and takes weeks if not months of work.

But growing a billion cows/sheep/mice/fruitflies, engineering their mutations and ensuring they’re being tested in identical genetic contexts, and measuring their relative fitness is… a bit of a challenge.

You understand the massive increase in difficulty is why biologists do most of their work on smaller organisms with much shorter generation times right? It’s not what Sanford suggests here. What he is insinuation with that line seems rather deceptive to me.

[Rumraket (Mikkel R.)]

@UncensoredPilgrims

You are also mistaken when you think this is a novel suggestion you’re making. It boils down to Kimura’s original proposed solution: mega-beneficial mutations. It has been addressed in Sanford’s book.

You misunderstand me here. I am not claiming that the idea that single large-effect beneficial mutations compensating for numerous small-effect deleterious ones is a novel idea at all.

I am talking about the idea of a DFE changing with fitness (the phenomenon called diminishing-returns epistasis) as a solution to Kondrashov’s paradox, being a novel idea.

And just to stave off any possible confusion about whether I think I have some unique insights people in the field should listen to, the only reason I suggest it is because I did some google scholar searches to see if I could find anyone suggesting such a thing, but didn’t find any.

Considering how even Fisher’s geometric model (and fitness landscape theory), which implies a DFE changing with fitness, to my mind suggests an obvious solution to the problem, I was all the more surprised I couldn’t find any such suggestions in the literature and was speculating on why that could be.
To be sure, my searches could just be incomplete. While the search terms yielded thousands of papers I could not find any that obviously related to the idea by quickly scanning a few dozen results.

And while on that topic, I am much less concerned about your replies (no hate) Paul, than I am about those of @talkpopgen here. He is, after all, quite obviously the one actual specialist in the field participating in this thread.

[Rumraket (Mikkel R.)]

@talkpopgen

@Rumraket

I can’t help wondering if some of the people working in the field don’t interact enough with fields like microbiology and molecular biology?

This leads me to this question. I would argue (to reveal my own bias) that it’s the reverse. These are theoretical questions that can be resolved with molecular biology, but the questions came first and as the data rolls in, we try to incorporate them into our models. Too often it seems like molecular biologists (e.g., the ENCODE consortium) make sweeping claims about evolution without reference to theory. Undoubtedly, we should all interact more often. I think a great example of this is Palazzo & Keijou (2022).

I take your point about ENCODE, and it’s definitely true that the world is full of self-appointed experts, with tangential credentials at best, opining on their latest revolutions of evolutionary biology.

The main reason for my suggestion, as I explained to Paul in another reply, was really that I couldn’t find any articles obviously discussing the phenomenon of diminishing-returns epistasis as a potential solution to Kondrashov’s paradox (or mutational load).

And yet there is good biological data coming from evolution experiments (though pretty much all of these are microbiology for reasons we shouldn’t have to explain, but creationists misrepresent it when we don’t so here we are) that shows how populations that climb novel fitness peaks have numerous large-effect mutations available to them.

[Dan_Eastwood]

@talkpopgen

Paul’s Behavior

I want to conclude by commenting on Paul’s behavior here.

This is in-part a moderation error. One of the ground rules here is we should not tell others what their faith is. I should not have accepted that portion of Paul’s comment. I can’t fix it now, but the mods will be more careful going forward, and we will cut off that line of discussion.

[Rumraket (Mikkel R.)]

@UncensoredPilgrims

I suppose what he means is that people have attempted to resolve the paradox, but there is no conclusive answer.

Taking a wild stab in the dark, I suspect instead he means that a consensus on which one (if any) of the many proposed solutions, or perhaps a combination, will be the one the population genetics community coalesces around.

Any one or even a combination of them might be entirely conclusive.