Well, we could posit that the pair, like inbred mouse strains, was the product of many generations of brotherxsister matings, selecting against the deleterious alleles… 
2 Likes
My sim took about 20 generations to reach carrying capacity. But there is no equilibrium to be found.
The extinction occurs because of mutation load. Rather than speculating about what scenario is under consideration, why not watch the debate?
Priorities.
4 Likes
Well, my priorities don’t include talking about a debate with people who refuse to watch it.
I can think of a number of reasons:
-
Because watching a 138 minute video for this small amount of information would appear be very inefficient.
-
Because many people find it easier to assimilate information that is read, rather than listened to.
-
There is no guarantee that your description of your scenario in the debate contains all the information that people might need to evaluate it.
Addendum:
It seems that Paul has published files to Github here:
And to Google here:
And some graphs here:
2 Likes
7 zebras, 2 hyenas… genetic variability is not going to be the cause of extinction.
5 Likes
@talkpopgen Actually I do have one last question. Could you please clear up for the record where you got those simulation charts you shared during the crossexam? Were those published anywhere, or are they simulations you ran personally? If the latter, could you please share the relevant SLiM code for each, so we can see what exactly you were modeling?
EDIT: Stern Cardinale is now confirming those charts were indeed from original unpublished work by Hancock. Silly me for giving him the benefit of the doubt that those were somehow published somewhere and could be independently checked.
Paul, Zach clearly says he’s modeling effectively and strictly neutral mutations. So there are slightly beneficial mutations above strictly neutral within the drift barrier of 1/(2Ne) (figure A), strictly neutral mutations (figure B), and slightly deleterious mutations with selection coefficients below strictly neutral within the drift barrier (figure C).
Despite this barrier, selection still exhibits some effect on these mutations. I could reproduce this effect easily using PopG (see results at the bottom).
Though to play devil’s advocate here (heh), it’s not clear to me why that would mean you concede the debate. So let me throw that bone to you here at least.
It does matter for the results how close to the barrier the mutations are in terms of their selection coefficients. Clearly those closer to strictly neutral are less affected by selection, and those closer to the drift barrier (1/(2Ne)) are more affected by selection.
But while the fraction of mutations selection manages to push to fixation increases the closer we move from strict neutrality to the drift barrier, the difference in fixation probability within this barrier is still rather small. It appears to be somewhere in the range of 2:1 to 3:1 (used Felsenstein’s popG: PopG Genetic Simulation Program). That is to say, a beneficial mutation with a selection coefficient within the drift barrier is 2 to 3 times more likely to go to fixation than a deleterious mutation with equal but negative magnitude of effect.
But if the ratio of beneficial to deleterious mutations is 1:1000, or even 1:100 within the drift barrier, that still seems to suggest that incorrectly assuming the DFE is fixed we get a fitness decline for effectively neutral mutations considered in isolation, as far as I can see.
Source data (let me know if anyone can’t access this):
2 Likes
These simulations were performed in R using the package learnPopGen, which can be accessed from CRAN. The function is drift.selection, which models stochastic allele frequency change with selection. The specific parameters used were N = 100, fitness for each genotype as 1, 0.99, 0.999 (additive), but it you can also test it in the case of dominance (1, 0.99, 0.99), performed 100 replicates for 500 generations. The code is run like so for the dominant case:
library(learnPopGen)
#beneficial dominant
drift.selection(p0=0.01, Ne=100, w=c(1,0.999, 0.999), ngen=500, nrep=100)
#deleterious dominant
drift.selection(p0=0.01, Ne=100, w=c(0.999,0.999, 1), ngen=500, nrep=100)
#truly neutral
drift.selection(p0=0.01, Ne=100, w=c(1,1, 1), ngen=500, nrep=100)
In the above, w is fitness for each genotype (pp, pq, and qq is the default ordering). In the first two, they are effectively neutral under the definition that Ns\leq 1.
Apologies for not showing the code during the debate, I had a slide that I meant to show during the cross-examination with it but got lost in the moment. I have also been in the field for several days with limited internet, and so only just able to respond. These are also not “original, unpublished work” in any sense of the word, they are merely numerical simulations of the classic population genetic equation of selection with drift on a per-generational basis:
\Delta p = \frac{sp(1-p)}{1+sp}+\frac{p(1-p)}{2N}
The first term is the change in p due to selection, the second due to drift. If you run the above code enough times (i.e., for enough reps), you should recapitulate the classic result from Kimura (1957) who showed that the probability of fixation is a function of N and s:
\text{Pr}(fixation)=\frac{2s}{1-e^{-4Ns}}
As Dan and I showed in our paper. I also provided the following citations during the debate itself in my opening (they were small, so maybe you didn’t see them) that performed virtually identical calculations across a much wider range of Ns: Hartl & Tauber (1996), Robertson (1960), and Hledick et al. (2022).
Happy to answer any additional questions you may have.
7 Likes
This is correct! And this is, as Paul pointed out, Kondrashov’s paradox. As I stated in the debate, our paper, nor these simulations, resolve this paradox. My attempt with these was to show that Sanford’s “No Selection Zone” does not truly exist, and that all mutations are affected by selection if s is not zero.
However, Paul made the case that this isn’t what Sanford meant, and that GE is actually Kondrashov’s paradox. If GE = Kondrashov’s paradox, as Paul plainly states, then these simulations are irrelevant. But that’s not how conversations between GE-proponents and opponents has gone - they have hinged on the existence of mutations that selection “cannot see.”
Regardless, if we let GE = Kondrashov’s paradox, the concept gains a great deal of clarity, makes specific predictions, and is built on a model that can be evaluated using standard population genetics. This is ideal and I look forward to engaging it in the future without reference to Sanford’s book, which has caused a great deal of confusion about what GE is.
8 Likes
A couple of quibbles:
- Kimura’s 1962 formula, for a population with initial frequency of the favored allele being 1/(2N), and additive fitnesses 1+2s : 1+s : 1, is (1-exp(-2s))/(1-exp(-4Ns)). If s is small this is close to 2s/(1-exp(-4Ns)).
- The formula for delta-p is not quite right. The expected change is sp(1-p)/(1+sp). The change once genetic drift is taken into account is the change from p to the frequency found in a binomial distribution where the variance of change is nearly p(1-p)/(2N). When fitnesses are (1+s)^2 : 1+s : 1, multiplicative fitnesses, it is a binomial variate with 2N draws from a binomial distribution with mean equal to p + sp(1-p)/((1+sp)^2).
All that is done properly in our lab’s program PopG. I don’t know about learnPopGen.
4 Likes
Can you please explain how pointing out that mice and humans are different in important ways with respect to GE is “special pleading”?
Thanks for providing this information, I’ll look it over.
@Dan_Eastwood Sorry if I’m nitpicking here, but this certainly doesn’t seem to me like “side comments”.
Yes, this is exactly how it’s modelled in learnPopGen, I should have been more exact thank you for the clarification.
You mean you don’t think Dan Stern Cardinale should be misleading his credulous and ill-informed followers that I conceded the debate “without realizing it”??
Show any real-world published genome-wide DFE for any large multicellular eukaryotes (like humans) that doesn’t imply fitness decline. Can you?
What about the sense of the word where you did the work and it isn’t published?
I want to be charitable here, but I just can’t. That is not an accurate description of what you claimed in your paper, and it certainly isn’t an accurate description of what Sanford ever claimed. In your paper, you stated:
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
Yet, that is also just a restatement of Kondrashov’s paradox. So yes, you very much were claiming to have resolved Kondrashov’s paradox (real-world parameters, allegedly, yet no fitness decline)!
But upon close inspection, it turned out that none of your parameters were anything remotely like real-world parameters, nor were they anything like Sanford’s DFE which, as he clearly stated in his paper, was just copied from Kimura’s for the deleterious side.
If this isn’t just the darndest case of masive backpedalling then I don’t know what ever would be. And to be clear, Sanford quoted from and made reference to Kondrashov liberally from cover to cover in his book, including Kondrashov’s 1995 paper itself. Over and over. It’s impossible that you could have actually been familiar with Sanford’s work and somehow not known that Kondrashov’s paradox is central to GE.
I did not respond to any of your previous claims and only answered your specific question because I had understood you to not want to be locked in an “indefinite back-and-forth on the matter in the forums,” but this response suggests you’d like to continue on this topic. If that’s the case, perhaps we should start a new thread and discuss the specifics of Kondrashov’s paradox and what the goal of our paper actually was, since I believe we’ve been somewhat talking past one another.
Lastly, saying that
is not the same thing as saying that Kondrashov’s paradox is GE, as you stated during the debate and in the comments of the debate. Again, if that is the case, we can avoid all the confusion here and just get to the heart of the issue.
2 Likes
Sure. By generation count since Ussher’s date of creation, mice, which like humans are mammals, have experienced 100 times the exposure to GE. Instead of dealing with that glaring dominant factor, proponents of GE such as yourself deflect attention to other purported minor factors. So that is special pleading.
Seeing as mice are showing no signs of genetic meltdown anytime soon, it would be useful to demonstrate what “realistic biological parameters” are required to reconcile this observation, and compare the parameters input for mice with those you use for human.
Actually I do think it would be best to cut it off for now, as I don’t want to be in an indefinite back-and-forth, but sadly I do find it hard to stop myself from being drawn in. I really think I’ve said all I need to say for the time being.
I cannot recall ever saying that Kondrashov’s paradox “is” GE, as if Sanford himself had nothing to add to the conversation. What I said is that Sanford expanded upon Kondrashov’s paradox, but that it was the heart of GE.
I agree. Dig up the parameters for mice just as I did for humans, and then use my code (it’s free) and use the mouse parameters instead of human. I’d be interested to see what it shows also. Remember, mice have larger effective population sizes and smaller per-generation mutation rates.
That’s fair!
I’ll add lastly then that you quoted Kondrashov during the debate as follows:
“Because the stochastic mutation load paradox [genetic entropy] appears real, it requires a resolution.”
You then stated “don’t let anyone tell you that genetic entropy is not in the literature, it certainly is, just not under that specific name.” You then wrote in the comments:
He said he had not resolved Kondrashov’s paradox (which is, in fact, GE!), which means he now effectively disavows his own published work
Emphasis mine. Again, I’ll hold-off on responding to any specific argument and just provide you the room to clarify these statements. Thanks.
1 Like