Genetic Load Clarifications
Given Paul’s response, I think I was unclear about the assumptions of the genetic load model so I want to begin by spelling them out explicitly:
- Mutations are assumed to impact viability. In this context, selection = death of the individual. If s = -0.01, then 1 out of every 100 individuals die without reproducing.
- Selection is assumed to act on each mutation independently.
- Each mutation has its own effect independent of the genomic context it is within – i.e., no epistasis and traits are relatively simple such that selection can “see” each individually.
- 1-3 is also true in all the SLiM models, both mine and Paul’s.
- The genetic load is a measure of the relative fitness difference between a population with no mutations and one with mutations. For example, a load of 50% means that the loaded population has 50% the number of offspring as a hypothetical population with no mutations. (Ask yourself: how many is that, exactly?)
Response
Now, to the specific content of Paul’s response.
What Sanford wrote:
…the universal tendency for things to run down or degrade apart from intelligent intervention. Genetic entropy specifically means entropy as it applies to the genome. It reflects the inherent tendency for genomes to degenerate over time apart from intelligent intervention.
Essentially every beneficial mutation must fall within Kimura’s “no selection zone”. All such mutations can never be selected for.
Notice the use of the words universal, specifically, and his emphasis on the word never. Furthermore, note that the first quote is the only time Sanford gives a definition of GE in the book. When you define a concept, it should be exact. And yet, Paul claims:
Paul seems to be arguing that when Sanford uses the word universal or never, so long as he uses different verbiage later on, then he has not in fact defined GE in such strong terms. The fact that you can find instances in which Sanford clearly does not mean that GE is universal or that un-selectable always means un-selectable doesn’t mean that I quote-mined him – it means that he contradicted himself. He could have said generally or rarely. Words have meaning.
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 clarify, it’s that the load itself depends on it. That is, the load is relative to a hypothetical, mutation-free individual. For example, for U = 2.2, then L = 0.89, so fitness of loaded individuals are only 11% of unloaded ones. But that means nothing demographically. If we imagine a mutation-free superhuman, how many children would they have on average? Maybe they’d have 50 children! But a typical loaded human, with only 11% their fitness, can have a max of 5.5.
The point here is that to translate the load into the question “will this population persist?” requires additional assumptions about how and when selection acts as Agrawal & Whitlock (2012) show.
It does not, it’s a mathematical certainty given our genome size. For such an individual to exist at equilibrium – which is what the stochastic load is measuring, to be clear – would require population sizes so large as to ensure that an individual could be born without any mutations. This assumption is reasonable in bacteria (Galeota-Sprung et al. (2020)), but certainly not humans.
Consider a mutation that kills you as a zygote with a probability of 0.0001. That means that 1 out of every 10,000 fertilization events will result in a selective death. This is, quite literally, a selection coefficient of 0.0001, but occurs in the womb. These mutations can still be inferred in the DFE because they will be slightly less represented in adults relative to their rate of occurrence.
Now consider a mutation that doesn’t kill you until you’re 15 – old enough to have used-up a lot of resources but not yet old enough for reproduction. This mutation – despite having the same selective coefficient – is demographically more harmful. A parent has wasted a great deal of reproductive potential funneling resources into an individual destined for death as opposed to a virtually unnoticed zygotic death. This is quite literally what the equation from Agrawal & Whitlock (2012) demonstrates that I showed in the OP.
You did not model soft selection in SLiM – you modelled hard selection. Both our simulations are irrelevant to soft selection. This is because each mutation had an effect on fitness irrespective of any other member of the population (i.e., density-independent). Ecological theory (e.g., Haldane (1956); Wallace (1975)) can’t just be thrown out. As any ecologist will tell you, most selection is density-dependent, driven by competition for space, resources, and mates.
As I explained, when selection is soft, the load is greatly reduced because it is drive solely by fitness variance, which is small in natural populations.
This is surprising. The entire agricultural enterprise is built on the fact that “traits” are selectable. The fact that dog breeds exist are because “traits” have selectable differences. This is a curious statement to me. And yet, underlying the vast majority of those traits are thousands of genes each of which have extremely small effects. This is what I explained in my opening in the debate. It also forms the theoretical foundation of quantitative genetics, going back to Fisher (1918). “Traits” are not amorphous – I gave several examples in the debate: corn oil production, beak depth, human height.
But we can go further. Imagine an enzyme that has an optimal expression level of 1000 transcripts per cell. If the initial expression level is 200, any mutation that increases expression is beneficial. This can occur via gene duplications, promoter recruitment from transposons, etc. Once at 1000 transcripts, any additional duplications are now deleterious, as are any deletions. The point of quantitative genetics is that mutational fitness effects are contextual.
I demonstrated mathematically that it is (see Charlesworth 2013), even at an optimum where all mutations would be harmful. My entire argument during the debate hinged on this fact. As Hledick et al. (2022) demonstrate, stabilizing selection on a great many alleles of extremely small effects maintained information with greater efficiency than strong selection. If you think this is incorrect, you need to demonstrate: 1) traits are not as polygenic as we think; 2) mutational effects are independent of genomic context; and 3) mutations have larger effects than we think they do.
I don’t think you realize that what you’re saying is “quantitative genetics is a rejection of basic population genetics.” This is especially odd given that both Kimura and Lynch started their careers in quantitative genetics. What is important to realize is that the degree to which classic population genetics is applicable vs. quantitative genetics is an empirical question. If we assume fairly simple traits – melanism in peppered moths, sickle-cell anemia, etc. – then classic population genetics works fine. But when traits are controlled by a very large number of genes, the underlying assumptions of classic population genetics fails. The degree to which these models fail is an area of active debate that can only be resolved with empirical data (e.g., how polygenic are traits? How do genes interact? What’s the relative importance of epistatic vs. additive genetic variance?).
I think this is a good time to reference Stephen’s response. My purpose in the OP (and the debate) is demonstrating we have resolutions to the paradox. 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. Joanna would say the same thing, as noted in Matheson et al. (2025), which offers one such resolution.
Paul is flustered that there are so many possible responses to Kondrashov’s paradox, but the fact is that there simply a multitude of possible resolutions. I listed a few in the OP, Joanna has others, and Kondrashov himself has his own (he suggests synergistic epistasis). The lingering question is which is correct – that is, which of these resolves the paradox? Likely it is a mix. It is “unresolved” insofar as we don’t yet know which of the many resolutions is actually the solution. This is an empirical question, and empirical work always lags behind theory.
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).
Under the infinitesimal model, Fisher’s geometric model of adaptation works beautifully. When traits are not polygenic or have large effect sizes, Wright’s shifting-balance theory works better (e.g., Lande & Arnold 1983).
I suppose this is good company to be in. Brian Charlesworth is perhaps the most famous living population geneticist (Joe, who I know is on this forum, is definitely in the running) with over 74,000 citations. His doctoral advisor was John Maynard Smith, who was the student of Haldane himself. Seems like it’d be worth it to read his work a little more carefully.
Lastly, as I mentioned above, Paul is flummoxed that more than one argument exists. This was particularly evident in the debate, where it seemed like he expected the debate to hinge on mine and Dan’s 2024 paper responding to Basener & Sanford (2018). However, the debate topic was “Are mutational effects a problem for evolution?” When he contacted me to request the debate, he did not say “I’d like to debate your paper” or “can you defend your paper”, but requested a broad debate about genetic entropy. In addition, he requested to be in the affirmative. When you are in the affirmative, you build a case – the negative deconstructs your case. Paul spent a great deal of his affirmative deconstructing things I had not said during the debate.
The argument I presented during the debate is what I consider the strongest argument against GE – that is, that most complex traits are highly polygenic, and thus selection is exceptionally effective despite being weak on each individual allele (e.g., Barton 2022). I chose this argument because it is much broader than Hancock & Cardinale (2024), is not restricted to a response to a single paper (Basener & Sanford 2018), and does not suffer from modelling assumptions (which we extensively discuss in the paper!). Furthermore, the infinitesimal predicts real, biological data, and has immense practical importance in agriculture.
Again, if Paul wished to debate specifically our paper, he should have said so and placed me in the affirmative (e.g., “Did Hancock & Cardinale 2024 disprove genetic entropy?”).
Paul’s Behavior
I want to conclude by commenting on Paul’s behavior here. Speaking to Paul directly, I understand that you feel as though you’re Daniel in the lion’s den in this forum, and that is enough to make anyone prickly. But by referencing Stephen and his son, attempting to pit them either against one another or me, is like walking up to the lion and slapping it in the face. Then, to say the following:
reveals the depth of your disrespect. You could have cited the paper or the Masel lab if you’d like, without specifically tagging a father in reference to his son. If you don’t understand why that is reprehensible, then spend some time away from the internet for a while. Touch some grass. Make some human connections. At the very least, keep your insults directed at me and don’t drag in bystanders.