Explaining the shape of a typical COVID 19 epidemic curve

We already know that’s wrong. The mutation rate is much, much lower than what Sanford is claiming.

Your doubt may not be warranted, as this passage shows:
Genetic bottlenecks are likely to occur quite frequently with RNA‐based respiratory viruses since respiratory droplets often contain only one to two infectious particles per droplet.7Modeling suggests that such bottlenecks likely drive down the virulence of a pathogen due to stochastic loss of the most virulent phenotypes
The whole article here:

We still have the observations that the virus isn’t changing that fast. Reality demonstrates that Sanford is wrong.

That’s a letter to the editor, not an article. The last one you cited was an editorial, also not an article.

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That doesn’t actually show that. It says bottlenecks might be common, which can mean quite a range of values significantly larger than 1. Reference 7 doesn’t seem to show the typical number of viral particles per droplet(as it’s a paper on modeling with ranges of parameters and conditions), but that’s not even the relevant measure anyway since a person can come into contact with many droplets over a short duration of time, as one person can breathe many out and another can breathe many in. Being stuck together in a bus, crowded restaurant, or other form of large gathering for minutes to hours.

The thing remains that with a replication error rate of ~ 1 mutation per genome per replication and a strong bottleneck whereby no more than 2 to 10 viral particles are transmitted from one host to the other, genetic entropy of sars-cov-2 is certain to occur quite rapidly.

You just don’t have any evidence that these values obtain, nor that Sanford’s distribution of fitness effects of mutations do.

Please show your work. Don’t forget to include the effects of purifying selection in both source and target, the fraction of mutants that are viable (and how you determined this), the fraction that are deleterious (ditto), and the effect of back mutations in the target.

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It’s not my work, it’s Sanford’s.
You will find answers to most of your questions in the mat&meth section of his article below:

Let’s look at Sanford’s numbers. A key bit of his paper is this: “We model 10% of all mutations as being perfectly neutral, with the remainder of mutations being 99% deleterious and 1% beneficial [35] […] We use the well-accepted Weibull distribution for mutation effects (a natural, exponential-type distribution [26]). In this type of distribution, low-impact mutations are much more abundant than high-impact mutations.”

Reference 35 is to this paper. In that paper, the authors report on 91 synthetic mutants of an RNA virus. They found 24 produced no virus and can be presumed lethal. If we ignore those, 31 (46%) had no statistically significant effect on fitness, 32 (48%) were deleterious, and 4 (6%) were beneficial. If we assume (without justification) that all mutants with lower measured fitness were deleterious, even if the value was not statistically significant, we have 76% deleterious and 18% neutral. They also found that the distribution of fitness effects detectably non-lethal deleterious mutations had a longer tail – more highly deleterious mutations – than could be fit well with an exponential-type distribution. Mean beneficial effect was 1%, mean/median deleterious effect (for non-lethals) was -13.9%/-9.2%

So let’s compare the Sanford model with the empirical results from the source they cite. Fraction neutral: 10% (model) vs 18-34% (empirical); fraction beneficial: 0.9% (model) vs 4-6% (empirical); fraction deleterious: 89% (model) vs 46-76% (empirical); size of beneficial effect: maximum of 1% (model) vs mean of 1% (empirical). Sanford’s paper doesn’t give the mean fitness effect of their deleterious mutations, but does report that 10% had an effect > 10%. The empirical median value for deleterious mutations (assuming all of the non-significant ones were actually deleterious) is just under 10% (9.2%), which means that Sanford’s distribution is weighted far more toward mutations of small effect than the empirical values, i.e. weighted toward mutations that can accumulate rather than be purged quickly by selection.

In summary, Sanford and colleagues took (and cited) a study of empirical values for the very thing they’re modeling, and then discarded every single one of the values and replaced it with one that suited their thesis. I’m not going to bother looking at the rest of their model, and I think I’ll skip characterizing the quality of this effort so I don’t get banned from PS.


Even assuming your corrected values, I don’t see how you could avoid genetic entropy. In particular, I don’t see how shifting the distribution of deleterious mutations toward higher effect mutations can help you, quite the contrary.
And you also have to consider that fitness decline of RNA viruses due to Muller’s ratchet has been experimentally documented.

Once again: show your work. This time with real values.

The whole point of Sanford’s ‘genetic entropy’ is that it’s caused by deleterious mutations of small effect, since mutations of large effect are easily removed.

No one disputes that Muller’s ratchet can occur, especially under artificially tight bottlenecks in the lab, or that RNA viruses have a mutation rate that is so high that they are close to the edge of failure. In fact, it’s thought that coronaviruses can only afford their relatively large genome because they have a relatively low mutation rate. The claim, though, is that RNA viruses must and do degrade during ordinary transmission. So far you’ve offered nothing to support that claim.


I would bet that the bottlenecks in the real Covid19 epidemic are tighter to the artificial one used in the experiment I refer you to.

So you are acknowledging up front you are making a wild guess?

Not really. I’ve offered a reference that supports the idea of very strong bottlenecks in the Covid19 epidemic.

That isn’t evidence @Giltil. Now might be a good time to wind down this conversation. Let’s see how Sanford responds.

I am really looking forward John’s answers and I I am grateful to you for taking the initiative to contact him on these issues of exceptional interest at this time of epidemic.

So how would you characterize his response?


Well, since @swamidass doesn’t seem to be chiming in, I’ll say that Sanford did respond by email. He declined to explain why he cited a source that gave quite different estimates than the ones he used, and he did not offer a justification for the numbers he did use.


That is an accurate summary.