Explaining the shape of a typical COVID 19 epidemic curve

Estimates of both the substitution rate and the generation time for SARS-CoV-2 vary. When I surveyed a number of estimates a couple of weeks ago, I ended up with an estimate of 0.4 substitutions per transmission.

What I was looking for is the mutation rate in the sense of the nb of mutations per genome per replication.

There are far more than 23 replications in a year. So this tells us that there is less than 1 neutral/positive mutation per replication. Mutation rates include deleterious mutations, but they are largely screened out in viral populations. Virulence reducing mutations often fix because they increase fitness, helping the virus spread by reducing the negative impact on the host.

Did you catch that? Reducing the lethality of the virus makes it more fit.

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@Giltil did you watch the video where it was shown how the SIR model reproduced the curve you found mysterious?

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Deleterious mutations are mostly screened out quickly ā€“ before transmission ā€“ but some do linger for a while. The substitution rate decreases as you increase the time over which you sample. (E.g. the measured substitution rate within Ebola virus outbreaks is higher than the measured rate between outbreaks.)

Not till the end, for time constraints. I will need time to swallow it, if I can ever do it!

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I donā€™t see how you can go from the nb of replication per year to the replication error rate I am interested in. I remember having read that it was about 1 error/substitution per genome per replication but was unable to find confirmation.

Figure 1 in Sanfordā€™s paper contradicts this claim, for it shows a regular increase in the accumulation of deleterious mutations as the number of generation increases.

I think this assumption doesnā€™t work in the case of Covid-19 for 1) the virus is infectious during the pre-symptomatic phase and 2) itā€™s lethality is much too weak.

Scientists have been monitoring the virus since it first emerged, so there should be data on how the viral genome has changed over the last 5 months or so.

Could you explain it?

The substitution rate(*) is right around 1e-3 mutations/bp/year, or 30 mutations per virus per year. Mean time between transmissions is less well known, but is around 5 days. That gives 0.4 mutations per transmission.

(*) Which is NOT the mutation rate ā€“ the mutation rate is much higher and very hard to measure, since most mutations are weeded out within a single host.

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Well to be fair, it isnā€™t really a contradiction to say that deleterious mutations can accumulate as generations increase, while most of those that occur are largely (but ofc not completely), as a proportion, screened out by selection.
This is a problem with keeping the discussion of these ideas at this kind of somewhat vague verbal level, as opposed to giving precise quantitative statements with actual numbers.

This is exactly what I meant when I stated ā€œlargelyā€ screened outā€¦

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Yes, this is a place where Sanford is saying something that contradicts what the data shows. We very much agree with you that his work, on this point, is in conflict with the evidence.

Your confutation of my hypothesis would have merit if it was the case that SARS-CoV-2 had a single origin but there are reasons to believe this is not true. For example, here is an interesting passage I found in a recent publication:
We look for the origin of SARSā€CoVā€2, because we see it as a single entity against which we could act using a series of established approaches, since the virus would follow a predictable route of contagion. The epidemic would resolve after ā€˜herd immunityā€™ had been created. Yet, SARSā€CoVā€2 is not a single entity (e.g., see Forster et al ., 2020) and may not have a single origin: contemplating herd immunity with a heterogeneous population of viruses may be very misleading, at best.
And here is the whole article:
https://sfamjournals.onlinelibrary.wiley.com/doi/full/10.1111/1462-2920.15053

I donā€™t think I can do better a better job than Sanford, so Iā€™m quoting him again:

The mutation rate in RNA viruses is so high that it becomes difficult

to speak of a given viral ā€œstrainā€, because any genotype quickly mutates into a

complex of genotypes, such that any patient is soon infected with a ā€œviral swarmā€.

With such a high mutation rate, the large majority of viral genotypes in a patient

must carry many deleterious mutations, and so will be inferior to the original

infecting genotype. This implies the lack of a realistic mechanism to preserve a

ā€œstandard genotypeā€, and all RNA viral swarms should typically be on the verge

of mutational meltdown.

When a virus is transmitted from one individual to the next, the first individual

harbors a viral swarm. The second individual becomes infected by a random

subset of that swarm (conceivably a single genotype). With this type of bottleneck-

ing, the ā€œbestā€ viral genotypes within the first swarm have a small probability of

being transmitted to the next host. This probability becomes especially small when

infection arises from a single viral particle. Given a high mutation rate and regular

bottlenecks, the operation of Mullerā€™s Ratchet becomes quite certain, which

should result in a continuous ratchet-like mutational degeneration of the viral

genome [6].

Sure, when that is what happens. But how often is it the case that host-to-host transmission is facilitated by a single viral particle? There must be some sort of distribution of typical transmission particle loads, and I highly doubt single or even double-digit transmission numbers are common.

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Well, good then, since SARS-CoV-2 had a single origin in humans. That much is overwhelmingly clear from the genetic data.

I have to hand it to you: you have a real talent for finding crackpottery even in the published literature.

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In the real world, natural selection works just fine to prevent the accumulation of deleterious mutations in RNA viruses within a host. Deleterious mutations can accumulate, with consequent loss of fitness, during transmission bottlenecks, but only if those bottlenecks are extremely and artificially tight. There is no loss of fitness for realistic bottlenecks, and in fact low fitness viruses that have accumulated deleterious mutations can regain fitness if the artificial bottlenecks are removed (thanks to that high mutation rate). See https://mmbr.asm.org/content/76/2/159 and Viral quasispecies.

We already know thatā€™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 RNAā€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:
https://onlinelibrary.wiley.com/doi/full/10.1002/jmv.26067

We still have the observations that the virus isnā€™t changing that fast. Reality demonstrates that Sanford is wrong.