Hi Andrew
The reasoning behind your assertion remains unclear. He is simply making an argument given genetic entropy as a working hypothesis that survival of an ancient living organism with small populations is unlikely. LUCA is a hypothetical construct so there is no basis to claim he is committing the TSS.
The sub-argument about who committed which fallacy can have a home here.
If we are going to talk about fallacies, I’ll just point out that LUCA is a hypothetical individual. And individuals don’t go extinct.
AFAICT including contradictory attributes in your terms (“first last universal common ancestor”) is too ridiculous to qualify as a fallacy.
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That’s a “those can’t be craters on the moon if there’s an invisible field preventing meteorite impacts” argument. There isn’t such a field, and we know that because we can see craters.
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Genetic Entropy isn’t real. Literally zero evidence for it.
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And there’s no reason to think the population of LUCA was ever small enough for something like error catastrophe to be a problem. Of course since we all now exist and descent from LUCA, it clearly wasn’t (see the craters analogy).
No, LUCA is a hypothetical population.