> (with p ~ 10%) in a single human-to-human transmission.
That math is absolute garbage. One, the odds of a C/T -> T/C double mutation in a single transmission for the clade-defining markers isn't the same as T/C -> C/T, so at the very least you need to state an ancestral lineage to do any math like this. It also doesn't take into account the different priors for reversions, synonymous mutations, and the C-T transition bias in humans.
> When they built the real tree, they observed that any single root fits badly.
No. Go read the paper again. ("Our unconstrained rooting strongly favors a lineage B or C/C ancestral haplotype...") It's when you try and root in lineage A that things go sideways.
> I believe you prefer to think in terms of construction of the phylogenetic tree for the real pandemic, like to frame the question of number of introductions in terms of the number of roots for the tree.
> More roots would fit better; but that's always true for any phylogeny unless there's a penalty for each additional root,
No, it's not multiple roots, they just place the likely MRCA of SARS-CoV-2 in animals. ("If lineages A and B arose from separate introductions...") It's one tree. With one root. However, that root is in an animal instead of a human.
You can calculate the MRCA for any portion of the tree, including the descendents from the two+ hypothesized introductions. This MRCA is distinct from the SARS-CoV-2 MRCA. Is this what you mean by multiple roots?
> It seems like we disagree as to what forms the paper's core result, though. I'm taking my own cue from Worobey's Twitter comments
If you're trying to understand the paper's core result, read the paper, not twitter.
The first paragraph in `Discussion` frames the crux of their argument I was trying to get across. Notice that they cite the paradox I'm trying to get you to understand, as well as citing genomic diversity as core evidence, as opposed to any argument about the exact timing of A and B samples, or the unlikelihood of multiple mutations.
That math is absolute garbage. One, the odds of a C/T -> T/C double mutation in a single transmission for the clade-defining markers isn't the same as T/C -> C/T, so at the very least you need to state an ancestral lineage to do any math like this. It also doesn't take into account the different priors for reversions, synonymous mutations, and the C-T transition bias in humans.
> When they built the real tree, they observed that any single root fits badly.
No. Go read the paper again. ("Our unconstrained rooting strongly favors a lineage B or C/C ancestral haplotype...") It's when you try and root in lineage A that things go sideways.
> I believe you prefer to think in terms of construction of the phylogenetic tree for the real pandemic, like to frame the question of number of introductions in terms of the number of roots for the tree.
> More roots would fit better; but that's always true for any phylogeny unless there's a penalty for each additional root,
No, it's not multiple roots, they just place the likely MRCA of SARS-CoV-2 in animals. ("If lineages A and B arose from separate introductions...") It's one tree. With one root. However, that root is in an animal instead of a human.
You can calculate the MRCA for any portion of the tree, including the descendents from the two+ hypothesized introductions. This MRCA is distinct from the SARS-CoV-2 MRCA. Is this what you mean by multiple roots?
> It seems like we disagree as to what forms the paper's core result, though. I'm taking my own cue from Worobey's Twitter comments
If you're trying to understand the paper's core result, read the paper, not twitter.
The first paragraph in `Discussion` frames the crux of their argument I was trying to get across. Notice that they cite the paradox I'm trying to get you to understand, as well as citing genomic diversity as core evidence, as opposed to any argument about the exact timing of A and B samples, or the unlikelihood of multiple mutations.