He did, four hours ago. 
Aha, Iâm not the only one who thinks the âphylogenetic signalâ doesnât indicate evolution.
From âCONSISTENCY INDICES AND RANDOM DATAâ
G. J. KLASSEN, R. D. MOOI, AND A. LOCKE
However, as pointed out by Faith and Cranston (1991) and Farris (1991), rejecting the null hypothesis of random permutation does not necessarily provide confidence in phylogenetic conclusions.
Thatâs not what the quote says.
The quote is saying just because we some inferred relationship is non random we cannot infer a phylogenetic relationship, e.g. A and B are placed in a certain relationship on a phylogenetic tree. If we cannot confidentally infer a phylogenetic relationship, then why can we confidentally infer an evolutionary tree? If A and B cannot be placed in a certain position on a tree, then why must they be placed on a tree in the first place? A DAG could do just as well.
Thatâs not what it says. It is saying that lower CI values for random data sets does not necessarily serve as a foolproof negative control for the specific phylogenetic method they are using. In no way are they saying phylogenetic signal is not evidence for shared ancestry.
Ewert has already stated that isnât the case. DAGâs should show a lack of features shared within taxonomic groups compared to phylogenetic trees.
Well, Iâll continue to flaunt my ignorance here, but how is that significantly different from what I am saying?
âspecific phylogenetic methodâ sounds to me like some metric for how well a tree model fits the data, or perhaps method for building a tree, and so rejecting the null hypothesis does not necessarily mean a tree model fits the data, at least as measured/constructed by said method.
Can you parse your sentence for me and show where I am misunderstanding? What exactly are they negatively controlling for? What is an example of something for which they fail to negatively control?
How do you get from âsolid, but not necessarily foolproof negative to control for phylogenetic signalâ to âphylogenetic signal doesnât indicate evolutionâ?
rejecting the null hypothesis of random permutation does not necessarily provide confidence in phylogenetic conclusions.
Doesnât sound like:
I donât get a sense of âsolidâ from the quote ânot necessarily provide confidenceâ. Lack of confidence indicates lack of solidity.
But, anyways, semantic disputes are not very interesting. Iâll just grant you for now the authors think phylogenetic signal is still solid, though not foolproof, and get back to the actual data where actually interestingness lies.
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Well put, and agreed.
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I redid my simulation using the consistency index (which turns out to be a normalized version of my SDS) and a null hypothesis where I randomly sample the leaves, and got the same result. DAGs and random leaves about neck and neck, followed by evolutionary trees. Hereâs an example from 30 runs:
Evotree hypothesis falsified 27 / 30 times.
Fake hypothesis falsified 16 / 30 times.
DAG hypothesis falsified 17 / 30 times.
UPDATE: actually if you run it longer, fake comes out ahead of DAGs.
I also used the CI cutoff for phylogenetic signal from the Klassen paper, source of this popular image, and same result: DAGs > fake > evolved trees
I used the CI cutoff to adjust the original CI score, by subtraction:
adjusted CI = original CI - CI cutoff
Here are some example values:
Average adjusted CI scores over 30 runs (> 0 statistically significant, higher is better phylogenetic signal):
DAG: 0.5149
Fake: 0.2775
Evotree: 0.2593
So, unless Iâm doing something dramatically wrong, or significantly misunderstanding something (all quite likely), it seems like the whole phylogenetic signal and perfectly nested clades doesnât tell us whether modern species have evolved. On the contrary, in true Chestertonian style, the phylogenetic signal seems to be evidence of intelligent design, i.e. Ewertâs dependency graph of life.
Someday Iâll find time to write it all up, but at least Iâve satisfied my personal interest in the matter.
For those interested in such things, here is the source code for my simulation. You can run it online to reproduce my results, and check parameters and algorithms. Apologies for the horrible state of the code.
https://repl.it/talk/share/The-Phylogenetic-Signal-Fallacy/52293
You have it the wrong way around as always.
The rationally 100% certain fact of dysteleological (apart from the theoretical possibility of a purposeful ground of being) evolution tells us that there is a phylogenetic signal.
If you can find a specific problem with my work, please let me know. The source code is provided above.
Itâs irrelevant Eric. The phylogenetic signal follows on evolution.
But does evolution follow on the phylogenetic signal? 
Now that is a profound question picked up best by Greg Bear in Darwinâs Radio and Darwinâs Children, therefore unfortunately not : ) like group selection. Teleology emerging from chance and necessity. We wish!
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Update, I had an error in calculating the normalization factor for the CI metric, so here are the new results:
Average adjusted CI over 100 runs:
evotree: 0.8676219452202528
dag: 0.7991580076656275
fake: 0.39394993245276183
And when comparing to the null hypothesis:
Tree hypothesis falsified 0 / 100 times.
DAG hypothesis falsified 17 / 100 times.
Fake hypothesis falsified 52 / 100 times.
Makes more sense!
Still shows CI is lacking when it comes to inferring evolution. Fake leaves still generate significantly positive adjusted CI, which is a strong phylogenetic signal. DAGs are almost at the same adjusted CI as evolved trees. All score in the same range or higher than the statistically significant points in the famous âperfectly nested cladeâ graph. And remember, the nested clade graph is using raw CI instead of adjusted CI, and raw CI is higher than adjusted CI.
For reference, the DAG and evotree trees have between 14-20 taxa (leaves), and the fake leaves tree has 10 taxa.
Hereâs the link to the updated source code. Run it in the browser to reproduce my results.
https://repl.it/talk/share/The-Phylogenetic-Signal-Fallacy/52293
Here are some example graphs, so you know what the numbers refer to.
Example DAG:
Corresponding inferred tree:
Example evotree:
Corresponding inferred tree:
Example fake leaves (all same length, randomly sampled genes):
Corresponding inferred tree:
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