Firstly, I see that I need to clarify the nature of the argument I made in the paper.
If my hypothesis is correct, this predicts that a dependency graph ought to be a better fit to the biological data than a tree. This prediction is fulfilled, thus providing some level of evidence that my hypothesis was correct. My argument is not that because the dependency graph model beats the tree model that the dependency graph model is correct. Such an argument would not be valid. Instead, I’m merely arguing that this fulfills a prediction.
The challenge this leaves to common descent is explaining why this prediction worked.
I expected 1 and 4 as obvious candidates (and mentioned them in my paper).
As for 2, I do have deletions in my model. But I’m curious about how you see large scale genome rearrangement playing into this. Since I’m just looking at the presence or absence of gene families, I’d think a rearrangement wouldn’t do anything interesting there. But presumably you know something about that which I don’t.
As for 3, it seems to me that this should be taken care of by the probabilistic analysis. I assume what you are thinking here is that some genes could end up in a similar set of species and thus look a lot like a module, but by pure coincidence. But the Bayesian analysis, and in the particular the penalty for the dependency graph should prevent that happening.
What I’m surprised by is you not bringing up horizontal gene transfer. Do you not think it is a good candidate?
My thinking is that none of these mechanisms seem like good candidates to explain my successful prediction. Obviously, my intuition on this point is worth diddly squat. It has to be backed up by cold hard evidence which I don’t have (yet).
So, yes, dealing with the exact sequence (instead of just gene family) and in particular the more neutral elements of that sequence is really key. If that can’t be done my proposal fails. It remains to be seen whether a model can be developed here.
It should be emphasized, the fact that human variability deviates from the expectations of tree does not automatically mean that it will fit a dependency graph better. So its very much an open question as to what the results will look like.
But more critically, I’m not sure what prediction I would make about the results of the test. Whether or not common descent produces a tree depends on various assumption you make about the evolutionary process. I suspect that neither a tree or a dependency graph is the right model in this case.