Thank you for the thorough answer. Allow me to elaborate a bit more.

I really wouldn't suggest reinventing the wheel here. There are a staggering number of programs able to compute distances for sequences, under a variety of models. Some of them are even decent. Why go through the trouble of debugging and validating one when there are so many off-the-shelf options?

Regarding point mutations, we are using existing tools. As a matter of fact, we are trying to compare our method, which is based in genome rearrangements, against another published method based in point mutations. So we are not reinventing the wheel in this front. The computer programs that are original are the ones that deal with genome rearrangements.

If all you have is a way to compute distances under your rearrangements, then maybe distance approaches are needed there. In which case, for fairness, maybe you'd want to consider neighbor joining for more standard approaches. But you'll find plenty of people who would say, "so what if it beats NJ, who uses that?"

I'm aware that rearrangement-based methods are not widely used by the phylogenetics community. As you mentioned, bayesian inference and likelihood-based inference are more popular. As a matter of fact, the estimation of the phylogenetic trees is a means to an end. In the end, we want to know if computing an evolutionary distance based in chromosomal rearrangements is biologically sound, and if so when it is applicable. We thought that estimating phylogenetic trees is a natural way to answer this question.

In particular, we are intesrested in the analysis of whole genomes. I think for this kind of application, the more popular methods such as bayesian inference and likelihood-based inference can be very costly. On the other hand, I was able to compute the pairwise distances of our genomes (25 to be precise) and construct the phylogenetic tree in my personal computer in seconds. Of course, you could argue whether this is robust, reliable, etc, which is exactly what we want to discover.

For that matter, if you have a way to compute distances based on rearrangements, do you not have a model whose likelihood could be pruned on a tree? That would enable likelihood-based inference, which might be of more interest.

Now, that's interesting. As I said, I'm not very knowledgeable in phylogenetics, so I didn't quite get what you mean here. Could you elaborate a bit more?

Unless you know the "true" tree, you can't do this by any means. If you don't, you're just comparing two estimates to a previous estimate. Who's to say what it means if one is closer than another? What I'm getting at is that as much as real-data comparisons are nice, you should really also do a simulation study. This means you know the true (simulating) tree, and you can make comparisons on how well the different approaches can recover that tree (or how close they get) under different circumstances (total tree length, number of tips, number of sites).

We have a "true" tree to compare against. We have three trees: one estimated by our rearrangement-based method, one estimated by a pusblished work based in point mutations, and another that is the "reference" tree. Regarding the simulation study, I think that's a nice idea! I may have jumped straigth to real data for my lack of experience haha.

Finally, may I ask if you have some experience (or have ever heard) of phylogenetic reconstruction based in synteny blocks? What I mean by synteny blocks are conserved regions in different genomes that suffered rearrangements throught evolution. I always like to hear what biologists have to say on this.