The ecological monograph linked below has generalized phylofactorization beyond compositional data (e.g. to presence/absence data, Poisson or multinomial counts, etc.).

The R package now follows the structure of the monograph, and an up-to-date tutorial is available on the "Resources" tab of my personal website (https://www.alexwashburne.com) . Among other things, you can now make much cooler...

Interesting paper. Since you have not cited them, I was wondering if you're aware of alternative methods also based on eigen decomposition that have been proposed and used in the "macro realm" of community ecology, such as those of Peres-Neto et al. 2012, [Peres-Neto & Kembel 2015](https://link.springer.com/article/10.1007/s11258-014-0...