Earlier quoted context omitted.
The phylogenetic tree of life is organized not on the characteristics, but on the evolutionary origin of species. Species are in a specific branch of that tree if they share a common ancestor species with the whole branch. Shared characteristica were a good proxy for ancestry back when the mechanism behind inheritance of genes was not discovered yet. Of course, the concept of a species is a bit fuzzy (even the possib…
> The phylogenetic tree of life is organized not on the characteristics, but on the evolutionary origin of species. My mother's old university biology textbook presents this as one of a few "equally valid" visions for how taxonomy should be organized. I agree with the modern view that it's the only valid vision, but it's interesting to see it presented in a "teach the controversy" way, and we can see from the comment…
The monophyletic grouping approach tells you something about the path through solution space taken by the algorithm.
The paraphyletic approach instead focuses on properties of the solutions.
I think it's fine to think of those as equally valid.