Let us start right at the beginning of the paper, with the introduction. This is where the state of the art is described, and so obviously we will find here the authors' view of the supposed shortcomings of phylogenetic systematics and how their own approach, evolutionary systematics, can supposedly rectify the situation.
Biological classification has been revolutionized by phylogenetic principles, and nowadays there is a broad consensus that shared ancestry is a primary criterion for grouping concepts.Of course there is also a virtual consensus that shared ancestry should be the only criterion for grouping species into higher order taxa.
However, beside this theoretical foundation, information content and practicability are also important criteria for classification (Mishler, 2009).First, because they patently mean some kind of phenetic "information content" (otherwise they would simply accept phylogenetic systematics) it demonstrates some chutzpah to cite a cladist for support in this sentence; and not only a cladist, but a PhyloCoder; and not only a PhyloCoder but one who even wants to make species monophyletic (not that I agree with him there, but that is not the point at the moment). Brent Mishler would hardly want his words taken out of context to manufacture some supposed justification for discarding the monophyly criterion.
Second, and more importantly, one could unfavorably read this as a deliberate attempt at conflating grouping and ranking, or grouping and the question of what nodes of the phylogeny to use for the acceptance of formal taxa. The only universal and objective grouping criterion is monophyly, but everybody agrees that that does not mean every possible monophyletic group is of great utility if formally recognized.
The combination of these features is the goal of evolutionary classification (e.g., Hörandl, 2007). Unlike traditional descriptive or phenetic concepts, evolutionary classifications are based on phylogenetic principles, i.e., taxonomic grouping is primarily based on shared ancestry.With regard to the absence of phylogenetic principles, H&E are correct as far as the (essentially extinct) phenetic school of classification is concerned, which really did not care about shared ancestry. But they claim evolutionary classifications represent some kind of methodological and conceptual advance over both the current paradigm of phylogenetic systematics and what came before, when really this approach is just going back to practice as it was in the first half of the 20th century. The idea that taxa should have a common ancestor (as in: be at least paraphyletic) goes back to Haeckel and even to Darwin's The Origin of Species:
If we extend the use of this element of descent, - the only certainly known cause of similarity in organic beings, - we shall understand what is meant by the natural system: it is genealogical in its attempted arrangement, with the grades of acquired difference marked by the terms varieties, species, genera, families, orders and classes.So unless H&E mean very outdated classifications indeed when they are talking about "traditional descriptive concepts", they err in assuming that what they suggest is any kind of conceptual advance over the systematics of say, the beginning of the 20th century. (Merely acknowledging that somebody else invented computers and tree building software in the meantime does not make a conceptual advance in classification.) Continuing with the paper:
Hybridization potentially can result in speciation both in plants and animals (Rieseberg and Willis, 2007; Mallet, 2007; Mavárez and Linares, 2008). Reticulate evolution may result in conflicting phylogenies that are based on different data sets, which complicates interpretations of phylogenetic reconstruction (McDade, 1992). Polyploidy, as a whole-genome duplication, is often followed by waves of diversification in all major groups of eukaryotes, and is often connected to hybridity (Van de Peer et al., 2009; Soltis et al., 2009).Here as well as in the rest of the paper H&E unfortunately use "hybridization" in a very loose way that makes it hard for me to understand what they are talking about. The only real problem for phylogenetic systematics would be if one very specific process, allopolyploid speciation, took place too frequently and/or between very distant lineages. If it only happens comparatively rarely, if high level polyploidy is often a dead end (as some people claim), or if it only takes place between very closely related species, then we have a certain percentage of nodes on the phylogeny that we cannot use to define clades but the rest of the system is fine.
Hybridization in the strict sense, as the sometime formation of subfertile or sterile offspring between two biological species, is of no import for this discussion whatsoever. Even introgression, rare gene flow between two biological species, is entirely irrelevant for phylogenetic systematics except as an epistemological issue (it makes it harder to infer the true species phylogeny) because phylogenetic systematics deals with grouping species and not with grouping introgressed sequence copies.
So knowing where H&E want to go with their argumentation, i.e. towards the conclusion that phylogenetic systematics cannot deal properly with these processes, one cannot help but feel uneasy about this first paragraph already. Specifically, one might suspect that, by generously throwing hybridization, reticulate evolution and polyploidy into one pot and stirring it all into a dense, confusing stew, by conceptually linking several irrelevant but frequent processes with the one very specific process, allopolyploid speciation, that is potentially problematic for phylogenetic systematics (and which, curiously, they don't even mention!), the authors attempt to imply that the current paradigm is in dire straights when it really isn't.