From a cladistic perspective, monophyly of taxa is desirable, but important evolutionary processes such as hybridization, anagenetic and anacladogenetic speciation (budding sensu Mayr & Bock, 2002) unavoidably result in non-dichotomous branching patterns (Hörandl, 2006; Hörandl & Stuessy, 2010).I am afraid I already find this first bit confused in several details. First, from a cladistic perspective, monophyly is not merely desirable but required. That is the entire point of cladism.
Second, non-dichotomous branching patters are polytomies, meaning the branch splits into more than two sub-branches. Polytomies are no problem for making supraspecific taxa monophyletic, so on the face of it, it is not clear what the argument is. But none of the mentioned processes necessarily produce polytomies anyway, and some of them do not even produce any branching at all.
Hybridisation - presumably the authors mean hybridogenic speciation, e.g. by allopolyploidy, and not actually hybridisation per se, which is usually a dead end - is not branching, it is the opposite. The problem for the argument here is that reticulation does not just mean there is no monophyly, it also means there no is paraphyly either, as there is no phyletic (tree-like) structure. It makes no sense to argue for paraphyly in a situation where there is no paraphyly. (More on that below.)
'Budding' speciation is dichotomous, just like any other lineage split, unless an ancestral species fractures into three or more descendant species at the exact same moment, just like could happen with a non-'budding' lineage split. It is no problem whatsoever for making supraspecific taxa monophyletic.
Third, anagenetic means that something happens along a lineage without a lineage split, so it is again odd to speak of a "non-dichotomous" branching pattern. If anagenesis is happening there is by definition no branching pattern, dichotomous or otherwise. Nor is there any problem for making supraspecific taxa monophyletic. So yes, the observation that there is no dichotomy is correct, but merely in the same trivial sense as the observation that a book isn't a car. You can go around saying that, but book authors or publishers will simply say, "we know, so what?" Cladists likewise when told that anagenesis happens.
Anacladogenesis is a case of peripatric speciation, in which a population or a group of populations from a species diverge, resulting in a derivative monophyletic species (Stuessy, Crawford & Marticorena, 1990). Unlike in cladogenetic processes, the ancestral species remains essentially unchanged and often becomes paraphyletic (Mayr & Bock, 2002; Crawford, 2010).With this the two closely related misconceptions at the heart of the paper's argumentation become clear. The first is that the cladist approach requires making species monophyletic. It doesn't. The second is that it makes sense to call species monophyletic or paraphyletic in the first place. It doesn't. (Although this is a very, very common and widespread misconception.)
As already indicated above, the concepts ending in -phyly apply in tree-like structures, such as the tree of life. The individuals of sexually reproducing species, however, do not form a tree-like but instead a net-like structure. Consequently, -phyly does not apply inside sexually reproducing species. Another attempt at an analogy: I can be asleep, but the molecules I consist of do not sleep. The concept "asleep or awake" does not apply to individual molecules, just as monophyly does not apply to individuals of the same sexually reproducing species. Fallacy of division is the keyword here.
This is not a new idea that cladists came up with only as a rearguard action, as frequently claimed by paraphyletists. We can go back all the way to the inventor of cladism, Willi Hennig. The central and best known figure in his book illustrates the different relationships that species, individuals, and life stages have to each other. Phylogenetic systematics ('cladism') is the approach to take when classifying species into supraspecific taxa, but not when classifying individuals into species. The claim that a species is monophyletic or paraphyletic is a category error.
Over time, the ancestral species may converge to monophyly through gene flow and lineage sorting (Baum & Shaw, 1995).Same as above, but in addition it has to be unclear what is meant with 'gene flow', as on the face of it such flow would work against lineage sorting. It is possible that the authors meant to say 'restriction of gene flow'.
This sentence also makes clear where the conceptual error is located that leads a surprising number of people to the idea that species can be something or other-phyletic. Lineage sorting happens to alleles, and yes, the alleles of a gene occurring inside a sexually reproducing species can be paraphyletic to the alleles occurring inside a different sexually reproducing species. But taxonomists do not classify alleles into species, they classify individuals into species, so this would be another category error.
Far from an exception, anacladogenetic speciation has been considered to be of main importance in plant evolution (Rieseberg & Brouillet, 1994; Anacker & Strauss, 2014). As integrative taxonomy advocates that taxa should reflect evolutionary processes (Stuessy, 2009; Schlick-Steiner et al., 2010), it may be necessary to recognize certain paraphyletic entities.The argument that Integrative Taxonomy requires paraphyly was not familiar to me. My understanding has always been that Integrative Taxonomy is about combining diverse kinds of evidence to support taxonomic decisions in species delimitation, e.g. a combination of ecological niche, population genetics, and morphology. The seminal Schlick-Steiner paper, for example, was clearly about alpha taxonomy, i.e. species delimitation. Searching it for the snippet "paraph" brings up only one entry in its reference list. (Stuessy is a different story, as he is one of the two or three most vociferous botanists still arguing for paraphyletic taxa; but then again he is not to my understanding a founding figure of Integrative Taxonomy.)
Again the central problem is, however, not what Schlick-Steiner et al may have thought about paraphyletic taxa, but that Integrative Taxonomy is about species delimitation, where paraphyly applies just as much as decibels apply to colours, and not about supraspecific taxa, where there concept properly applies.
The paragraph ends with something like an argumentum ad populum.
Indeed, examples of recognized paraphyletic taxa exist at various taxonomic levels (e.g. class Reptilia: Mayr & Bock, 2002; Pozoa coriacea Lag.: López et al., 2012; Helichrysum Mill.: Galbany- Casals et al., 2014; Plethodon wehrlei Fowler & Dunn: Kuchta, Brown & Highton, 2018; Columnea strigosa Benth.: Smith, Ooi & Clark, 2018).The individual species used as examples are irrelevant for the reasons outlined above, because unless they are reproducing clonally, in which case they should have been circumscribed to be monophyletic, they are not paraphyletic but instead tokogenetic (net-like), and cladism does not apply inside tokogenetic structures. That leaves two supraspecific taxa that the taxonomic community has long recognised as ill-circumscribed due to their paraphyly: reptilia and Helichrysum.
One might point out that Mayr, for example, remained opposed to phylogenetic classification even as he saw it being adopted by the scientific community around him, and that recognition of reptilia as a paraphyletic taxon is not state of the art in zoology today. The vast majority of animal systematists today classify animals consistently by relatedness.
But more importantly, there is no way to base the acceptance of paraphyletic reptilia or Helichrysum on the argumentation presented in this paper, which argues entirely from the existence of hybridogenic and 'budding' speciation. This illustrates an extremely common pattern in papers arguing for paraphyletic taxa: an argument is made that applies inside a species (although even that only if we misconstrue the conceptual basis and actual practice of phylogenetic systematics), and then the entirely unwarranted jump is made to the conclusion that paraphyly should be accepted at a much higher level of classification, where the argument would not apply even if it were correct.