During a discussion about species, a visiting colleague has argued that I am misusing the word "tokogenetic" (see here, here and basically everywhere I discuss phylogenetic systematics). Apparently the way Hennig originally intended the concept of a tokogenetic relationship to be used was not as a synonym for "net-like" but instead to describe the ancestor-descendant relationship, as from mother to daughter across generations.
If that is so, I will from now on try to avoid making that mistake. That being said, my previous misuse, both on this blog and in research papers, does not appear all too problematic because nearly everybody else seems to use the term in the same way, as a Google search easily demonstrates.
The important point, however, is that this insight does not change anything that matters: Regardless of whether they can or cannot be called tokogenetic in the original sense of the word, networks, or net-like structures, definitely do not contain monophyly or paraphyly. Only tree-like, phylogenetic structures can contain monophyly or paraphyly.
This is why anybody arguing that reticulation makes it necessary to accept paraphyletic taxa only demonstrates their own conceptual confusion. As do those arguing that the members of the same sexually reproducing species form a monophyletic group or clade, of course.