The ICTV code uses the phrase “monophyletic group” several times, including in its definition of an MGE species. The code does not, however, define the word “monophyletic”. Defining such a commonly used word may feel unnecessary to many people, but is complicated by the fact that there are two main usages of the word.
The first usage of the word essentially considers a group that shares a common ancestor to be monophyletic.
In the second usage of the word, a group is monophyletic if it includes all the descendants of some ancestor, and only those descendants. In contrast to Usage 1, this second usage makes “monophyletic” mutually exclusive with “paraphyletic”.
Unfortunately, perhaps, preference for one usage over the other has historically been polarized by taxonomic philosophy. The “cladistic” or “phylogenetic systematic” school recommends Usage 2, whereas the “evolutionary taxonomic” school says that Usage 1 is more correct, and uses the word “holophyletic” as a synonymous alternative for Usage 2.
The most lucid description of the difference between the two usages that I have found is a chapter by Sober in ‘Keywords in evolutionary biology’, edited by Keller and Lloyd (1992).
I am considering writing a Taxonomy Proposal to reduce this ambiguity by adding a working definition for ICTV purposes and thereby recommending one usage over the other. I think that the Executive Committee has made clear that polyphyletic taxa are undesirable, but I have noticed that polyphyly and paraphyly are sometimes confused or conflated. I do not necessarily think that the Executive Committee should make further statements about the desirability of paraphyletic taxa at this time, but I am not sure what their current stance is, because of the terminological ambiguity. (I interpret last year's consensus statement paper as favoring Usage 2 of the word to some extent.) I would be interested in feedback that anyone might have, especially if they think I am confused or confusing!
p.s. congratulations to all ICTV contributors on the release of MSL39.