I am interested in two questions here. The first is the justification for doing something at all, or, to be perhaps more precise, the justification for believing that an activity is conductive to a given goal. Assume, for example, that you are paying a company to build a house for you. One day you walk past and you notice that the builders do not actually seem to be raising any walls, instead they are sitting around a sandpit playing with mud pies. The question is now why they are playing mud pies. You are paying this hour's work in the belief that it goes towards your house - how does this further the undertaking?
Now maybe there is a good reason. Perhaps the foreman could reply that you are not actually looking at mud pies but at a revolutionary new brick-making technology. Who knows? But if he just replies, well, we fancied making mud pies, then you would most likely not consider that to be a very good justification, because there is no connection between that answer and the goal of getting your house up. Similarly, if we want to build a sensible classification, we need an approach that is justified as logically leading to a sensible classification, and not just an answer on the lines of, well, we fancied the result this approach produces.
I should also add that I am not really interested in trying to invent a justification myself, or in examining some post-hoc rationalisation that a completely different pro-paraphyly taxonomist may have developed several years later. I am primarily interested in how the paper originally presenting patrocladistics to the community justified the approach.
The second question is why the analysis should be conducted in the very specific way suggested by the authors, independently of the answer to the first question. In the case of the builders, regardless of whether they have convinced you of the virtues of mud pies as a replacement for bricks, you may still ask why they would be using chopsticks to form their mud pies when little shovels or even spoons would perhaps be more efficient. In the case of patrocladistics, I will likewise temporarily put aside the issue of whether it makes sense and ask if any justification is provided for the specific way in which patrocladistics are conducted in the paper.
1. Why do a patrocladistic analysis? What is it good for?
Unfortunately, I do not find it easy to answer this first question based on the original publication. As far as I can tell, two rationales are implied, but I hesitate to call them justifications because I do not see them progressing from a biological consideration to a methodology that will demonstrably provide data on the relevant biological pattern. Instead, we first find the following considerations in the introduction:
the crux of the problem lies with character divergence within lineages, which strict cladistic classification does not take into account*. We propose here a method of incorporating patristic distances, or evolutionary divergence within lineages, into an explicit method of producing a branching diagram (called a patrocladistic tree or patrocladogram).And later in the results section:
For those workers wishing to incorporate divergence within lineages in their classifications, this simple example shows how it can be done quantitatively.To the best of my understanding then, the logic here is pretty much as follows: Some species look quite different from their closest surviving relatives, and because they are so different-looking we would really, really like to recognise them at the same supraspecific taxonomic rank as those relatives, which will then form a paraphyletic group. But the current paradigm is to accept only monophyletic groups. Hm. Maybe the real problem is that we don't have an explicit and quantitative method to recognise paraphyletic taxa, like the cladists have for their monophyletic ones. Here, we have invented such a method.
Maybe it is just me, but I find that rather unsatisfying. To clarify my problem with this, the rationale does not seem to be biological, theoretical or philosophical but instead strategical: The authors are trying to make paraphyletic taxa more palatable not by explaining why they are meaningful but by hunting around for some analysis that produces paraphyletic groupings. Or in other words, the logic of the paper doesn't start with a biological pattern and then finds that it is best described using paraphyletic groups, but it rather explicitly starts with the desire to have paraphyletic taxa and works backwards from there.
In the end there is an explicit and quantitative method, that much is true. The underlying controversy is unsolved, however, because that is still about whether to classify consistently by relatedness or by some other criterion.
The second implied justification is even odder, and it became the focus of E.O. Wiley's response to and criticism of the method (Wiley 2009, Taxon 58: 2-6). Again the relevant parts of the original patrocladistics paper, starting with the abstract:
... (patrocladogram). This diagram can serve for classification using cladistic rules, because the patristic dimension has already been taken into account in the analysis.Introduction:
This dendrogram, because it already contains a measure of the patristic relationships among the taxa under study, can be used directly in classification by applying strict cladistic rules (especially the holophyletic criterion). (...) This should eliminate, or at least significantly reduce, the controversy over how to deal with paraphyletic groups.Methods:
This new diagram, then, can be used in an explicit cladistic holophyletic (monophyletic) evaluation for classification.Results:
... now the genus Nablonium is again supported by the patrocladistic topology. Both genera are now holophyletic.This is as strange as it is plain in the text. The authors appear to assume that as phylogenetic systematists want to recognise only clades as taxa, the solution to the controversy is to find a clustering method that will manipulate the phylogeny to turn non-clades into clusters. Clusters in a phenogram have the same shape as clades on the tree of life, so they can then point a cladist at the cluster and say, here you go, now the group looks monophyletic in this figure! Surely you will now agree that we should accept this paraphyletic taxon? Oops, sorry, this now holophyletic taxon, I mean.
The best analogy I can come up with would be the builders carefully constructing a little sandcastle with four walls and demanding their money for having build a three bedroom brick house with central heating. Yes, we might then reply, that sandcastle has the same general shape as a house, but it is not really a house. Yes, a cluster in a patrocladogram has the same shape as a clade in a phylogenetic tree, but only at the level of lines of ink on paper. It is still the case that a paraphyletic group contains species that are more closely related to species outside the group than they are to any other species inside the group. That is still the issue, and as no manner of manipulating the tree to take a different shape will distract from that fact, mainstream systematists have so far remained rather uninterested in patrocladistics.
It is possible that I am missing something, but I have gone through the paper several times, and if there is a biological justification for patrocladistics then I do not see it. There really seems to be only the observation that "divergent single taxa may be very different in character composition from its [sic] closest relatives" followed, without argument, by the implication that that justifies paraphyletic taxa. And then some method is sought that will turn paraphyletic groups into clusters. How these clusters are meaningful is, as far as I can tell, never established. What is more, there is no indication at all that the authors have considered the theoretical or practical implications of extinct (or undiscovered) intermediate ancestors and of the gradualism of evolution in general.
2. The specifics
In the previous posts and their comment threads, the choice of clustering method has already been discussed. I consider the single-linkage method used in the original paper to be accurate and honest: In the absence of saltationist gaps it does not find any clusters, and that is exactly how it should be. As all of life is seamlessly connected through intermediate ancestors, breaking the tree of life into clusters along its branches would be arbitrary, artificial and accordingly meaningless. That this consequence of their choice of clustering method had not occurred to the inventors of patrocladistics could be seen as another indication that they may not have considered the implications of including intermediate ancestors into a classification.
Personally, I would be more interested in why the distance matrix used for patrocladistics is produced by adding cladistic to patristic distances. Putting, as mentioned above, aside the question of how the whole approach is to be justified, I understand the use of patristic distances: the hope is to get different clusters where extant species are separated by a long branch of extinct intermediates. But I do not understand the cladistic distances. In effect, each branch is unaccountably lengthened by one apomorphy count. Why? As more intermediate ancestors are included, the patrocladistic distances converge on 2 x patristic distances, making the results equivalent to using only the latter. Sadly, it never seems to be explained why cladistic distances are added at all.
In addition, the paper features some discussion about weighting cladistic against patristic distances. No clear suggestions are made, and decisions are left to "the evolutionary convictions of the particular worker".
This is rather vague. Again, at least in this paper the method is presented not so much as following logically and necessarily from a biological process that one wants to elucidate but simply as an option "for those workers wishing to incorporate divergence within lineages in their classifications". Those who wish to do so can use it; those who don't wish to do so won't use it anyway. I am afraid I will have to be counted among the latter.
* I consider this a PRATT. Such divergence is used to recognise subclades, so it is taken into account.