Having written about paraphyletic groups and the use of the term ‘rhamphorhynchoid‘ when talking about pterosaurs I thought it wise to discuss the issue in a slightly broader context and highlight the problem of such names. As I mentioned, I think ‘rhamphorhyncoids’ is a perfectly acceptable term as long as it is made clear that this is a paraphyletic group. But assuming you don’t want to do that (which is an understandable position), what are the alternatives?
First off some researchers prefer to use the term long-tailed pterosaurs and short-tailed pterosaurs for the rhamphoprhynchoids and pterodactyloids respectively. There are immediate and obvious problems with this approach. Firstly it is longwinded, and while clarity is to be valued in science communication, so too is brevity. Secondly, by using what are effectively colloquial terms it does not make clear the monophyly of pterodactyloids, since the both are given non-technical names. Thirdly and most obviously are the problems of the anuroganthids and Pteranodon since the former have a short tail unlike the rest of the rhamphorhynchoids, and the latter a long one. Thus the anuroganthiuds are then short-tailed, long-tailed pterosaurs and Pteranodon becomes a long-tailed, short-tailed pterosaur. Thus the use of long- and short-tailed is neither clear nor concise. Other variations (I guess you could point to the 5th toe, or the neck length) run similar risks.
Next we can use a nice general term such as ‘basal’ and ‘derived’ to refer to them. However, as above this suffers from ambiguity, since Rhamphorhynchus for example is a very derived rhamphorhynchoid and thus is a derived basal pterosaur, and equally Pterodactylus could be called a basal derived pterosaur. You would have to be explicit every time you used the word basal or derived and again this gets confusing and requires you make exact statements about what context you are using the words in each time you want to refer to a taxon.
Next you have the use of replacement words or phrases such as non-pterodactyloid pterosaurs, or basal clades, or others. These I do not have a problem with, again as long as they are clear (as non-pterodactyloid pterosaur certainly is). However, again, I do not think these terms are especially nice to use (rhamphorhynchoid is so much more succinct, and its worse in other groups – compare ‘prosauropods’ to ‘non-sauropodan sauropodomorph’) and they are hardly ‘time saving’ in as much as in any paper where you refer to them you will still have to include a sentence along the lines of “the non-pterodactyloid pterosaurs are a paraphyletic collection of basal taxa” just as you would when defining the rhamphorhynchoids.
Overall I find the putsch against paraphyletic terms annoying. I can’t see the harm in using them when they are clear and succinct and are carefully defined (and that is the case here). I don’t see icthyologists putting the word ‘fish’ in quotes constantly or writing about ‘non-tetrapod vertebrates’ (or if they are, I have missed it). People will even still use ‘reptile’ in its polyphyletic sense (i.e. not including birds or mammals) when convenient to do so (admittedly rarely), without problems. The only time this approach is problematic is where one term is synonymous with two different things (like dinosaurs can mean, well ‘dinosaurs’ [i.e. non-avian dinosaurs] or all dinosaurs including birds) and here distinction is necessary. For pterosaurs though, this is not the case. ‘Rhamphorhynchoids’ are paraphyletic, everyone knows they are and accepts that they are, so why replace one term (rhamphorhynchoid) with another longer one (e.g. non-pterodacyloid pterosaur) that still represents the exact same paraphyletic assemblage and still requires the same clarification?
As I recently wrote in a technical note on this issue in a paper “I prefer therefore the systematic term ‘rhamphorhyncoid’ which, despite being paraphyletic, is succinct, accurate and unambiguous”. I find it hard to fault that statement (even if I wrote it).