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What do terms like monophyletic, paraphyletic and polyphyletic mean?

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                       Aves                        /                       /          Crocodilia  /Mammalia    \    Dinosauria     \       \      /      \       \    /       \       \  /   Synapsida  Reptilia         \      /          \    /           \  /         Amniota

Here are examples of all three types of group:

• Consider the group consisting of all the animals in this diagram- that is, Amniota. This group ismonophyletic because it consists of a single animal togetherwith all of its descendants. The Dinosauria, including themodern birds, is another monophyletic group, sometimes definedas the most recent common ancestor ofIgunanodon andMegalosaurus together with all its descendants.

  Monophyletic groups are also calledclades, and aregenerally considered as the only ``natural'' kind of group.They are very important in phylogenetic classification.

• Now consider the group consisting of the non-avian dinosaurs(which is what people usually mean by the informal term``dinosaurs''). This is a paraphyletic group, because itcan't be defined simply as ``this animal plus all itsdescendants'', but must be described as one clade minusanother: in this case, Dinosauria minus Aves.

  The ``non-avian dinosaurs'' make up a singly paraphyleticgroup because only one clade need be omitted from its basedefinition.Groups may also be doubly paraphyletic, thrice paraphyletic,etc., depending on how many sub-clades they omit.

• Finally, consider the group of ``warm-blooded animals'', whichconsists of Mammalia and Aves.This is a polyphyletic group - a totally unnatural assemblage- because it can't even be expressed as a paraphyletic group,that is, a clade minus one or more of its subclades. Suchgroups are not used at all in phylogenetic work since they area purely artificial construct. In terms of common descent, a``warm-blooded animals'' grouping makes no more sense than aSynapsida-plus-Crocodilia group - though this is not to saythe notion of a warm-blooded group may not be useful in someinformal discussions.

So far, so straightforward. The only wrinkle in this scheme is thatsome workers use the word ``monophyletic'' in a sense that includeswhat we have described here as paraphyletic groups. These people thenuse ``holophyletic'' to describe what are usually called monophyleticgroups. It's tempting in the face of this ambiguity just to abandonthe word ``monophyletic'' and use a holophyletic/paraphyleticdichotomy, but this terminological abuse is probably not widespreadenough to merit such extreme measures. It's just something to be onthe watch for.

Because clades are so important, there is common notation forspecifying them (taken from the Phylocode: see note 9.4.1 inhttp://www.ohiou.edu/phylocode/art9.html).

• Clade(A+B) is anode-based definitionmeaning ``the most recent common ancestor of A and B, togetherwith all its descendents'', or equivalently, ``the leastinclusive clade containing A and B''.This may be extended to forms such as Clade(A+B+C),Clade(A+B+C+D),etc., in the obvious way.

  For example, Neosauropoda is defined asClade(Saltasaurus +Diplodocus), that is, themost recent common ancestor ofSaltasaurus andDiplodocus together with all its descendants. AndEutitanosauria, the ``true titanosaurs'' can be defined asClade(Saltasaurus +Argyrosaurus +Lirainosaurus).

• Clade(A<--B) is astem-based definitionmeaning ``A together with everything that shares a more recentcommon ancestor with A than with B''.This too may be extended into forms such as Clade(A<--B, C)

  For example, Coelurosauria is often defined asClade(Neornithes <--Allosaurus),that is, modern birds and everything sharing a more recentcommon ancestor with them than withAllosaurus.And Eusauropoda, the group of ``true sauropods'', is definedessentially by listing a lot of taxa that arenot includedin it, as Clade(Saltasaurus <--Barapasaurus,Ohmdenosaurus,Vulcanodon,Zizhongosaurus).

  Stem-based clades are useful for neatly partitioning anode-based clade. For example, within the Avetheropoda,which is defined as Clade(Neornithes +Allosaurus), thetwo subgroups are the Carnosauria, defined asClade(Allosaurus <-- Neornithes), and theCoelurosauria, defined as its complement: Clade(Neornithes<--Allosaurus).

• Clade(X in A) is anapomorphy-based definitionmeaning ``the first species to possess character Xsynapomorphic with that in A, together with all itsdecendants.''

  Whatever the hell that means.

These notations are not standard in formal technical literature, butappear frequently on the Dinosaur Mailing List.

It's unfortunate that this notation is so clumsy. The following,more concise, alternative notation is sometimes used (notably in MikeKeesey's admirableDinosauricon):

• {A+B} is equivalent to Clade(A+B)
• {A>B} is equivalent to Clade(A<--B).(Yes, the arrow points in the opposite direction. That's atragedy, but we seem to be stuck with it.)
• There's no way to indicate apomorphy-based definitions, butthat's OK because no-one ever uses these anyway.
• {A-B} can be used, in the absence of the prejuducial word``Clade'' in the notation, to indicate the paraphyletic groupformed by removing the clade B from the enclosing clade A.Mildly naughty, but pragmatic.

As examples of this last, we might describe the informal grouping``non-avian dinosaurs'' as {Dinosauria-Aves}, and the ``traditionalreptiles'' as {Reptilia-Aves}.