>>Hypothetical taxon: frogs birds
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>>Is this a polyphyletic group, or is it paraphyletic?
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>>Thanks.

If this taxon consists only of frogs and birds, then it is considered polyphyletic by any systematist, whether he/she is a cladist, a pheneticist or a Darwinian.

The closest living relatives of frogs are salamanders and caecilians. Thus frogs, salamanders and caecilians have a nearest common ancestor that is different than the common ancestor of the birds and frogs. The closest living relatives of birds are the crocodilians, and of course birds are also more closely related to the reptiles and even the mammals than they are to the frogs. The common ancestor of the birds, mammals and reptiles is the common ancestor of the amniotes. The common ancestor of the frogs, salamanders and caecilians is the common ancestor of the lissamphibians.

Therefore a taxon consisting or birds and frogs only would consist of one group from the amniotes and one group from the lissamphibians. That taxon would of course be unambiguously polyphyletic, no ifs, ands, or buts about that.

The common ancestor of the frogs and birds is also the common ancestor of the tetrapods. If one removes frogs (a crown group) from the tetrapods and puts them in a new higher taxon, the remaining tetrapods (excluding frogs) is a basal group that lacks some of the crown groups. Such a group (i.e. the basal tetrapods) would be considered paraphyletic by the cladists. The Darwinians and pheneticists, however, do not make a distinction between paraphyletic and monophyletic groups. Therefore the basal tetrapods (excluding the frogs) would be considered monophyletic by Darwinians and pheneticists. If one then removes birds (also a crown group) from the remaining tetrapods and classify the birds as another higher taxon, then the remaining tetrapods (excluding frogs and birds) would again be paraphyletic according to the cladists but monophyletic according to the Darwinians. But if one lumps frogs and birds (2 different crown groups with different common ancestors) into a single taxon, the such a taxon would be polyphyletic according to the Darwinians, the cladists, or the pheneticists.

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