Uses for paraphyletic groups
When the appearance of significant traits has led a subclade on an evolutionary path very divergent from that of a more inclusive clade, it often makes sense to study the paraphyletic group that remains without considering the larger clade. For example, the Neogene evolution of the Artiodactyla (even-toed ungulates, like deer) has taken place in an environment so different from that of the Cetacea (whales, dolphins, and porpoises) that the Artiodactyla are often studied in isolation even though the cetaceans are a descendent group. The prokaryote group is another example; it is paraphyletic because it excludes many of its descendent organisms (the eukaryotes), but it is very useful because it has a clearly defined and significant distinction (no cell nucleus) from its excluded descendants.
Also, paraphyletic groups are involved in evolutionary transitions, the development of the first tetrapods from their ancestors for example. Any name given to these ancestors to distinguish them from tetrapods—"fish", for example—necessarily picks out a paraphyletic group, since the descendent tetrapods are not included.[15]
The term "evolutionary grade" is sometimes used for paraphyletic groups.[16]
Paraphyly cannot be based on independently evolved traits
Vivipary, the production of offspring without the involvement of a fertilized egg, developed independently in the lineages that led to humans (Homo sapiens) and southern water skinks (Eulampus tympanum, a kind of lizard). Put another way, at least one of the lineages that led to these species from their last common ancestor contains nonviviparous animals, the pelycosaurs ancestral to humans for example; vivipary appeared subsequently in the human lineage.
Independently-developed traits like these cannot be used to distinguish paraphyletic groups since paraphyly requires the excluded groups to be monophyletic. Pelycosaurs were descended from the last common ancestor of skinks and humans, so vivipary could be paraphyletic only if the pelycosaurs were part of an excluded monophyletic group. Since this group is monophyletic, it contains all descendents of the pelycosaurs; since it is excluded, it contains no viviparous animals. This doesn't work, since humans are among these descendents. Vivipary in a group that includes humans and skinks cannot be paraphyletic.
Though the last common ancestor of skinks and humans was not viviparous, this is not essential to the argument. The last common ancestor of porpoises and sharks, like these extant animals, probably had a dorsal fin on its back, but the Mesozoic ancestors of porpoises (a mammal group) did not have the fin, so it does not define a paraphyly. The presence of a trait in a last common ancestor is not sufficient for paraphyly.
Not Paraphyly
Amphibious fish are not a paraphyletic group because although they appear similar several different groups of amphibious fishes evolved independently, see Convergent evolution.
Flightless birds are also not paraphyletic because their flightless charasteristics evolved independently.
Quadrupedal archosaurs are not a paraphyletic group. Bipedal dinosaurs like Eoraptor, ancestral to quadrupedal ones, were descendents of the last common ancestor of quadrupedal dinosaurs and other quadrupedal archosaurs like the crocodilians.
