The term was coined to apply to well-known taxa like Reptilia (reptiles) which, as commonly named and traditionally defined, is paraphyletic with respect to mammals and birds. Reptilia contains the last common ancestor of reptiles and all descendants of that ancestor, including all extant reptiles as well as the extinct synapsids, except for mammals and birds. Other commonly recognized paraphyletic groups include fish, monkeys, and lizards.
Groups that include all the descendants of a common ancestor are said to be monophyletic. A paraphyletic group is a monophyletic group from which one or more subsidiary clades (monophyletic groups) are excluded to form a separate group. Ereshefsky has argued that paraphyletic taxa are the result of anagenesis in the excluded group or groups.
Paraphyletic groupings are considered problematic by many taxonomists, as it is not possible to talk precisely about their phylogenetic relationships, their characteristic traits and literal extinction. Related terminology that may be encountered are stem group, chronospecies, budding cladogenesis, anagenesis, or 'grade' groupings. Paraphyletic groups are often a relic from previous erroneous assessments about phylogenic relationships, or from before the rise of cladistics.
The prokaryotes (single-celled life forms without cell nuclei), because they exclude the eukaryotes, a descendant group. Bacteria and Archaea are prokaryotes, but archaea and eukaryotes share a common ancestor that is not ancestral to the bacteria. The prokaryote/eukaryote distinction was proposed by Edouard Chatton in 1937 and was generally accepted after being adopted by Roger Stanier and C.B. van Niel in 1962. The botanical code (the ICBN, now the ICN) abandoned consideration of bacterial nomenclature in 1975; currently, prokaryotic nomenclature is regulated under the ICNB with a starting date of 1 January 1980 (in contrast to a 1753 start date under the ICBN/ICN).
Among animals, several familiar groups are not, in fact, clades. The order Artiodactyla (even-toed ungulates) is paraphyletic because it excludes Cetaceans (whales, dolphins, etc.). In the ICZN Code, the two taxa are orders of equal rank. Molecular studies, however, have shown that the Cetacea descend from artiodactyl ancestors, although the precise phylogeny within the order remains uncertain. Without the Cetacean descendants the Artiodactyls must be paraphyletic. The class Reptilia as traditionally defined is paraphyletic because it excludes birds (class Aves) and mammals. In the ICZN Code, the three taxa are classes of equal rank. However, mammals hail from the synapsids (which were once described as "mammal-like reptiles") and birds are descended from the dinosaurs (a group of Diapsida), both of which are reptiles. Alternatively, reptiles are paraphyletic because they gave rise to (only) birds. Birds and reptiles together make Sauropsids. Osteichthyes, bony fish, are paraphyletic when they include only Actinopterygii (ray-finned fish) and Sarcopterygii (lungfish, etc.), excluding tetrapods; more recently, Osteichthyes is treated as a clade, including the tetrapods. The wasps are paraphyletic, consisting of the narrow-waisted Apocrita without the ants and bees. The sawflies (Symphyta) are similarly paraphyletic, forming all of the Hymenoptera except for the Apocrita, a clade deep within the sawfly tree. Crustaceans are not a clade because the Hexapoda (insects) are excluded. The modern clade that spans all of them is the Tetraconata.
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 descendant group. The prokaryote group is another example; it is paraphyletic because it excludes many of its descendant organisms (the eukaryotes), but it is very useful because it has a clearly defined and significant distinction (absence of a cell nucleus, a plesiomorphy) from its excluded descendants.
Independently-developed traits like these cannot be used to distinguish paraphyletic groups because 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. Because this group is monophyletic, it contains all descendants of the pelycosaurs; because it is excluded, it contains no viviparous animals. This does not work, because humans are among these descendants. Vivipary in a group that includes humans and skinks cannot be paraphyletic.
The concept of paraphyly has also been applied to historical linguistics, where the methods of cladistics have found some utility in comparing languages. For instance, the Formosan languages form a paraphyletic group of the Austronesian languages because they consist of the nine branches of the Austronesian family that are not Malayo-Polynesian and are restricted to the island of Taiwan.