Just as synapomorphic features indicate common ancestry (monophyletic origin), the extent and distinctiveness of synapomorphies reflect proximity of relationship. The term "monophyletic" was long used to indicate descent from a common ancestor, but following Hennig (1966), mono-phyly now usually connotes not just single origin but also inclusion of all descendants from that ancestor (holophyly of Ashlock, 1971). Monophyletic groups or taxa are called clades. Groups believed to have evolved from more than one ancestor are referred to as polyphyletic and, once demonstrated, are rejected. Such was the case with the original concept of Edentata, which consisted of xenarthrans, pangolins, and aardvarks. Each is now known to constitute a distinct order with a separate origin. However, bats, pinnipeds, rodents, odontocetes, and Mammalia itself have all been claimed to be diphyletic or polyphyletic at some time during the past several decades, but recent analyses once again suggest that all are monophyletic.
The term paraphyletic is often applied to groups that are monophyletic in origin but do not include all descendants. Such groups lack unique synapomorphies. Some authors prefer to avoid paraphyletic taxa, or to enclose their names in quotation marks. That convention is not adopted here. Although at first glance elimination of paraphyletic groups would seem to streamline taxonomy, it may instead introduce new problems, including a highly cumbersome hierarchy and taxonomic instability. These problems arise in part because some taxa once thought to be paraphyletic, when better known, are now regarded as monophyletic, and vice versa. Some groups seem to be obviously paraphyletic (e.g., the current conception of condylarths, the stem group of many ungulate orders), but for many others, their status is less clear. For example, phenacodontid condylarths could be either the monophyletic sister taxon of perissodactyls and paenungulates or their paraphyletic stem group. Mesony-chia, for the last 30 years regarded as the paraphyletic stem group of Cetacea, is now considered by some to be a mono-phyletic side branch, as Cetacea appear to be more closely related to artiodactyls. Artiodactyla, long held to be one of the most stable monophyletic groups, could in fact be para-phyletic unless Cetacea are included. These examples highlight the uncertainty of identifying and verifying paraphyly even in the face of a good fossil record.
Carroll (1988: 13) concluded that as many as half of all species are paraphyletic and that "the existence of paraphyletic groups is an inevitable result of the process of evolution." In fact, it is often the paraphyletic taxa—especially those that gave rise to descendants that diverged sufficiently to be assigned to separate higher taxa—that are of greatest evolutionary interest. Undoubtedly we have only begun to recognize which taxa are paraphyletic. Consequently no attempt is made in this text to eliminate para-phyletic groups. Some, such as Condylarthra, Plesiadapi-formes, Miacoidea, and Palaeanodonta, are retained for convenience, and their probable paraphyletic nature noted, pending a better understanding of their relationships.
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