In phylogenetics, a group of organisms is said to be paraphyletic (Greek para = near and phyle = race) if the group contains its most recent common ancestor, but does not contain all the descendants of that ancestor.
Groups that do include all the descendants of the most recent common ancestor are commonly said to be monophyletic.
Sometimes the term holophyletic is used. Technically these two terms are not quite equivalent: originally a monophyletic group was simply one including the most recent common ancestor of its members (Greek monos = one) and would thus be either monophyletic or paraphyletic in the modern sense; while a holophyletic group included all descendants of the most recent common ancestor (Greek holos = whole), thus being monophyletic in the modern sense. However, in actual practice monophyletic has lost this original meaning and has displaced holophyletic which has mostly dropped out of use.
Technically, in the original meaning of the words, a paraphyletic group is a monophyletic group from which one of the clades is excluded to form a separate group (as in the paradigmatic example of reptiles and birds, shown in the picture). A paraphyletic group can be fixed either by expanding it, and including the missing clade, or by splitting it into its component parts.
A group which does not contain the most recent common ancestor of its members is said to be polyphyletic (Greek polys = many).
These formulations were developed during the debates of the 1960s and 70s accompanying the rise of cladistics (a clade is a term for a monophyletic group). Before that period the distinction between mono- and polyphyletic groups was based on the inclusion or exclusion of the most recent common ancestor. It was shown, however, that the inclusion of ancestors in the classification leads to unavoidable logical inconsistencies, and, in some schools of taxonomy, the phylogenetic pattern is described exclusively in terms of nested patterns of the sister group relationships between the known representatives of taxa without referring to the ancestor-descendant relationships.
Many of the older classifications contain paraphyletic groups, especially the traditional 2–6 kingdom systems and the classic division of the vertebrates. For example, the class Reptilia as traditionally defined is paraphyletic because that class excludes birds (class Aves), which are descended from reptiles. Paraphyletic groups are often erected on the basis of (sym)-plesiomorphies (ancestral similarities) instead of (syn)apomorphies (derived similarities).
In most cladistics-based schools of taxonomy, the existence of paraphyletic groups in a classification is regarded as an error. Some groups in currently-accepted taxonomies may later turn out to be paraphyletic, in which case the classifications may be revised to eliminate them. Some, however, feel that having paraphyletic groups is an acceptable sacrifice if it makes the taxonomy more understandable. Others argue that paraphyletic groups are necessary for a comprehensive classification including extinct groups, since each species, genus, and so forth necessarily originates from part of another. It has been suggested that paraphyletic groups should be allowed, but clearly marked as such, for instance with asterisks: Reptilia*. The term "evolutionary grade" is sometimes used for such groups.