their traits, and contain fossil members that lived before the last common ancestors of the living groups or, like the mammal Haldanodon, were not descended from that ancestor although they lived later. Crown-Aves and Crown-Mammalia therefore differ slightly in content from the common definition of Aves and Mammalia. This has caused some confusion in the literature. Other groups under the crown group concept The cladistic idea of strictly using the topology of the phylogenetic tree to define groups necessitates other definitions than crown groups to adequately define commonly discussed fossil groups. Thus, a host of prefixes have been defined to describe various branches of the phylogenetic tree relative to extant organisms. Pan-group A pan-group or total group is the crown group and all organisms more closely related to it than to any other extant organisms. In a tree analogy, it is the crown group and all branches back to (but not including) the split with the closest branch to have living members. The Pan-Aves thus contain the living birds and all (fossil) organisms more closely related to birds than to crocodilians (their closest living relatives). The phylogenetic lineage leading back from Neornithes to the point where it merges with the crocodilian lineage, along with all side branches, constitutes pan-birds. In addition to non-crown group primitive birds like Archaeopteryx, Hesperornis and Confuciusornis, therefore, pan-group birds would include all dinosaurs and pterosaurs as well as an assortment of non-crocodilian animals like Marasuchus. Pan-Mammalia consists of all mammals and their fossil ancestors back to the phylogenetic split from the remaining amniotes (the Sauropsida). Pan-Mammalia is thus an alternative name for Synapsida. Stem groups A stem group is a paraphyletic assemblage composed of the members of a pan-group or total group, above, minus the crown group itself (and therefore minus all living members of the pan-group). This leaves primitive relatives of the crown groups, back along the phylogenetic line to (but not including) the last common ancestor of the crown group and their nearest living relatives. It follows from the definition that all members of a stem group are extinct. The "stem group" is the most used and most important of the concepts linked to crown groups, as it offers a means to reify and name paraphyletic assemblages of fossils that otherwise do not fit into systematics based on living organisms. While often attributed to Jefferies (1979), Willmann (2003) traced the origin of the