In the above figure, the number of clades possible for species A-H is as follows:
The relationship between a taxonomic group and a phylogenetic tree or cladogram is important for phylogenetic systematics. There can be three types of relationships:
• A taxon is monophyletic if it includes the most recent common ancestor of the group and all descendants of that ancestor.
• A taxon is paraphyletic if it includes the most recent common ancestor of all members of a group and some but not all descendants of that ancestor.
• A taxon is polyphyletic if it does not include the most recent common ancestor of all members of a group; this condition requires that the group has had at least two separate evolutionary origins, usually requiring independent evolutionary acquisition of similar features.
Both evolutionary and cladistic taxonomy accept monophyletic groups and reject polyphyletic groups.
In Evolutionary taxonomy, taxa may be either monophyletic or paraphyletic. Recognition of paraphyletic taxa requires that this taxonomy distort patterns of common descent.
In this diagram we see that the recognition of the families Pongidae and Hominidae distort the relationships between the three families to emphasize the uniqueness of the group Hominidae.
In cladistic taxonomy, all taxa must be monophyletic.
Taking the same example, as the most recent common ancestor of the paraphyletic family Pongidae is also an ancestor of the Hominidae, recognition of this family Pongidae is incompatible with cladistic taxonomy.
A cladogram is the nested hierarchy of clades, while the phylogenetic tree gives more correct and accurate information of the species.
The cladogram is constructed by using only synapomorphies among the species. The branches of a cladogram are only a formal device for indicating the nested hierarchy of clades within clades. A phylogenetic tree has more information than a cladogram. It is much more specific. Its branches represent real lineages that occurred in the evolutionary past.
The additional information needed to obtain a phylogenetic tree is important additional interpretations concerning ancestors, the durations of evolutionary lineages or the amount of evolutionary change that occurred on the lineages.