How Cladistic Analysis Works
Cladistics begins by selecting a group of species, then analyzing characteristics shared by members of the group. In cladistics, the emphasis is on keeping all groups monophyletic and avoiding groups that are paraphyletic or polyphyletic.
A monophyletic group includes all the descendants of a common ancestor and no species that did not descend from that ancestor.
A paraphyletic group contains only some descendants of a common ancestor, while a polyphyletic group does not contain the common ancestor at all.
For example, "non-flying mammals" is paraphyletic because it does not include bats, which share a common ancestor with non-flying mammals. "Flying vertebrates" is polyphyletic because it does not include the LCA of vertebrates, which did not fly.
In order to ensure that all resulting groups are monophyletic, the characteristics used in a cladistic analysis are described relative to the group under study by the terms plesiomorphy, apomorphy, and synapomorphy. A plesiomorphy is a characteristic that arose before the group's last common ancestor (LCA), an apomorphy is one that arose after the LCA, and a synapomorphy is one that arose in the LCA. An apomorphy can be distinguished because it will be present in only some members of the group. Plesiomorphies and synapomorphies are present in all members of the group; they can be distinguished by comparing the group to other groups (outgroups). A plesiomorphy will be found in at least one outgroup, while a synapomorphy will not be present in any outgroup.
Once these determinations have been made, researchers can use computer software to generate a cladogram of the group under study.