Cladistics is a relatively recent method for uncovering the evolutionary relationships between living things, intended to provide explicit and testable hypotheses. Different possibilities are presented on trees called cladograms, as in the example
,--- Beetles | ---+ ,--- Wasps, bees, ants | | `---+ ,--- Butterflies, moths | | `---+ | `--- Flies
In a cladogram, all organisms lie at the endpoints, and each split is ideally binary. A correct cladogram would have all the organisms in each branch, or clade, share a common ancestor which they do not share with the other organisms on the diagram. Each clade should be set off by a series of characteristics that appear in its members but not in the forms it diverged off of, called synapomorphies. For instance hardened front wings are a synapomorphy of beetles.
Typically an analysis begins by collecting information on certain features of all the organisms in question, and then deciding which versions were present in their common ancestor (plesiomorphies) and which have been derived since (apomorphies). Usually this is done by considering some outgroup of organisms we know are not too closely related to any of the organisms in question. Only apomorphies are any use in characterising clades.
Next different possible cladograms are drawn up and evaluated. Clades are typically chosen to have as many synapomorphies as they can. The idea is that a sufficiently large number of characteristics should be large enough to overwhelm any examples of convergent evolution, and in practice neutral features like exact ultrastructure tend to do just that. When equivalent possibilties turn up they are usually selected from according to the principle of parsimony: the most compact arrangement is likely the best.
Cladistics has taken a while to settle in - a matter not helped by the variety of jargon used - and there is some questioning over in just what sort of circumstances cladistics is appliable. In particular, apomorphies are not always easy to distinguish and data is often unavailable thanks to a sparsity in available forms or lack of knowledge of characters, and these may invalidate cladograms. There is also concern that use of widely different data sets, for instance structural versus genetic characteristics, may produce widely different trees. However by and large cladistics has proven a useful and coherent extension of other methods and has gained general support.