ABSTRACT
This chapter discusses formal methods to find ancestral character state reconstructions for which the maximum possible number of similarities is traceable to common ancestry; this process is known as “optimization”. When it is not possible to simultaneously trace all similarities to common ancestry, the transformation costs between states must be considered. The transformation costs express the degree of difference between the states, with transformations between more different states being more costly. Consideration of these transformation costs is an unavoidable part of ancestral character state reconstruction. In all the cases discussed in this chapter, the problem of finding the globally optimal reconstruction can be decomposed into a series of local subproblems, examined during two passes to the tree. When all transformation costs are similar, the process can be simplified with Fitch optimization; in the case of lineal additive characters, Farris optimization simplifies the process. For more complex transformation costs (possibly including asymmetries in transformation costs), so-called step-matrix optimization can be used. Optimization is the most fundamental process in cladistic analysis; as it allows any tree to be evaluated, it forms the basis of all methods for selecting trees on the basis of parsimony. The implementation of all these methods in the computer program TNT is described and illustrated, as well as its use for producing diagnoses of groups or mapping characters on given trees.
