Phylogenetic tree-building. 
Cladistic analysis is an approach to phylogeny reconstruction that groups taxa in such a way that those with historically more-recent ancestors form groups nested within groups of taxa with more-distant ancestors.  This nested set of taxa can be represented as a branching diagram or tree (a cladogram), which is an hypothesis of the evolutionary history of the taxa.  The analysis is performed by searching for nested groups of shared derived character states.  These shared derived character states define monophyletic groups of taxa (clades), which include all of the descendants of the most recent common ancestor.  If all of the characters for a set of taxa are congruent, then reconstructing the phylogenetic tree is unproblematic.  However, most real data sets contain incongruent characters, and consequently a wide range of tree-building methods has been developed.  These methods differ in a variety of characteristics, and they may produce topologically distinct trees for a single data set.  None of the currently-available methods are simultaneously efficient, powerful, consistent and robust, and thus there is no single ideal method.  However, many of them appear to perform well under a wide range of conditions, with the exception of the UPGMA method and the Invariants method.