Mathematical conditions which showed where parsimony was not consistent for four taxa were first introduced by Felsenstein in 1978. This was subsequently labelled the "Felsenstein zone". Following Felsenstein's findings, 'frequentists' conjectured that for five taxa there would also be a region in parameter space where parsimony is not consistent. In response, 'cladists' claimed that parsimony was consistent in a different region of parameter space, which is called the "Farris zone". However, no analytical description of the region in which this consistency occurs has been made. Furthermore, no mathematical extensions of this Felsenstein theory to five taxa or more has been made. The same is true for the Farris zone. In this thesis, we give a complete account for the Felsenstein zone and Farris zone for four and five taxa and interpret these in terms of the shape of the phylogenetic tree.