Figure 1. Cladistic relationships among three Great Apes depicted in the form of a tree or cladogram. The cladogram represents the hypothesis that the last common ancestor of humans and chimpanzees was more recent than the last common ancestor of humans, chimpanzees and gorillas. Thus humans and chimpanzees are cladistically more closely related to each other than to gorillas.

Figure 2. Incongruence between two simple characters, the presence or absence of halteres and of piercing mouths. For both characters absence is the plesiomorphic character state. As a potential synapomorphy, halteres provide evidence that the fruitfly and mosquito are more closely related to each other than either is to the aphid. This follows if halteres had a single origin in their common ancestor. As a potential synapomorphy, piercing mouths provide evidence that the mosquito and aphid are more closely related to each other than either is to the fruitfly. Both hypotheses of cladistic relationships cannot be true if there is only one true Tree of Life. Incongruence between the characters may be resolved either by more detailed study (which would reveal that the piecing mouthparts of mosquitoes and aphids are quite dissimilar and unlikely to be homologous) or through parsimony analysis in which other characters supporting the close relationship of the mosquito and fruitfly would outweigh the misleading and limited evidence provided by the superficial similarity in mouth parts.