By Ward C. Wheeler
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Hexapods (including insects), myriapods (centipedes, millipedes, and kin), and crustaceans exhibit sensory antennae. Those of Crustacea may be biramous (two branches as opposed to one; Fig. 4). 4: Biramous crustacean antennae of Daphnia. 25 26 Fundamental Concepts could be coded in an additive fashion with state 0 = absence of antennae; 1 = presence of antennae; and 2 = presence of biramous antennae. Since biramous antennae are treated as a special case of the more general (uniramous) antennae and logically cannot occur independently of antennae, the character can be linearly ordered and transformations treated as additive.
Simple graphs forbid parallel edges and loops. These are the sorts of graphs we will deal with here. By convention, edges are referred to by their incident vertices [(u, v) ∀eu,v ∈ E]. The degree of a vertex is the number of edges incident upon it. In Fig. 8, vertex v1 has degree 2. Directed graphs can specify in-degree and out-degree edges, their sum being the degree. Vertex v3 (Fig. 8 left) has in-degree 1 and out-degree 2. It is possible to have a vertex that is unconnected to any other vertex, hence with degree 0.
De minimus, a taxon must consist of at least two creatures. Some, however, would limit the minimal taxon to be a “species” however defined, not allowing subspecific distinctions. 2 Taxa 27 advocated using individual specimens as terminals on trees. The term “terminal entities” was used specifically to avoid referring to a single creature as a taxon. Any other group, however, could be. Since all groups (size > 1) are arbitrary in their level (although “real” in the sense of monophyly), “higher taxa” are arbitrary.