The semaphorontic view of homology.

The relation of homology is generally characterized as an identity relation, or alternatively as a correspondence relation, both of which are transitive. We use the example of the ontogenetic development and evolutionary origin of the gnathostome jaw to discuss identity and transitivity of the homology relation under the transformationist and emergentist paradigms respectively. Token identity and consequent transitivity of homology relations are shown to be requirements that are too strong to allow the origin of genuine evolutionary novelties. We consequently introduce the concept of compositional identity that is grounded in relations prevailing between parts (organs and organ systems) of a whole (organism). We recognize an ontogenetic identity of parts within a whole throughout the sequence of successive developmental stages of those parts: this is an intra-organismal character identity maintained throughout developmental trajectory. Correspondingly, we recognize a phylogenetic identity of homologous parts within two or more organisms of different species: this is an inter-species character identity maintained throughout evolutionary trajectory. These different dimensions of character identity--ontogenetic (through development) and phylogenetic (via shared evolutionary history)--break the transitivity of homology relations. Under the transformationist paradigm, the relation of homology reigns over the entire character (-state) transformation series, and thus encompasses the plesiomorphic as well as the apomorphic condition of form. In contrast, genuine evolutionary novelties originate not through transformation of ancestral characters (-states), but instead through deviating developmental trajectories that result in alternate characters. Under the emergentist paradigm, homology is thus synonymous with synapomorphy.