First, I need to admit that I am not a taxonomist nor a taxidermist, even of my back yard, and that my continuums of evolutionary taxonomy across geological time are also neither linear nor complete. I have ceased the independent trick of concocted Latin. I believe that taxonomic terminology attempts a description of increasingly accurate yet fragmented descriptions of evolutionary pathways.
Archaeopteryx is theorized to be a very important arcane speciation from a herpetological lineage which at the point of said speciation diverged into archaeopteryx; the first species of the class Aves.
The Caduceus, with wings perhaps of Icarus or Daedalus, depicts a brood of serpents upon the staff of AEsculphius.