Accompanying the above intriguing illustration, John Wilkins has written a really good essay on the concept of homology, which we are taught (and go on to teach) as a really basic concept in evolution, but has surprising ambiguities and potential circularities (not unlike a few other evolutionary terms I can think of). John very helpfully traces some of the history of the term, and how its application has evolved as we've become better at building and testing phylogenies as hypotheses of evolutionary relationships. I have to agree with him when he says:
The notion of homology is complex, and as we recently saw when I asked about the use in mathematics, it has a slew of other meanings, but the one that seems to me to be consistent across all uses is this: a homology is a mapping or “agreement” of parts of organisms with other parts of organisms. A mapping relation is not a similarity, and it is not the explanation of the relation (such as evolutionary common ancestors, which are proposed to explain the homology). It is an identity relation: this is the same as that. The identity may be an identity of place, of sequence, of developmental process, or just of a shared name, but what it is not is similarity or common ancestry. Similarity may be how we identify homology (and what kinds of similarity depends on what we use), and common ancestry may be how we explain homology, but in both cases homology is the relation itself.You know you'll be reading the rest of that essay for sure if you are in my class the next time I teach Evolution!