Perhaps the most obvious way to show relations between animals (besides the brute-force method of manually punching them in) would be to do what is done in real life: Taxonomically categorize animals from broad categorical kingdoms down to narrow and specific genus and species.
While it would probably be overkill to go for the full Kingdom, Phyllum, Class, etc, however, having four or five layers of categories added onto the raws of every creature would not be unreasonable. A very broad class distinguishing "natural animals" from something more exotic like "living magical rock creature" is a more meaningful distinction than the distinction between different types of lizard. Comparably, a combined family/genus type of category would be useful in putting brown bears and black bears and polar bears together while only having to add the number of tokens as you have layers of taxa per creature.
The side-positives of this sort of system would be that it could work well with future changes to the creature system, such as if you wanted to make part of the sphere/god/magic system that relates to specific creatures work by having relationships between specific types of animals. It could also help ease in notions of "breeds", such as having the capability to cross-breed horses and donkeys (or maybe wolf and dog or even dingo). It would also work well with regards to
something like the alchemical properties of the materials of an animal to have taxa for their creature type for algorithmic association of chemical properties to specific taxa.
Finally, it could be useful in the creation of a full-scale procedural generation of creatures to simply have a "family tree" of "real" animals, while the game just populated the holes with new creatures.
The negative side of this, however, is that taxonomy obviously does not denote behavior. When trying to train behavior, in some ways, a spider has more in common with a crocodile than it does with an ant, even if ants are closer neighbors as fellow invertebrates.