Subtitle: A Curious Case of Batesian Mimicry. During late August in Arkansas it is often possible to glimpse a black-bodied insect darting through the tree tops. Looking closer, the dorsal side of the hind wings reflects a blue-green hue. You might naturally wonder, what species is that? On the running trail: https://0x0.st/z4Wy.JPG On U of A campus: https://0x0.st/z4Wt.JPG Or At Devil's Den State Park: https://0x0.st/z4Wv.JPG https://0x0.st/z4Ww.JPG It could easily be confused for a swallowtail, either pipevine or spicebush, when in fact the creature is from family Nymphalidae rather than Papilionidae. During a flight, it is impossible to closely observe the fore-wing venation, so humans nor birds can be blamed for falling fool to an effective mimic (at least at first). Even upon a closer look at the ventral side, the poorly-named red-spoted purple admiral ( why not orange-spotted blue? ) appears very similar to the pipevine swallowtail. Both butterflies have seven orange ocelli along the border of the hind wing. The ocelli are homologous under biological definitions, but they certainly are not mathematical homologs. Compare data: https://www.butterfliesandmoths.org/species/Battus-philenor https://www.butterfliesandmoths.org/species/Limenitis-arthemis Roughly speaking, if evolution acts as an anatomical homotopy, then two organisms along separate branches of a family tree should end up biological homologs. With Batesian mimicry, survival depends on homology, because predators need to see similar biological features to confuse a palatable species (here arthemis) with an unpalatable species (here philenor). However, biological homology is a looser concept than mathematical homology, and it is very possible that evolution introduces additional structures that disrupt mathematical homology. Comparing arthemis and philenor, the idea of a common ancestor is easy to accept. As it so happens, evolution has produced mathematically distinct ocelli. With arthemis, the eyespots are usually sole orange disks, each possibly connected to another black disk. Philenor has more complicated geometry involving an orange disk with black and white surroundings. To characterize the homology of two typical patterns for Philenor eyespots, I made the following disk-edge-vertex decomposition graphs: https://0x0.st/z4WA.png A next step would be to collect lots of data and measure area of disks, length of edges, and angles around each vertex. This would associate each graph vertex to a metric, thus would give a decent idea as to what an average philenor eyespot looks like. Of course, the same could be done for Arthemis. It would be an interesting exercise of bio-statistics to compare the orange-disk area metric between species. It looks that Arthemis has smaller spots, but survival of the species implies that the spots are not too small to ruin the mimicry effect. Another interesting question: is there a tolerance limit for pattern agreement, which bounds the ability of one species to effectively mimic another? Cheers --Brad