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Below is a tweet thread where I will try my best to describe how I use the help of a dental formula to ID skulls belonging to groups of mammals. Many times the dental formula will ID to species level, other times, a number of species in a genus can share the same dental formula.
Learning your teeth and how to count them will goes far in oneās ability to ID skulls, even partial ones. I personally primarily use teeth to attempt skull ID, but of course there are other widely used distinguishing features across species in their skull shape.
Transparency: while my area of study is mammalogy and I have taken courses that teach basic skull ID, I am primarily self-taught simply out of interest. After a few solid years of personally (ethically) collecting and studying, Iāve become pretty experienced.
To continue being proficient, I have to continue looking at skulls, reading, being open to correction, and seeking opportunities to learn from others with much more experience than me. So this thread is just what I know and what I use when given a chance to ID a skull.
Also, Iām most knowledgeable in Texas mammal species. Iām not near as efficient in my ID in bird, herp, or some other groups of non-N.A mammal species. Just a big FYI! If I am incorrect on an ID, please let me know. 
Iām going to be using my personal skulls from my Texas natives collection for this thread. A lot of my early ones were not degreased in ammonia and I need to go back and do so to pull the stubborn areas that the dish soap method couldnāt! Also some are specimens = not degreased.
Letās talk teeth! Firstly in the formula are the incisors (i for ābabyā/deciduous teeth; I for āadultā/permanent teeth) used in cutting food items. These are located in the front of the mouth between the canines (c; C). I have the incisors of this raccoon outlined in blue.
Firstly in the formula are the incisors (i for ābabyā/deciduous teeth; I for āadultā/permanent teeth) used in cutting food items. These are located in the front of the mouth between the canines (c; C). I have the incisors of this raccoon outlined in blue.
Next are the canines, used in biting and tearing food. They are between the incisors and the premolars (p/Pm). I have outlined them in pink on the same raccoon. Incisors are colored blue. Some animals, such as rodents (N.A. beaver in the second and third pictures) lack canines.
Behind the canines are the premolars (outlined in orange in the raccoon) used in crushing and grinding food items. Premolars can vary greatly in number and shape across mammals. For example raccoons can have up to 16 total premolars, while N.A badgers have 12 (2nd photo).
Lastly are the molars (m; M), which can also vary considerably in number and shape. In our raccoon (highlighted in yellow), we have a total of 8 molars. Our badger (third photo) has 6 (2 on top/maxilla; 4 on bottom/mandible).
There are large exceptions to these general rules. An example: armadillos (nine-banded pictured), which lack incisors/canines and instead have uniform peg-like teeth in place of pre/molars known as cheek teeth. Pinnipeds (flippered marine mammals) have similar peg-like dentition.
Now that we know teeth, time to understand the formula. The formula is written as: I (# teeth on half of the ātop jawā/ # teeth on half bottom); C (half on top/half on bottom); Pm (half top/half bottom); M (half top/half bottom) x2 = n.
I split our raccoon skull into halves. The dental formula for this raccoon is I 3/3; C 1/1; Pm 4/4; M 2/2 x2 = 40 total teeth. The formula is written this way because not all species have the same number of teeth on both the maxilla and the mandible, like with our badger.
Here is our badger with a dental formula of I 3/3; C 1/1; Pm 3/3; M 1/2 x 2 = 34.
Bonus: Virginia opossum with a dental formula of I 5/4; C 1/1; Pm 3/3; M 4/4 x 2 = 50.
I hope this super long thread (Iām so sorry) was helpful! Also, I hope it encourages folx to include views of the teeth in photos to be used in ID requests! Here are some great views you can include in photos when requesting for ID (N.A. river otter pictured):
Here are some great views you can include in photos when requesting for ID (N.A. river otter pictured):
