I was recently at the State Zoology Museum of Munich, studying their amazing plethora of orangutan bones. Jaw bones are especially useful skeletal remains when you study growth, because different teeth come in at different points in one’s life. Remember when your 1st permanent molar teeth came in? You were probably 5 or 6 years old at the time. It was a big deal, your first permanent teeth! What about your 4th permanent molars, after your wisdom teeth, remember those?
|An adult male orangutan mandible, with bilateral supernumerary molars. Or more simply, “an extra molar on both sides of the jaw.”
I hope not. As a good eutherian
, you should never have more than 3 molars in each half of each jaw. And as a modern human, there’s a good chance you’ve only got 2 in each half (but that’s a whole other story). So when I was looking at orangutan skulls to get an idea of individuals’ ages, I was shocked to find specimen after specimen with at least one extra molar. So far as I could tell, 27 out of 181 (14.9%) adult orangutans in this collection had extra molars.
Supernumerary (fancy word for “extra”) molars manifest a number of ways in this collection. Sometimes there’s only one extra tooth. Sometimes there are extra teeth in both upper and lower jaws but only on one side. Sometimes there’s a full set (4). Et cetera. One poor bastard even had a 5th molar lurking behind one of his four 4ths! Deplorable.
|An adult male with a fairly normal 4th (blue arrow) and even a weird, unerupted 5th (red arrow) molar. Gross!
This is rather strange, such a regular occurrence of supernumerary teeth – what gives? A starting clue is the fact that all specimens with extra molars are of the species Pongo pygmaeus from Borneo
(173 of 181 specimens). The remaining eight specimens, with a normal dental formula
, are Pongo abelii
from the island of Sumatra
. But how much of this difference in frequency is due to the fact we’re looking at 181 Bornean, vs. only eight Sumatran orangutans?
Resampling to the rescue! Is it weird that 27/181 (15%) Bornean orangutans have extra teeth, while 0/8 Sumatran orangs do not? Another way to ask the question is, what are the chances of sampling 8 Bornean orangs, none of which have extra molars
? This is very easy to program and test in R
Set up a vector (basically, a string of numbers) to represent your Bornean orangs, each entry representing an individual, assigning “0” for no extra teeth and “1” for at least one (this admittedly oversimplifies the nature of extra teeth). Then simply randomly sample – lots and lots of times – eight individuals from this Bornean vector, to see how often you get a set in which 0/8 have extra molars.
|“b” is our vector of Bornean orangutans, consisting of 0s and 1s for whether there are extra teeth. “n” tells us how many individuals had extra teeth in that subsample. The “(i in 1:10000)” means for each of 10,000 resamplings.
Following this resampling procedure, there’s about a 25.5% chance that none of them will have extra molars. That means the remaining 74.5% of the time, a random subsample of the Bornean orangutans will contain at least one individual with at least one extra tooth.
A number of interesting questions arise from this – if we were to examine more Sumatran orangutans, would we eventually find one with an extra molar? After all, the 25.5% chance of sampling 0/8 suggests maybe we just missed some Sumatrans with extra molars. Regardless, within the Bornean orangs, why is the frequency so high? Does one pattern of extra teeth (say, just in the lower jaw, or on both sides, etc.) predominate? Are there differences between the sexes? These are questions for another day….