Premolars in primates

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Different kinds of primates have different numbers of premolars in their dentitions. The ancestral number of premolars in primates is three in each quadrant of the jaw. From this ancestral number, the common ancestors of the Old World monkeys, apes and humans lost their most mesial premolars, the P2 and P2. That leaves us only two premolars where many primates have three.

The last common ancestor of the primates had three premolars in each quadrant. Four superfamilies, including lemuroids (lemurs), lorisoids (lorises and galagos), tarsioids (tarsiers) and ceboids (New World monkeys), still have members with the ancestral three premolars. Lemurs are variable today, as some species have lost one of the premolars. Hominoids (apes and humans) and cercopithecoids (Old World monkeys) evolved from a common ancestor that had also lost its premolars. These two superfamilies belong to the group called the Catarrhini, so that we are catarrhine primates as well as hominoids.

Additionally, the anatomy of the premolars can vary. Many catarrhines have lower P3 with a single, large cusp. Some of them have a cutting edge running from the cusp mesially (toward the front). This acts in a scissor-action against the upper canine, and is called a sectorial P3. In species with three premolars, many have a sectorial P2 instead.

At this station, there are some primates with different kinds of premolars. Is there any way of predicting which primates have three premolars in each quadrant? What determines whether the mandible has a sectorial P3?

The two incisors, one canine, two premolars and three molars on both top and bottom are called the human dental formula. We write a dental formula as follows:

2 1 2 3
2 1 2 3

What is the dental formula of primates who have three premolars in each quadrant?