Modeling the distance between the molar tooth rows in mammals

The sum of all possible bite forces along a mammalian tooth row is related to the area under the curve when bite force is plotted from one end of the tooth row to the other. Integrating the equation of this plot and dividing by the length of the entire jaw, from joint to incisor, gives the average bite force along the entire jaw (as opposed to along the tooth row). Calculations indicate that for any jaw shape there is only one location for the tooth row relative to the midline of the skull, where the average bite force is maximized; the average force is lower when the tooth row is closer to, or farther from, the midline. In addition, for animals with long narrow jaws, the location where this maximum is realized is relatively closer to the midline than it is for animals with short wide jaws. In many mammals, the distance between the jaw joints (jaw width) often varies between 60 and 80% of the distance from the jaw joints to the incisor (jaw length) in narrow and wide jaws, respectively. Length is measured perpendicular to the resultant force of the jaw muscles. Accepting that average bite force will be maximized, the model predicts that in the longer, narrower jaws the distance between the two molar rows will be approximately half the width of the jaw (and will approach 60% in the shorter, wider jaws).