On the control of tooth replacement in reptiles and its relationship to growth

The teeth of nearly all non-mammalian vertebrates are replaced in waves which sweep through alternate tooth positions. It is argued that tooth replacement in these animals represents growth of the dentition. It is shown that the pattern of tooth replacement could be described by the exponential equation t_(n)r, = k e^ar+bn when t(n)r is the time at which the rth replacement erupts in the nth position and k, a and b are constants. The length of a replacement wave (w) which is visible in the mouth, can be calculated from the equation w = 2(a?b)/a?2b for forward travelling waves. The effect of different ratios, $\text{a}\text{b}$, on wavelength is described. The model can be interpreted as describing the effect of a zone of inhibition which (it is argued) temporarily surrounds any newly initiated tooth. The increasing time required to dissipate the inhibition around successive replacement teeth is related to the age of the animal. This increasing time permits successive teeth to grow for longer periods than their predecessors and can account for a gradual increase in the size of successive teeth. A similar mechanism could account for the phasic nature of bone growth. It is indicated that the model could be difficult to test.