It is now well established both theoretically and, more recently, experimentally, that steady-state spatial chemical concentration patterns can be formed by a number of specific reaction–diffusion systems. Reaction–diffusion models have been widely applied to biological pattern formation problems. Here we propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator, Alligator mississippiensis, which, from a reaction–diffusion theory, introduces, among other things, a new element, namely the effect of domain growth on dynamic spatial pattern formation. Detailed embryological studies by Westergaard and Ferguson (B. Westergaard and M. W. J. Ferguson, J. Zool. Lond., 1986, 210, 575; 1987, 212, 191; Am. J. Anatomy, 1990, 187, 393) show that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. Based on biological data we develop a reaction–diffusion mechanism, which crucially includes domain growth. The model can reproduce the spatial pattern development of the first seven teeth primordia in the lower half jaw of A. mississippiensis. The results for the precise spatio temporal sequence compare well with detailed developmental experiments.