The vertebrate enteric nervous system is formed by a rostro-caudally directed invasion of the embryonic gastrointestinal mesenchyme by neural crest cells. Failure to complete this invasion results in the distal intestine lacking intrinsic neurons. This potentially fatal condition is called Hirschsprung's Disease. A mathematical model of cell invasion incorporating cell motility and proliferation of neural crest cells to a carrying capacity predicted invasion outcomes to imagined manipulations, and these manipulations were tested experimentally. Mathematical and experimental results agreed. The results show that the directional invasion is chiefly driven by neural crest cell proliferation. Moreover, this proliferation occurs in a small region at the wavefront of the invading population. These results provide an understanding of why many genes implicated in Hirschsprung's Disease influence neural crest population size. In addition, during in vivo development the underlying gut tissues are growing simultaneously as the neural crest cell invasion proceeds. The interactions between proliferation, motility and gut growth dictate whether or not complete colonization is successful. Mathematical modeling provides insights into the conditions required for complete colonization or a Hirschsprung's-like deficiency. Experimental evidence supports the hypotheses suggested by the modeling.