Topographic maps are the primary means of relaying spatial information in the brain. Understanding the mechanisms by which they form has been a goal of experimental and theoretical neuroscientists for decades. The projection of the retina to the superior colliculus (SC)/tectum has been an important model used to show that graded molecular cues and patterned retinal activity are required for topographic map formation. Additionally, interaxon competition has been suggested to play a role in topographic map formation; however, this view has been recently challenged. Here we present experimental and computational evidence demonstrating that interaxon competition for target space is necessary to establish topography. To test this hypothesis experimentally, we determined the nature of the retinocollicular projection in Math5 (Atoh7) mutant mice, which have severely reduced numbers of retinal ganglion cell inputs into the SC. We find that in these mice, retinal axons project to the anteromedialj portion of the SC where repulsion from ephrin-A ligands is minimized and where their attraction to the midline is maximized. This observation is consistent with the chemoaffinity model that relies on axon-axon competition as a mapping mechanism. We conclude that chemical labels plus neural activity cannot alone specify the retinocollicular projection; instead axon-axon competition is necessary to create a map. Finally, we present a mathematical model for topographic mapping that incorporates molecular labels, neural activity, and axon competition.