The highly ordered wiring of retinal ganglion cell (RGC) neurons in the eye to their synaptic targets in the superior colliculus of the midbrain has long served as the dominant experimental system for the analysis of topographic neural maps. Here we describe a quantitative model for the development of one arm of this map--the wiring of the nasal-temporal axis of the retina to the caudal-rostral axis of the superior colliculus. The model is based on RGC-RGC competition that is governed by comparisons of EphA receptor signalling intensity, which are made using ratios of, rather than absolute differences in, EphA signalling between RGCs. Molecular genetic experiments, exploiting a combinatorial series of EphA receptor knock-in and knockout mice, confirm the salient predictions of the model, and show that it both describes and predicts topographic mapping.