Neural spike rate data are more restricted in range than related psychophysical data. For example, several studies suggest a compressive (roughly cube root) nonlinear relationship between wavelength-opponent spike rates in primate midbrain and color appearance in humans, two rather widely separated domains. This presents an opportunity to partially bridge a chasm between these two domains and to probe the putative nonlinearity with other psychophysical data. Here neural wavelength-opponent data are used to create cortical competition models for hue opponency. This effort led to creation of useful models of spiking neuron winner-take-all (WTA) competition and MAX selection. When fed with actual primate data, the spiking WTA models generate reasonable wavelength-opponent spike rate behaviors. An average psychophysical observer for red-green and blue-yellow opponency is curated from eight applicable studies in the refereed and dissertation literatures, with cancellation data roughly every 10 nm in 18 subjects for yellow-blue opponency and 15 subjects for red-green opponency. A direct mapping between spiking neurons with broadband wavelength sensitivity and human psychophysical luminance yields a power law exponent of 0.27, similar to the cube root nonlinearity. Similarly, direct mapping between the WTA model opponent spike rates and psychophysical opponent data suggests power law relationships with exponents between 0.24 and 0.41.