Optimal design of photoreceptor mosaics: why we do not see color at night.

While color vision mediated by rod photoreceptors in dim light is possible (Kelber & Roth, 2006), most animals, including humans, do not see in color at night. This is because their retinas contain only a single class of rod photoreceptors. Many of these same animals have daylight color vision, mediated by multiple classes of cone photoreceptors. We develop a general formulation, based on Bayesian decision theory, to evaluate the efficacy of various retinal photoreceptor mosaics. The formulation evaluates each mosaic under the assumption that its output is processed to optimally estimate the image. It also explicitly takes into account the statistics of the environmental image ensemble. Using the general formulation, we consider the trade-off between monochromatic and dichromatic retinal designs as a function of overall illuminant intensity. We are able to demonstrate a set of assumptions under which the prevalent biological pattern represents optimal processing. These assumptions include an image ensemble characterized by high correlations between image intensities at nearby locations, as well as high correlations between intensities in different wavelength bands. They also include a constraint on receptor photopigment biophysics and/or the information carried by different wavelengths that produces an asymmetry in the signal-to-noise ratio of the output of different receptor classes. Our results thus provide an optimality explanation for the evolution of color vision for daylight conditions and monochromatic vision for nighttime conditions. An additional result from our calculations is that regular spatial interleaving of two receptor classes in a dichromatic retina yields performance superior to that of a retina where receptors of the same class are clumped together.