The retina provides an excellent system for understanding the trade-offs that influence distributed information processing across multiple neuron types. We focus here on the problem faced by the visual system of allocating a limited number neurons to encode different visual features at different spatial locations. The retina needs to solve three competing goals: 1) encode different visual features, 2) maximize spatial resolution for each feature, and 3) maximize accuracy with which each feature is encoded at each location. There is no current understanding of how these goals are optimized together. While information theory provides a platform for theoretically solving these problems, evaluating information provided by the responses of large neuronal arrays is in general challenging. Here we present a solution to this problem in the case where multi-dimensional stimuli can be decomposed into approximately independent components that are subsequently coupled by neural responses. Using this approach we quantify information transmission by multiple overlapping retinal ganglion cell mosaics. In the retina, translation invariance of input signals makes it possible to use Fourier basis as a set of independent components. The results reveal a transition where one high-density mosaic becomes less informative than two or more overlapping lower-density mosaics. The results explain differences in the fractions of multiple cell types, predict the existence of new retinal ganglion cell subtypes, relative distribution of neurons among cell types and differences in their nonlinear and dynamical response properties.
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