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We examine how the prior probability distribution of a sensory variable inthe environment influences the optimal allocation of neurons and spikes in apopulation that represents that variable. We start with a conventional responsemodel, in which the spikes of each neuron are drawn from a Poisson distributionwith a mean rate governed by an associated tuning curve. For this model, weapproximate the Fisher information in terms of the density and amplitude of thetuning curves, under the assumption that tuning width varies inversely withcell density. We consider a family of objective functions based on the expectedvalue, over the sensory prior, of a functional of the Fisher information. Thisfamily includes lower bounds on mutual information and perceptualdiscriminability as special cases. For all cases, we obtain a closed formexpression for the optimum, in which the density and gain of the cells in thepopulation are power law functions of the stimulus prior. Thus, the allocationof these resources is uniquely specified by the prior. Since perceptualdiscriminability may be expressed directly in terms of the Fisher information,it too will be a power law function of the prior. We show that these resultshold for tuning curves of arbitrary shape and correlated neuronal variability.This framework thus provides direct and experimentally testable predictionsregarding the relationship between sensory priors, tuning properties of neuralrepresentations, and perceptual discriminability.

Implicit embedding of prior probabilities in optimally efficient neural populations