  The mammalian brain is a metabolically expensive device, and evolutionary
pressures have presumably driven it to make productive use of its resources.
For sensory areas, this concept has been expressed more formally as an
optimality principle: the brain maximizes the information that is encoded about
relevant sensory variables, given available resources. Here, we develop this
efficiency principle for encoding a sensory variable with a heterogeneous
population of noisy neurons, each responding to a particular range of values.
The accuracy with which the population represents any particular value depends
on the number of cells that respond to that value, their selectivity, and their
response levels. We derive the optimal solution for these parameters in closed
form, as a function of the probability of stimulus values encountered in the
environment. This optimal neural population also imposes limitations on the
ability of the organism to discriminate different values of the encoded
variable. As a result, we predict an explicit relationship between the
statistical properties of the environment, the allocation and selectivity of
neurons within populations, and perceptual discriminability. We test this
relationship for three visual and two auditory attributes, and find that it is
remarkably consistent with existing data.
