This figure is taken from our paper on place-cell reconstruction (J. Neurophysiol., 1998). It shows that the accuracy of a variable encoded by the activity of a population of coarsely tuned neurons depends on the dimension D of this variable. For example, orientation tuning in V1 at a fixed spatial location is one-dimensional, while a place field or a visual receptive field is two-dimensional. It is rather counterintuitive that no matter what's the size of the place fields, the accuracy of the position encoded in the whole population of cells is exactly the same.
Initially, our analysis assumed Gaussian tuning functions and Poisson spike statistics. As it turns out, this tuning law is very general: The accuracy of population coding by tuned neurons as a function of tuning width follows the same power law regardless of the exact shape of the tuning function and the exact probability distribution of spikes. Sharpening the tuning width can increase (D=1), decrease (D=3 or D>3), or not change (D=2) the coding accuracy per neuron, depending on the dimension D of the encoded variable. This tuning law holds true even when exist weak correlated noises exist among neurons. The general results and mathematical proofs will be published in Neural Computation (manuscript available online).