Optimal sizes of dendritic and axonal arbors

I consider a topographic projection between two neuronal layers with dif-ferent densities of neurons. Given the number of output neurons con-nected to each input neuron (divergence or fan-out) and the number of input neurons synapsing on each output neuron (convergence or fan-in) I determine the widths of axonal and dendritic arbors which minimize the total volume ofaxons and dendrites. My analytical results can be sum-marized qualitatively in the following rule: neurons of the sparser layer should have arbors wider than those of the denser layer. This agrees with the anatomical data from retinal and cerebellar neurons whose morphol-ogy and connectivity are known. The rule may be used to infer connec-tivity of neurons from their morphology.