Optimal Sizes of Dendritic and Axonal Arbors

I consider a topographic projection between two neuronal layers with different densities of neurons. Given the number of output neurons connected 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 summarized 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 morphology and connectivity are known. The rule may be used to infer connectivity of neurons from their morphology.