HVCRA axons with simple morphology increase the number of possible combinations of postsynaptic contacts. We made a simple model in which 400 out of a fixed population of 1,000 RA neurons are required to generate a segment of song. (The number and pattern of mathematical combinations will vary depending on what proportion of RA neurons are activated in order to produce a short segment of sound; our estimate of the proportion of RA neurons activated was intermediate between those of Leonardo and Fee, 2005, and Sober et al., 2008.) If each HVC axon contacts only a single RA neuron, then a very large number of sound combinations can be generated (1,000 choose 400; log value = 291). However, if a single HVC axon contacts four axons then the number of possible combinations drops sharply (1,000 choose 100; log value = 140). Thus, fewer axons with a limited branching pattern are required to activate different combination of RA neurons compared to axons with complex branching patterns. See text.