  We propose a theory for ocular dominance (OD) patterns in mammalian primary
visual cortex. This theory is based on the premise that OD pattern is an
adaptation to minimize the length of intra-cortical wiring. Thus we can
understand the existing OD patterns by solving a wire length minimization
problem. We divide all the neurons into two classes: left-eye dominated and
right-eye dominated. We find that segregation of neurons into monocular regions
reduces wire length if the number of connections with the neurons of the same
class differs from that with the other class. The shape of the regions depends
on the relative fraction of neurons in the two classes. If the numbers are
close we find that the optimal OD pattern consists of interdigitating stripes.
If one class is less numerous than the other, the optimal OD pattern consists
of patches of the first class neurons in the sea of the other class neurons. We
predict the transition from stripes to patches when the fraction of neurons
dominated by the ipsilateral eye is about 40%. This prediction agrees with the
data in macaque and Cebus monkeys. This theory can be applied to other binary
cortical systems.
