  Neurons in the primary visual cortex are more or less selective for the
orientation of a light bar used for stimulation. A broad distribution of
individual grades of orientation selectivity has in fact been reported in all
species. A possible reason for emergence of broad distributions is the
recurrent network within which the stimulus is being processed. Here we compute
the distribution of orientation selectivity in randomly connected model
networks that are equipped with different spatial patterns of connectivity. We
show that, for a wide variety of connectivity patterns, a linear theory based
on firing rates accurately approximates the outcome of direct numerical
simulations of networks of spiking neurons. Distance dependent connectivity in
networks with a more biologically realistic structure does not compromise our
linear analysis, as long as the linearized dynamics, and hence the uniform
asynchronous irregular activity state, remain stable. We conclude that linear
mechanisms of stimulus processing are indeed responsible for the emergence of
orientation selectivity and its distribution in recurrent networks with
functionally heterogeneous synaptic connectivity.
