Neurons in the visual cortex respond preferentially to edge-like stimu
li of a particular orientation(1). It is a long-standing hypothesis th
at orientation selectivity arises during development through the activ
ity-dependent refinement of cortical circuitry(2-4). Unambiguous evide
nce far such a process has, however, remained elusive(5-7). Here we ar
gue that, if orientation preferences arise through activity-dependent
refinement of initially unselective patterns of synaptic connections,
this process should leave distinct signatures in the emerging spatial
pattern of preferred orientations. Preferred orientations typically ch
ange smoothly and progressively across the cortex(1). This smooth prog
ression is disrupted at the centres of so-called pinwheels(8,9), where
neurons exhibiting the whole range of orientation preferences are loc
ated in close vicinity(10). Assuming that orientation selectivity deve
lops through a set of rules that we do not specify, we demonstrate mat
hematically that the spatial density of pinwheels is rigidly constrain
ed by basic symmetry principles. In particular, the spatial density of
pinwheels, which emerge when orientation selectivity is first establi
shed, is larger than a model-independent minimal value. As a consequen
ce, lower densities, if observed in adult animals, are predicted to de
velop through the motion and annihilation of pinwheel pairs.