Meng et al. conjecture that pinwheel density scales with body and brain size. Our data, spanning a 40-fold range of body sizes in Laurasiatheria and Euarchonta, do not support this conclusion. The noncolumnar layout in Glires also appears size-insensitive. Thus, body and brain size may be understood as a constraint on the evolution of visual cortical circuitry, but not as a determining factor. W e presented a comparative study of visual cortical orientation columns and pinwheels in three mammalian species whose evolutionary paths separated more than 65 million years ago (1). For this purpose, we introduced methods to measure pinwheel density objectively-i.e., insensitive of image data preprocessing [(1) and supporting online material (SOM) of (1), pp. 3-12 and 29-41]. We found that statistical measures characterizing the spatial layout of pinwheels from the scale of individual hypercolumns to the entire primary visual cortex (V1) were virtually identical, agreeing with an accuracy of a few percent. To understand how distinct evolutionary lineages can independently evolve this common design, we examined a broad set of mathematical models for the developmental self-organization of orientation columns [(1) and SOM of (1), pp. 13-62]. We found that models from a symmetry-defined class, exhibiting a universal (i.e., model-independent) solution set, robustly predict every aspect of the common design when suppressive long-range interactions are dominant [(1) and SOM of (1), pp. 13-41)]. This suggests that developmental network self-organization has canalized the evolution of neuronal circuitry underlying orientation maps in these species into the common design. A predicted signature of this mechanism is a pinwheel density close to the mathematical constant p. Confirming this prediction, we found that mean pinwheel density was indeed statistically indistinguishable from p (T2%).Meng et al. claim that pinwheel density is not an invariant but a function of V1 size (2). They conjecture a pinwheel density scaling law that can be approximated by , and 450 mm 2 V1 size, respectively (3, 4), pinwheel density in cats (galagos) should be 53% (28%) larger than in ferrets/tupaias. Our methods to accurately estimate pinwheel density are well suited to test this prediction. Figure 1A presents measured pinwheel densities for the four species graphed against body weight. Pinwheel densities appear invariant with respect to body weight. The hypothesis that mean pinwheel density in cat (galago) is more than 50% (20%) larger than in ferrets can be rejected with virtual certainty [P < 0.0001(0.0001), bootstrap test]. Meng et al. suggest greater variation in pinwheel density across species; however, those data were derived from studies with small sample sizes using first-generation optical imaging methods that are subject to various systematic errors described in detail in [SOM of (1),. Our analysis unambiguously indicates that pinwheel density is a genuine invariant feature of orientation column layout over a wide range of V1 sizes and th...