the number of neurons be much larger than the number of independently fluctuating fields. If the relevant fields are generated by retinal neurons that provide input to the ganglion cells, then changing the effective dimensionality of the stimulus—from full field flicker to natural movies to random checkerboards—would change the number of effective fields, and at one extreme this number is comparable to or larger than the number of neurons from which we record. Nonetheless we see near–critical behavior in all these cases. It is also not clear how such models with fluctuating fields would explain the fact that networks with slightly stronger or weaker correlations among neurons both deviate from criticality (Fig \[alpha\_fig\]).

The evidence for criticality that we find in the analysis of 160 neurons is consistent with extrapolations from the analysis of smaller populations under similar conditions [@tkacik+al_06; @tkacik+al_09]. The basis for those predictions was the assumption that the smaller populations were typical of the larger one, i.e. that the spike probabilities and pairwise correlations that we could observe were drawn from the same distribution as in the full system, and that these distributions (rather than the detailed structure of the correlation matrix, for example) were sufficient to 