This procedure was repeated 1,000 times to give an estimate of the null distribution (ρnull-modelρnull-model; see Figure S5B). The model correlation, ρmodelρmodel, was tested against the null distribution for significance (p = 0.05, Bonferroni corrected for M multiple comparison, where M is the number of significant spatial locations for each neuron). The model was considered to have significant predictive power for a neuron if there was at least one spatial location that was significant, according to the above criteria. We also

investigated two reduced versions of the pooling model (Figure S5C). The space-only version was obtained by averaging across orientation at each fine-grid location (Figure S5C, right upper panel). This model did not have any local orientation Dorsomorphin price tuning. The orientation-only version was obtained by subtracting the average orientation response (as in the space-only model) from the measured data at each fine-grid location (Figure S5C, right lower panel). Thus, this model did not contain any local spatial information. The model correlations and null distributions for these reduced models were calculated using the same procedure described above for the full model. The explained variance of our model was estimated by first calculating the model correlation, ρmodelρmodel,

Akt inhibitor as above, but on different jackknifed fractions of the data. Specifically, we calculated ρmodelρmodel between the predicted response map and the observed response maps from (1) the full data set, (2) 95% of trials (3) 90% of trials, (4) 85% of trials and (5) 80% of trials. We then performed a linear regression on the resulting ρmodelρmodel values against the reciprocal of the corresponding jackknife fraction values (1, 1/0.95, 1/0.9, 1/0.85, and 1/0.8). This procedure is designed to correct for the bias due to finite data set size (Brenner et al., 2000; Sahani and Linden, 2003; Machens et al., 2004). The square of the y-intercept of the regression

line was taken as the explainable variance for that RF location. The explained variances of the reduced space-only and orientation-only models during were calculated using the same procedure. This research was supported by grants from the NIH (R01 EY019493), the Alfred P. Sloan Foundation, the W.M. Keck Foundation, the Ray Thomas Edward career award in Biomedical Sciences, and the McKnight Scholar Award (to T.O.S.); NIH grant R01 EY013802 and the Gatsby Charitable Foundation (to J.H.R.); NIH grant R01 EY013802 and the Swartz Foundation (to J.F.M.); and by a Pioneer Fund postdoctoral fellowship (to A.S.N.). A.S.N. and J.F.M. designed the experiments, collected data, and developed the model and the statistical methods; A.S.N analyzed the data and ran the model simulations; A.S.N., J.F.M., J.H.R., and T.O.S. wrote the manuscript.