The spatial selectivity of FOF neurons were best explained by the gain-field model. A, Raster plots and PETHs of an example neuron. Trials were grouped by the start position (left panel), the direction (middle panel), and the target position (right panel). The gray bar at the bottom indicates the 500 ms time window after the visual cue onset, the time window used for firing rate estimation, and model fitting in B–E. B, Estimated mean firing rate in each movement trajectory using a maximum a posterior estimator, same as in Figure 3. C, Predicted firing rates of four fit models (lines) and the mean and s.e. (circles and error bars) of firing rates in each trial condition. CV R2, cross-validated R2 (see Methods for definition). D, Left axis, fraction of neurons best fit by a specific model, among neurons whose mean cross-validated R2s over the four models was larger than the x-axis indicated value. Best fit was defined as having the largest cross-validated R2 among the four models. Error bars were 95% confidence intervals of the binomial distribution. Right axis, neurons that crossed the mean CV R2 criteria for each x-axis value. E, Each panel plots the cross-validated R2s of the x-axis model versus the y-axis model. Each circle indicates a neuron. The red line indicates the total least-square fit to the data. The dashed black line marks the diagonal. Only neurons whose mean of cross-validated R2s in the four models were larger than 0.05 were included (n = 199). The mean R2 in the gain-field model was larger than the x-axis models in all of these panels. ***, p < 0.001 (gain field vs additive, p = 8 × 10−5; gain field vs direction, p = 2 × 10−5; gain field vs start, p = 2 × 10−5. Permutation test against the null hypothesis that the Fisher-z transformed cross-validated R2s in the x-axis model and the y-axis model was not significantly different from zero, with 105 shuffles). F, The cross-validated R2s of the additive model versus the gain-field model in synthetic neurons, designed to have additive or gain-field selectivity, respectively. Only synthetic neurons whose cross-validated R2s in the four models were larger than 0.05 were included. Both panels had p = 2 × 10−5 (permutation test same as in E).
