a, Log-odds excited metric. This metric uses a non-parametric bootstrap procedure to estimate the chance of observing average responses to photostimulation of a target from random sampling of a neuron’s activity (see Methods). An influence value of 0.1 corresponds to a log-odds of ~1.259, or a probability of being excited above shuffles of ~0.557. This metric adapts to the varyingly sparse, heavy-tailed, and skewed response distributions of each neuron’s activity, and so complements the ΔActivity measure. Key analyses from Figs. 2, 3 were repeated using this log-odds metric. b, Calculation of influence using the activity of a non-targeted neuron. Examples are shown for two pairs of neurons. Left, deconvolved activity of a non-targeted neuron on trials photostimulating a different neuron (red). Black lines indicate 5% and 95% bounds from resampling all trials. Data were smoothed with a 67-ms s.d. Gaussian filter for display only. Right, mean deconvolved activity for non-targeted neuron averaged over 0.367 s following photostimulation of target (red). Probabilities for obtaining a given deconvolved activity from the shuffle distribution of the non-targeted neuron are shown (black). c, Influence bias (average of signed influence values) as a function of distance between the targeted site and non-targeted neurons., plotted for both neuron and control photostimulation targets. Mean ± s.e.m. Same pairs as in Fig. 2g, n = 153,689 neuron site pairs, 90,705 control site pairs. d, Influence magnitude measured as the absolute value of influence values for all pairs following neuron or control site photostimulation. The non-zero value for control sites is expected because of noise due to random sampling of neural activity and potential off-target effects. Mean ± s.e.m. n = 153,689 neuron site pairs, 90,705 control site pairs. Neuron versus control: P = 2.31 × 10−5, Mann–Whitney U-test. e, Influence bias for a single target was the mean of influence values for the targeted neuron across all non-targeted neurons. Mean ± s.e.m. across targets. n = 518 neuron targets, 295 control targets. P = 7.40 × 10−4, Mann–Whitney U-test. f, Influence dispersion for a single target was the s.d. of influence values for the targeted neuron across all non-targeted neurons. Mean ± s.e.m. across targets. n = 518 neuron targets, 295 control targets. P = 2.3 × 10−6, Mann–Whitney U-test. g, Mean influence for all values for a single target was calculated. The s.d. of these values for neuron sites and control sites is plotted. The similar values indicate that it is unlikely that some neurons tended to have much larger positive or negative influence than expected based on control sites. n = 518 neuron sites, 295 control sites. P = 0.88, two-sample F-test. h, Running average of influence with noise correlation, for nearby (black) or distant (grey) pairs, with bin half-width of 20% (percentile bins). i, Running average of influence with signal correlation, with bin half-width of 15% (percentile bins). j, Running average of influence with difference in preferred orientation, with bin half-width of 12.5°. k, Coefficient estimates for linear regression of influence values. Plots show bootstrap distribution with median estimate as grey line, 25–75% interval as box, 1–99% interval as whiskers. Left, coefficients for piece-wise linear distance predictors from the model. Significance estimated by bootstrap: 25–100 μm, offset P = 0.0006, slope P < 1 × 10−4; 100–300 μm, offset P < 1 × 10−4, slope P < 1 × 10−4; > 300 μm, offset P = 0.68, slope P = 0.056. Right: coefficients for activity predictors from the same model. Signal correlation, P = 0.0002; signal–distance interaction, P = 0.96; noise correlation P = 0.0010; noise–distance interaction, P = 0.0024; signal–noise interaction P = 0.14; n = 64,485 pairs. l, Coefficient estimates from separate models in which the specified tuning correlation replaced signal correlation in the influence regression model of k, same bootstrap and boxplot conventions. Each model used only pairs in which targeted and non-targeted neurons exhibited tuning. Direction, P = 0.21, n = 36,565 pairs; orientation, P = 0.0026, n = 36,565; spatial frequency, P = 0.30, n = 47,810; temporal frequency, P = 0.011, n = 26,526; running speed, P = 0.11, n = 46,634.