Fig. 1: Effect size analysis to quantify the coding of reward probability on a trial-by-trial basis.

a Schematics of the pursuit and saccade eye movement tasks. The spots represent the target and the arrows show the direction of continuous motion (pursuit) or instantaneous jump of the target (saccade). The numbers represent the probability of receiving a reward. b Ten example traces of eye position from a single pursuit (top) and saccade (bottom) session aligned to target motion onset. c The fraction of trials in which the monkey selected the P = 0.75 target on an additional choice task averaged across sessions. Gray dots represent individual sessions (Monkey A: n = 71, Monkey G: n = 87). The dashed line represents the chance level. All error bars represent the standard error of the mean. d–g PSTHs (top) and rasters (bottom) aligned to the onset of the cue for the P = 0.25 (red) and P = 0.75 (blue) conditions in a vermis Purkinje cell (d), vermis local neuron (e), SNpr neuron (f), and caudate neuron (g). The black diamonds in (d) represent complex spikes recorded in the same Purkinje cell. Error bars on PSTHs represent SEMs over trials. h An illustration of the calculation of the \({\omega }_{p}^{2}\) effect size. The parts represent the partition of the trial-by-trial variability into the variance explained by a specific variable (yellow), the variance explained by other variables (pink), and the variance unexplained by any of the task variables (blue). i Average \({\omega }_{p}^{2}\) (gray) and partial \({\eta }^{2}\) (black) effect sizes as a function of the number of conditions in a simulation in which the neural responses were independent of the condition. j Reward probability \({\omega }_{p}^{2}\) effect sizes of neurons in (d–g) calculated in bins of 50 ms. Entire trial effect sizes that represent the total coding of reward probability throughout the cue epoch are shown in (d–g).