Experimental paradigm.

Each trial began with a fixation display followed by a 600-ms spatial cue indicating one of eight possible target locations. After a 200-ms fixation interval, a search display appeared containing either four or eight items (one target digit and distractor letters) for 75 ms, followed by a mask display that remained until response. Masks were presented only at locations that had contained a search item (i.e., four masks in easy displays, eight in hard displays). Participants reported the identity of the target digit via unspeeded keypress. Expectation was manipulated across blocks: in easy-expectancy blocks, most trials (80%) contained sparse displays with four items; in hard-expectancy blocks, most trials contained dense displays with eight items. The cue predicted the target location with 75% validity.

Behavioral results.

Mean accuracy for validly and invalidly cued trials as a function of expected search difficulty (easy vs. hard blocks) and search display (easy = 4 items; hard = 8 items). Left and right panels show easy and hard search displays, respectively. Bars represent mean accuracy, with overlaid points indicating individual participant means. Error bars represent 95% within-subject confidence intervals (Morey, 2008). Significance markers reflect conventional pairwise t-tests comparing performance between expectation conditions within each cue validity and display type; both easy and hard displays showed higher accuracy when participants expected hard (dense) displays (counter to GLMM results reported in the main text, where only hard displays yielded a significant effect). The inset panel shows accuracy on invalid trials as a function of absolute distance between cue and target, illustrating that performance declined with increasing distance and was largely unaffected by expectation.

Spatial tuning functions and slope time courses derived from the IEM analysis.

(A) Reconstructed channel tuning functions (CTFs) for expect-easy (left panel) and expect-hard (right panel) conditions, averaged across participants. Tuning to the cued location emerged at ∼100 ms following stimulus onset in both conditions, indicating reliable deployment of spatial attention. (B) Time course of CTF slopes (mean ± bootsrapped SEM) for each expectancy condition. The dashed grey/red bar along the x-axis marks a significant cluster (cluster-based permutation test, p < 0.05) where slopes were steeper in the expect-hard condition, indicating enhanced spatial selectivity when participants anticipated difficult search displays.

Parameter estimates from CTF fits reveal expectancy-related gain modulation.

(A) Boxplots showing participant-level estimates of amplitude, concentration (reported as FWHM), and baseline from 316–425 ms after cue onset. Individual data points are overlaid to illustrate between-participant variability; no consistent differences were observed for concentration. (B) Example fitted exponentiated-cosine CTFs from the significant time window (316–425 ms), illustrating higher amplitude but comparable width (concentration k) in the expect-hard condition. Note that baselines were artificially shifted to zero for plotting purposes. (C) Time-resolved amplitude estimates (mean ± bootsrapped SEM) from cue onset through the pre-target interval. A significant cluster (p < 0.05) indicated higher amplitude in expect-hard relative to expect-easy blocks, whereas concentration and baseline parameters showed no significant clusters. The black line shows decoding (indexed by auc) of the expected search condition within the same time interval. Together these results indicate that expectancy modulated the gain—but not the spatial precision—of cue-evoked attentional signals.