A mathematical model of saccadic reaction time as a function of the fixation point brightness gain

The gap effect refers to a reduction in saccadic reaction time (SRT) to an eccentric target, when the fixation point is removed before the target onset. Though it is known that the gap effect peaks when the fixation point is offset about 200 ms before the onset of the eccentric target, it is unknown how this effect is modulated by stimulus variations. In this paper, we propose and investigate a model of saccadic reaction time as a function of the fixation point brightness gain. The brightness gain is defined as the ratio of the final and initial intensities of the stimulus. We have conducted a typical gap effect experiment with 15 participants, where the brightness of the fixation point was manipulated under four conditions and two gap intervals, at the same time and 200 ms before the onset of the eccentric target. The conditions included removing the fixation point (offset), leaving it with constant brightness (overlap), reducing, and increasing its brightness (lower and higher brightness conditions). Experimental data showed a significant gap effect in the offset and lower brightness conditions when compared to the overlap condition. On the other hand, the SRT was significantly longer for the higher brightness condition than the SRT for the overlap condition. Linear regression analysis using ten values of brightness gain shows that our model fits the data well for the 0- and 200-ms gap, with a coefficient of determination of .89 and .94, respectively.