Sequences of predictive eye movements form a fractional Brownian series - Implications for self-organized criticality in the oculomotor system

When human subjects are presented with a pair of visual targets that alternate periodically, they track the targets with rapid eye movements known as saccades. In previous work we demonstrated that at low pacing rates (<0.5 Hz), saccades have a latency of about 180 ms, and the latencies are uncorrelated from trial to trial. At high pacing rates (>0.6 Hz), latencies are much shorter: subjects make predictive saccades that anticipate target motion. The predictive latencies are correlated and appear to form a fractional Brownian motion. Here we confirm this finding by examining the rate of decay of nonlinear forecasting of predictive latencies. We further characterize the nature of predictive saccade latencies through the use of detrended fluctuation analysis and surrogate data. These results lead us to conclude that predictive saccades may exhibit a form of self-organized criticality, which enables rapid response to changes in stimulus timing. We provide an experimental demonstration of this.