Inter-Trial Correlations in Predictive-Saccade Endpoints: Fractal Scaling Reflects Differential Control along Task-Relevant and Orthogonal Directions

Pamela Federighi, Aaron L. Wong, Mark Shelhamer

Saccades exhibit variation in performance from one trial to the next, even when paced at a constant rate by targets at two fixed locations. We previously showed that amplitude fluctuations in consecutive predictive saccades have fractal structure: the spectrum of the sequence of consecutive amplitudes has a power-law (f(-α)) form, indicative of inter-trial correlations that reflect the storage of prior performance information to guide the planning of subsequent movements. More gradual decay of these inter-trial correlations coincides with a larger magnitude of spectral slope α, and indicates stronger information storage over longer times. We have previously demonstrated that larger decay exponents (α) are associated with faster adaptation in a saccadic double-step task. Here, we extend this line of investigation to predictive saccade endpoints (i.e., movement errors). Subjects made predictive, paced saccades between two fixed targets along a horizontal or vertical axis. Endpoint fluctuations both along (on-axis) and orthogonal to (off-axis) the direction of target motion were examined for correlations and fractal structure. Endpoints in the direction of target motion had little or no correlation or power-law scaling, suggesting that successive movements were uncorrelated (white noise). In the orthogonal direction, however, the sequence of endpoints did exhibit inter-trial correlations and scaling. In contrast, in our previous work the scaling of saccade amplitudes is strong along the target direction. This may reflect the fact that while saccade amplitudes are neurally programmed, endpoints are not directly controlled but instead serve as a source of error feedback. Hence, the lack of correlations in on-axis endpoint errors suggests that maximum information has been extracted from previous movement errors to plan subsequent movement amplitudes. In contrast, correlations in the off-axis component indicate that useful information still remains in this error (residual) sequence, suggesting that saccades are less tightly controlled along the orthogonal direction.