Does saccadic undershoot minimize saccadic flight-time? A Monte-Carlo study

Visually guided saccades to single targets undershoot by about 10% of the target distance, and require additional secondary saccades to foveate the target. We examine theoretically the hypothesis that undershooting is an economical strategy for maximizing the time for clear vision by minimizing saccadic flight-time. Using a simple stochastic model, Monte-Carlo simulations show that when the standard deviation of saccadic error is about 10% of the target distance the optimal gain of primary saccades is about 0.93-0.97 depending on the main sequence for saccade duration. When the standard deviation of saccadic error is large, as occurs in the human infant, the optimal gain decreases to about 0.6, which agrees with empirical observations. We conclude that saccadic undershoot is consistent with an adaptive controller that attempts to minimize total saccadic flight-time during sequences, rather than retinal error. The ethology and physiology of such a controller is discussed in the context of visual scanning and visual development.