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The Main Sequence of Saccades Optimizes Speed-accuracy Trade-off

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Abstract

In primates, it is well known that there is a consistent relationship between the duration, peak velocity and amplitude of saccadic eye movements, known as the ‘main sequence’. The reason why such a stereotyped relationship evolved is unknown. We propose that a fundamental constraint on the deployment of foveal vision lies in the motor system that is perturbed by signal-dependent noise (proportional noise) on the motor command. This noise imposes a compromise between the speed and accuracy of an eye movement. We propose that saccade trajectories have evolved to optimize a trade-off between the accuracy and duration of the movement. Taking a semi-analytical approach we use Pontryagin’s minimum principle to show that there is an optimal trajectory for a given amplitude and duration; and that there is an optimal duration for a given amplitude. It follows that the peak velocity is also fixed for a given amplitude. These predictions are in good agreement with observed saccade trajectories and the main sequence. Moreover, this model predicts a small saccadic dead-zone in which it is better to stay eccentric of target than make a saccade onto target. We conclude that the main sequence has evolved as a strategy to optimize the trade-off between accuracy and speed.

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Authors and Affiliations

  1. SensoriMotor Laboratory, Centre for Theoretical and Computational Neuroscience, University of Plymouth, Plymouth, PL4 8AA, UK

    Christopher M. Harris

  2. Sobell Department of Motor Neuroscience, Institute of Neurology, University College London, Queen Square, London, WC1N 3BG, UK

    Daniel M. Wolpert

  3. Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

    Daniel M. Wolpert

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  1. Christopher M. Harris
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  2. Daniel M. Wolpert
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Correspondence to Christopher M. Harris.

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Harris, C.M., Wolpert, D.M. The Main Sequence of Saccades Optimizes Speed-accuracy Trade-off. Biol Cybern 95, 21–29 (2006). https://doi.org/10.1007/s00422-006-0064-x

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  • DOI: https://doi.org/10.1007/s00422-006-0064-x

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