Fitts’ Theorem in Oculomotor Control: Dissociable Movement Times for Amplitude and Width Manipulations

ABSTRACT

The authors examined whether movement times (MT) for discrete saccades are constant given equivalent index of difficulty (ID) values (i.e., unitary nature of Fitts’ theorem). To that end, we contrasted ID/MT relations for saccades equated for ID but differing with respect to their target amplitudes and widths. Results showed that MT increased with increasing ID within amplitude and width conditions; however, the ID/MT slope was markedly steeper in the former condition. Thus, the amplitude condition imposed greater information processing demands than the width condition—a result indicating that the constituent elements of Fitts’ theorem are dissociable (i.e., nonunitary). Further, examination of saccade kinematics demonstrated that the optimal MT for a given target amplitude was largely independent of target width.

Keywords:

• Fitts’ theorem
• movement time
• oculomotor
• saccade
• speed-accuracy

Funding

The study was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada and Faculty Scholar and Major Academic Development Fund Awards from the University of Western Ontario.

Notes

1. The present study provides an account of index of difficulty (ID) based on (a) Fitts’ (1954) formulation and (b) effective target width (i.e., We) wherein the denominator for ID is based on the 95% confidence interval for movement endpoints (see Meyer et al., 1988; Patla et al., 1985; Schmidt et al., 1979). Thus, throughout the manuscript the subscript Fitts (i.e., ID_Fitts) and We (i.e., ID_We) are included in each mention of ID to alert the reader as to which formulation we refer to.

2. Chi and Lin (1997) examined a reciprocal saccade task involving different target amplitudes (the authors reported the amplitudes as 4 and 16 cm) and widths (the authors reported the widths as 1° and 2°) and reported a grand average MT of 841 ms. The extremely long MT values reported by Chi and Lin are difficult to reconcile and perhaps represent a metric that included not only the time to complete a saccade but also the time spent fixating on a target prior to the initiation of a subsequent saccade. For that reason, we did not highlight Chin and Lin's work in the Introduction.

3. We did not compute endpoint variability for a secondary saccade (i.e., vAMP_S) because participant-specific cells for each condition by ID_Fitts combination did not always contain greater than three trials. For that same reason, we did not compute ID_We values for a secondary saccade.

4. The location of target stimuli in left and right visual fields (i.e., target left or right of fixation) did not elicit main effects or interactions for movement time or peak velocity. Thus, for our main analyses visual field is not included as a variable in our ANOVA model.

5. Target amplitudes of less than 3° produce longer RTs than saccades directed to targets of greater amplitude (Bell et al., 2000; Gillen & Heath, 2014; Kalesnyskas & Hallett, 1994). This finding is attributed to the continuum of saccade- and fixation-related neurons in the motor maps of the superior colliculus. In particular, targets located proximal to a fixation create conflicting saccade generation and fixation commands that require additional time to resolve (Bell et al., 2000).