Each voluntary eye movement provides physical evidence of a visuomotor choice about where and when to look. Primates choose visual targets with two types of voluntary eye movements, pursuit and saccades, although the exact mechanism underlying their coordination remains unknown. Are pursuit and saccades guided by the same decision signal? The present study compares pursuit and saccadic choices using techniques borrowed from psychophysics and models of response time. Human observers performed a luminance discrimination task and indicated their choices with eye movements. Because the stimuli moved horizontally and were offset vertically, subjects' tracking responses consisted of combinations of both pursuit and saccadic eye movements. For each of two signal strengths, we constructed speed–accuracy curves for pursuit and saccades. We found that speed–accuracy curves for pursuit and saccades have the same shape, but are time-shifted with respect to one another. We argue that this pattern occurs because pursuit and saccades share a decision signal, but utilize different response thresholds and are subject to different motor processing delays.

^{2}; target luminance, 33.6 or 33.8 cd/m

^{2}), but with the same standard deviation (

*SD*= 3.2 cd/m

^{2}). The difference in means was adjusted to produce stimuli with discriminability of

*d*′ = 0.05 or 0.10 (Green & Swets, 1988). Because these

*d*′ (sensitivity) values represent a measurement of the distance between the luminance distributions and not performance values for an ideal observer on our task, we will refer to these as conditions of low and high signal, respectively. To ensure consistency in the distance between the luminance distributions, we tested each unique pair of noise strips, using only pairs whose measured

*d*′ value was within 1% of the value reported.

*d*′, correcting for infinite sensitivity values using established methods (Macmillan & Creelman, 1991). To minimize noise in our sensitivity measurements, we defined the speed–accuracy curve for one session to be the mean of 1000 speed–accuracy curves bootstrapped using the data from that session (Efron & Tibsshirani, 1994). We retained time bins that contained at least five sensitivity measurements (i.e., measurements from at least half of the 10 possible experimental sessions).

*p*< .05, two-way ANOVA).

*p*> .05, two-way ANOVA). Nonetheless, the pursuit and saccade data occupy different temporal regions of the same speed–accuracy curves. For instance, if subject N's pursuit curve is time-shifted by 50 ms, the two curves do not completely overlap. The pursuit curve includes short-latency time points of low sensitivity, whereas the saccade curve includes long-latency time points of near-asymptotic sensitivity. Finally, the time shifts we observed between the speed–accuracy curves for pursuit and saccades are related to a difference in their latencies. We compared the best time shift for each pair of speed–accuracy curves (see Materials and methods) to the median latency difference on those trials. As shown in Figure 4, the best time shifts were significantly correlated with the differences in latency (Pearson's

*R*,

*r*= .72,

*p*< .05).

*F*

_{independent}=

*F*

_{pursuit}×

*F*

_{saccades}+ (1−

*F*

_{pursuit}) (1−

*F*

_{saccades}), in which

*F*

_{pursuit}and

*F*

_{saccades}are the fraction of correct pursuit and saccade trials for a given stimulus condition, respectively.

*p*< .05, 2-way ANOVA). Thus, our data did not match the predictions based on independent response-selection mechanisms for pursuit and saccades.

*R*,

*p*< .05).

*C*, which is the input time delay (Stone, 1960) based on the latency of visual responses in eye movement-related brain structures (see Materials and methods). After this delay, the decision signal rises at a constant rate from an initial level

*S*

_{0}(Carpenter & Williams, 1995; Reddi & Carpenter, 2000). The pursuit response begins at time lat

_{P}, corresponding to the moment at which the decision signal crosses the threshold

*P*. The saccadic system is subject to an unshared motor delay

*U*, based on the motor time delay (Stone, 1960) in the output pathways of the saccadic system (see Materials and methods), offsetting its response by

*U*ms. If pursuit and saccades share a decision signal, then the ratio of the latencies is related to the ratio of the thresholds, once the internal delays

*C*and

*U*have been taken into account. Hence, we defined the quantity

*P*/

*S*to be the threshold ratio, according to the equation:

*P*/

*S*= (lat

_{P}−

*C*) / (lat

_{S}−

*C*−

*U*).

*P*/

*S*) by comparing the latencies of pursuit and saccades from single trials. In Figure 6, left column, we show a plot of pursuit latency (minus the common visual delay) as a function of saccade latency (minus common visual and unshared motor delays) for data from the final experimental session. Each point in these plots represents one trial on which pursuit and saccade choices agreed. The Pearson's

*R*values of these correlations range from .72 to .76, indicating a mostly linear decision signal. A perfectly linear decision signal would yield a correlation with an

*R*value of 1.0. The right column of Figure 6 shows the distribution of threshold ratio estimates. We defined the threshold ratio as the mean of this distribution, and made individual measurements across sessions and signal strengths. The average threshold ratio was .81, indicating that the pursuit threshold was about 19% lower than the saccade threshold; the threshold ratio estimates also showed slight differences across subjects (averaged across all 10 sessions: subject N, .75; subject C, .75; subject D, .91).

*R*,

*r*= −.67,

*p*< .01), indicating that the difference in threshold ratio can account for 45% of the variance in the time shifts between the speed–accuracy curves. Within subjects, this correlation was also significant (subjects N and D at

*p*< .05, subject C at

*p*< .10, Pearson's

*R*). In absolute terms, the time shift attributable to the difference in threshold is simply the time shift minus the putative motor delay (15 ms), which, on average, was 34 ms (subject N, 39; subject C, 51; subject D, 11) or 64% of the total time shift (subject N, 72%; subject C, 77%; subject D, 42%).

*C*and

*U*(50 and 15 ms, respectively) were taken from the physiological literature and represent reasonable median values for the visual and motor delays. Increases in

*C*decrease the value of threshold ratio estimates, and increases in

*U*increase the value of the threshold ratio estimates. Table 1 summarizes how threshold ratio estimates change as

*C*varies from 40 to 80 ms and

*U*varies from 10 to 20 ms, showing that changes in these physiological delays have modest effects on our threshold ratio estimates. As

*C*increases from 40 to 80 ms, our threshold ratio estimates decrease by less than 9%. As

*U*increased from 10 to 20 ms, these estimates increase by less than 9%. Changes in these delays shift the values of the two quantities (lat

_{P}−

*C*) and (lat

_{S}−

*C*−

*U*), but not the relationship between them. Therefore, the correlation between pursuit latency and saccade latency remains unchanged as the values for

*C*and

*U*change, with an average

*r*value of .69 across subjects (subject N, .66; subject C, .69; subject D, .71), which was always significant (Pearson's

*R*,

*p*< .00001).

Subject N | Subject C | Subject D | All | ||
---|---|---|---|---|---|

C | U | P/S | P/S | P/S | P/S |

40 | 10 | .75 ± .05 | .74 ± .03 | .90 ± .04 | .79 ± .08 |

15 | .77 ± .05 | .76 ± .04 | .92 ± .05 | .81 ± .09 | |

20 | .79 ± .06 | .78 ± .04 | .94 ± .05 | .84 ± .09 | |

50 | 10 | .73 ± .05 | .73 ± .04 | .89 ± .05 | .79 ± .09 |

15 | .75 ± .06 | .75 ± .05 | .91 ± .05 | .81 ± .09 | |

20 | .78 ± .06 | .77 ± .05 | .94 ± .05 | .83 ± .10 | |

60 | 10 | .72 ± .05 | .71 ± .04 | .89 ± .05 | .77 ± .09 |

15 | .74 ± .06 | .73 ± .04 | .91 ± .05 | .80 ± .10 | |

20 | .77 ± .06 | .76 ± .06 | .94 ± .06 | .82 ± .10 | |

70 | 10 | .71 ± .06 | .70 ± .05 | .88 ± .05 | .76 ± .10 |

15 | .73 ± .06 | .72 ± .04 | .91 ± .05 | .79 ± .10 | |

20 | .76 ± .06 | .74 ± .05 | .94 ± .06 | .81 ± .11 | |

80 | 10 | .69 ± .06 | .68 ± .04 | .88 ± .05 | .75 ± .10 |

15 | .72 ± .06 | .70 ± .03 | .91 ± .06 | .77 ± .11 | |

20 | .75 ± .07 | .72 ± .04 | .94 ± .06 | .80 ± .11 |