How do primates anticipate uncertain future events?

Abstract

The timing of an upcoming event depends on two factors: its temporal position, proximal or distal with respect to the present moment, and the unavoidable stochastic variability around this temporal position. We searched for a general mechanism that could describe how these two factors influence the anticipation of an upcoming event in an oculomotor task. Monkeys were trained to pursue a moving target with their eyes. During a delay period inserted before target motion onset, anticipatory pursuit responses were frequently observed. We found that anticipatory movements were altered by the temporal position of the target. Increasing the timing uncertainty associated with the stimulus resulted in an increase in the width of the latency distribution of anticipatory pursuit. These results show that monkeys relied on an estimation of the changing probability of target motion onset as time elapsed during the delay to decide when to initiate an anticipatory smooth eye movement.

Figure 1.

Experimental protocol. A, Sequence of events during a trial. An initial fixation period was followed by a delay period without a stimulus on the screen. At the end of the delay, a target moving at 65°/s appeared at an eccentric position. After 500 ms of target motion, the target stopped for a final fixation period of 500 ms. B, Probability distribution of the time of target motion onset (T_ON) in the two-choices experiment. Target motion could start either 400 ms after fixation offset (first choice) or 1200 ms after fixation offset (second choice) with the same probability (p = 0.5). C, Bimodal density experiment. Target motion onset T_ON was drawn from a bimodal density function f_ON. Black curve, σ = 100 ms; gray curve, σ = 200 ms.

Figure 2.

Examples of the different types of anticipatory pursuit movements observed in the two-choices experiment. A, Short delay, single response. Eye velocity is represented as a function of time. The duration of the fixation period is represented with a filled bar below the eye velocity trace. The delay period is represented by a gray area. The target motion period is represented with an open bar. Eye velocity crossed the threshold (dashed line; velocity, 1.5°/s) at the time indicated with a dashed downward arrow. B, Long delay, single response. Eye velocity increased at the time of the first choice (solid upward arrow) and then decreased. Only a single anticipatory pursuit response occurred. C, Long delay, double response. Eye velocity increased before the time of the first choice (solid upward arrow), then decreased and increased again before the time of the second choice (solid downward arrow). Two latencies were measured (1^st mov., first movement; 2^nd mov., second movement), because eye velocity decreased below the detection level during the intermovement period.

Figure 3.

Two-choices experiment. A, C, Average eye velocity and SD as a function of time for double responses during long delays. B, D, Latency distributions of double responses composed of a first and a second movement. Filled symbols, Latency distribution of first movements; open symbols, latency distribution of second movements; solid lines, Hermite interpolation curves. Data for monkey P are in A and B; data for monkey T are in C and D.

Figure 4.

Scalar variability. Three single choices (400, 800, and 1200 ms) were tested independently (indicated with bold and italic characters). A, Distributions of anticipatory pursuit latency when the single choice of target motion onset was either 400 ms (filled squares, continuous line), 800 ms (open circles, continuous line), or 1200 ms (filled circles, dotted line). B, Relationship between mean latency (open circles, dotted line) and SD (Std dev.; filled squares, continuous line) for the three choices tested independently. The mean and the SD covary, and the CV (open squares, continuous line) is approximately constant.

Figure 5.

Bimodal density experiment. A, B, Average eye velocity as a function of time for responses when σ = 100 ms (black curves) or σ = 200 ms (gray curves). C–F, Distributions of anticipatory pursuit latency in the bimodal density experiment. Black curves, σ = 100 ms (C, D); gray curves, σ = 200 ms (E, F); filled symbols, first movements; open symbols, second movements. Data for monkey P are in A, C, and E; data for monkey T are in B, D, and F.

Figure 6.

Hazard rates. A comparison of the latency hazard rate functions (gray curves) for σ = 100 ms (A, C) and σ = 200 ms (B, D) with the f_ON (dashed curves) and model hazard rates (black curves) is shown. Data for monkey P are in A and B; data for monkey T are in C and D.

Figure 7.

Model predictions and validation. A, Transformation of the f_ON density (black curve; σ = 100 ms) into the model density (red curve). The blue curve shows the results of the application of the scalar property alone to the f_ON density (Scalar; downward arrow). B, The dashed curve indicates the latency density for σ = 100 ms in monkey P. The red curve indicates the model density.