A Population Decoding Framework for Motion Aftereffects on Smooth Pursuit Eye Movements

Adaptation of the direction and speed of pursuit

Effects of adaptation on the direction of pursuit appeared when we included pursuit target motion in directions that were different from that of the adapting patch. Figure 2A schematizes an experiment in which the adapting motion was rightward and pursuit target motions were in polar directions that were 30 or 60° upward and downward relative to rightward. The results of this experiment are summarized in the polar plot of Figure 2C, where each line is a vector showing the direction and speed of post-saccadic pursuit. Comparison of the average vectors of pursuit in the control block (bold, black lines) and the vectors for individual trials in the adaptation block (colored vectors) reveals two effects. First, the direction of pursuit in individual responses during the adaptation blocks (colored vectors) is consistently repelled away from the direction of the adapting stimulus. For target motions in polar directions of -30 and -60°, the responses in the adaptation block are rotated clockwise relative to the average from the control block. The average directions moved to -52.7° from -41.1° and to -26.4° from -20.8° (p < 0.02; Watson-Williams test). For target motions in polar directions of 30 and 60°, adapted responses were rotated counterclockwise to 38.0° from 33.0° and to 64.3° from 54.8° (p < 0.01; Watson-Williams test). Second, the speed of post-saccadic pursuit tends to be lower in the adaptation blocks than in the control blocks. The median eye speeds for the four directions of pursuit motion were adapted to 12.5°/sec from 12.9°/sec, to 9.2°/sec from 16.4°/ sec, to 10.2°/sec from 14.4°/sec, and to 11.1°/sec from 12.9°/sec (all p < 0.01; log-transformed Student's t test).

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Figure 2.

The effect of adaptation on subsequent pursuit, and how adaptation generalizes to targets moving in different directions. The right and left panel summarize two sets of experiments that used different directions of pursuit target motion to explore the effects of adaptation. A, B, Schematic diagram of the target motions. The light gray outline shows the location of the adapting patch, the light gray arrow shows the direction of the adapting motion, and the “+” indicates the fixation position during adaptation. The colored arrows show the trajectory of the first 500 msec of motion of the pursuit targets. C, D, Polar plots where each arrow is a vector showing the direction and amplitude of eye velocity. The colors of the vectors correspond to the target motion vectors in A and B. In C, the bold black vectors indicate the average responses in control blocks, without adaptation, and the colored vectors indicate responses in individual trials in the adaptation block. In D, all the responses in the adaptation block have been normalized relative to the average responses in the control block so that the bold black vectors are in the directions of target motion with unity length. The colored vectors show the normalized average responses in each of seven experiments. E, F, Summary of all 29 experiments plotting normalized eye direction (E) and speed (F) as a function of the difference between the direction of motion of the pursuit target and the adapting stimulus. The colored symbols plot the data from D, the gray symbols plot the results for 22 additional experiments, and the open circles plot the averages across all experiments. Error bars show the 95% confidence intervals.

An experiment that used a larger number of directions of pursuit target motion is summarized in Figure 2, B and D, now using a data presentation that normalizes the responses in the adaptation block relative to those in the control block. Pursuit was tested for target motions in polar directions 0, ±22.5, ±45, ±90, ±135, and 180°. For each response in the adaptation block, eye speed has been normalized for the average eye speed in the control block, and eye direction has been computed relative to the average direction of the responses in the control block. As a result, the average responses in the control block (bold, black vectors) have lengths of unity and directions equal to target direction. Figure 2D plots seven vectors of each color, to show the average responses in the adaptation block for seven experiments conducted with the design illustrated in Figure 2B. In each experiment, the repellant effects of adaptation extended to directions of target motion up to 90° away from the adapting direction (all differences p < 0.03 and p < 0.01 for target motion with upward and downward components; Watson-Williams test). In contrast, the pursuit directions in the adaptation block were not significantly different from those in the control block for target motion in polar directions 180, 135, -135, and 0° (p > 0.2; Watson-Willams test). Adaptation reduced the speed of pursuit for directions close to the adapting direction with significant differences for polar directions of 0, -22.5, and -45 (p < 0.01; log-transformed Student's t test); pursuit speed was not affected for other directions of target motion. Although we have represented the position and direction of the adapting patch to be on the right with motion to the right in Figure 2B, the seven experiments summarized in Figure 2D included all possible combinations of patch locations either on the left or right side of the fixation position with directions of adapting motion either to the left or right. Pursuit targets always were presented on the same side of the fixation position as the adapting patch. Because there were no consistent differences in the amount of reduction in speed or spread of the repellant effect to different directions of pursuit, the results have been rotated so that they could be presented as if the adapting motion were rightward.

All 29 adaptation experiments of the designs similar to those illustrated in Figure 2, A and B (n = 7 for the full set of directions as in B; n = 22 that examined fewer directions), are summarized by showing the normalized eye direction and speed in Figure 2, E and F, as a function of the difference between the polar direction of pursuit target motion and that of the adapting stimulus. The circular symbols with error bars show means and 95% confidence intervals for the full set of experiments, whereas the gray and colored dots show the average normalized effects of adaptation based on ∼20 pursuit responses in each direction. The direction of pursuit (Fig. 2E) is clearly repelled from the direction of the adapting stimulus, showing positive effects for positive directions of target motion and negative effects for negative directions of target motion. The average effect on pursuit direction peaked for polar directions ±30-60° from the adapting direction, and statistical significance was present for pursuit target motions up to 90° from the adapting direction. The speed of pursuit (Fig. 2F) is maximally depressed for pursuit target motion in the adapting direction and retains statistical significance for pursuit target directions <90° from the adapting direction. We did not observe significant enhancement of pursuit speed when the pursuit target moved in directions opposite to the adapting direction.

To determine limits on how quickly adaptation can be induced by our experimental design, we conducted four experiments that consisted of a control block, an adaptation block with a reduced duration of exposure of 1-1.5 sec for each adapting stimulus, and a second control block and adaptation block with our standard exposure time of 7-7.5 sec. The experiments had the same design as the one diagrammed in Figure 2A, with four directions of motion for the pursuit target. The pursuit in both adaptation blocks was normalized to their respective control blocks. The adaptation of pursuit direction was statistically significant for the shorter adapting stimuli but not as strong as for the longer adapting stimuli. For the shorter-duration adapting stimulus, the effects on pursuit direction averaged 59% of those for the longer-duration adapting stimulus. There were no differences in the extent of adaptation of pursuit speed, which averaged 84.1 and 85.2% of the control response for the short- and long-duration adapting stimuli.

We also conducted three experiments on one monkey to ask whether the effects of adaptation were stored from trial to trial: would control and adaptation trials in separate blocks show stronger effects of adaptation than if the trials were interleaved? Each experiment consisted of a “mixed” block that contained randomly interleaved control and adaptation trials as well as a standard adaptation block, both using our standard adaptation period of 7-7.5 sec. The effects of adaptation in the standard adaptation block were compared with the control trials in the mixed block. We found that the direction of pursuit was weakly repelled from the adapting direction in the mixed block: the effects on pursuit direction averaged 39% of those for the standard blocked experiment. There were no significant differences in the reduction of speed of pursuit after adaptation between the mixed and the standard blocked experiment, which averaged 90.8 and 87.8% of the control response, respectively. At least for adaptation of the direction of pursuit, our results parallel those for the perception of motion in which adaptation in one exposure has a strong influence on the adaptation caused during the next exposure (Wohlgemuth, 1911).

Spatial specificity of adaptation

As a first test of the spatial specificity of adaptation, we examined whether any effects of adaptation could be seen when the pursuit targets appeared in the opposite visual hemifield from where the adapting patch had been shown. In the experiments summarized above, both the control and adaptation blocks included pursuit targets that started either on the same (Fig. 3A) or opposite (Fig. 3B) side of the fixation position as the adapting stimulus. In contrast to the results when the pursuit stimulus moved through the same visual hemifield as the adapting stimulus (Fig. 3C), we did not observe adaptation of pursuit direction or speed for pursuit targets that moved through the same eccentricity in the opposite hemifield (Fig. 3D). The results of all 29 experiments are summarized in Figure 3, E and F, where the mean and 95% confidence intervals are shown as a function of the difference between the direction of motion of the pursuit target and the direction of the adapting motion. As before, these graphs plot the eye direction and speed in the adapting block relative to those in the control blocks. The data in Figure 2 have been replotted here (red symbols) for pursuit targets that moved through the same hemifield as the adapting stimulus. In contrast, the black symbols in Figure 3, E and F, show that there was no evidence of adaptation when the pursuit target moved through the opposite visual hemifield.

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Figure 3.

Failure of adaptation to generalize to the opposite hemifield from the adapting stimulus. A, B, Stimulus configuration. The light gray patch shows the location of the adapting stimulus, the gray arrow shows the direction of the adapting motion, the “+” indicates the fixation position, and the colored arrows show pursuit targets presented in the same (A) or opposite (B) hemifields from the adapting stimulus. C, D, Polar plots where each vector shows the normalized average eye velocity: black vectors show control responses, and colored vectors show responses from individual experiments in the adaptation block. The colors correspond to the arrows in A and B, and the two plots show responses for pursuit targets that moved through the same (C) or opposite (D) hemifield from the adapting stimulus. E, F, Summary of average effects of adaptation showing the normalized direction (E) and speed (F) in the adapting block as a function of the difference between the directions of motion of the pursuit target and the adapting stimulus. Red and black symbols show responses for pursuit targets in the same or opposite hemifield from the adapting stimulus. Error bars show 95% confidence intervals.

As a more stringent test of the spatial specificity of the effect of motion adaptation on pursuit, we used adapting patches that appeared simultaneously in the two visual hemifields and provided adapting motion in opposite directions. For the experiment in Figure 4, for example, we showed leftward adapting motion in the right visual hemifield and rightward adapting motion in the left hemifield (Fig. 4A). Subsequent pursuit targets moved in polar directions -120, -60, -30, 30, 60, and 120° through location of the adapting patch in the left hemifield and in polar directions -150, -120, -60, 60, 120, and 150° through the location of the adapting patch in the right hemifield (Fig. 4B,C; bold black vectors). The choice of directions represents a compromise between good coverage around the adapting direction in each hemifield and overlap in the directions of motion through the two hemifields.

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Figure 4.

Effects of simultaneous adaptation with different directions of motion in the two visual hemifields. A, Stimulus configuration. The light gray patches show the locations of the two adapting stimuli, the gray arrows show the direction of the adapting motion in each patch, the “+” indicates the fixation position, and the colored arrows show pursuit targets presented in the two hemifields. B, C, Polar plots where each vector shows the normalized average eye velocity: black vectors show control responses, and colored vectors show responses from individual experiments in the adaptation block. The colors correspond to the arrows in A, and the two plots show responses for pursuit targets that moved through the left (B) or right (C) hemifield. D, E, Normalized eye direction is plotted as a function of the absolute target direction for pursuit targets that moved through the left (D) or right (E) hemifield. F, G, Normalized eye speed is plotted as a function of the absolute target direction for pursuit targets that moved through the left (F) or right (G) hemifield. In D-G, the colors of the symbols correspond to the arrows in A. H, I, Eye direction (H) and speed (I) as a function of the difference between the directions of motion or the pursuit target and the adapting stimulus. Red and black symbols show average responses across all experiments for targets that moved through the left and right visual hemifield, respectively. Error bars show 95% confidence intervals when there was enough data to compute them by bootstrapping.

The adaptation in pursuit for targets that moved through the visual field locations of the adapting patches in either hemifield was always appropriate to the motion of the relevant adapting patch. To document these effects, the two columns of Figure 4 summarize responses to target motion through the two hemifields. At each location on the abscissa in the graphs of Figure 4, D-G, each symbol shows results from an individual experiment. Here, the data are plotted as a function of the actual direction of target motion, so that the adapting direction corresponds to 0° in Figure 4D (and F) and ± 180° in Figure 4E (and G). Comparison of Figure 4, D and E, shows that eye direction was repelled from the direction of the adapting stimulus in each hemifield. It was rotated clockwise for pursuit targets with negative polar angles when the targets moved through the left hemifield and counterclockwise when the targets moved through the right hemifield (and in the opposite sense in each case for pursuit targets with positive polar angles). As a result, adaptation had different effects on the responses to pursuit target motion in a given absolute polar direction when the targets moved through different hemifields. For example, adaptation caused a negative shift for a direction of -120 on the left (Fig. 4D) and a positive shift for the same direction of target motion on the right (Fig. 4E). Adaptation of speed shows the same general effect. For targets in the left visual hemifield, which had rightward adapting motion, the eye speed was reduced for targets with a rightward component of motion and increased for targets with a leftward component of motion (Fig. 4F). The U-shaped curve suggested by Figure 4F is contrasted by the upside-down U-shaped curve suggested by Figure 4G, which shows the eye speed of pursuit for targets that moved through the right hemifield after adaptation with leftward motion. Eye speeds were higher than control for targets with rightward components of motion and the same or slightly lower than control for targets with leftward components of motion. As with direction, there are examples of polar directions of motion in which the effect of adaptation on pursuit speed was opposite for the target motion through the two visual hemifields.

Figure 4, H and I, confirm that the effects in the two hemifields are the same as those we documented in Figures 2 and 3 when the data are plotted as a function of the difference between the direction of motion of the pursuit target and the adapting direction. For pursuit targets in both the right (black symbols) and left (red symbols) hemifield, the adaptation causes eye direction to be repelled away from the adapting direction (Fig. 4H). The 95% confidence intervals (error bars) indicate that the adaptation is statistically significant. The adaptation of eye speed is also similar for targets moving through the two visual hemifields, although there was very little reduction in eye speed for targets in the left hemifield and small numbers of trials precluded computation of 95% confidence intervals for some of the key points. We also note that simultaneous adaptation with opposite direction motion in the two hemifields caused eye speed to be considerably larger than control for targets that moved in the opposite direction from the adapting patch, in both hemifields. More data would be needed to determine the veracity of this apparent difference from the results with single adapting patches.

Spatial generalization of the effects of adaptation

We tested the spatial generalization of the adaptation effect more systematically in seven experimental sessions by presenting pursuit targets starting from multiple positions across the horizontal meridian (Fig. 5A) after adaptation with a 10 × 10° patch (Fig. 5A, white rectangle) located 10° to the left (or right) of the fixation target. Pursuit targets moved in directions that were either +30 or -30° from horizontal, starting at positions chosen so that the targets would cross the horizontal meridian 250 msec after motion onset at locations -15, -10, -5, 0, 5, and 10° from the fixation point. The post-saccadic pursuit direction (Fig. 5B, open circles) and speed (Fig. 5C, open circles) underwent spatially specific adaptation. For pursuit targets that moved near the region of the adapting patch (target position -15, -10, and -5° on the abscissa), both the direction and speed of smooth eye velocity are below the horizontal dashed lines, indicating effects of adaptation. For pursuit targets that started central enough to cross the position of fixation or that moved through the opposite visual hemifield (target position 0, 5, and 10° on the abscissa), there was little to no difference between the control and adaptation blocks in either the direction or speed of smooth eye movement.

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Figure 5.

Spatial generalization of adaptation tested for peripheral and central adapting locations. A, Stimulus configuration. White and gray rectangles indicate the locations of the two adapting patches, used in different experiments, and arrows indicate the first 300 msec of motion of the pursuit targets. B, C, Normalized eye direction (B) and speed (C) are plotted as a function of the starting location of the pursuit target along the horizontal axis. White and gray symbols show effects of peripheral and central adaptation, respectively. Error bars show 95% confidence intervals. White and gray rectangles indicate the region of the visual field covered by the peripheral and central adapting stimuli. Horizontal dashed lines show control values of eye direction and speed. For eye direction, negative values indicate that the response was repelled away from the direction of the adapting motion.

To test the effects of adaptation of the central visual field, we conducted nine similar experiments with a 5 × 5° adapting patch that was centered at the position of fixation (Fig. 5A, gray rectangle). The effects of adaptation with the central patch were weaker than with the peripheral patch, but they show a complementary pattern of results (Fig. 5B,C; gray symbols). When the pursuit target moved through the central visual field, near the position where the adapting patch had been shown, both direction and speed were adapted relative to control. In contrast, when the pursuit target moved through peripheral positions, far from the location of the adapting patch, we did not see evidence of significant adaptation in either the direction or speed of smooth eye movement. We conclude that adaptation with a central a patch is specific to the retinal location of the adapting patch.

With a central patch, it was especially difficult for the monkeys to suppress smooth eye movements during adaptation. We therefore trained the monkeys over many experimental sessions to hold fixation with a central patch, decreasing the size of the fixation window over days until the monkeys were competent at performing the task. Even after training, the residual eye movements in the direction of the adapting patch were 1.01°/sec, slightly larger than the 0.355°/sec found for trials with peripheral adapting patches. In neither case did average eye position over the course of the adaptation period differ by more than one-tenth of a degree from the center of the fixation position. We therefore conclude that any difference in the residual tracking movements occurring during central patch presentation will have a minimal effect on the retinal velocity of the adapting patch (<5%) and should not affect our results greatly.

Time course of expression of adaptation

For 1967 trials from 23 experiments in which the pursuit target direction was between 10 and 60° from the adapting direction, we analyzed the effect of adaptation on the direction (Fig. 6A) and speed (Fig. 6B) of pursuit in 10 ms bins for 200 msec after the end of the first saccade. The direction of pursuit (Fig. 6A) is plotted so that it has negative values if the response was repelled away from the adapting direction, showing that the expression of adaptation in pursuit recovers within 150-200 msec after the end of the first saccade. The speed of pursuit (Fig. 6B) returned to control over approximately the same time course. The short duration of the behavioral expression of adaptation does not imply that the underlying neural adaptation recovers as quickly. The initial position of the pursuit target was chosen so that the motion of the target would be presented at the same eccentric retinal location as the adapting patch, whereas after the first saccade, the target motion would be near the fovea, which had not been adapted. Therefore, our results agree well with the expectation that feedback about the errors in pursuit direction and speed would cause pursuit to recover within two latent periods after the first feedback indicated differences between target and eye velocity, despite persistent sensory adaptation. Because the configuration of target position and motion in our paradigm evoked early saccades and generally weak pre-saccadic pursuit, the pre-saccadic eye speed was low, and eye direction was poorly defined, thus precluding meaningful analysis of pre-saccadic adaptation effects in general. Furthermore, we found a small but significant difference in the average saccade latency in control and adaptation trials (202.9 vs 214.8 msec; p = 0.013; Student's t test). To avoid confounds that might be caused by this difference, we have presented a conservative estimate of adaptation effects based on data aligned on the end of the saccades.

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Figure 6.

Time course of adaptation effects on post-saccadic pursuit. Normalized pursuit eye direction (A) and speed (B) are plotted as a function of time of the measurement relative to the saccade. Negative values of normalized eye direction indicate that the response was repelled away from the direction of the adapting motion. Error bars show 95% confidence intervals.

Generalization of adaptation across target speeds

In five experiments summarized in Figure 7, we provided adapting motion at our standard speed of 16°/sec and tested pursuit with targets that moved in the adapting direction at speeds of 4, 8, 16, 24, 32, and 48°/sec. As reported previously, adaptation caused a reduction in post-saccadic eye speed for pursuit targets of the same speed as the adapting patch. The reduction was to a value that averaged 91.7% of control (p = 0.07; log-transformed Student's t test). For other speeds of pursuit target motion, eye speed seemed to be repelled from target speed, much as it was in the direction domain. For target speeds of 4 and 8°/sec, post-saccadic eye speed averaged 66.0 and 78.3% of control (p < 0.05; log-transformed Student's t test). For faster target speeds of 24 and 32°/sec, post-saccadic eye speed averaged 104.2 and 107.2% of control (p = 0.23 and 0.05) For pursuit target motion at 48°/sec, the adaptation was not present (although this speed was only tested for two experiments).

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Figure 7.

Effects of adaptation on the post-saccadic eye speed evoked by different speeds of target motion in the adapting direction. The graph plots normalized eye speed as a function of the difference between target speed and adapting speed. Targets moved at 4, 8, 16, 24, 32, and 48°/sec, and the adapting stimulus always moved at 16°/sec. Error bars show 95% confidence intervals. The target speed of 48°/sec (the point at 32°/sec on the graph) was only tested in two experiments and therefore lacks error bars.

Relationship of effects of adaptation on speed versus direction of pursuit

To analyze whether the adaptation effects on the direction and speed of pursuit were coupled, Figure 8 plots the degree of adaptation of eye speed as a function of the adaptation of eye direction. Different points show averages of the effects in different experiments, and we made separate plots for pursuit targets that moved in directions that were 30° (n = 34) (Fig. 8A) or 60° (n = 20) (Fig. 8B) away from the adapting direction. There was no significant correlation between the magnitude of adaptation effects on speed and direction for either direction of pursuit target motion (r² < 0.02; p > 0.35). The same analysis of percentage of deviation in direction and speed in individual trials compared with the means for each experiment also did not reveal any correlation between the two effects of adaptation (r² < 0.01; p > 0.3; n = 812).

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Figure 8.

Absence of correlation in the magnitudes of the adaptations of eye speed versus eye direction. Data are plotted for each pursuit trial in which the direction of target motion was 30° (A) or 60° (B) from the adapting direction. Each point represents the average effect from ∼20 trials in a single daily experiment. Negative values of normalized eye direction on the abscissa indicate that the response was repelled away from the direction of the adapting motion.

Computational analysis of adaptation of pursuit direction

We have used a computer model to ask whether the effects of adaptation on the direction and speed of pursuit could be understood in terms of plausible estimates of the effect of adaptation on the population code for the direction of motion in area MT. Unfortunately, the available experimental data about the effect of adaptation on responses of MT neurons are disparate: previous recordings either provide data only about the effects of adaptation at the preferred and nonpreferred directions for each neuron (Petersen et al., 1985; Van Wezel and Britten, 2002; Kohn and Movshon, 2003) or have found qualitatively different results of adaptation on direction-tuning curves depending on the adapting stimulus (Kohn and Movshon, 2004). In our analysis of direction adaptation, we therefore modeled four different types of effects of adaptation that have been found or suggested by recording studies on MT and V1 neurons.

In the first model, implemented as Equations 1 and 2, the response gain of MT neurons is decreased after adaptation (Petersen et al., 1985; Van Wezel and Britten, 2002; Kohn and Movshon, 2003). Adaptation extended to neurons with preferred directions near to the adapting direction, but the magnitude of adaptation decreased as a Gaussian function of the difference between the direction of the adapting stimulus and the preferred direction of the neuron. Adaptation was simulated as a multiplicative operation that scaled the Gaussian direction-tuning function by the same percentage for target motion in all directions. Neurons with preferred directions opposite or nearly opposite to the adapting direction were modeled as not being affected by adaptation (Van Wezel and Britten, 2002; Kohn and Movshon, 2003). Comparison of the red and black curves in the first column of Figure 9A shows the effect of response gain adaptation on the direction-tuning curves for a family of model neurons. The amplitude of the adapted tuning curve (red) was smallest for the neuron with a preferred direction near the adapting direction and increased as the preferred direction of the neurons moved away from the adapting direction.

The effects of adaptation on a population of 10,000 model neurons with randomly chosen preferred speeds and directions can be appreciated qualitatively by examining the second and third columns of Figure 9A, each of which shows the population response to a given target motion. Each point plots the responses of one model neuron before (black) and after (red) adaptation, in which the position along the x-axis indicates the preferred direction of motion for the model neuron and the position along the y-axis indicates the response amplitude. When the direction of target motion was the same as the adapting direction (Fig. 9A, first column), adaptation reduces the amplitude of the population response, but the change in response is symmetrical around the direction of motion. As a result, the population vector is in the same direction before and after adaptation (red and black arrows, respectively). In contrast, if the direction of motion of the pursuit target is in a polar direction that is 30° from the adapting direction (Fig. 9A, third column), then adaptation depresses the response of model neurons asymmetrically on the side of the population response closest to the adapting direction. The direction of the population vector (red arrow) is repelled from the adapting direction, exactly as we observed in the initiation of pursuit. Similar logic has been used by others (Mather, 1980; Lee et al., 1988; Gilbert and Wiesel, 1990; Clifford et al., 2000; Clifford, 2002).

We fitted the 256 neuron model to the observed effect of adaptation on the direction of pursuit by allowing the amplitude, center, and SD of the adaptation function in Equation 2 to vary, as described in Materials and Methods. We obtained a best-fitting equation (Fig. 9E, black curve) that accounted for 95% of the variance in the data using a maximum reduction of 33% of the response that was centered 3° from the adapting direction, with the spread of adaptation characterized by a SD of 37°.

In the second model, implemented by Equations 1 and 3, the effect of adaptation was to narrow tuning widths (Kohn and Movshon, 2004). The best-fitting model (Fig. 9E, red curve) could account for 93% of the variance in the pursuit direction data by having a maximal effect for neurons with preferred directions 5° from the direction of adaptation, where tuning widths were narrowed to 65% of their preadaptation values. The spread of adaptation was characterized by a SD of 28°. Inspection of the population responses from the 10,000 neuron model shows that narrowing the direction tuning has the same effect on the direction of the population vector as does adaptation by gain reduction, but without causing a large change in the amplitude of the population response. When the target direction is matched to the adapting direction (Fig. 9B, second column), the population response is symmetrically narrowed so that the direction of the population vector is unchanged. When the target direction is offset from the adapting direction (Fig. 9B, third column), the population response is altered asymmetrically, with a larger effect on the side closer to the adapting direction: the direction of the population vector is repelled from the adapting direction.

The third and fourth models were mirror images of each other, implementing adaptation by shifting the preferred direction of each neuron either toward (Kohn and Movshon, 2004) or away from the adapting direction, the latter similar to what has been found for orientation-tuning curves in V1 (Dragoi et al., 2000). Neither of these models of adaptation, implemented using Equations 1 and 4, did a good job of mimicking our data. For shifts in preferred direction away from the adapting direction, the best-fitting model accounted for only 18% of the variance in our pursuit direction data (Fig. 9E, cyan curve), using a maximum repulsion of 15° that occurred for neurons with preferred directions 24° from the adapting direction; the width of the adaptation effect was characterized by a SD of 16° (Fig. 9C, first column). For shifts in the preferred direction toward the adapting direction, the predictions of the model depended on how tightly the effects of adaptation were localized to the adapting direction. When adaptation effects were constrained to be localized near the adapting direction, the effect of attraction was essentially the opposite to that of repelling the tuning curves from the adapting direction. However, if we allowed adaptation to shift tuning by a maximum of 12° over a larger range of angles (Fig. 9D), then the best-fitting model accounted for 44% of the variance.

The example population responses in Figure 9, C and D, illustrate the reason for failure of the models in which adaptation caused attraction and repulsion of the preferred direction of MT neurons toward or away from the adapting direction. If changes in preferred direction are localized to neurons with direction tuning near the adapting direction (Dragoi et al., 2000; Kohn and Movshon, 2004), then the effects on the population response are biphasic, causing the shift in population response to be in one direction near the adapting direction but in the opposite direction far from the adapting direction. For the repulsion mechanism of adaptation (Fig. 9C), the population response was repelled from the adapting direction for target motion of a direction 30° different from the adapting direction (middle column), in agreement with our data on adaptation of the direction of pursuit. However, the population response was attracted toward the adapting direction for target motion in a direction 90° different from the adapting direction (right column), in contradiction to our data. The model was never able to achieve a good fit to our data because of these two conflicting tendencies. The attraction mechanism of adaptation had the opposite problems, causing adaptation in the wrong direction for targets that moved in directions near the adapting direction and in the correct direction for targets that were further from the adapting direction.

If adaptation attracts or repels the preferred directions of MT neurons having a wider range of preferred directions, then the attraction model can predict the correct direction of adaptation in pursuit for targets that move in directions far from, but not near to, the adapting direction (Fig. 9D). When the direction of target motion was 60° different from the adapting direction (right column), the population response was repelled from the adapting direction, in agreement with our data on the effect of adaptation on the direction of pursuit. However, when target motion was 15° different from the adapting direction (middle column), the breadth of the adaptation function caused the same effects to occur on both sides of the population response. The population response broadened on both sides but did not change its vector average, predicting an absence of adaptation that we did not see in our data on pursuit. The repulsion model also failed to predict adaptation in pursuit for target motion in directions near the adapting direction and made the incorrect prediction that pursuit should be attracted toward the adapting direction for target motion in directions farther from the adapting direction.

Computational analysis of adaptation of pursuit speed

Two changes in the population response might contribute to the effects of adaptation of the speed of pursuit. First, there is abundant evidence that target speed is estimated by a neural implementation of Equation 6, where the presence of ϵ in the denominator means that adaptation will reduce eye speed if it also reduces the amplitude of the population response. Second, adaptation may have different effects on the speed tuning of MT neurons depending on the difference between the adapting speed and their preferred speeds. Because of the absence of neural data to predict the effect of adaptation on speed tuning, we have chosen not to extend our simulations along that axis. However, we can evaluate whether adaptation can be expected to cause changes in the speed of pursuit given the population responses for the different models in Figure 9 and reasonable values of ϵ. In our data, the average effect of adaptation on the speed of pursuit when direction and speed are matched was ∼80%. Previous models have predicted that the value of ϵ is <25% of the normal population response. Equation 6 predicts that the population response must be reduced in amplitude to <47% of control to match these constraints. For the four models we considered, the population responses to target motion in the adapting direction fell short of these predictions: the total population response was reduced to only 73% of the control amplitude for the gain model, to 90% of control for the narrowing model, and to 92% of control for the repelling model. Furthermore, the population response increased to 143% of control for the attraction model, in the wrong direction to account for the effect of adaptation on the speed of pursuit. We conclude that Equation 6 is adequate to account for the effects of adaptation on the speed of pursuit only if adaptation also affects the responses of MT neurons in a way that depends on the difference between the adapting speed and the preferred speed of the neuron.

Coordinate system for motion adaptation in pursuit

The spatial specificity of motion adaptation in pursuit demonstrates the coordinate frame of adaptation is retinal and not motor. If adaptation were localized in motor circuits, it would have been expressed for pursuit of targets that moved across the parts of the visual field outside the site of the adapting motion. Thus, adaptation cannot be caused by a residual smooth eye movement left over from a larger response generated to suppress smooth tracking during presentation of the adapting stimulus. Furthermore, our results are distinct from those for pursuit motor learning, which shows partial generalization to targets presented even in the opposite hemifield (Chou and Lisberger, 2002) and is specific for the direction of target/eye motion rather than the direction of visual motion (Kahlon and Lisberger, 1996). Thus, motion adaptation in pursuit occurs in a sensory coordinate system, whereas pursuit learning occurs in an intermediate, sensory-motor coordinate system.

Underlying effects of adaptation on neuronal populations

Of the four possible effects of adaptation on the responses of MT neurons we tested in computer simulations, only changes in response gain or narrowing of tuning width could account for the effects of adaptation on the direction of pursuit. Neither attractive nor repellant changes in the preferred direction of tuning for MT neurons by themselves could account for the effects in our data. Kohn and Movshon (2004) found that a combination of response gain, narrowing, and attraction could account for the magnitude of perceptual effects of adaptation. Our study corroborates and extends their results by testing separately each of the mechanisms found in their study and comparing the predictions to quantitative data about the effect of adaptation on motor output. To account for both the magnitude and extent of adaptation effects on the direction of pursuit movements, only the neural adaptations comprising response gain and narrowing are critical. Although MT neurons do display attractive shifts of preferred direction after adaptation with sinusoidal gratings, there is preliminary evidence that this is not the case when the visual stimuli consist of the random dot patterns used in our study (Kohn and Movshon, 2004). We also note that a combination of changes in response gain and narrowing of tuning would work synergistically, allowing smaller neural adaptations of each type to account for the behavioral adaptation we have observed in the direction of pursuit.

Our models were based on the assumption that the response of each neuron contributes to the decoded estimate of target direction in the same way before and after adaptation. In principle, repellant shifts of preferred tuning away from the adapting direction still could account for our data if the value used to weigh each neurons response according to its preferred direction (θ_pref in Eq. 5) shifted with adaptation. As a consequence, tuning preferences would no longer be distributed uniformly across directions but would acquire a hole around the adapting direction. The effect on the vector-averaging decoding computation of Equation 5 would be to bias the estimate of target direction away from the adapting direction.

In all but the case just mentioned, the use of maximum-likelihood methods for estimating target direction from the population response would not have changed our conclusions. For populations of neurons that have direction tunings distributed equally across all directions, vector-averaging is mathematically equivalent to fitting a sinusoid to the population response, and maximum-likelihood is equivalent to fitting a tuning curve to the population response (Pouget et al., 2000). Each estimates the center of mass of the population response. If, in the repellant or attractive model of neural adaptation, we allow the “label” or weight in the population computation of each neuron to shift with preferred direction, then a maximum-likelihood computation would take account of the shift and would be resilient against the effects of neural adaptation, in disagreement with our pursuit data. These are important theoretical issues, but we do not want to give the impression that the exact decoding computation (or its neural implementation) is constrained by our report. We prefer to emphasize the value of the population coding and decoding framework for understanding the relationship between neural and behavioral expressions of sensory adaptation.

Population decoding for speed versus direction

In principle, the computation used to estimate target direction must be distinct from that used to estimate speed. The encoding of direction and speed by MT neurons is orthogonal in the sense that neurons have similar tuning curves for direction regardless of the speed of stimulus, and vice versa (Rodman and Albright, 1987). From the perspective of pursuit, estimates of target direction and speed have rather different consequences for motor programming. In the cerebellum and brainstem, the estimate of direction must specify the relative activity of different sets of neurons that drive the horizontal and vertical components of smooth eye velocity, whereas the estimate of speed will determine the overall level of activity in the different groups of neurons. At the very least, the computations used to decode speed and direction must assign different profiles of weights across the population of MT neurons. In our data, the absence of a correlation between the magnitudes of the effects of adaptation on pursuit speed and direction supports the idea that pursuit uses separate and mostly independent neural computations to estimate target speed and direction.

Our experiments and analysis leave open the question of how to account for the effect of adaptation on the speed of pursuit eye movements as well as the apparent repulsion of eye speed from the adapting speed. Because of the relative smallness of our data set on the effects of target speed along with the absence of knowledge of the effects of adaptation on the speed tuning of MT neurons, we have chosen to defer this issue for later, more extensive experiments and modeling.

Comparison of adaptation effects for perception and action

Our data show greater similarities to the perceptual motion aftereffects studied with dynamic stimuli than to those for static stimuli, such as the waterfall effect. The latter is thought to be an effect on low-level vision because it shows incomplete ocular transfer (Wohlgemuth, 1911) and is not produced by “second-order motion” (Derrington and Badcock, 1985; Cropper and Hammett, 1997). Motion aftereffects tested on dynamic stimuli (Blake and Hiris, 1993) show almost complete ocular transfer (Raymond, 1993; Nishida et al., 1994) and can be induced by second-order motion (Ledgeway and Smith, 1994; Nishida and Sato, 1995). These and other results (for review, see Mather et al., 1998) indicate that tests with dynamic stimuli probe higher stages of visual processing. We think that the effects we see for pursuit are probing similar visual processing in the same brain areas that are responsible for motion aftereffects on dynamic stimuli.

The repellant adaptation effects on pursuit speed and direction mirror similar repellant effects in perceptual tests using tilt (Gibson, 1937), spatial frequency (Blakemore and Sutton, 1969), and image blur (Webster et al., 2002). Furthermore, perceived directions deviate away from the adapting direction in a way that appears quantitatively analogous to what we found for pursuit (Levinson and Sekuler, 1976). Although there is some heterogeneity of results concerning the perception of target speed after adaptation, the consensus of various tests show that adaptation affects perceived speed in a way similar to what we found (Carlson, 1962; Rapoport, 1964; Thompson, 1981; Smith, 1985). Thus, there is excellent agreement between the effects of motion adaptation on motor outputs and perceptual reports. We suggest that the locus of adaptation occurs early in the visual motion processing pathways, presumably in MT, so that the same adaptation affects both perception and action.

Adaptation can be a beneficial process for visual perception by keeping neurons sensitive to small changes in the baseline sensory stimulus across a wide range of baselines. Adaptation may serve a similar function for the perception of motion but would have potentially detrimental consequences for motion-based movements like pursuit, in which adaptation would degrade the ability to successfully match eye velocity to target velocity.

A population decoding explanation for motion adaptation

Our analysis has allowed us to take the next step beyond most previous physiology (Barlow and Hill, 1963; Vautin and Berkley, 1977; von der Heydt et al., 1978; Hammond et al., 1985, 1989; Petersen et al., 1985; Müller et al., 1999; Van Wezel and Britten, 2002; Kohn and Movshon, 2003) (but see Kohn and Movshon, 2004) and functional imaging experiments (Tootell et al., 1995; Huk et al., 2001) that understood adaptation based on responses of neurons to stimuli that moved in their preferred and nonpreferred directions (Sutherland, 1961). The strong causal linkage from visual responses in MT to pursuit eye movements has allowed us to create a broader framework for understanding adaptation based on population coding and decoding. The similarity of the motion aftereffects on pursuit and perception implies that our framework holds for both visual and movement systems, suggesting the existence of unifying principles of sensory coding and decoding for perception and action.