Article Figures & Data
Figures
- Fig. 1.
Evidence for an illusion of increased target speed in monkey pursuit. A, Illustration of the pursuit task. The two rectangles show the temporal sequence of the task. The monkey first fixated a small point (cross), and then pursued a patch of dots that appeared to the left of the extinguished fixation point and immediately moved rightward. The starting position of the center of the dot patch relative to the fixation point was set to equal the average receptive field eccentricity of the MT neurons recorded in that monkey (6.4° and 5.2° left of fixation for Mo and Q, respectively).B, Pursuit responses of monkey Mo to a 16°/sec target with different values of Δt. The tracesplot average eye velocity and acceleration as a function of time. Traces begin at the time the patch target appeared and began to move. Different line types plot responses for different values of Δt, as indicated in the key. C, The average peak eye acceleration evoked by a 16°/sec target (circles) and the average acceleration latency (triangles) are plotted as a function of Δt. Peak eye acceleration is plotted as a percentage of that when Δt was 4 msec. Latency is plotted as the change from the latency when Δt was 4 msec. Longer latencies are plotted downward. Thus, for both peak acceleration and the acceleration latency, symbols below thedashed line indicate deficits relative to the pursuit evoked when Δt was 4 msec. Measurements of peak acceleration and latency were made for each individual trial and averaged. Error bars indicate SEM.
- Fig. 2.
Human judgment of the speed of apparent motion.A, Illustration of the task. Subjects fixated a central spot (cross) throughout each trial. A patch of moving dots appeared briefly above fixation (top panel). A second patch then appeared briefly below fixation (bottom panel). Subjects pressed one of two buttons to indicate which patch was moving faster. B, Symbols plot the proportion of responses in which the 16°/sec standard patch was judged faster, as a function of the speed of the comparator patch.Filled symbols plot, for each of five subjects, responses when the two patches both had a Δt of 4, and differed only in speed. Open gray symbols plot responses when the comparator patch had a Δt of 4 msec and the standard patch had a Δt of 32–64 msec. The exact value of Δt used depended on the subject (see Results). The black and gray lines show sigmoidal least-square fits.
- Fig. 3.
Effect of changing Δt on the responses of two MT neurons to apparent motion at 16°/sec.A, C, Histograms showing firing rate as a function of time for two MT neurons, with preferred speeds of 13.1°/sec (A) and 8.2°/sec (C). Bin width was 32 msec. Upward and downward histograms show the response to stimulus motion in the preferred and null directions of the neurons. The length of the arrowsat the right of the last histogram provides a scale, and indicates a firing rate of 100 spikes/sec in A and 50 spikes/sec in C. Stimulus duration was 500 msec and is indicated by the sequence of dots above each histogram. The locations of the dots indicate the timing of the flashes. The label above each pair of histograms inA indicates the value of Δt.B, D, The directional response of the neurons in A and C, plotted as a function of flash separation. The directional response is the mean firing rate evoked by motion in the preferred direction, minus that evoked by motion in the null direction. Error bars indicate SEM and are suppressed when smaller than the symbol size. The fits are sigmoidal least squares fits.
- Fig. 4.
Responses of two MT neurons to smooth motion at different speeds and to apparent motion at 16°/sec. A,C, Speed tuning. The directional response to effectively smooth motion (Δt = 4 msec) is plotted as a function of stimulus speed. Fits are least squared fits as described in Materials and Methods. The peak of the fit is at 8.0°/sec inA and 24°/sec in C. B,D, The directional response of the neurons inA and C to 16°/sec stimulus motion, plotted as a function of Δt. The inflection point of the sigmoidal fits is at 20 msec in B and 42 msec inD. Error bars in B and Dindicate SEM and are suppressed when smaller than the symbol size.
- Fig. 5.
Scatterplots showing the relationship between preferred speed and the limit of directionality. Each symbol corresponds to one cell. The limit of directionality was calculated as the inflection point of sigmoidal fits such as that in Figure4B. Data are shown separately for monkey Mo (left column) and monkey Q (right column) and for stimulus speeds of 16°/sec (top row) and 32°/sec (bottom row). The histogram at thetop of each column shows the distribution of preferred speeds recorded from each monkey. The histograms on theright show distributions of the limit of directionality for each of the two stimulus speeds, collapsed across both monkeys (for whom they were similar but not identical). A small number of neurons, with high or low preferred speeds, had such weak directional responses to stimulus speeds of 16 and/or 32°/sec that their limit of directionality could not be calculated with any confidence. For the relevant stimulus speed, such neurons were excluded from the analysis shown in this figure, but are included in subsequent analyses.
- Fig. 6.
Effect of apparent motion on the population response of MT neurons to stimulus motion at 16°/sec. Each point corresponds to one neuron and plots its response to a 16°/sec stimulus against its preferred speed. Red andblack symbols show responses to motion with values of Δt of 32 and 4 msec. The top andbottom graphs show data for monkey Mo (73 neurons) and Q (34 neurons), respectively. A, C, The “raw population response.” The response of each neuron to motion in its preferred direction is plotted on the right-hand side (positive preferred speeds), while its response to motion in its null direction is plotted on the left-hand side(negative preferred speeds). Each neuron thus contributes two data points for each value of Δt. B,D, The “opponent population response.” Each point plots the directional response of that neuron, computed as the difference between the responses to stimulus motion in the preferred and null directions. For all panels, the response of each cell has been normalized by the peak of the fit to the speed tuning data, so that its directional response to its preferred speed is one when Δt is 4 msec. Vertical black andred lines show the centers of mass of the population when Δt was 4 and 32 msec, respectively.
- Fig. 7.
Comparison of pursuit responses with estimates of target speed extracted from the population response using a variety of computations. All quantities are plotted as a function of Δt. Open black symbols show mean peak pursuit eye acceleration, calculated and normalized as for Figure 1. Error bars indicate SEM. Colored traces show estimates of target speed extracted via four methods: three versions of the vector average (VA) and a weighted sum, as indicated in the key. These computations were applied to the recorded population response of the relevant monkey for each speed and value of Δt. For comparison with pursuit data, estimates of target speed are shown as a percentage of the estimated speed when Δt was 4 msec. Error bars indicate the SE of the estimates, computed based on the SE of the firing rate of the neurons providing the input to the estimation. A, Data for monkey Mo and a target speed of 16°/sec. Peak eye acceleration was significantly increased when Δt was 32 and 44 msec (p < 10−7 for each).B, Data for monkey Mo and a target speed of 32°/sec. Eye acceleration was significantly increased when Δtwas 16 and 24 msec (p < 0.03 for each) and was decreased for larger values of Δt(p < 10−4 for each).C, Data for monkey Q and a target speed of 16°/sec. Eye acceleration was significantly increased when Δtwas 20, 24, and 32 msec (p < 0.05 for each) and was decreased for larger values of Δt(p < 10−9 for each).D, Data for monkey Q and a target speed of 32°/sec. Eye acceleration was significantly increased when Δtwas 12 msec (p < 0.005) and was decreased for values of Δt that were ≥24 msec (p < 10−7 for each).
- Fig. 8.
The influence of the parameter ɛon the behavior of the three vector average methods for estimating speed. All graphs plot pursuit data (open circles) and estimates of target speed (filled symbolsconnected by lines) for a stimulus speed of 16°/sec, derived and plotted as described in Figure 7. The three sets offilled symbols in each panel show estimates of speed created using different values of ɛ, as indicated by the keys. The top panels (A–C) each show data for monkey Mo (with the same pursuit data reproduced in each), and the bottom panels(D–F) show data for monkey Q. A,D, Estimates of speed were produced by the raw vector average. B, E, Estimates of speed were produced by preferred-only vector average. C,F, Estimates of speed were produced by opponent vector average.
- Fig. 9.
Illustration of the impact of the parameterɛ on the normalization provided by the vector average methods. The three curved traces show, for different values of ɛ, how the output of the vector average computations changes with the strength of the input, assuming the center of mass of the input is constant. The diagonal line shows the outcome if there were no normalization, and thehorizontal line shows the perfect normalization that results when ɛ is zero. The value of ɛ is expressed as a percentage of the denominator of the vector average when the input is at 100%.
- Fig. 10.
Time-varying estimates of target speed based on the time-varying population responses in area MT. Neural responses and estimates of speed are shown as a function of time for monkey Mo (left column) and Q (right column). Different trace types correspond to different values of Δt, as indicated by the numbers inA. A, B, Average responses of MT neurons to preferred direction motion at 16°/sec. Averages were made separately for each monkey, by summing the activity of all recorded neurons for a given stimulus, after normalization and filtering as described in Results. C,D, Average directional responses (the response to the preferred direction minus the response to the null direction) for the same stimuli as in A and B.E, F, Time-varying estimates of speed produced by the opponent vector average. Estimates were made by applying Equation 4 to the same neural responses that produced the averages in the above panels. All example traces in Figure 10 were computed after artificially shifting in time the responses of all MT neurons so that each had a latency of 100 msec for target motion of the preferred speed and direction.
- Fig. 11.
Comparison of pursuit with estimates of speed produced by the time-based version of the opponent vector average, applied to the recorded population response. Open symbols plot pursuit performance. Circles andtriangles plot, respectively, average peak acceleration and acceleration latency for each value of Δt, computed as in Figure 1. The small gray symbols andtraces plot measurements made from the estimate of speed. The estimate of speed for each stimulus was obtained by applying the opponent vector average to the time-varying population response recorded for that stimulus, resulting in traces such as those in Figure10, E and F. Small gray circles plot the peak estimate of speed (plotted against the left vertical axis), and small gray triangles plot the latency of the estimate of speed (plotted against the right vertical axis). Gray symbols connected by continuous lines show the results obtained when all neural responses were shifted to have a latency of 100 msec. Gray symbolsconnected by dashed lines show the results when the latency of each neuron was left at its natural value. All data are plotted relative to their values when Δt was 4 msec. Each graph shows results for a different monkey and target speed, as indicated.
- Fig. 12.
Comparison of pursuit with estimates of speed produced by the time-based version of the preferred-only vector average, applied to the recorded population response. Open symbols plot pursuit performance, as in Figure 11. Thesmall gray symbols and traces plot measurements made from the estimate of speed. The estimate of speed for each stimulus was obtained by applying the preferred-only vector average to the time-varying population response recorded for that stimulus. Small gray circles plot the peak estimate of speed (plotted against the left vertical axis), and small gray triangles plot the latency of the estimate of speed (plotted against the right vertical axis). Gray symbols connected by continuous lines show the results obtained when all neural responses were shifted to have a latency of 100 msec.Gray symbols connected by dashed linesshow the results when the latency of each neuron was left at its natural value. All data are plotted relative to their values when Δt was 4 msec. Each graph shows results for a different monkey and target speed, as indicated.
- Fig. 13.
Illustration of three hypothetical MT population responses. Neural response is plotted as a function of preferred speed, with rightward preferences on the right and leftward preferences on the left. The solid trace(A) shows an ideal population response with no baseline firing or nondirectional component. The thin trace (B) shows a population response with a small amount of baseline firing that contributes a nondirectional component. The dashed trace(C) shows a population response with a large nondirectional response component.
Tables
Δt (msec) Monkey M Monkey Q 16°/sec target 32°/sec target 16°/sec target 32°/sec target 4 0.15°/sec 0.10°/sec 0.55°/sec 0.63°/sec 12 0.10°/sec 0.14°/sec 0.61°/sec 0.55°/sec (4%) 16 0.16°/sec 0.22°/sec (−5%) 0.55°/sec 0.40°/sec 20 0.11°/sec 0.45°/sec (7%) 24 0.14°/sec 0.12°/sec (−5%) 0.36°/sec (12%) 0.19°/sec 32 0.13°/sec (1%) 0.09°/sec 0.22°/sec (22%) 0.07°/sec 44 0.01°/sec (3%) −0.02°/sec 0.13°/sec −0.01°/sec 64 −0.02°/sec 0.03°/sec Means were calculated as the average smooth eye velocity in the direction of the stimulus, over the 500 msec time the stimulus was present, after excision of saccades. Means are shown for both monkeys, two target velocities, and the full range of values of Δt. For those values of Δt that evoked statistically significant increases in pursuit eye acceleration, parentheses show the percentage of the increase in estimated speed (calculated using the static version of the opponent vector-average) that could be accounted for by the change in smooth eye velocity from when Δt was 4 msec. Negative percentages indicate that the artifact introduced by smooth eye movements would actually produce a decrease in estimated speed.
