Decision-making with multiple alternatives

Abstract

Simple perceptual tasks have laid the groundwork for understanding the neurobiology of decision-making. Here, we examined this foundation to explain how decision-making circuitry adjusts in the face of a more difficult task. We measured behavioral and physiological responses of monkeys on a two- and four-choice direction-discrimination decision task. For both tasks, firing rates in the lateral intraparietal area appeared to reflect the accumulation of evidence for or against each choice. Evidence accumulation began at a lower firing rate for the four-choice task, but reached a common level by the end of the decision process. The larger excursion suggests that the subjects required more evidence before making a choice. Furthermore, on both tasks, we observed a time-dependent rise in firing rates that may impose a deadline for deciding. These physiological observations constitute an effective strategy for handling increased task difficulty. The differences appear to explain subjects' accuracy and reaction times.

Figure 1

Task and performance, (a–c) Sequence of events on 2- and 4-choice direction discrimination tasks. The monkey fixates a central point until the random dot motion appears and is then permitted to indicate its decision by making a saccadic eye movement to a choice target. The motion is in one of 2 or 4 directions (trials randomly interleaved in a 1:2 ratio). A liquid reward is given for choosing the target along the axis of random dot motion, or it is given with probability ½ or ¼ when the motion strength is zero. Random intervals (truncated exponential distributions) separate fixation, appearance of choice targets and motion onset. The random-dot motion is extinguished when the monkey initiates a saccade to one of the choice targets. This interval, from motion onset to saccade initiation, is the RT. One of the choice targets is in the RF of an LIP neuron recorded during the task (shading). The shading is only meant as a guide: actual RF size varied considerably, (a) 2-choice task. The directions are 180° apart. One direction is toward the target in the neuron’s RF (T_in), (b) 4-choice task. The directions are 90° apart, (c) 90° control task, (d–g) Speed and accuracy of decisions. Smooth curves in all panels are fits to the bounded diffusion model described at the end of Results. The fits were performed separately for panels (d,f) and for panels (e,g). (d) Psychometric functions. The probability of a correct choice is plotted as a function of motion strength. All experiments contribute to these graphs. At 0% motion strength, choices are rewarded randomly (open symbols), (f) Psychometric functions for the 29 experiments that included the 90° control, (e) Chronometric functions. Mean RT for correct trials is plotted as a function of motion strength. Each point reflects correct responses from all experiments. Error bars are s.e.m.; some are smaller than the symbols, (g) Chronometric functions for the 29 experiments that included the 90° control.

Figure 2

Responses of LIP neurons on the 4-choice task are consistent with bounded accumulation. Firing rates are aligned to key events in the course of a trial, which are marked by vertical lines. For the trials depicted here, motion was either random (0% coherence) or in the T_in direction, (a) Average firing rates from 1 neuron. Left: responses aligned to onset of the choice targets; middle: responses aligned to the onset of stimulus motion; right: responses aligned to saccade initiation. For saccade-aligned responses, only T_in choices are shown. For purposes of display, traces are smoothed with a 30 ms exponential filter, (b) Responses reflect termination of the decision. Responses are grouped by RT at the values indicated (± 25 ms). The averages are aligned to saccade initiation and exclude neural activity within 200 ms of motion onset. Only correct T_in choices are included, and for clarity, every other RT group is not displayed. (c,d) Population average responses (N=70 neurons). Same conventions as in (a) and (b), except that no smoothing was performed; firing rates were computed in 20 ms non-overlapping bins. Arrow in (c) indicates the dip in firing rate seen shortly after motion onset. Arrow in (d) indicates the time when responses appear to coalesce, approximately 60 ms before the saccade.

Figure 3

Neural responses in the pre-motion epoch are larger on the 2-choice task, (a) Average firing rate from a single neuron during the pre-motion epoch when 2 or 4 choice-targets were displayed. Vertical black line indicates the onset of the choice targets. Insets are a schematic of the target configurations used in this experiment. One target is in the neuron’s RF (shading). (b) Population average response. Same conventions as in (a) except that traces are average firing rates from 70 neurons. All trials contribute to these averages. Insets illustrate that one target is in the RF of the neuron; the location of this RF varies from neuron to neuron, (c) Comparison of firing rates from individual neurons on the 2- and 4-choice tasks. Responses were measured from 200 to 300 ms after choice target onset. The green circle marks the neuron shown in (a). Points for three neurons with high background firing rates are omitted from the plot to facilitate an appropriate scale for the remaining points (^{{227,174}, {132,99}, {144,127}}) Error bars are s.e.m. and are occasionally obscured by the points. Histogram displays the firing rate differences for all 70 neurons. Shading indicates significance (p<0.05). (d) Comparison of firing rates from individual neurons on the 2-choice and the 90° control tasks. Same conventions as in (c). Two neurons were omitted from the scatter plot ({131,138}, {227,226}).

Figure 4

Neural responses during motion viewing depend on difficulty, (a–d) Population average firing rates (N=70 neurons) are shown for three motion strengths. Panels group together trials based on the direction of motion and the number of choices (cartoon insets). Correct and incorrect trials are included in these averages. The traces for 0% coherent motion are identical in panels (a,b) and in panels (c,d). Only three motion strengths are shown for clarity. Shaded rectangle indicates the epoch used to estimate the buildup rates (190–320 ms after the onset of stimulus motion), (a) 2-choice trials when the motion direction was toward T_in. Arrow indicates the stereotyped firing rate “dip” that occurs after motion onset, (b) 2-choice trials when the motion direction was toward T_out. (c) 4-choice trials when the motion direction was toward T_in. (d) 4-choice trials when the motion direction was toward T_out (dashed line) or toward an orthogonally positioned (T₉₀) target (dot-dash line). The five traces on this panel are largely superimposed. The single cyan trace is for 0% coherent motion averaged across all choices (T_in, T_out and T₉₀; same as cyan trace in c) (e–g) Effect of motion strength on buildup rates, (e) Single neuron example. Buildup rates were estimated for each motion strength; these buildup rates (±s.e.) are plotted as a function of motion strength. The slope of the fitted line estimates the effect of a unit change in motion strength on the buildup rate. Black, 2-choice; Red, 4-choice. 5 motion strengths were tested for this neuron (methods) (f) Same conventions as in (e) except that buildup rates were calculated in individual neurons and then averaged across the population (N=70 neurons) before fitting the line. Error bars are s.e. of buildup rates across neurons, (g) Population analysis for the 29 neurons tested with the 90° control condition in addition to 2- and 4-choice trials. Blue lines correspond to the 90° control condition; error bars are s.e. of buildup rates across neurons. Points corresponding to 51.2% motion strength are not included on this plot because this motion strength was tested in only 3 neurons.

Figure 5

Neural responses just preceding the eye movement responses. Population average firing rates (N=70 neurons) are shown aligned to the initiation of saccades (vertical line). Panels group together trials based on the direction of the saccade with respect to the RF of the neuron (cartoon insets). Only 3 motion strengths are shown for clarity, (a) T_in choices in the 2-choice task, (b) T_out choices in the 2-choice task, (c) T_in choices in the 4-choice task, (d) T_out (dashed) and T₉₀ (dot-dash) choices in the 4-choice task.

Figure 6

Firing rate excursion is larger on the 4-choice task, (a) Firing rates on 2- and 4-choice trials at the beginning and end of the motion-viewing period for a single example neuron. Responses are aligned to motion onset (left) and saccade initiation (right). Black and red traces indicate responses on the 2- and 4-choice tasks, respectively. For purposes of display, traces are smoothed with a 30 ms exponential filter. Excursion is the difference between firing rates in the shaded regions. All responses leading to correct T_in choices and with RT>450 ms are used in this analysis. Firing rate excursion was 29.7±8.4 sp/s larger for 4-choice than for 2-choice. (b) Same as (a) except that traces reflect the average firing rate from 70 neurons and no smoothing was performed; firing rates were computed in 20 ms nonoverlapping bins, (c) Comparison of firing rate excursion on 2- and 4-choice tasks. Points are estimates of the firing rate excursion from single neurons. One point {170,159} was omitted from the scatter plot to facilitate scaling of the remaining points. Error bars show s.e. of the excursion (Eq. 2) and are occasionally obscured by the points. Green circle marks the example neuron in (a). Histogram depicts the differences in excursion on 2- minus 4-choice tasks. Arrow indicates the mean. Only correct responses to T_in targets were used for this analysis. Gray shading indicates individual neurons with significant differences (p<0.05). (d) Comparison of firing rate excursion on 2-choice and 90°-control tasks. Same conventions as in (b). The same neuron {170,157} was omitted from the scatter plot.

Figure 7

Neural responses and RTs are inversely correlated on single trials, (a) Trial-by-trial correlation between RT and buildup rate for one representative neuron (Kendall τ=−0.30, p<10⁻⁴). Values are expressed in units of standard deviations from mean. This detrending was performed for each motion strength using all correct T_in choices and all T_in choices for 0% coherence, (b) Same as (a) but for 4-choice trials (τ=−0.42, p<10⁻⁴). (c–d) Distribution of correlation coefficients (Kendall τ) for each neuron in the data set. Gray shading indicates individual neurons with significant correlation (p<0.05). (c) 2-choice task. Arrow indicates the mean, (d) 4-choice task. Arrow indicates the mean.