Figure 1.
The motion discrimination task.
Target colors cue the magnitude of rewards for correct responses, red denoting a value twice that of blue. The four panels in the reward segment show the possible reward conditions. See text for full description.
Figure 2.
A typical state space of the LCA model, showing nullclines on which for
(thin curves), fixed points (filled circles with arrows indicating stability types) and slow manifold (dashed line).
Diagonal solid line represents one-dimensional state space of reduced OU model, with associated probability distribution
of sample paths.
Figure 3.
Psychometric functions showing fraction of T1 choices as a function of coherence for constant reward bias
applied before and during motion period.
(A) ; (B)
; (C)
; each panel shows the cases
and −0.1 (left to right). Remaining parameters are
and
(arbitrary time units). Green lines indicate slopes for zero bias; arrows show shifts.
Figure 4.
Optimal shifts as a function of the reward ratio r1/r2 for fixed coherences (solid blue curves) and for coherence ranges centered on the fixed coherences (dashed red curves).
(A): = 10; 20 and 30% (top left to bottom right, solid blue), and [C1;C2] = [5; 15]; [15; 25] and [25; 35] (top left to bottom right, dashed red). (B): Coherence bands centered on
= 20% (solid blue curve) with widths 10; 20; 30 and 40% (bottom left to top right, dashed red). Approximation of Eq. (30) shown in green. The slope b1 is fixed at 0.06 throughout.
Figure 5.
Fits of accuracy data from monkeys A (A) and T (B) to the PMF (15), for the four reward conditions averaged over all sessions.
Bars denote standard errors. See text for details.
Figure 6.
Optimal shifts b2 for a range of reward ratios r1/r2 and b1 = 0.0508 (solid, black) and b1 = 0.0432 (dot-dashed, red), corresponding to slopes of PMFs fitted to equal rewards data for monkeys A and T.
Vertical dotted lines at r1/r2 = 0.5 and 2 intersect the curves at the symmetrically-placed optimal shifts for those reward ratios. (A) Predictions for the different sets of nonuniformly-distributed coherences viewed by each animal. (B) Results for coherences distributed uniformly from −48% to 48%: note smaller optimal shifts and reversal of order of curves for A and T compared to panel A. Triangles and crosses respectively indicate shifts determined from data for monkeys A and T for r1/r2 = 0.5, 1 and 2 (cf. Table 1).
Table 1.
Parameter values for data fits for monkeys A and T, averaged over all sessions, to the PMF (15).
Figure 7.
Contours (black curves) of expected rewards for
for monkeys A (A) and T (B) over the (
)-plane, based on the coherences viewed by each animal.
Vertical dashed lines indicate values fitted to pooled equal rewards data. Note that gradients in
in either direction away from ridges of maximum expected rewards (blue curves) become smaller as
decreases, that gradients are smaller for overshifts in
than for undershifts, that this asymmetry increases as
decreases, and that gradients are steeper for T than for A. See text for discussion.
Figure 8.
Optimal PMFs (black curves) and bands (color) in which 99.5% of maximal possible rewards are gained, compared with session-averaged HL, LL and HH, and LH data (triangles, left to right on each panel) for monkeys A (A) and T (B).
See text for details.
Figure 9.
Slope and shift values for individual sessions and the four reward conditions, plotted as points in the for monkeys A (four panels in (A)) and T (four panels in (B)).
Asterisks indicate values averaged over all sessions (cf. top two rows of Table 1). Performance curves and bands show optimal values for given
values (central blue curves) and values that gain 99% and 97% of maximum rewards are also shown (flanking magenta curves closest to and farthest from blue curves, respectively).