Slowing of Movements in Healthy Aging as a Rational Economic Response to an Elevated Effort Landscape

Reward quickens reaction time in both groups, but older adults are less willing to increase their movement speed (Experiment 2). A, Participants performed out-and-back reaches to alternating targets projected along a ring 14 cm from the home circle. The desired quadrant was indicated with a marker centered at the middle of the quadrant. Visual feedback of the cursor was removed during the outward portion of the movement and was re-displayed during the return portion of the reach once the hand was 9 cm from the home target. The protocol consisted of a baseline period with no reward followed by four experimental blocks. Each experimental block had one quadrant paired with a reward (RWD). Audiovisual reward stimulus was delivered upon crossing any region of the 100° target arc. The gray areas indicating reward were not visible to the participant, but are presented in the figure to convey which quadrant was paired with reward. B, We used a nonparametric kernel density estimation method to calculate the probability distribution for each individual when making movements to rewarded (RWD, solid curves) and nonrewarded (NRWD, dashed curves) quadrants as well as a difference (dotted curve) in these distributions at each bin (bin size = 5 ms). Younger adults (green curves) initiated movements earlier than older adults (red curves), but both groups responded to reward by reacting sooner. C, Effects of reward on movement execution in young (green) and older (red) adults. Young adults made movements toward quadrants paired with reward (RWD, solid curves) with greater peak speed when compared to that same quadrant when not rewarded (NRWD, dashed curves). Older adults reached with a peak speed that was independent of reward status. Inset graph depicts enlarged region highlighted peak speed. D–F, Scatter plot representing the relationship between rewarded (RWD, vertical axis) and nonrewarded (NRWD, horizontal axis) movements according to mean reaction time (D), movement duration (E), and peak speed (F). Dots represent individual participants. Crosses represent the mean for each age group, and the length of the bars represents ±SEM. The mean effect of reward for each age group is indicated with the inset bar graph, reported as mean ± SEM. G, Proportion of time savings due to reaction time (RT) and movement time (MT) in young vs older adults. The proportion of time saved by reacting faster is larger in older adults

A rational response to increased effort costs is to slow movements and reaction times. A, Logistic function representing the speed–accuracy tradeoff for reaction times. B, Logistic curves fit to endpoint data of older (red) and young (green) adults representing the speed–accuracy tradeoff for movement times. For a given reach duration, older adults saw a lower probability of success than the young. C, Effect of effort costs on optimal reaction times (dotted lines) and movement times (solid lines) across arbitrary reward values, using (Eq. 7). Fitted metabolic parameters (Fig. 1B) and associated speed–accuracy curves were used for the young and older curves. D, Effect of reward devaluation on optimal reaction times and movement times. Green curves represent optimal solutions based on the younger adult metabolic fits, accuracy, and nominal reward valuation (k = 1). Red curves are optimal solutions with the same effort costs, but older adult accuracy and reduced reward valuation (k = 0.8). E, F, The proportions of time saved (ΔRT/(ΔRT + ΔMT)) due to reducing reaction time or movement time for an arbitrarily selected increase in reward from 45 J to 50 J (gray region in C, D). Compared to young, older adults should allocate a larger proportion of time savings to reducing reaction times due to higher metabolic costs (E). If older adults were instead valuing reward less, their proportion of time savings from reaction time should instead be lower (F).