Range-adapting representation of economic value in the orbitofrontal cortex

Abstract

While making economic choices, individuals assign subjective values to the available options. Values computed in different behavioral conditions, however, can vary substantially. The same person might choose some times between goods worth a few dollars, and other times between goods worth thousands of dollars, or more. How does the brain system that computes values -- the "valuation system" -- handle this large variability? Here we show that the representation of value in the orbitofrontal cortex (OFC), an area implicated in value assignment during economic choice, adapts to the behavioral condition of choice and, more specifically, to the range of values available in any given condition. In the experiments, monkeys chose between different juices and their choice patterns provided a measure of subjective value. Value ranges were varied from session to session and, in each session, OFC neurons encoded values in a linear way. Across the population, the neuronal sensitivity (defined as the change in neuronal activity elicited by the increase in one value unit) was inversely proportional to the value range. Conversely, the neuronal activity range did not depend on the value range. This phenomenon of range adaptation complements that of menu invariance observed in a previous study. Indeed, the activity of each neuron adapts to the range values it encodes but does not depend on other available goods. Our results thus suggest that the representation of value in the OFC is at one time instantiative of preference transitivity (menu invariance) and computationally efficient (range adaptation).

Figure 1.

Experimental design and preliminary analysis. a, At the beginning of each trial, the monkey fixated the center of a computer monitor. Two sets of squares appeared on opposite sides of the fixation point (“offer”). Different colors of the squares indicated different juice types and the number of squares indicated the juice amount. After a randomly variable delay (1–2 s), two saccade targets appeared near the offers (“go”). The monkey indicated its choice and maintained fixation on the saccade target for 0.75 s before juice delivery. The trial was aborted if the monkey broke fixation before the go. For any juice pair, the quantities of the two juices varied randomly. For any given pair of offers (offer type), left/right positions were randomly counterbalanced. b, Neuronal response encoding the offer value A. In the left, black circles represent the behavioral choice pattern, i.e., the percentage of B choices (y axis) recorded for different offer types (x axis). The relative value, obtained from a sigmoid fit, is indicated in the panel. In the same panel, red symbols represent the neuronal firing rate ± SEM. Diamonds and circles represent trials in which the monkey chose juice A and juice B, respectively. On the right, the same firing rate (y axis) is plotted against the encoded variable offer value A (x axis). The black line is obtained from the linear regression and the regression parameters (slope and intercept) are indicated. c, Neuronal response encoding the offer value B plotted against the offer type (left) and against the encoded variable (right). d, Neuronal response encoding the chosen value plotted against the offer type (left) and against the encoded variable (right). Regression slopes are expressed in conventional value units uV, corresponding to uA for offer value A and uB for offer value B and chosen value (see Materials and Methods). sp, Spikes.

Figure 2.

Slope distributions. a–c, Distribution of signed slopes. The histograms represent the number of responses (y axis) recorded with a given regression slope (x axis), separately for the three encoded variables. For each variable, the two distributions obtained for the subsets of responses with positive and negative slopes are statistically indistinguishable (all p > 0.15, Wilcoxon test). d–f, Distribution of rectified slopes. The distribution obtained for offer value A responses is significantly broader than that obtained for offer value B responses (p < 10⁻¹⁰, Wilcoxon test). For each variable, the median of the distribution is indicated in the corresponding panel. sp, Spikes.

Figure 3.

Model of range adaptation. a, Firing rate. The model describes the activity of a value-encoding neuron recorded in different behavioral conditions. The generic variable value of X corresponds either to the variable offer value X (if X is one particular juice) or to the variable chosen value (if X is the chosen juice). The relationship between the neuronal firing rate (y axis) and the value variable (x axis) is assumed to be linear. Different behavioral conditions are characterized by different value ranges. The fundamental assumption of the model is that the neuronal activity range remains constant and independent of the value range. In other words, the relationship between the neuronal firing rate and the encoded value depends on the value range: the neuron adapts in such a way that its activity range describes, in any behavioral condition, the entire range of available values. b, c, Slope. According to the model, the slope of the encoding (corresponding to the neuronal sensitivity) is proportional to the inverse value range.

Figure 4.

Regression slope versus value range. a–c, Slope distributions. The three panels refer to neuronal responses encoding offer value A (a), offer value B (b), and chosen value (c). In each panel, the regression slope (y axis) is plotted against the value range (x axis) and each black cross represents one neuronal response. Value ranges are measured in conventional units. Color diamonds represent the mean slopes computed for the corresponding subpopulation. In the case of chosen value responses, means are computed binning value ranges (see Materials and Methods). For all encoded variables, the mean regression slope decreases as a function of the value range. d, e, Mean slopes. Mean slopes are plotted against the value range (ΔV, d) and against the inverse value range (1/ΔV, e). The three colors represent the three encoded variables. The relationship slope ∝ 1/ΔV can be observed in both panels and is confirmed by a linear fit (see Results).

Figure 5.

Population firing rate for offer-value responses. a, Individual responses. The entire population of 937 neuronal responses encoding the offer value is shown (offer value A and offer value B responses are combined). Neuronal responses were baseline-subtracted, rectified and plotted here (y axis) against the offer value (x axis). Different colors highlight different value ranges. Qualitatively, we observe that for each value range neuronal activities are broadly distributed. However, the distributions recorded for different value ranges appear rather similar. b, Average neuronal responses. Each line represents the average neuronal response obtained for given value range (see color legend). Neuronal adaptation can be observed for any value, as average neuronal responses recorded with different value ranges are well separated throughout the value spectrum (e.g., compare the activity recorded at V = 2 for various ranges ΔV). c, Distribution of activity ranges. Each histogram illustrates the distribution of activity ranges obtained for the subpopulation of responses recorded with the corresponding value range (color codes as in b). Small triangles indicate the medians. Several statistical tests failed to find any significant correlation between activity range and value range (p > 0.13, Kruskal–Wallis test; p > 0.7, correlation analysis). Analyses in b and c were performed only for subpopulations of at least 40 responses. sp, Spikes.

Figure 6.

Population firing rate for chosen value responses. a, Individual responses. The entire population of 817 neuronal responses is shown. Neuronal responses were baseline subtracted and rectified, and they are plotted here (y axis) against the baseline-subtracted chosen value (x axis). Different colors highlight different value ranges. b, Average neuronal responses. We binned value ranges and divided neuronal responses in subpopulations recorded with different value ranges. Each line in the plot represents the average neuronal response obtained for a given value range (see color legend). Average neuronal responses recorded with different value ranges are separated throughout the value spectrum (e.g., compare the activity recorded at V = 2 for various ranges ΔV). c, Distribution of activity ranges. Each histogram illustrates the distribution of activity ranges obtained for the subpopulation of responses recorded with the corresponding value range (color codes as in b). Small triangles indicate the medians. Several tests failed to find any significant correlation between activity range and value range (p > 0.05, Kruskal–Wallis test; p > 0.4, correlation analysis). Analyses in b and c were performed only for subpopulations of at least 40 responses. sp, Spikes.

Figure 7.

Invariance of the neuronal activity range. a, The activity range does not depend on the juice preference. Of the 100 neuronal responses encoding the offer value of cranberry juice in our dataset, 26 responses were recorded in sessions in which cranberry juice was preferred (juice A) and 74 responses were recorded in sessions where cranberry juice was nonpreferred (juice B). These two groups of responses are plotted separately here (black, preferred; gray, nonpreferred). The histogram shows the percentage of responses (y axis) recorded with different activity ranges (x axis). A comparison revealed that the distributions measured for the two groups of responses are very similar (p > 0.2, Wilcoxon test). b, The activity range does not depend on the value. Our dataset includes 47 chosen value responses recorded in sessions in which monkeys chose between apple juice and peppermint tea. The relative value of the two juices varied from session to session. In the scatter plot, each circle represents one neuronal response, and the activity range (y axis) is plotted against the relative value of the two juices (x axis). No systematic relation between the two measures was found (95% confidence interval, linear fit). sp, Spikes.

Figure 8.

Scale invariance. For each response in the main dataset, we computed the inverse value range and the regression slope expressing values either in uA or in uB. We then binned the inverse value range (bin size 0.05–0.2, see Materials and Methods). In the scatter plot, mean regression slopes (y axis) are plotted against the inverse value range (x axis), separately for different encoded variables (offer value or chosen value) and different value units (uA or uB, see color legend). Thus, each neuronal response contributes to this plot twice (once for each value unit). Regression lines are obtained from an analysis of covariance of the mean regression slope using the inverse value range as predictor and the dividing data in four groups (2 encoded variables × 2 value units). Computing the full statistical model amounts to testing whether the regression lines differ significantly from each other for their intercepts (main factor group) and/or for their slopes (interaction). The results did not find any such significant effect (both p > 0.1).

Figure 9.

Range adaptation for individual neurons. a, One response. The figure illustrates the activity of one chosen value response recorded with a small value range (left, ΔV = 4.3 uB) and with a large value range (center, ΔV = 8.1 uB). In both panels, filled black circles represent the behavioral choice pattern and empty color symbols represent the firing rate (all conventions as in Fig. 1b). Right, The same neuronal response is plotted against the chosen value separately for the two trial blocks. The emerging picture closely resembles that of the adaptation model (Fig. 3). b, Change in regression slope. In the scatter plot, slopes recorded with small ΔV (x axis) are plotted against slopes recorded with large ΔV (y axis). Each circle represents one neuronal response, and different colors identify offer value and chosen value responses (see legend). A square represents one outlier (y = 3.58). Consistent with adaptation, the vast majority of responses lie below the identity line. c, Change in activity range. Axes represent the activity ranges recorded with small ΔV (x axis) and large ΔV (y axis). Each circle represents one response, and different colors identify offer value and chosen value (same colors as in b). A square represents one outlier (y = 21.45). Activity ranges were approximately stable across trial blocks. sp, Spikes.

Figure 10.

Partial adaptation on the time scale of individual trials. a, One response. Red symbols represent the response computed pooling all trials. Trials were then separated in two groups, with V(n) > V(n − 1) (blue symbols) and V(n) < V(n − 1) (green symbols). For each trial type, trials with V(n) = V(n − 1) were assigned to the group with fewer trials. For most trial types, the “blue firing rate” [trials V(n) > V(n − 1)] was slightly higher than the “green firing rate” [trials V(n) < V(n − 1)], consistent with neuronal adaptation. For each trial type, we computed the difference between the blue firing rate and the green firing rate, and we normalized it by the red firing rate. This normalized difference averaged across trial types defined δ. Thus, δ represents the mean percentage modulation of trial n − 1 on the activity recorded on trial n. For this particular response, δ = 0.14. b, Population analysis, distribution of δ for trial n − 1. For both offer value (top) and chosen value (bottom) responses, the x axis represents δ and the y axis represents the number of responses. Both variables present a large variability. However, δ was greater than zero in a significant majority of cases [binomial test (bino)], and mean(δ) was significantly larger than zero (t test; p values indicated in inserts). c, Population analysis, mean(δ) over trials. The mean(δ) (±SEM) (y axis) is plotted against the trial number (x axis) separately for offer value and chosen value responses. Filled squares indicate data points statistically different from zero (binomial test, p < 0.01; same results for t test, p < 0.01). Mean(δ) is ∼6% for trial n − 1, ∼2% for trial n − 2, and statistically indistinguishable from zero for earlier trials. As expected, mean(δ) is also indistinguishable from zero for trial n + 1. sp, Spikes.