a, Left, all data points (trials) from an example cell. The solid lines are linear fits to the positive and negative domains, and the shaded areas show 95% confidence intervals calculated with Bayesian regression. Right, the same cell plotted in the format of Fig. 4b. b, Cross-validated model comparison on the dopamine data favours allowing each cell to have its own asymmetric scaling (P = 1.4 × 10−11 by paired t-test). The standard error of the mean appears large relative to the P value because the P value is computed using a paired test. c, Although the difference between single-asymmetry and diverse-asymmetry models was small in firing-rate space, such small differences correspond to large differences in decoded distribution space (more details in Supplementary Information). Each point is a TD simulation; colour indicates the degree of diversity in asymmetric scaling within that simulation. d, We were interested in whether an apparent correlation between reversal point and asymmetry could arise as an artefact, owing to a mismatch between the shape of the actual dopamine response function and the function used to fit it. Here we simulate the variable-magnitude task using a TD model without a true correlation between asymmetric scaling and reversal point. We then apply the same analysis pipeline as in the main paper, to measure the correlation (colour axis) between asymmetric scaling and reversal point. We repeat this procedure 20 times with different dopamine response functions in the simulation, and different functions used to fit the positive and negative domains of the simulated data. The functions are sorted in increasing order of concavity. An artefact can emerge if the response function used to fit the data is less concave than the response function used to generate the data. For example, when generating data with a Hill function but fitting with a linear function, a positive correlation can be spuriously measured. e, When simulating data from the distributional TD model, where a true correlation exists between asymmetric scaling and reversal point, it is always possible to detect this positive correlation, even if the fitting response function is more concave than the generating response function. The black rectangle highlights the function used to fit real neural data in c. f, Here we analyse the real dopamine cell data identically to Fig. 4d, but using Hill functions instead of linear functions to fit the positive and negative domains. Because the correlation between asymmetric scaling and reversal point still appears under these adversarial conditions, we can be confident it is not driven by this artefact. g, Same as Fig. 4d, but using linear response function and linear utility function (instead of empirical utility).