Fig. 2.

The choice model characterizes individual biases and strategies and predicts variation of performance with reference orientation, as found in the data. (A) Choice model schematic. The angles of two oriented Gabor patches (white dashed lines, Left Column) are estimated as samples from circular distributions (density: purple, estimates: black crosses). Their absolute values are measured as angular distances to the vertical and compared with each other (Middle Column), which generates a choice. (B) Distribution $p({\theta }_R^{\ast },{\theta }_L^{\ast })$ of orientation estimates, as in A, in 2D space for $\left({\theta }_L,{\theta }_R\right)=(30°,0°)$ (red cross) in an unbiased model with $({\kappa }_R,{\kappa }_L)=(2,2)$, and a sample from this distribution (black cross). Probability mass inside the shaded areas ($\left|{\theta }_R^{\ast }\right|<\left|{\theta }_L^{\ast }\right|$) is equal to the probability of right choice P(R). Dashed lines: distribution quartiles. (C, Left) P(R) of model in B evaluated at all stimulus pairs $\left({\theta }_L,{\theta }_R\right)$. Red and black lines are one example branch of $\Delta \theta =18°$ and $\Delta \theta =-18°$, respectively. (Right) P(R) along the branches of constant $\Delta \theta$ marked on the Left with red and black lines. (D) Effect of model parameters on animals’ likelihood distributions over percepts (Top Row), P(R) surface assuming uniform priors (Middle Row), and the corresponding psychometric curves (Bottom Row). Red crosses: distribution means before parameter manipulation; green arrows: transformation of the distributions with parameter change; blue psychometric curves: before parameter change; red curves: after parameter change. The Center panel in the Middle Column shows P(R) values displaced relative to $\Delta \theta$ isolines (solid black: example isoline for $\Delta \theta$  =  15°). (E) Choice priors $p_b(x,y)$ with ${\kappa }_b$ equal to −1 (Left; left-choice bias) and 1 (Right; right-choice bias). (F, Left) Population average P(R) (n = 40 mice), with an example branch of $\Delta \theta =9°$ and $\Delta \theta =-9°$ marked with red and black lines, respectively. (Center) Population average of the model P(R), n = 40. (Right) P(R) values along the $\Delta \theta =\pm 9°$ branches in data (dots with error bars represent mean ± CI) and model (black lines with shaded areas are mean ± CI). Reference SI Appendix, Fig. S3 for P(R) of every animal. (G) Example mouse, Left to Right: 1) data P(R); 2) P(R) of the fitted model; 3) P(R) along the red dashed and solid lines on the Left predicted by the model (lines) and computed from the data (dots with error bars, darker dots correspond to the dashed line); and 4) P(R) along the black dashed and solid lines on the Left, as predicted by the model (lines) and computed from the data (dots with error bars, darker dots correspond to the dashed line). Reference SI Appendix, Fig. S3D for the model of P(R) for every animal. (H, Left) Population summary of model parameters fitted to all mice (n = 35; n = 5 animals with ${\kappa }_R$ or ${\kappa }_L$ estimated on the edge of the allowed range of values are excluded). (Middle) Ratio of $\text{log}({\kappa }_R+1)$ and $\text{log}({\kappa }_L+1)$ with the smaller of the two values divided by the larger value for each mouse (n = 35). Circles: individual animals; Box plot: population summary; Red line: median value; Box borders: 25th and 75th percentiles. Whiskers are up to most extreme parameter values. Red crosses: outliers. (Right) $\text{log}({\kappa }_R+1)$ and $\text{log}({\kappa }_L+1)$ across the population are significantly anticorrelated. Linear regression line for all animals together. Red circles: 10 mice with best performance.