(A) Recording sites. Left: Two regions of interest were recorded through single electrodes in macaque monkeys. Middle and right: Specific recording sites in three monkeys. AS, arcuate sulcus; CS, central sulcus; IPS, intraparietal sulcus; SPD, superior precentral dimple. L, left hemisphere; R, right hemisphere; A, anterior; P, posterior; M, medial. The straight dash gray line separated the dorsal and ventral part of the premotor cortex in the middle panel. The straight dash gray line indicates the middle of IPS and CS. The circular dash lines indicate the recording chambers. (B) Temporal structure of a single trial for the visual-proprioceptive conflict (VPC) task. (C) Neural information of arm locations in premotor and parietal cortices. Upper: No significant difference between the brain regions for the neural information of VP arm (Wilcoxon rank-sum test, W=0.64, dfpremotor = 411, dfparietal = 237, p=0.52, false-discovery rate [FDR] corrected, rrb = 0.030) and P arm (W=0.51, dfpremotor = 411, dfparietal = 237, p=0.52, FDR corrected, rrb = 0.031), respectively. Bottom: There were significant differences between the brain regions for both the neural information of proprioceptive arm (Wilcoxon rank-sum test, W=–3.92, dfpremotor = 411, dfparietal = 237, p<0.001, FDR corrected, rrb = 0.18) and visual arm (W=6.34, dfpremotor = 411, dfparietal = 237, p<0.001, FDR corrected, rrb = 0.30) in VPC task, respectively. Both brain regions conveyed significant information about the arm location in the three tasks (premotor: VP arm, Wilcoxon signed-rank test, W = 27,712.0, df = 474, p<0.001, FDR corrected, rrb = 0.35; P arm, W = 25,614.0, df = 411, p<0.001, FDR corrected, rrb = 0.40; proprioceptive arm (VPC), W=22,316.0, df = 411, p<0.001, FDR corrected, rrb = 0.48; visual arm (VPC), W=14,874.0, df = 411, p<0.001, FDR corrected, rrb = 0.65. Parietal: VP arm, W=9466.0, df = 237, p<0.001, FDR corrected, rrb = 0.33; P arm, W=7414.0, df = 237, p<0.001, FDR corrected, rrb = 0.48; proprioceptive arm (VPC), W=3745.0, df = 237, p<0.001, FDR corrected, rrb = 0.74; visual arm (VPC), W=10,138.0, df = 237, p<0.001, FDR corrected, rrb = 0.29). Each circle indicates a neuron. The effect sizes (rrb) were performed using the rank-biserial correlation. (D) Raster plots and mean firing rates from an example neuron in the parietal cortex that exhibited responses varied with visual disparity, showing the preference for the P task during the target-holding period (gray zones). The yellow curve was fitted with a von Mises distribution. (E) Schematic drawing of VP weight analysis (see Materials and methods) in one example trial for the VPC task. In brief, we first mapped the tuning curves of arm position in VP (left red curve) and P (left blue curve) tasks as integration and segregation templates, respectively. Then, during the VPC task, for a single trial, we mapped the visual and proprioceptive arm position onto the these templates to get the probabilities of integration and segregation. Then, we normalized the probability to get the VP weight. (F) Two examples of causal inference neurons in premotor and parietal cortices during the target-holding period (the same neurons shown in Figure 3—figure supplement 2 and (D), respectively). Each point represents one single trial, and the color represents the value of VP weight. The color bar represents VP weight, larger values indicate higher VP weights (higher probability of integration). (G) Population causal inference patterns in two brain regions. Each point was a pseudo-trial that was generated through bootstrapping, and the color represents the value of VP weight. (H) An example neuron in the parietal cortex shows the causal inference pattern defined by a significant positive correlation between VP weight and Pcom (Pearson correlation). Each point represents the average Pcom and VP weight in a cluster from the behavioral Pcom pattern. The solid line was fitted with linear regression, and the shaded area indicates the 95% confidence interval. The bar plot represents the fraction of causal inference neurons in the premotor cortex and parietal cortex. ***p<0.001.