Fig. 3: Conjunctive tuning to head position and conventional navigational variables.

a The contribution of each variable to model performance (log-likelihood increase (LLI) in information compared to a mean firing rate model; median [1st–3rd quartile], n = # of cells significantly encoding the variable of interest and at least one other variable; B = 0.64 [0.38–0.84], n = 394; H_a = 0.32 [0.14–0.58], n = 327; B_s = 0.15 [0.06–0.34], n = 332; H_p = 0.13 [0.07–0.18], n = 44; H_r = 0.17 [0.10–0.31], n = 44; \(\dot H_a\) = 0.06 [0.02–0.13, n = 64]). b Comparison of variable contributions. Boxplots; box, interquartile range; solid line, median; whiskers, range; outliers plotted separately ₍number of cells as in (a); Χ² = 410.3, P = 1.8e−86, df = 5; Kruskal–Wallis test followed by post hoc two-sided Wilcoxon rank-sum comparisons with α = 0.0033 after Bonferroni correction for multiple comparisons). ***for all significant pairwise comparisons, P < 0.00055. c The spike-normalized average log-likelihood increase in information across 10 folds of held-out data for all cells significantly encoding at least one variable (median [1st–3rd quartile]; 0.11 [0.04–0.26], n = 869). d Joint tuning curves. Examples where the cell encoded variable a but not b are labeled “a w/o b” (w/o; without). Examples where the cell encoded both variables are labeled “a × b”. Minimum and maximum firing rates are shown at top, with warmer colors indicating higher firing rates. Unvisited bins are shown in gray. Only model-derived tuning curves for significantly encoded variables are shown. e For each head position variable we constructed a two-dimensional “tuning curve profile space” (Methods, Supplementary Fig. 11). Within a plot, each circle represents a cell whose tuning curve was projected onto the first two principal components. Subplots are colored according to whether the cell significantly encoded each additional variable. f Example tuning curves from a subset of cells are shown at the cell’s position in the tuning curve profile space. B, body position; B_s, body speed; H_a, azimuthal head direction; H_p, pitch; H_r, roll; \(\dot H_a\), azimuthal head velocity.