Fig. 2

Model of modulation by heading direction relative to a reference point. a Definitions of the reference point and reference-heading (RH) angle. b RH-angle tuning for the recorded population of neurons compared to the tuning for surrogate data with randomly shuffled heading directions. Green circle is defined as in Fig. 1. 86% of the neurons are above the equality line (dashed line), and 56% are above the 95% confidence line (dotted line). c Variance explained by the model with both RH angle and place modulation compared to a purely spatial description. d Histogram of the fractional change in variance, defined as the change in variance due to RH modulation divided by the variance explained solely by place modulation. e Heading-direction tuning with spatial tuning removed over the full range of ±180 degrees divided into 10 bins. The eccentricity (around the circle of mean rate) of the polar plot represents the heading-direction modulation of the firing rate. f Same example cells as in e, showing spatial tuning (heat map), heading-direction tuning (blue arrows), and RH-angle tuning as fitted by the model (red arrows). Black circles are the reference points obtained by the model. Reference point far from the arena enclosure is noted by an arrow with the word “distant” pointing toward the reference point. g RH-angle tuning responses fitted by the model. Shaded area is the ±std.dev. These tunings are comparable with reports in bats¹⁵