Finding the way home
How does sensory information shape a bat’s sense of direction?
We reanalyzed the flight paths of Kuhl’s pipistrelle bats from Goldshtein et al. (2024). By expressing each movement relative to its recorded destination, we separated orientation, directional precision, and the prevalence of concentrated headings.
The fitted circular models connect these three features to sensory treatment and individual variation. Echolocation remained available in every group.
A path through space
We resampled each trajectory every 60 m of traveled distance.
A bearing to the goal
Zero degrees points toward the roost or along the lake’s approach field.
A distribution of directions
We fitted a von Mises distribution and a von Mises–uniform mixture.
From flight paths to fitted bearings
67 bats · 4,942 headingsEach path leads toward a recorded destination. The selected heading links its location on the map to the fitted distribution on the circle.
Loading flight paths and model fits…
The flight path
Recorded trajectoriesThe solid arrow shows movement; the dashed arrow shows the goal reference. North is up. Distances use UTM zone 36N. Tracking gaps are dashed; they are not reconstructed flight paths.
Bearings relative to the goal
Observed + fittedDots lie on the unit circle. Radius beyond it represents density. The band describes uncertainty in the density.
Component membership is a statistical attribution, not an observed behavioral state.
One peak, or a peak and a background?
von Mises + uniformA single von Mises distribution summarizes the headings with one mean direction and one concentration. The mixture allows a concentrated directional tendency to coexist with broadly distributed headings.
How the fitted density adds up
- Orientation · μ
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- Precision · κ
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- Concentrated weight · w
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Median and central 90% posterior interval for the selected bat. Larger κ means a narrower peak. Weight describes prevalence among sampled headings, approximately along distance traveled.
The histogram and fitted curve use this bat’s full set of modeled headings, regardless of the playback position.
What changes across treatments?
Population termsWe allowed each treatment to change the mean direction, concentration, and, in the mixture, component weight. Individual effects captured differences among bats within the same treatment.
Orientation · μ
Degrees from the goalPrecision · κ
Higher = narrowerConcentrated weight · w
Fraction of sampled headingsDots show medians; lines span central 90% intervals. These are treatment predictions with individual effects set to zero, not averages over a population of new bats. All destinations contribute to each fitted treatment effect. “+ magnet” includes eye cover; “+ anosmia” includes eye cover and magnet.
Numerical treatment summaries
| Treatment | Bats / headings | μ (degrees) | κ | w |
|---|
Predictive comparison
The saved analysis favored the mixture overall in leave-one-heading-out prediction. Support varied across treatments.
This evaluates held-out headings from observed bats, not generalization to entirely new bats. Serial dependence and the sampling limitations below still matter.
Mixture − single von Mises
ELPD difference ± 1 SEData, model assumptions, and limitations
The ATLAS tracking tables contain 28,350 raw positions for 67 retained bats. Resampling produces 5,072 positions; 4,942 headings have the quantities required for fitting. The analysis uses full usable tracks, without restricting the data to a behavior-defined homing phase.
Each bearing is the backward movement difference at a sampled position, relative to the local destination reference. The roost is a point; the lake uses the negative gradient of a harmonic field around its shoreline. A recorded destination supplies a reference, not a direct observation of the bat’s intention.
Tracking jumps greater than 600 m or time gaps greater than 120 seconds split resampling segments. The original fitted table can nevertheless include bearings across gaps because heading differences were taken within each bat. This explorer preserves those observations, marks them explicitly, and never draws a solid trajectory across a gap.
The models include treatment and individual effects. Distance is not a predictor in these fitted formulas. Repeated headings are conditionally independent in the likelihood; individual effects do not explicitly model remaining serial dependence. Bats contribute unequal numbers of headings.
Sampling qualification. These are the saved R/brms v2 fits, with 8,000 retained draws per model across four chains. The notebook reports that divergence information was not retained, and its diagnostic helper flattened chains before computing convergence summaries. We therefore do not present those summaries as verified convergence evidence. No models were refitted for this explorer.
The pointwise density bands use all retained posterior draws. Component membership is the posterior mean of the concentrated component’s conditional responsibility for the selected heading. Predictive density is a density per radian, not the probability of an exact angle; its logarithm can be positive. The map’s color represents membership in the mixture, and switches to one treatment color for the single-distribution model.
Sources and reproducibility
The explorer uses the saved bat analysis and model specification in unwrap, and the tracking data and v2 model caches in unwrap-data.
The exported headings were checked against both fitted response tables, with maximum angular error below 3 × 10−10 radians before rounding for display. Coordinates and the shoreline are derived from the supplied data; no online basemap or map service is used.