Determine the cause of contrast-dependent changes in the fitted decay exponent

Determine whether the observed decrease in the fitted harmonic-decay exponent of the Drosophila compass activity bump with increasing cue contrast reflects composition by filters with different decay profiles or a change in the shape of an individual filter.

Background

The compass bump becomes narrower and develops stronger higher harmonics as cue contrast increases. A flexible decay-exponent fit changes from approximately Gaussian-like in darkness toward a heavier-tailed profile at high contrast. Harmonic composition theory allows this change to arise either from altered contributions of multiple filters or from a change in one filter itself, and the available data do not distinguish these possibilities.

References

A shape-flexible check fits a single decay exponent \alpha per fly: in darkness the fitted exponent, 1.93, is indistinguishable from the Gaussian \alpha=2 against a calibrated null, and it decreases to 1.72 at high contrast --- a drift whose interpretation, via the composition rule of Sec.~\ref{sec:general-kernel}, remains open (S7).

— Selection rules for the harmonic spectroscopy of animal decisions  (2610.00990 - Salahshour, 1 Oct 2026) in Section 3.5.3, “Contrast sharpens the compass, and the sharpening predicts the spectrum” (S7)