Data from: On the use of double quantile regression and visual assessment to estimate performance constraints

Quantile regression (QR) is a widely used tool for estimating performance
limits in behavioral data. In Vazquez-Cardona et al. (2023, Behavioral
Ecology), we applied mixed QR to estimate motor constraints in Adelaide’s
warbler song, and measured performance as deviations from these estimated
limits. A recent critique (Cardoso, 2024, Behavioral Ecology) raised two
concerns about that analysis: (1) QR-based deviation scores arbitrarily
emphasize one of the two variables in the trade-off, and (2) uneven
sampling may produce the illusion of constraint, compromising the validity
of visual assessments and QR. Here, we evaluate these claims by applying
double quantile regression (DQR)—Cardoso’s proposed remedy—and by testing
whether rarefaction alters the observed constraints. We introduce a novel
method to characterize DQR results using bisecting lines and show that,
for some distributions, DQR improves fit to the constrained edge. However,
DQR performs poorly under some conditions and can falsely identify
constraints in unconstrained data. Rarefaction analyses reveal that uneven
sampling does not account for the appearance of constraint in our bird
song data, which show sharp, bounded edges unlike the smooth gradients of
unconstrained simulations. Finally, we demonstrate that the warm-up effect
in vocal performance, previously reported in Vazquez-Cardona et al.
(2023), is robust to both DQR-based estimation and rarefaction. We
conclude that while DQR can be a useful complement to QR, visual
inspection remains essential, and caution is warranted when applying DQR
to datasets with complex geometries or potential false boundaries.