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Double quantile regression accurately assesses distance to boundary trade‐offs

ABSTRACT

1‐ Boundary trade‐offs are common among ecological, life‐history, behavioural and other traits. Depending on the traits studied, distances of data points to boundary trade‐offs can indicate ecological or life‐history strategies, or behavioural performance. Quantile regression tests the statistical significance of boundary trade‐offs, but it is unknown whether it provides meaningful benchmarks for evaluating distances to the true trade‐offs shaping the data. This is especially relevant when traits limit each other mutually, rather than one independent trait limiting another dependent trait. 2‐ I used empirical and simulated data to evaluate how quantile regression assesses distance to boundary trade‐offs. First, I reanalysed empirical datasets showing upper‐bound trade‐offs between acoustic traits, which is a field where distances to trade‐offs are often used to infer behavioural performance. Second, I simulated data under different assumptions of how boundaries influence density distributions, to test the accuracy of assessing distance to the true trade‐offs generating the data. 3‐ Quantile regression assessed distance to upper‐bound trade‐offs incongruently in most empirical datasets, strongly influenced by arbitrary decisions on which trait to use as dependent. Simulated data showed that a double quantile regression approach — the consensus of two reciprocal quantile regressions — accurately and robustly assesses distance to the true trade‐offs generating the data. The method was robust to low sample sizes and to different assumptions on how boundary trade‐offs influence the density distribution of data. 4‐ Double quantile regression can assess distances to the boundary trade‐offs observed in various branches of ecology, from functional and behavioural ecology, to population and macro‐ecology.

REFERENCE

Cardoso, G. C. 2019. Double quantile regression accurately assesses distance to boundary trade‐offs. Methods in Ecology and Evolution. 10. 1322-1331.

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