Permutation tests for phylogenetic comparative analyses of high-dimensional shape data: what you shuffle matters

Area of Science:

• Comparative Biology
• Phylogenetic Statistics
• Evolutionary Biology

Background:

• High-dimensional phenotypes present statistical challenges in comparative biology due to the ratio of traits to species.
• Existing methods like permuting phylogenetic independent contrasts (PICs) and distance-based phylogenetic generalized least squares (D-PGLS) attempt to address these challenges.

Purpose of the Study:

• To evaluate the statistical validity of permuting PICs versus permuting original data in phylogenetic comparative analyses.
• To identify and explain the reasons for discrepancies in statistical outcomes between these two permutation approaches.

Main Methods:

• Comparison of statistical outcomes between permuting phylogenetic independent contrasts (PICs) and permuting original data within a phylogenetic generalized least squares (PGLS) framework.
• Analysis of the theoretical underpinnings of exchangeable units under the null hypothesis for each permutation method.
• Simulation or re-analysis demonstrating the impact of different permutation strategies on Type I error rates.

Main Results:

• Permuting PICs is not statistically equivalent to permuting the original data as performed in D-PGLS.
• Phylogenetic independent contrasts (PICs) are not the correct exchangeable units under the null hypothesis, leading to inflated Type I error rates.
• Shuffling original data and recalculating contrasts yields significance levels consistent with D-PGLS, validating this approach.

Conclusions:

• The method of permuting phylogenetic independent contrasts (PICs) can produce misleading statistical and biological inferences due to inflated Type I error rates.
• Permuting the original data, either directly or by recalculating contrasts iteratively, is a statistically sound approach for hypothesis testing in high-dimensional phylogenetic comparative studies.
• Researchers should carefully consider the permutation strategy employed in phylogenetic comparative analyses to ensure the reliability of their findings.