Which Variable Should Be Dependent in Phylogenetic Generalized Least Squares Regression Analysis

ABSTRACT Phylogenetic generalized least squares (PGLS) regression is one of the most commonly used methods in examining evolutionary correlations between two traits. Unlike the conventional correlation methods like Pearson and Spearman’s rank tests, the two analyzed traits are in different positions when correcting the phylogenetic non-independence in PGLS regression. In examining the correlations of CRISPR-Cas and prophage contents with optimal growth temperature and minimal doubling time, we noticed that a remarkable frequency (26.3%) of conflicting results appears after swapping the independent and dependent variables. Then, we generated 12000 simulations of the evolution of two traits (X1 and X2) along a binary tree containing 100 terminal nodes with different models and variances. In this simulated dataset, swapping the dependent and independent variables gave conflicting results at a frequency of 17.2%. By conventional correlation analysis of the trait changes along the phylogenetic branches (ΔX1 and ΔX2), we established a golden standard for whether X1 and X2 correlate in each simulation. With this golden standard, we compared six potential criteria for dependent variable selection, log-likelihood, Akaike information criterion, R2, p-value, Pagel’s λ, and the estimated λ in Pagel’s λ model. The last two criteria were found to be equivalent in their performance of dependent variable selection and superior to the other four criteria. Because Pagel’s λ values, as indicators of phylogenetic signals, are generally calculated at the beginning of phylogenetic comparative studies, for practical convenience, we recommend the trait with a higher λ value to be used as the dependent variable in future PGLS regressions. Logical analysis of cause and effect should be done after establishing a significant correlation by PGLS regression rather than providing an indicator for the choice of the dependent variable.