Testing for correlation between traits under directional evolution.

Being confounding factors, directional trends are likely to make two quantitative traits appear as spuriously correlated. By determining the probability distributions of independent contrasts when traits evolve following Brownian motions with linear trends, we show that the standard independent contrasts can not be used to test for correlation in this situation. We propose a multiple regression approach which corrects the bias caused by directional evolution. We show that our approach is equivalent to performing a Phylogenetic Generalized Least Squares (PGLS) analysis with tip times as covariables by providing a new and more general proof of the equivalence between PGLS and independent contrasts methods. Our approach is assessed and compared with three previous correlation tests on data simulated in various situations and overall outperforms all the other methods. The approach is next illustrated on a real dataset to test for correlation between hominin cranial capacity and body mass.