Ignoring phylogenetic history can lead to incorrect conclusions about the nature of evolutionary associations between traits.

<p>In this hypothetical example, eight species have been measured for two traits, x and y, as indicated by pairs of values at the tips of the phylogenetic tree (A). Ordinary least-squares linear regression (OLS) indicates a statistically significant positive relationship (B; <i>r²</i> = 0.62, <i>P</i> = 0.02), potentially leading to an inference of a positive evolutionary association between x and y. However, inspection of the scatterplot (B) in relation to the phylogenetic relationships of the species (A) indicates that the association between x and y is <i>negative</i> for the four species within each of the two major lineages. Regression through the origin with phylogenetically independent contrasts (computed using <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1001080#pgen.1001080-Midford1" target="_blank">[34]</a> and setting all branches to length 1.0), which is equivalent to phylogenetic generalized least squares (PGLS) analysis, accounts for the nonindependence of species and indicates no overall evolutionary relationship between the traits (C, standardized contrasts, <i>r²</i> = 0.01, <i>P</i> = 0.82; basal contrast indicated in red). The apparent pattern across species was driven by positively correlated trait change only at the basal split of the phylogeny; throughout the rest of the phylogeny, the traits mostly changed in <i>opposite</i> directions (A; basal contrast in red). Notes: In A, the estimated nodal values for both traits are shown in parentheses. These are intermediate steps in the independent contrasts algorithm and are not to be taken as optimal estimates of the states at internal nodes; rather, they are a type of “local parsimony” estimate (except the estimate at the basal node, which is equivalent to the estimate under squared-change parsimony). Contrasts are taken between sister nodes on a phylogeny, not along each branch segment <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1001080#pgen.1001080-Felsenstein1" target="_blank">[15]</a>, <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1001080#pgen.1001080-Garland1" target="_blank">[16]</a>, <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1001080#pgen.1001080-Garland2" target="_blank">[18]</a>.