New multivariate tests for phylogenetic signal and trait correlations applied to ecophysiological phenotypes of nine Manglietia species

Summary 1. Phylogenetic signal – the similarity in trait values among phylogenetically related species – is pervasive for most types of traits in most organisms. Traits can often be categorized a priori into groups based on the level of biological organization, functional relations, developmental origins, or genetic underpinnings. Traits within such groups are often expected to be correlated and hence show similar levels of phylogenetic signal. 2.  We developed multivariate statistical methods to test for phylogenetic signal in groups of traits while also incorporating estimates of trait measurement error (including within‐species variation) that can obscure phylogenetic signal. Simultaneously, these methods produce estimates of correlations between traits that are corrected for phylogenetic relationships among species. 3. We applied these methods to data for 13 morphological and physiological traits gathered in a common‐garden study of nine species of Manglietia (Magnoliaceae). The 13 traits fell into four groups: three traits involved photosynthesis [maximum net photosynthesis ( A max ), light saturation point (LSP), light compensation point]; three described leaf morphology (thickness of leaves, palisade tissue, sponge tissue); four related to plant growth (basal stem diameter, crown volume, leaf area, relative growth rate); and three measured thermal tolerance [critical temperature ( T ch ), peak temperature ( T max ), temperature of half‐inactivation ( T 50 )]. We also constructed a molecular phylogeny for these species from 219 AFLP markers via maximum likelihood estimation under the assumption of sequential binary changes in DNA sequences. 4. Of the 13 traits, only two photosynthesis traits ( A max and LSP) exhibited statistically detectable phylogenetic signal ( P  < 0·05) when analysed separately, whether using previously published univariate tests or our new univariate tests that incorporate measurement error. In contrast, multivariate analyses of the four trait groups, estimating simultaneously the phylogenetic signal for all traits and the correlations between traits, revealed a statistically significant phylogenetic signal for two of the four groups (photosynthesis and plant growth), comprising seven traits in total. 5.  Our results demonstrate that even when the number of species in a comparative study is small, resulting in low power for univariate tests, phylogenetic signal can nonetheless be detected with multivariate tests that incorporate measurement error. Furthermore, our simulations show that the joint estimation of phylogenetic signal and trait correlations can lead to better (less biased and more precise) estimates of both.