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UW-Madison BOTANY 940 - New multivariate tests for phylogenetic signal and trait correlations applied

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New multivariate tests for phylogenetic signal and traitcorrelations applied to ecophysiological phenotypes ofnine Manglietia speciesLi Zheng1, Anthony R. Ives*,2, Theodore Garland Jr3, Bret R. Larget4, Yang Yu5and KunfangCao*,11Xishuangbanna Tropical Botanical Garden, Chinese Academy of Sciences, Kunming 650223, China;2Department ofZoology, UW-Madison, Madison, Wisconsin 53706, USA;3Department of Biology, University of California, Riverside,Riverside, California 92521, USA;4Departments of Botany and Statistics, UW-Madison, Madison, Wisconsin 53706,USA; and5Yunnan Provincial Environmental Protection Department, Appraisal Center for Environment and Engineering,27 Xiyuannan Road, Kunming 650032, ChinaSummary1. Phylogenetic signal – the similarity in trait values among phylogenetically related species – ispervasive for most types of traits in most organisms. Traits can often be categorized a priori intogroups based on the level of biological organization, functional relations, developmental origins,or genetic underpinnings. Traits within such groups are often expected to be correlated andhence show similar levels of phylogenetic signal.2. We developed multivariate statistical methods to test for phylogenetic signal in groups of traitswhile also incorporating estimates of trait measurement error (including within-species variation)that can obscure phylogenetic signal. Simultaneously, these methods produce estimates ofcorrelations 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 acommon-garden study of nine species of Manglietia (Magnoliaceae). The 13 traits fell into fourgroups: three traits involved photosynthesis [maximum net photosynthesis (Amax), light satura-tion point (LSP), light compensation point]; three described leaf morphology (thickness ofleaves, palisade tissue, sponge tissue); four related to plant growth (basal stem diameter, crownvolume, leaf area, relative growth rate); and three measured thermal tolerance [critical tempera-ture (Tch), peak temperature (Tmax), temperature of half-inactivation (T50)]. We also constructeda molecular phylogeny for these species from 219 AFLP markers via maximum likelihood esti-mation under the assumption of sequential binary changes in DNA sequences.4. Of the 13 traits, only two photosynthesis traits (Amaxand LSP) exhibited statistically detect-able phylogenetic signal (P <0Æ05) when analysed separately, whether using previously pub-lished univariate tests or our new univariate tests that incorporate measurement error. Incontrast, multivariate analys es of the four trait groups, estimating simultaneously the phylo-genetic signal for all traits and the correlations between traits, revealed a statistically significantphylogenetic signal for two of the four groups (photos ynthesis and plant growth), comprisingseven 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 withmultivariate tests that incorporate measurement error. Furthermore, our simulations show thatthe joint estimation of phylogenetic signal and trait correlations can lead to better (less biasedand more precise) estimates of both.Key-words: character syndromes, comparative methods, Magnoliaceae, phylogenetic inertia,phylogenetic signal, shade tolerance, strategy*Correspondence authors. E-mail: [email protected], [email protected] 2009 The Authors. Journal compilation  2009 British Ecological SocietyFunctional Ecology 2009, 23, 1059–1069 doi: 10.1111/j.1365-2435.2009.01596.xIntroductionStatistical methods that incorporate phylogenetic informa-tion are now common in comparative analyses of trait var-iation and covariation (e.g. Clobert, Garland & Barbault1998; Housworth, Martins & Lynch 2004; Hansen, Pienaar& Orzack 2008; Lavin et al. 2008), because these methodsenhance both biological insight and statistical validity.Biologically, shared ancestry should cause related speciesto resemble each other for many traits, a pattern referredto as phylogenetic signal (Blomberg & Garland 2002). Forexample, in a survey of traits taken from many studies,Blomberg, Garland & Ives (2003) demonstrated that phy-logenetic signal was pervasive. Nonetheless, they foundthat phylogenetic signal was weaker on average forbehavioural traits than for body size or size-adjusted mor-pholometric traits. This finding may indicate that behavio-ural traits experience selection that breaks downphylogenetic patterns (Revell, Harmon & Collar 2008),giving inferential information about evolution of behavio-ural traits (although the possibility that they exhibitgreater measurement error cannot be discounted; Ives,Midford & Garland 2007).Statistically, analyses that require interspecific compari-sons are challenging, because species cannot be assumed to beindependent data points, violating the foremost assumptionof many standard statistical analyses. When standard statisti-cal methods are applied to phylogenetically related data, typeI errors (rejecting the null hypothesis when in fact it is true)are often inflated, and coefficients estimated from statisticalmodels (such as regression slopes) may not be minimum vari-ance (e.g. Grafen 1989; Diaz-Uriarte & Garland 1996; Gar-land & Dı´az-Uriarte 1999; Rohlf 2006). To address bothbiological and statistical issues, a large number of phylogenet-ically informed approaches have been developed for a widerange of analyses (reviewed in Garland, Bennett & Rezende2005; Lavin et al. 2008).Here, we extend this programme by developing new meth-ods that estimate the correlation in trait values among specieswhile simultaneously estimating the strength of phylogeneticsignal and accounting for measurement error. This over-comes a limitation of the most commonly used phylogeneticstatistical methods; they require an aprioriassumption aboutthe strength of phylogenetic signal in the data to be analysed.For example, Felsenstein’s independent contrasts method(Felsenstein 1985) assumes that evolution follows a ‘Brown-ian motion’ process in which trait values increase or decreaserandomly as evolution proceeds incrementally up a hierarchi-cal phylogenetic tree. The assumption would be invalid, how-ever, if trait evolution did not proceed in a Brownian motionfashion (e.g. Diaz-Uriarte & Garland 1996). In


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UW-Madison BOTANY 940 - New multivariate tests for phylogenetic signal and trait correlations applied

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