Functional Ecology 2009 23 1059 1069 doi 10 1111 j 1365 2435 2009 01596 x New multivariate tests for phylogenetic signal and trait correlations applied to ecophysiological phenotypes of nine Manglietia species Li Zheng1 Anthony R Ives 2 Theodore Garland Jr3 Bret R Larget4 Yang Yu5 and Kunfang Cao 1 1 Xishuangbanna Tropical Botanical Garden Chinese Academy of Sciences Kunming 650223 China 2Department of Zoology 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 and 5Yunnan Provincial Environmental Protection Department Appraisal Center for Environment and Engineering 27 Xiyuannan Road Kunming 650032 China 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 Amax 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 Tch peak temperature Tmax temperature of half inactivation T50 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 Amax 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 signi cant 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 Key words character syndromes comparative methods Magnoliaceae phylogenetic inertia phylogenetic signal shade tolerance strategy Correspondence authors E mail arives wisc edu caok xtbg en 2009 The Authors Journal compilation 2009 British Ecological Society 1060 L Zheng et al Introduction Statistical methods that incorporate phylogenetic information are now common in comparative analyses of trait variation and covariation e g Clobert Garland Barbault 1998 Housworth Martins Lynch 2004 Hansen Pienaar Orzack 2008 Lavin et al 2008 because these methods enhance both biological insight and statistical validity Biologically shared ancestry should cause related species to resemble each other for many traits a pattern referred to as phylogenetic signal Blomberg Garland 2002 For example in a survey of traits taken from many studies Blomberg Garland Ives 2003 demonstrated that phylogenetic signal was pervasive Nonetheless they found that phylogenetic signal was weaker on average for behavioural traits than for body size or size adjusted morpholometric traits This nding may indicate that behavioural traits experience selection that breaks down phylogenetic patterns Revell Harmon Collar 2008 giving inferential information about evolution of behavioural traits although the possibility that they exhibit greater measurement error cannot be discounted Ives Midford Garland 2007 Statistically analyses that require interspeci c comparisons are challenging because species cannot be assumed to be independent data points violating the foremost assumption of many standard statistical analyses When standard statistical methods are applied to phylogenetically related data type I errors rejecting the null hypothesis when in fact it is true are often in ated and coef cients estimated from statistical models such as regression slopes may not be minimum variance e g Grafen 1989 Diaz Uriarte Garland 1996 Garland D az Uriarte 1999 Rohlf 2006 To address both biological and statistical issues a large number of phylogenetically informed approaches have been developed for a wide range of analyses reviewed in Garland Bennett Rezende 2005 Lavin et al 2008 Here we extend this programme by developing new methods that estimate the correlation in trait values among species while simultaneously estimating the strength of phylogenetic signal and accounting for measurement error This overcomes a limitation of the most commonly used phylogenetic statistical methods they require an a priori assumption about the strength of phylogenetic signal in the data to be analysed For example Felsenstein s independent contrasts method Felsenstein 1985 assumes that evolution follows a Brownian motion process in which trait values increase or decrease randomly as evolution proceeds incrementally up a hierarchical phylogenetic tree The assumption would be invalid however if trait evolution did not proceed in a Brownian motion fashion e g Diaz Uriarte Garland 1996 In contrast our methods estimate phylogenetic signal simultaneously with trait correlations rather than making a priori assumptions about its strength and so they should improve the
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