An important aim of plant ecology is to identify leading dimensions of ecological variation among species and to understand the basis for them. Dimensions that can readily be measured would be especially useful, because they might offer a path towards improved worldwide synthesis across the thousands of field experiments and ecophysiological studies that use just a few species each. Four dimensions are reviewed here. The leaf mass per area-leaf lifespan (LMA-LL) dimension expresses slow turnover of plant parts (at high LMA and long LL), long nutrient residence times, and slow response to favorable growth conditions. The seed mass-seed output (SM-SO) dimension is an important predictor of dispersal to establishment opportunities (seed output) and of establishment success in the face of hazards (seed mass). The LMA-LL and SM-SO dimensions are each underpinned by a single, comprehensible tradeoff, and their consequences are fairly well understood. The leaf size-twig size (LS-TS) spectrum has obvious consequences for the texture of canopies, but the costs and benefits of large versus small leaf and twig size are poorly understood. The height dimension has universally been seen as ecologically important and included in ecological strategy schemes. Nevertheless, height includes several tradeoffs and adaptive elements, which ideally should be treated separately. Each of these four dimensions varies at the scales of climate zones and of site types within landscapes. This variation can be interpreted as adaptation to the physical environment. Each dimension also varies widely among coexisting species. Most likely this within-site variation arises because the ecological opportunities for each species depend strongly on which other species are present, in other words, because the set of species at a site is a stable mixture of strategies.

Fitting a line to a bivariate dataset can be a deceptively complex problem, and there has been much debate on this issue in the literature. In this review, we describe for the practitioner the essential features of line-fitting methods for estimating the relationship between two variables : what methods are commonly used, which method should be used when, and how to make inferences from these lines to answer common research questions.A particularly important point for line-fitting in allometry is that usually, two sources of error are present (which we call measurement and equation error), and these have quite different implications for choice of linefitting method. As a consequence, the approach in this review and the methods presented have subtle but important differences from previous reviews in the biology literature.Linear regression, major axis and standardised major axis are alternative methods that can be appropriate when there is no measurement error. When there is measurement error, this often needs to be estimated and used to adjust the variance terms in formulae for line-fitting. We also review line-fitting methods for phylogenetic analyses.Methods of inference are described for the line-fitting techniques discussed in this paper. The types of inference considered here are testing if the slope or elevation equals a given value, constructing confidence intervals for the slope or elevation, comparing several slopes or elevations, and testing for shift along the axis amongst several groups. In some cases several methods have been proposed in the literature. These are discussed and compared. In other cases there is little or no previous guidance available in the literature.Simulations were conducted to check whether the methods of inference proposed have the intended coverage probability or Type I error. We identified the methods of inference that perform well and recommend the techniques that should be adopted in future work.

Summary1. The Standardised Major Axis Tests and Routines (SMATR) software provides tools for estimation and inference about allometric lines, currently widely used in ecology and evolution. 2. This paper describes some significant improvements to the functionality of the package, now available on R in smatr version 3. 3. New inclusions in the package include sma and ma functions that accept formula input and perform the key inference tasks; multiple comparisons; graphical methods for visualising data and checking (S)MA assumptions; robust (S)MA estimation and inference tools.Key-words: common slope testing, model II regression, principal component analysis, robust estimation, standardised major axis Biologists often wish to estimate how one variable scales against another and to test hypotheses about the nature of this relationship and how it varies across samples. The most common example of this is allometry (Reiss 1989); hence, we refer to this problem as one of estimation and testing about allometric lines. An example is given in Fig. 1a, where we wish to understand how leaf lifespan (longev) scales against leaf mass per area (lma) and how this relationship changes across sites with different rainfall (rain). longev and lma are log-transformed prior to analysis and are approximately linearly related on the transformed scale. This is common in allometry, and it means that their relationship approximately follows a power law, longev¼ alma b . The 'scaling exponent' b is the slope on log-transformed axes, and the magnitude of this parameter describes how steep the leaf lifespan-leaf mass per area relationship is. The 'proportionality coefficient' a, related to the elevation on log-log axes, is needed to understand how longlived leaves of a given mass per area will be.Estimating a and b is not a simple linear regression problem because we are not interested in predicting one variable from another -we are interested in estimating some underlying line of best fit (Warton et al., 2006 ). Another way to understand this is to see that the problem is symmetric -the basic problem does not change if we plot lma on the Y axis instead of the X axis (Smith 2009). Hence, the appropriate methods for analysis have more in common with principal component analysis, a multivariate approach, than with linear regression (Warton et al., 2006). Common approaches to estimating the line of best fit are standardised major axis (SMA) and major axis (MA) estimation, which will be collectively referred to as (S)MA, and which are widely used in ecology and evolution.Warton et al. (2006) reviewed (S)MA techniques, proposed routines for comparing the parameters a and b amongst groups and developed software to implement the methods. The Standardised Major Axis Tests and Routines (SMATR) software, available in both R (R Development Core Team 2010) and C++, has since been used in over 200 publications. We have made significant improvements to the software in the recently released version 3 of the smatr R package, and this paper briefly describe...

AimOur aim was to quantify climatic influences on key leaf traits and relationships at the global scale. This knowledge provides insight into how plants have adapted to different environmental pressures, and will lead to better calibration of future vegetation-climate models.Location The data set represents vegetation from 175 sites around the world.Methods For more than 2500 vascular plant species, we compiled data on leaf mass per area (LMA), leaf life span (LL), nitrogen concentration (N mass ) and photosynthetic capacity (A mass ). Site climate was described with several standard indices. Correlation and regression analyses were used for quantifying relationships between single leaf traits and climate. Standardized major axis (SMA) analyses were used for assessing the effect of climate on bivariate relationships between leaf traits. Principal components analysis (PCA) was used to summarize multidimensional trait variation.Results At hotter, drier and higher irradiance sites, (1) mean LMA and leaf N per area were higher; (2) average LL was shorter at a given LMA, or the increase in LL was less for a given increase in LMA (LL-LMA relationships became less positive); and (3) A mass was lower at a given N mass , or the increase in A mass was less for a given increase in N mass . Considering all traits simultaneously, 18% of variation along the principal multivariate trait axis was explained by climate.Main conclusions Trait-shifts with climate were of sufficient magnitude to have major implications for plant dry mass and nutrient economics, and represent substantial selective pressures associated with adaptation to different climatic regimes.

Phenotypic traits and their associated trade-offs have been shown to have globally consistent effects on individual plant physiological functions 1-3 , but how these effects scale up to influence competition, a key driver of community assembly in terrestrial vegetation, has remained unclear 4 . Here we use growth data from more than 3 million trees in over 140,000 plots across the world to show how three key functional traits-wood density, specific leaf area and maximum height-consistently influence competitive interactions. Fast maximum growth of a species was correlated negatively with its wood density in all biomes, and positively with its specific leaf area in most biomes. Low wood density was also correlated with a low ability to tolerate competition and a low competitive effect on neighbours, while high specific leaf area was correlated with a low competitive effect. Thus, traits generate trade-offs between performance with competition versus performance without competition, a fundamental ingredient in the classical hypothesis that the coexistence of plant species is enabled via differentiation in their successional strategies 5 . Competition within species was stronger than between species, but an increase in trait dissimilarity between species had little influence in weakening competition. No benefit of dissimilarity was detected for specific leaf area or wood density, and only a weak benefit for maximum height. Our traitbased approach to modelling competition makes generalization possible across the forest ecosystems of the world and their highly diverse species composition.Phenotypic traits are considered fundamental drivers of community assembly and thus species diversity 1,6 . The effects of traits on individual plant physiologies and functions are increasingly understood, and have been shown to be underpinned by well-known and globally consistent trade-offs 1-3 . For instance, traits such as wood density and specific leaf area capture trade-offs between the construction cost and longevity or strength of wood and leaf tissues 2,3 . By contrast, we still have a limited understanding of how such trait-based trade-offs translate into competitive interactions between species, particularly for long-lived organisms such as trees. Competition is a key filter through which ecological and evolutionary success is determined 4 . A long-standing hypothesis is that the intensity of competition decreases as two species diverge in trait values 7 (trait dissimilarity). The few studies [8][9][10][11][12][13] that have explored links between traits and competition have shown that linkages were more complex than this, as particular trait values may also confer competitive advantage independently from trait dissimilarity 9,13,14 . This distinction is fundamental for species coexistence and the local mixture of traits. If neighbourhood competition is driven mainly by trait dissimilarity, this will favour a wide spread of trait values at a local scale. By contrast, if neighbourhood interactions are mainly driven by the c...