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%Title : Functional traits have globally consistent effects on plant competition
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%Authors: Georges Kunstler; David A Coomes; Daniel Falster; Francis Hui;
  Rob Kooyman; Daniel Laughlin Lourens Poorter; Mark Vanderwel;
  Ghislain Vieilledent; Joe Wright; Masahiro Aiba; John Caspersen;
  Sylvie Gourlet-Fleury; Marc Hanewinkel; Bruno Herault; Hiroko Kurokawa;
  Yusuke Onoda; Maria Uriarte; Sarah Richardson; Paloma Ruiz;
  I-Fang Sun; Goran Ståhl; Nathan Swenson; Jill Thompson; Miguel Zavala;
  Hongcheng Zeng; Jess Zimmerman; Niklaus E Zimmermann; and Mark Westoby.
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# Summary paragraph outline (max 200 words)
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Competition is a very important type of ecological interaction, especially in terrestrial vegetation where plants greatly modify the local environment for each other. Competition has influence on growth of individuals and survival, on how species mixtures will change over time into the future, and on community composition. However firm generalizations have yet to be established about outcomes of competition among tree species. Here we show how key species traits have consistent influences on growth and competition. The data sources are very large, including national forest inventories monitoring growth in sometimes millions of trees, and we here synthesize across a global set of such inventories plus also several large forest-monitoring plots. Some traits have strong effect on the growth rate of the species. Then traits in part determine the tolerance to competition and the impact of the competitor. A notable generalization is that trait values that favour tolerance to competition also render species slow growing in absence of competition. There is also a small but detectable benefit in reducing competition from trait-dissimilarity between focal plant and its competitors.  The trait-based picture that emerges is much simpler and more general than a quantification of competition coefficients between each pair of species, which is intractable at the global scale. Our results demonstrate that traits may be used to predict competitive interactions between forest tree species at a large scale. We anticipate that our results can have profound influence on trait model of community assembly.
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# Main text
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**(MAX 1500 words till the end of Methods = 1494)**
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Competition is a fundamental type of interaction in ecological communities. Each individual modify their neighbouring environment and thus influences the performance of neighbouring individuals [@keddy_competition_2001]. Competition influences species composition and its changes over time.  Maybe competition is especially important for vegetation on land because most vegetation types have high enough cover that shading and water and nutrient depletion are conspicuous. There have thus been a very large number of studies on competition among plants [@goldberg_patterns_1992], but firm generalizations have yet to be established about its outcomes.
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When competition is described as interactions between pairs of species (as it traditionally has been), the number of different interactions to be measured grows explosively with the number of species ($N^2$), and becomes quickly intractable. Also this species-pair approach does not lead naturally to generalization across forests on different continents with different composition. Here we quantify competition between trees (in the sense of influence of neighbours on growth of a focal tree) within a framework, which is novel in two important ways: (i) competition is modelled as a function of traits rather than of species and (ii) we partition how traits drive the outcome of competition in four different key processes (Fig. \ref{ilustr}). Competition can select trait values that are the most competitive. This competitive advantage of trait values can arise because (1) there are correlated with higher potential growth (in absence of competition) [@wright_functional_2010], (2) they are correlated with a higher tolerance to competition [@goldberg_competitive_1996], or (3) they are correlated with higher competitive impact [@gaudet_comparative_1988]. In contrast, competition can promotes the coexistence of a mixture of traits values, if (4) competition decrease with increasing dissimilarity of the traits of the competitors and the focal tree [@macarthur_limiting_1967]. These four processes are likely to be connected to the key traits used to describe plant strategies[@hillerislambers_rethinking_2012; @lasky_trait-mediated_2014], however there is no agreement on their relative contributions to each of these processes and whether the magnitude and direction of these effects are conserved across large scale.
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Here we dissect how three key traits[@westoby_plant_2002; @chave_towards_2009] (maximum height, wood density and specific leaf area - *SLA*) affect these four processes involved in competition between trees using neighbouring modeling approach[@uriarte_neighborhood_2004]. We compiled data of growth along side local abundance of their competitor for more than 7 million trees representing more than 2500 species covering all the major biomes of the earth (Fig. \ref{res2}b). We analysed how the potential growth of each individual tree was reduced by the local abundance of its competitors. Our analysis accounts for the trait of both the focal tree and its competitors estimating the trait effect for each of the processes presented in Fig. \ref{ilustr}.
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Across all biomes we found that strongest drivers of individual growth
was first-ranked the local abundance of competitors; and second ranked
the direct influence of the focal plant’s traits on its growth
(Fig. \ref{res1} Extended data Table D1). We detected only negative
effect of the abundance of competitors showing that competition was
predominant. Among the three traits wood density had the strongest
direct effect, followed by maximum height  whereas SLA had no
detectable effect (Fig. \ref{res1}). Then our results show the
influence of neighbour traits on their competitive impact, and of
focal species traits on tolerance of competition
(Fig. \ref{res1}). Taken together these two effects are in the range
of half or quarter as big as the direct trait effect (Extend data
Table D1), down to zero influence depending on the trait (Fig
\ref{res1}). Finally, there is a small but consistent effect whereby
the wider is the absolute trait separation between focal and neighbour
species, the weaker is competitive suppression of growth
(Fig. \ref{res1}). This may arise because of negative density
dependence arising for species with similar trait because, for
instance, a higher load of  herbivores or pathogens
[@bagchi_pathogens_2014] or less efficient use of resources (such a
less efficient light use[@sapijanskas_tropical_2014] or less efficient
litter recylcing[@sapijanskas_beyond_2013]). An analysis using a multiple-traits distance rather than a single trait distance didn't show different pattern (extended data Figure **\color{red}?[^todo]**). Analyses allowing for different effect between biomes did no show strong evidence for any particular biome behaving consistently differently from the others (Fig. \ref{res3}). The exception is the temperate biomes where SLA showed much stronger effect, probably ought to the dominance of deciduous species in this biome (Fig. \ref{res2}).
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[^todo]: **\color{red}Still running.**
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  The direction of the traits effect agree well with the existing
  literature. High wood density was lined with
  slow potential growth rate but high tolerance to competition, in
  agreement with shade-tolerant
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  species having high wood density[@wright_functional_2010]. High wood density also resulted in a
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  higher competitive impact, that may be related to deeper crown
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  [@poorter_architecture_2006; @aiba_architectural_2009]. The lack of direct effect of *SLA* on maximum growth (but with a positive tendency)
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  agree well with the weak correlation previously reported for adult
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  trees [@wright_functional_2010]. Increasing *SLA* was also weakly
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  related to decreased competitive impact and no effect or possible
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  weakly decreased competitive tolerance, which agree with previous
  study reporting a weak negative correlation betwen *SLA* and shade
  tolerance[@wright_functional_2010]. Finally, maximum height was
  positively related to maximum growth as previously
  reported[@wright_functional_2010]. Species with small maximum height
  were also much more tolerant to competition than taller species, in
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  line with the idea that sub-canopy tree are more shade-tolerant. For
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  wood density and *SLA* the  link with competitive impact and
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  competitive response was opposed, in agreement with a coordinated
  selection under which trait value that confer high competitive
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  impact also confer high competitive tolerance (a competitive
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  hierachy[@kunstler_competitive_2012; @mayfield_opposing_2010]). This
  was not the case for maximum height because short species were more
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  tolerant to competition but had a lower competitive impact. This
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  match well the observation of the persistence of sub-canopy species
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  under a close cover of tall tree and the stratification theory of
  species coexistence[@kohyama_stratification_2009].
  Finally our study show that trait values that favour tolerance to
  competition also render species slow growing in absence of
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  competition. Our results just demonstrate that the wood density based trade-off (Fig. \ref{res3}) between fast growth in the absence of competition and lower tolerance to competition is a global phenomenon common to all forested biomes. For the two other traits their effect on competition was not sufficient to counteract the effect on maximum growth. This important because this is one of the most
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  classical process proposed to explain species coexistence in forest
  [@rees_long-term_2001].

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The globally consistent link between competition effect on growth and traits that we report is promising to simplify the complex interaction governing forest communities. Our results also demonstrates that most assumptions about the link between traits and competition that are use to tease out community assembly are too simplistic[@adler_trait-based_2013]. Analysis for other fitness component (survival and recruitment) are now need to be able to scale up these short-term interactions to population dynamics impacts on traits composition.
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<!-- TODO ADD TRAITS RANDOMISATION TO -->
<!-- SEE NOT AN ARTIFACT. -->
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# Methods summary
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To examine the link between competition and traits we first compiled
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forest plot data from both national forest inventories and long-term
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permanent plots from 14 countries covering all the major biomes of the
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world (Fig. 1b, see extended methods Table M1 \& M2). We restricted our analysis to
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tree with trunk diameter $>= 10cm$ to have a common minimum size
across all data set. Second, we extracted traits mean per species (not
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accounting for intra-specific variability) from either a global
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([TRY](http://www.try-db.org/) data base[@kattge_try_2011] or local
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data base (extended Table 1), for three key traits: wood density, SLA,
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and Maximum height. Third, we computed the local abundance (measured
as the basal area - $m^2/ha$) of competitors per species in the
neighborhood of each tree. The neighborhood was defined as a 15m
radius around the focal tree in large plot with xy coordinates of all
trees or as the whole plot for national forest inventory data that are
based on small plot (the plot size correspond to a circular plot
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ranging from 10 to 25m in radius). Fourth, for each traits, we computed for each individual, four
crowding indices that where representing (i) the overall crowding
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irrespective of the species trait (as the sum of basal area of local
competitors), (ii) the overall crowding times the trait of focal
species, representing how traits affect tolerance to competition,
(iii) the mean traits of the competitor weighted by their abundance
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(basal area), representing how traits affect the competitive impact,
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and (iv) the mean of the trait absolute distance between the focal
tree and the competitor species weighted per their abundance (basal
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area), representing how the trait similarity affect competition. Finally, for each trait, we fitted a model estimating how
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individuals tree basal area growth was affected by the focal species
traits (direct traits effect) and by these four crowding indexes,
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while accounting for size effect. To
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facilitate comparison between parameters and traits all traits and
variable were standaridised to a SD of one. We report these
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standardized parameters for each traits. Two models were fitted, (i)
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we included biomes as a random effect in each parameters to estimate
the overall effect across all biomes and (ii) we included biomes as a
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fixed effect to analyse the difference between biomes.
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**Supplementary Information** is available in the online version of the paper.
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**Acknowledgements**
We are thankful that people whose long term commitment allowed the  established and
maintained the forest plots and their associated databases, granted us access to forest inventory data and long term forest plots of NVS, Japan, Spain, France, Switzerland, Sweden, US, Canada (for the following provinces: Québec, ...), CTFS plots (BCI, Fushan and Luquillo) and Cirad permanent plots (Paracou, M'Baiki).  GK
was supported by a Marie Curie International Outgoing Fellowship
within the 7th European Community Framework Program (Demo-
traits project, no. 299340).
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**Author contributions**
G.K. conceived the study with feedback from M.W and D.F. G. K., M. W and ... wrote the manuscript. G.K. devised the main
analytical approach, wrote the computer code and performed analyses.
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**Author information**
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\newpage
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# FIGURES & TABLES
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![**Assessing competitive interactions at global scale.** **a,** Precipitation-temperature space occupied by the natural forest communities studied (NFI data : national forest Inventories, LPP data : large permanent plots) . Biomes follow the definition of Whittaker [@ricklefs_economy_2001]:
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 1, tundra; 2, taiga; 3, woodland/shrubland; 4, temperate forest; 5,
 temperate rainforest; 6, desert; 7, tropical seasonal forest; 8,
 tropical rainforest. **b,** Sampled patches vary in the density of
 competitors from species $c$ around individuals from a focal species
 $f$. For each tree we record the stem diameter $D_i$ across multiple
 censuses, and link this with records for the traits of the focal and
 competitor species, $t_f$ and $t_c$ respectively. **c,** We use a
 neighbourhood modelling framework to model the effects of the traits
 and size of the focal tree, and the total basal area ($B_c$) and
 traits of competitor species on growth of the focal tree. These
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 effects can be broken down into those influencing maximum growth
 rate (red) and those influencing reduction in growth per unit basal area of competitor (blue), $\alpha_{c,f}$. Trait value of focal tree ($t_f$) can influences the tree growth without competition (maximum growth, $m_1$). The trait value of the focal tree can influences its tolerance to competition ($t_f \, \alpha_r$) and the trait values of the competitors can influence their competitive impact ($t_c \, \alpha_i$). Finally, the trait similarity between the focal tree and its competitors can influences competitive interactions ($\alpha_s \, \vert t_c-t_f \vert$) (see extended methods). The parameters $m_1, \gamma, \alpha_0, \alpha_i, \alpha_r$ and $\alpha_s$ are fitted from data. \label{ilustr2}](image/fig1e.pdf)
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\newpage
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![**Traits effects on maximum growth and competition.** Standardized regression coefficients of the growth models in function of the trait of the focal tree and its competitors fitted separately for each traits (Wood density, *SLA*, and maximum height).  The parameters estimate represents the traits effect explained in the Fig 1c.: the direct trait effect on maximum growth of the focal tree, the competition trait independent, the trait of the competitors effect on their competitive impact, the trait of the focal tree effect on its competitive response, and trait similarity between the focal tree and its competitors effect on competition.  The points represent the mean estimate and the line the 95\% confidence interval.  \label{res1}](../../figs/figressp1b.pdf)
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\newpage
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![**Variation of traits effects on maximum growth and competition between biomes.** Standardized regression coefficients of the growth models in function of the trait of the focal tree and its competitors fitted separately for each traits as in Fig. 2, but with a different estimates for each biomes (see Fig 1a. for the definitions of the biomes). **NEED TO UPDATE WITH FIGURE WITH FIXED BIOMES EFFECT**.  \label{res2}](../../figs/figresspBLUP1.pdf)
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\newpage
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![Trade off between growth without competition and growth with competition underpinned by Maximum height, SLA (specific leaf area), and wood density (**I need to update the name of the traits**). The growth of a focal tree with low or high trait value (respectively 5 and 95\% quantile) in function of the local basal area of competitors with trait value resulting in a high competitive impact. The shaded area represents the 95% confidence interval of the prediction.  \label{res3}](../../figs/figres3.pdf)
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<!-- # POINTS TO DISCUSS WITH DANIEL -->
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<!-- 1. Fig 1 include size effect or not. Size effect is not interesting -->
<!--    here. -->
<!-- 2. set on biomes ? -->
<!-- 3. Split param between trait and not trait? The comparison of trait -->
<!--    effect and mean comp is interesting. -->
<!-- 4. Biomes effect ..... -->
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# References
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