Commit 4b01aba9 authored by kunstler's avatar kunstler
Browse files

update paper

parent 1a76605c
......@@ -202,8 +202,8 @@ segments( unlist(x + 1.96*sd), y-small.bar, unlist(x +1.96*sd), y+small.bar, .
}
fun.col.param <- function(){
t.col <- c('black', '#e41a1c', '#377eb8', '#4daf4a',
'#984ea3', '#ff7f00')
t.col <- c('black', '#e41a1c', '#377eb8',
'#984ea3', '#4daf4a', '#ff7f00')
names(t.col) <- c('logD', "Tf","sumBn", "sumTnBn",
"sumTfBn", "sumTnTfBn.abs")
return(t.col)
......@@ -685,15 +685,25 @@ for (i in traits){
extract.param <- function(trait, list.res,
model = 'lmer.LOGLIN.ER.AD.Tf.r.biomes.species',
param.vec = c("Tf","sumBn", "sumTnBn",
param.vec = c("logD", "Tf","sumBn", "sumTnBn",
"sumTfBn", "sumTnTfBn.abs")){
list.temp <- list.res[[paste("all.no.log_", trait ,
list.temp <- list.res[[paste("simple_", trait ,
"_", model,
sep = '')]]$lmer.summary
param.mean <- list.temp$fixed.coeff.E[param.vec]
return(param.mean)
}
extract.R2c <- function(trait, list.res,
model = 'lmer.LOGLIN.ER.AD.Tf.r.biomes.species',
param.vec = c("logD", "Tf","sumBn", "sumTnBn",
"sumTfBn", "sumTnTfBn.abs")){
list.temp <- list.res[[paste("simple_", trait ,
"_", model,
sep = '')]]$lmer.summary
return(list.temp$R2c)
}
## get fixed biomes
......
......@@ -32,16 +32,22 @@ source.root("R/utils/plot.R")
##+ ComputeTable_Effectsize, echo = FALSE, results = 'hide', message=FALSE
list.all.results <-
readRDS.root('output/list.lmer.out.all.NA.no.log.rds')
readRDS.root('output/list.lmer.out.all.NA.simple.set.rds')
library(pander)
mat.param <- do.call('cbind', lapply(c('Wood.density', 'SLA', 'Max.height'),
extract.param, list.res = list.all.results,
model = 'lmer.LOGLIN.ER.AD.Tf.r.ecocode.species'))
model = 'lmer.LOGLIN.ER.AD.Tf.r.set.species'))
mat.R2 <- do.call('cbind', lapply(c('Wood.density', 'SLA', 'Max.height'),
extract.R2c, list.res = list.all.results,
model = 'lmer.LOGLIN.ER.AD.Tf.r.set.species'))
mat.param <- rbind(mat.param, mat.R2)
colnames(mat.param) <- c('Wood.density', 'SLA', 'Max.height')
row.names(mat.param) <- c('Direct trait effect', 'Mean competition',
'Competitive effect', 'Competitive response',
'trait similarity')
row.names(mat.param) <- c('Size', 'Direct trait effect', 'Competition trait indep',
'Competitive impact', 'Competitive response',
'Trait similarity', 'R2c')
##+ Table2_Effectsize, echo = FALSE, results='asis', message=FALSE
pandoc.table(mat.param, caption = "Standaridized parameters estimates presented in Fig 2.")
pandoc.table(mat.param, caption = "Standaridized parameters estimates presented in Fig 2. and R2 of models")
## We report the conditional $R^2$ of the models using the methods of Nakagawa, S. & Schielzeth, H. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution 4, 133–142 (2013).
......@@ -35,18 +35,24 @@ source.root("R/utils/plot.R")
``` {r ComputeTable_Effectsize, echo = FALSE, results = 'hide', message=FALSE}
list.all.results <-
readRDS.root('output/list.lmer.out.all.NA.no.log.rds')
readRDS.root('output/list.lmer.out.all.NA.simple.set.rds')
library(pander)
mat.param <- do.call('cbind', lapply(c('Wood.density', 'SLA', 'Max.height'),
extract.param, list.res = list.all.results,
model = 'lmer.LOGLIN.ER.AD.Tf.r.ecocode.species'))
model = 'lmer.LOGLIN.ER.AD.Tf.r.set.species'))
mat.R2 <- do.call('cbind', lapply(c('Wood.density', 'SLA', 'Max.height'),
extract.R2c, list.res = list.all.results,
model = 'lmer.LOGLIN.ER.AD.Tf.r.set.species'))
mat.param <- rbind(mat.param, mat.R2)
colnames(mat.param) <- c('Wood.density', 'SLA', 'Max.height')
row.names(mat.param) <- c('Direct trait effect', 'Mean competition',
'Competitive effect', 'Competitive response',
'trait similarity')
row.names(mat.param) <- c('Size', 'Direct trait effect', 'Competition trait indep',
'Competitive impact', 'Competitive response',
'Trait similarity', 'R2c')
```
``` {r Table2_Effectsize, echo = FALSE, results='asis', message=FALSE}
pandoc.table(mat.param, caption = "Standaridized parameters estimates presented in Fig 2.")
pandoc.table(mat.param, caption = "Standaridized parameters estimates presented in Fig 2. and R2 of models")
```
We report the conditional $R^2$ of the models using the methods of Nakagawa, S. & Schielzeth, H. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution 4, 133142 (2013).
......@@ -21,18 +21,24 @@ opts_chunk$set(dev= c('pdf','svg'), fig.width= 10, fig.height = 5)
---------------------------------------------------------------
&nbsp; Wood.density SLA Max.height
-------------------------- -------------- -------- ------------
**Direct trait effect** -0.1366 0.06761 0.07342
-----------------------------------------------------------------
&nbsp; Wood.density SLA Max.height
----------------------------- -------------- ------- ------------
**Size** 0.4262 0.4088 0.4224
**Mean competition** -0.2153 -0.186 -0.227
**Direct trait effect** -0.1255 0.1081 0.05803
**Competitive effect** -0.04333 0.06167 -0.03017
**Competition trait indep** -0.3231 -0.2461 -0.3358
**Competitive response** 0.04628 -0.04506 -0.1399
**Competitive impact** -0.02219 0.08218 -0.02344
**trait similarity** 0.04945 0.08251 0.06553
---------------------------------------------------------------
**Competitive response** 0.0582 0.01802 -0.08021
Table: Standaridized parameters estimates presented in Fig 2.
**Trait similarity** 0.04117 0.05546 0.06229
**R2c** 0.7072 0.7514 0.7156
-----------------------------------------------------------------
Table: Standaridized parameters estimates presented in Fig 2. and R2 of models
We report the conditional $R^2$ of the models using the methods of Nakagawa, S. & Schielzeth, H. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution 4, 133–142 (2013).
......@@ -2,25 +2,25 @@
# Model and analysis
We use a neighbourhood modelling framework[@canham_neighborhood_2006; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] to model the growth of a focal tree of species $f$ as a product of its intrinsic potential rate (determined by its traits and size) and reductions due to competition with individuals growing in the local neighbourhood. Specifically, we assumed a relationship of the form
We use a neighbourhood modelling framework[@canham_neighborhood_2006; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] to model the growth of a focal tree of species $f$ as a product of its maximum growth rate (determined by its traits and size) and reductions due to competition with individuals growing in the local neighbourhood. Specifically, we assumed a relationship of the form
\begin{equation} \label{G1}
G_{i,f,p,s,t} = G_{\textrm{max} \, f,p,s} \, D_{i,f,p,s,t}^{\gamma_f} \, \exp\left(\sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s,t}}\right),
G_{i,f,p,s} = G_{\textrm{max} \, f,p,s} \, D_{i,f,p,s}^{\gamma_f} \, \exp\left(\sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s}}\right),
\end{equation}
where:
- $G_{i,f,p,s,t}$ and $D_{i,f,p,s,t}$ are the the annual basal area growth and diameter of individual $i$ from species $f$, plot $p$ and dataset $s$ in census $t$,
- $G_{i,f,p,s}$ and $D_{i,f,p,s}$ are the the annual basal area growth and diameter of individual $i$ from species $f$, plot $p$ and dataset $s$,
- $G_{\textrm{max} \, f,p,s}$ is the potential growth rate in basal area growth for species $f$ on plot $p$ in data set $s$, i.e. in absence of competition,
- $\gamma_f$ determines the rate at which growth changes with size for species $f$, modelled with a normally distributed random effect of species $\epsilon_{\gamma, f}$ (as $\gamma_f = \gamma_0 + \epsilon_{\gamma, f}$)
- $N_p$ is the number of competitor species on plot $p$ ,
- $\alpha_{c,f}$ is the per unit basal area effect of individuals from species $c$ on growth of an individual in species $f$, and
- $B_{c,p,s,t}= 0.25\, \pi \, w_i \sum_i D_{i,c,p,s,t}^2$ is the basal area of the species $c$ within the plot $p$ and dataset $s$ at census $t$, where $w_i$ is a constant based on plot size.
- $B_{c,p,s}= 0.25\, \pi \, w_i \sum_i D_{i,c,p,s}^2$ is the basal area of the species $c$ within the plot $p$ and dataset $s$, where $w_i$ is a constant based on plot size.
Values of $\alpha_{c,f}< 0$ indicate competition, whereas $\alpha_{c,f}$ > 0 indicates facilitation. Log-transformation of eq. \ref{G1} leads to a linearised model of form
\begin{equation} \label{logG1}
\log{G_{i,f,p,s,t}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,t,p,s}} + \sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s,t}}.
\log{G_{i,f,p,s}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,p,s}} + \sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s}}.
\end{equation}
......@@ -38,18 +38,18 @@ To include traits effects on competition presented in Fig. 1, competitive intera
\end{equation}
where:
- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ (as $\alpha_{0,f} = \alpha_0 + \epsilon_{0, f}$),
- $\alpha_r$ is the **competitive response** of the focal species, i.e. change in competition response due to traits $t_f$ of the focal tree,
- $\alpha_{i}$ is the **competitive impact**, i.e. change in competition impact due to traits $t_c$ of the competitor tree, and
- $\alpha_s$ is the effect of **trait similarity**, i.e. change in competition due to absolute distance between traits $\vert{t_c-t_f}\vert$.
- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ and a normally distributed random effect of data set $s$ (as $\alpha_{0,f} = \alpha_0 + \epsilon_{0, f}+ \epsilon_{0, s}$),
- $\alpha_r$ is the **competitive response** of the focal species, i.e. change in competition response due to traits $t_f$ of the focal tree and include a normally distributed random effect of data set $s$,
- $\alpha_{i}$ is the **competitive impact**, i.e. change in competition impact due to traits $t_c$ of the competitor tree and include a normally distributed random effect of data set $s$, and
- $\alpha_s$ is the effect of **trait similarity**, i.e. change in competition due to absolute distance between traits $\vert{t_c-t_f}\vert$ and include a normally distributed random effect of data set $s$.
[^GK1]: With basal area of species $c$ this equation can be simplified as a function of total basal area, the weighted mean of the traits of the competitors and the weighted mean of the traits similarity.
Eqs. \ref{logG1}-\ref{alpha} were then fitted to empirical estimates of growth, given by
\begin{equation} \label{logGobs} G_{i,f,p,s,t} = 0.25 \pi \left(D_{i,f,p,s,t+1}^2 - D_{i,f,p,s,t}^2\right).
\begin{equation} \label{logGobs} G_{i,f,p,s} = 0.25 \pi \left(D_{i,f,p,s,t+1}^2 - D_{i,f,p,s,t}^2\right).
\end{equation}
To estimate standardised coefficients (one type of standardised effect size)[@schielzeth_simple_2010], response and explanatory variables were standardized prior to analyse (divided by standard deviation). Moreover, trait and diameter were also centred to facilitate convergence. The model were fitted using $lmer$ in [lme4](http://cran.r-project.org/web/packages/lme4/index.html). We fitted two versions of this model. In the first version parameters $m_{0}, m_1, \alpha_0,\alpha_r,\alpha_i,\alpha_s$ were estimated with ecoregion as random effects to account for the variation between data set and different abiotic region. In the second version, we repeated the same analysis but including different fixed estimates of these parameters fort each biome. This enabled us to explore variation between biomes.
To estimate standardised coefficients (one type of standardised effect size)[@schielzeth_simple_2010], response and explanatory variables were standardized prior to analyse (divided by standard deviation). Moreover, trait and diameter were also centred to facilitate convergence. The model were fitted using $lmer$ in [lme4](http://cran.r-project.org/web/packages/lme4/index.html). We fitted two versions of this model. In the first version parameters $m_{0}, m_1, \alpha_0,\alpha_r,\alpha_i,\alpha_s$ were estimated as constant across all biomes, we repeated the same analysis but including different fixed estimates of these parameters fort each biome. This enabled us to explore variation between biomes. Because some biomes had very few observation we merged several biomes with climatically closest biome: tundra was merged with taiga, tropical rainforest and tropical seasonal forest were merged in tropical forest, and desert were not include in this final analysis as to few data was available.
**\color{red}TO BE DONE** Because traits similarity may be more strongly related to multi-traits distance than a single trait distance we also explored a model with all three traits and a traits distance based on the euclidean distance of the three traits (standardized). This model expand the equation 1 with a parameter $m_1$, $\alpha_i$ and $\alpha_r$ per trait and an effect of multi-traits similarity (with the parameter $\alpha_s$).
......@@ -62,7 +62,7 @@ Our main objective was collate data sets spanning the dominant forest biomes of
the world. Datasets were included if they (i) allowed both growth rate of individual trees and the local abundance of competitors to be estimated, and (ii) had good (>50%) coverage for at least one
of the traits of interest (SLA, wood density, and maximum height).
The datasets collated fell into two broad categories: (1) national forest inventories (NFI), in which trees above a given diameter are sampled in a network of small plots (often on a regular grid) covering the country; (2) large permanent plots (LPP) ranging in size from 0.5-50ha, in which the x-y coordinates of all trees above a given diameter were recorded. These LPP were mostly located in tropical regions. The minimum diameter of recorded trees varied among sites from 1-12cm. To allow comparison between data sets, we restricted our analysis to trees greater than 10cm. Moreover, we excluded from the analysis any plots with harvesting during the growth measurement period, that was identified as a plantation, or overlapping a forest edge. See the section *Details on sites* and Table M1 for more details on the individual datasets.
The datasets collated fell into two broad categories: (1) national forest inventories (NFI), in which trees above a given diameter are sampled in a network of small plots (often on a regular grid) covering the country; (2) large permanent plots (LPP) ranging in size from 0.5-50ha, in which the x-y coordinates of all trees above a given diameter were recorded. These LPP were mostly located in tropical regions. The minimum diameter of recorded trees varied among sites from 1-12cm. To allow comparison between data sets, we restricted our analysis to trees greater than 10cm. Moreover, we excluded from the analysis any plots with harvesting during the growth measurement period, that was identified as a plantation, or overlapping a forest edge. Finally, we selected only two consecutive census for each tree to avoid to have to account for repeated measurements, as only less than a third of teh data had repeated measurements. See the section *Details on sites* and Table M1 for more details on the individual datasets.
Basal area growth was estimated from diameter measurements recorded across successive time points. For the French NFI, these data were obtained from short tree cores. For all other datasest, diameter at breast height ($D$) of each individual was recorded at multiple censuses. We excluded trees with extreme positive or negative diameter growth rates, following criteria developed at the BCI site [@condit_mortality_1993] and implemented in the R package [CTFS R](http://ctfs.arnarb.harvard.edu/Public/CTFSRPackage/).
......@@ -75,7 +75,7 @@ We extracted mean annual temperature (MAT) and mean annual sum of precipitation
## Traits
Data on species functional traits was extracted from existing sources. We focused on wood density, species specific leaf area (SLA) and maximum height, because these traits have previously been related to competitive interactions and are available for large numbers of species [@wright_functional_2010; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] (see Table M2 for traits coverage). Where available we used data collected locally; otherwise we sourced data from the [TRY](http://www.try-db.org/) trait data base [@kattge_try_2011]. Local data were available for most tropical sites and species (see Table S1). Several of the NFI datasets also provided height measurements, from which we computed a species' maximum height as the 99% quantile of observed values (France, US, Spain, Switzerland; for Sweden we used the estimate from the French data and for Canada we used the estimate from the US data). Otherwise, we extracted measurement from the TRY database.
Data on species functional traits was extracted from existing sources. We focused on wood density, species specific leaf area (SLA) and maximum height, because these traits have previously been related to competitive interactions and are available for large numbers of species [@wright_functional_2010; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] (see Table M2 for traits coverage). Where available we used data collected locally; otherwise we sourced data from the [TRY](http://www.try-db.org/) trait data base [@kattge_try_2011]. Local data were available for most tropical sites and species (see Table M1). Several of the NFI datasets also provided height measurements, from which we computed a species' maximum height as the 99% quantile of observed values (France, US, Spain, Switzerland; for Sweden we used the estimate from the French data and for Canada we used the estimate from the US data). Otherwise, we extracted measurement from the TRY database.
For each focal tree, our approach requires us to also account for the traits of all competitors present in the neighbourhood. Most of our plots had good coverage of competitors, but inevitably there were some trees were trait data were lacking. In these cases we estimated trait data as follows. if possible, we used the genus mean, and if no genus data was available, we used the mean of the species present in the country. However, we restricted our analysis to plots were the percentage of basal area of trees with (i) no species level trait data was less than 10%, and (ii) no genus level data was less than 5%.
......
......@@ -2,25 +2,25 @@
# Model and analysis
We use a neighbourhood modelling framework[@canham_neighborhood_2006; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] to model the growth of a focal tree of species $f$ as a product of its intrinsic potential rate (determined by its traits and size) and reductions due to competition with individuals growing in the local neighbourhood. Specifically, we assumed a relationship of the form
We use a neighbourhood modelling framework[@canham_neighborhood_2006; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] to model the growth of a focal tree of species $f$ as a product of its maximum growth rate (determined by its traits and size) and reductions due to competition with individuals growing in the local neighbourhood. Specifically, we assumed a relationship of the form
\begin{equation} \label{G1}
G_{i,f,p,s,t} = G_{\textrm{max} \, f,p,s} \, D_{i,f,p,s,t}^{\gamma_f} \, \exp\left(\sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s,t}}\right),
G_{i,f,p,s} = G_{\textrm{max} \, f,p,s} \, D_{i,f,p,s}^{\gamma_f} \, \exp\left(\sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s}}\right),
\end{equation}
where:
- $G_{i,f,p,s,t}$ and $D_{i,f,p,s,t}$ are the the annual basal area growth and diameter of individual $i$ from species $f$, plot $p$ and dataset $s$ in census $t$,
- $G_{i,f,p,s}$ and $D_{i,f,p,s}$ are the the annual basal area growth and diameter of individual $i$ from species $f$, plot $p$ and dataset $s$,
- $G_{\textrm{max} \, f,p,s}$ is the potential growth rate in basal area growth for species $f$ on plot $p$ in data set $s$, i.e. in absence of competition,
- $\gamma_f$ determines the rate at which growth changes with size for species $f$, modelled with a normally distributed random effect of species $\epsilon_{\gamma, f}$ (as $\gamma_f = \gamma_0 + \epsilon_{\gamma, f}$)
- $N_p$ is the number of competitor species on plot $p$ ,
- $\alpha_{c,f}$ is the per unit basal area effect of individuals from species $c$ on growth of an individual in species $f$, and
- $B_{c,p,s,t}= 0.25\, \pi \, w_i \sum_i D_{i,c,p,s,t}^2$ is the basal area of the species $c$ within the plot $p$ and dataset $s$ at census $t$, where $w_i$ is a constant based on plot size.
- $B_{c,p,s}= 0.25\, \pi \, w_i \sum_i D_{i,c,p,s}^2$ is the basal area of the species $c$ within the plot $p$ and dataset $s$, where $w_i$ is a constant based on plot size.
Values of $\alpha_{c,f}< 0$ indicate competition, whereas $\alpha_{c,f}$ > 0 indicates facilitation. Log-transformation of eq. \ref{G1} leads to a linearised model of form
\begin{equation} \label{logG1}
\log{G_{i,f,p,s,t}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,t,p,s}} + \sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s,t}}.
\log{G_{i,f,p,s}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,p,s}} + \sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s}}.
\end{equation}
......@@ -38,18 +38,18 @@ To include traits effects on competition presented in Fig. 1, competitive intera
\end{equation}
where:
- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ (as $\alpha_{0,f} = \alpha_0 + \epsilon_{0, f}$),
- $\alpha_r$ is the **competitive response** of the focal species, i.e. change in competition response due to traits $t_f$ of the focal tree,
- $\alpha_{i}$ is the **competitive impact**, i.e. change in competition impact due to traits $t_c$ of the competitor tree, and
- $\alpha_s$ is the effect of **trait similarity**, i.e. change in competition due to absolute distance between traits $\vert{t_c-t_f}\vert$.
- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ and a normally distributed random effect of data set $s$ (as $\alpha_{0,f} = \alpha_0 + \epsilon_{0, f}+ \epsilon_{0, s}$),
- $\alpha_r$ is the **competitive response** of the focal species, i.e. change in competition response due to traits $t_f$ of the focal tree and include a normally distributed random effect of data set $s$,
- $\alpha_{i}$ is the **competitive impact**, i.e. change in competition impact due to traits $t_c$ of the competitor tree and include a normally distributed random effect of data set $s$, and
- $\alpha_s$ is the effect of **trait similarity**, i.e. change in competition due to absolute distance between traits $\vert{t_c-t_f}\vert$ and include a normally distributed random effect of data set $s$.
[^GK1]: With basal area of species $c$ this equation can be simplified as a function of total basal area, the weighted mean of the traits of the competitors and the weighted mean of the traits similarity.
Eqs. \ref{logG1}-\ref{alpha} were then fitted to empirical estimates of growth, given by
\begin{equation} \label{logGobs} G_{i,f,p,s,t} = 0.25 \pi \left(D_{i,f,p,s,t+1}^2 - D_{i,f,p,s,t}^2\right).
\begin{equation} \label{logGobs} G_{i,f,p,s} = 0.25 \pi \left(D_{i,f,p,s,t+1}^2 - D_{i,f,p,s,t}^2\right).
\end{equation}
To estimate standardised coefficients (one type of standardised effect size)[@schielzeth_simple_2010], response and explanatory variables were standardized prior to analyse (divided by standard deviation). Moreover, trait and diameter were also centred to facilitate convergence. The model were fitted using $lmer$ in [lme4](http://cran.r-project.org/web/packages/lme4/index.html). We fitted two versions of this model. In the first version parameters $m_{0}, m_1, \alpha_0,\alpha_r,\alpha_i,\alpha_s$ were estimated with ecoregion as random effects to account for the variation between data set and different abiotic region. In the second version, we repeated the same analysis but including different fixed estimates of these parameters fort each biome. This enabled us to explore variation between biomes.
To estimate standardised coefficients (one type of standardised effect size)[@schielzeth_simple_2010], response and explanatory variables were standardized prior to analyse (divided by standard deviation). Moreover, trait and diameter were also centred to facilitate convergence. The model were fitted using $lmer$ in [lme4](http://cran.r-project.org/web/packages/lme4/index.html). We fitted two versions of this model. In the first version parameters $m_{0}, m_1, \alpha_0,\alpha_r,\alpha_i,\alpha_s$ were estimated as constant across all biomes, we repeated the same analysis but including different fixed estimates of these parameters fort each biome. This enabled us to explore variation between biomes. Because some biomes had very few observation we merged several biomes with climatically closest biome: tundra was merged with taiga, tropical rainforest and tropical seasonal forest were merged in tropical forest, and desert were not include in this final analysis as to few data was available.
**\color{red}TO BE DONE** Because traits similarity may be more strongly related to multi-traits distance than a single trait distance we also explored a model with all three traits and a traits distance based on the euclidean distance of the three traits (standardized). This model expand the equation 1 with a parameter $m_1$, $\alpha_i$ and $\alpha_r$ per trait and an effect of multi-traits similarity (with the parameter $\alpha_s$).
......@@ -62,7 +62,7 @@ Our main objective was collate data sets spanning the dominant forest biomes of
the world. Datasets were included if they (i) allowed both growth rate of individual trees and the local abundance of competitors to be estimated, and (ii) had good (>50%) coverage for at least one
of the traits of interest (SLA, wood density, and maximum height).
The datasets collated fell into two broad categories: (1) national forest inventories (NFI), in which trees above a given diameter are sampled in a network of small plots (often on a regular grid) covering the country; (2) large permanent plots (LPP) ranging in size from 0.5-50ha, in which the x-y coordinates of all trees above a given diameter were recorded. These LPP were mostly located in tropical regions. The minimum diameter of recorded trees varied among sites from 1-12cm. To allow comparison between data sets, we restricted our analysis to trees greater than 10cm. Moreover, we excluded from the analysis any plots with harvesting during the growth measurement period, that was identified as a plantation, or overlapping a forest edge. See the section *Details on sites* and Table M1 for more details on the individual datasets.
The datasets collated fell into two broad categories: (1) national forest inventories (NFI), in which trees above a given diameter are sampled in a network of small plots (often on a regular grid) covering the country; (2) large permanent plots (LPP) ranging in size from 0.5-50ha, in which the x-y coordinates of all trees above a given diameter were recorded. These LPP were mostly located in tropical regions. The minimum diameter of recorded trees varied among sites from 1-12cm. To allow comparison between data sets, we restricted our analysis to trees greater than 10cm. Moreover, we excluded from the analysis any plots with harvesting during the growth measurement period, that was identified as a plantation, or overlapping a forest edge. Finally, we selected only two consecutive census for each tree to avoid to have to account for repeated measurements, as only less than a third of teh data had repeated measurements. See the section *Details on sites* and Table M1 for more details on the individual datasets.
Basal area growth was estimated from diameter measurements recorded across successive time points. For the French NFI, these data were obtained from short tree cores. For all other datasest, diameter at breast height ($D$) of each individual was recorded at multiple censuses. We excluded trees with extreme positive or negative diameter growth rates, following criteria developed at the BCI site [@condit_mortality_1993] and implemented in the R package [CTFS R](http://ctfs.arnarb.harvard.edu/Public/CTFSRPackage/).
......@@ -75,7 +75,7 @@ We extracted mean annual temperature (MAT) and mean annual sum of precipitation
## Traits
Data on species functional traits was extracted from existing sources. We focused on wood density, species specific leaf area (SLA) and maximum height, because these traits have previously been related to competitive interactions and are available for large numbers of species [@wright_functional_2010; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] (see Table M2 for traits coverage). Where available we used data collected locally; otherwise we sourced data from the [TRY](http://www.try-db.org/) trait data base [@kattge_try_2011]. Local data were available for most tropical sites and species (see Table S1). Several of the NFI datasets also provided height measurements, from which we computed a species' maximum height as the 99% quantile of observed values (France, US, Spain, Switzerland; for Sweden we used the estimate from the French data and for Canada we used the estimate from the US data). Otherwise, we extracted measurement from the TRY database.
Data on species functional traits was extracted from existing sources. We focused on wood density, species specific leaf area (SLA) and maximum height, because these traits have previously been related to competitive interactions and are available for large numbers of species [@wright_functional_2010; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] (see Table M2 for traits coverage). Where available we used data collected locally; otherwise we sourced data from the [TRY](http://www.try-db.org/) trait data base [@kattge_try_2011]. Local data were available for most tropical sites and species (see Table M1). Several of the NFI datasets also provided height measurements, from which we computed a species' maximum height as the 99% quantile of observed values (France, US, Spain, Switzerland; for Sweden we used the estimate from the French data and for Canada we used the estimate from the US data). Otherwise, we extracted measurement from the TRY database.
For each focal tree, our approach requires us to also account for the traits of all competitors present in the neighbourhood. Most of our plots had good coverage of competitors, but inevitably there were some trees were trait data were lacking. In these cases we estimated trait data as follows. if possible, we used the genus mean, and if no genus data was available, we used the mean of the species present in the country. However, we restricted our analysis to plots were the percentage of basal area of trees with (i) no species level trait data was less than 10%, and (ii) no genus level data was less than 5%.
......@@ -303,48 +303,38 @@ For each focal tree, our approach requires us to also account for the traits of
```
##
## Attaching package: 'pander'
##
## The following object is masked from 'package:knitr':
##
## pandoc
```
----------------------------------------------------------------------------------------
set # of trees # of species # of % of angiosperm % of evergreen
plots/quadrats
-------- ------------ -------------- ---------------- ----------------- ----------------
Sweden 2e+05 26 22552 0.27 0.73
NVS 53775 117 1415 0.94 0.99
-----------------------------------------------------------------------------------
set # of trees # of species # of % of % of evergreen
plots/quadrats angiosperm
-------- ------------ -------------- ---------------- ------------ ----------------
Sweden 2e+05 26 22552 0.27 0.73
NVS 53775 117 1415 0.94 0.99
US 1370497 492 59840 0.63 0.37
US 1369862 492 59840 0.63 0.37
Canada 5e+05 75 14983 0.34 0.65
Canada 5e+05 75 14983 0.34 0.65
NSW 906 101 63 1 0.92
NSW 906 101 63 1 0.92
France 184316 127 17611 0.74 0.28
France 184316 127 17611 0.74 0.28
Swiss 28260 59 2597 0.36 0.55
Swiss 28287 61 2597 0.36 0.55
Spain 418805 122 36462 0.35 0.82
Spain 418805 122 36462 0.35 0.82
BCI 27081 237 2033 1 0.78
BCI 27097 237 2033 1 0.78
Paracou 46367 715 2157 1 0.83
Paracou 46368 710 2157 1 0.84
Japan 4663 136 318 0.73 0.7
Japan 4645 138 318 0.73 0.7
Fushan 14701 72 623 0.92 0.75
Fushan 14701 72 623 0.92 0.75
Luquillo 14011 82 399 1 0.99
Luquillo 14011 82 399 1 0.99
Mbaiki 17611 207 989 0.99 0.72
-----------------------------------------------------------------------------------
Mbaiki 17575 204 989 0.99 0.73
----------------------------------------------------------------------------------------
Table: Table M1. Data description
......
......@@ -23,13 +23,11 @@ When competition is described as interactions between pairs of species (as it tr
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}.
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
were tree size and the local abundance of competitors. Then amomg the trait effect, the direct influence of the focal plant’s traits on its growth was the most important effect
(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
direct effect, followed by SLA whereas confidence interval for maximum height intercepted zero (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
......@@ -43,10 +41,10 @@ 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}).
litter recylcing[@sapijanskas_beyond_2013])[^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}). For Wood density only taiga which has relatively small sample size and few species showed a different competitive response parameter (Fig. \ref{res2}). The results were more variable for SLA (Fig. \ref{res2}), which may be related to different relationship between shade-tolerance and SLA between deciduous and evergreeen species[@lusk_why_2008].
[^todo]: **\color{red}Still running.**
[^todo]: **I'M PLANNING TO ADD An analysis using a multiple-traits distance rather than a single trait distance didn't show different pattern (extended data Figure **\color{red}?**). \color{red}BUT Still running.**
The direction of the traits effect agree well with the existing
literature. High wood density was lined with
......@@ -54,38 +52,32 @@ litter recylcing[@sapijanskas_beyond_2013]). An analysis using a multiple-traits
agreement with shade-tolerant
species having high wood density[@wright_functional_2010]. High wood density also resulted in a
higher competitive impact, that may be related to deeper crown
[@poorter_architecture_2006; @aiba_architectural_2009]. The lack of direct effect of *SLA* on maximum growth (but with a positive tendency)
agree well with the weak correlation previously reported for adult
trees [@wright_functional_2010]. Increasing *SLA* was also weakly
related to decreased competitive impact and no effect or possible
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
[@poorter_architecture_2006; @aiba_architectural_2009]. The small direct effect of *SLA* on maximum growth agree well with the weak correlation previously reported for adult
trees [@wright_functional_2010]. Increasing SLA was also related to decreased competitive impact, in agrement with the postive relation ship between leaf life span and light interception [@niinemets_review_2010]. No effect of SLA on competitive tolerance were found. Finally, maximum height was
positively related to maximum growth in most biomes (but with large confidence interval in tropical forest) as previously
reported[@wright_functional_2010]. Species with small maximum height
were also much more tolerant to competition than taller species, in
line with the idea that sub-canopy tree are more shade-tolerant. For
wood density and *SLA* the link with competitive impact and
wood density [^note] the link with competitive impact and
competitive response was opposed, in agreement with a coordinated
selection under which trait value that confer high competitive
impact also confer high competitive tolerance (a competitive
hierachy[@kunstler_competitive_2012; @mayfield_opposing_2010]). This
was not the case for maximum height because short species were more
tolerant to competition but had a lower competitive impact. This
hierachy[@kunstler_competitive_2012; @mayfield_opposing_2010]). For *SLA* the coordinations between competitive impact and response was variable between biomes which may again be related to differences between deciduous and evergeen species. For maximum height there was no coordination, with short species being more
tolerant to competition but with a tendency for a lower competitive impact. This
match well the observation of the persistence of sub-canopy species
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
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
classical process proposed to explain species coexistence in forest
competition. Our results just demonstrate that traits 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. This important because this trade-off is one of the most
classical process proposed to explain species coexistence in forest along succession
[@rees_long-term_2001].
[^note]: the sign of the SLA competitive response is variable depending on the resampling.
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.
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 species coexistence.
<!-- TODO ADD TRAITS RANDOMISATION TO -->
<!-- SEE NOT AN ARTIFACT. -->
# Methods summary
......@@ -119,10 +111,9 @@ traits (direct traits effect) and by these four crowding indexes,
while accounting for size effect. To
facilitate comparison between parameters and traits all traits and
variable were standaridised to a SD of one. We report these
standardized parameters for each traits. Two models were fitted, (i)
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
fixed effect to analyse the difference between biomes.
standardized parameters for each traits. We included the data set as a random effect in each parameters to account for variation in protocol between data set. Two models were fitted, (i) estimating an overall trait effect across all data set
and (ii) we included biomes as a
fixed effect to analyse the difference between biomes.
**Supplementary Information** is available in the online version of the paper.
......@@ -144,7 +135,7 @@ G.K. conceived the study with feedback from M.W and D.F. G. K., M. W, D. F. and
![**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]: 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 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)
![**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]: 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 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{ilustr}](image/fig1e.pdf)
\newpage
......@@ -155,7 +146,7 @@ G.K. conceived the study with feedback from M.W and D.F. G. K., M. W, D. F. and
\newpage
![**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). \label{res2}](../../figs/figres2.pdf)
![**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). Note that tropical rainforest and tropical seasonal forest were merged togetherin tropical forest, tundra was merged with taiga, and desert were not included in this analysis as to few data were available. \label{res2}](../../figs/figres2.pdf)
\newpage
......
......@@ -27,6 +27,17 @@
file = {Uriarte et al_2010_Trait similarity, shared ancestry and the structure of neighbourhood.pdf:/home/georges/Dropbox/biblio/pdfNEW/Uriarte et al_2010_Trait similarity, shared ancestry and the structure of neighbourhood.pdf:application/pdf}
}
@article{niinemets_review_2010,
title = {A review of light interception in plant stands from leaf to canopy in different plant functional types and in species with varying shade tolerance},
volume = {25},
issn = {0912-3814},
number = {4},
journal = {Ecological Research},
author = {Niinemets, Ülo},
year = {2010},
pages = {693--714}
}
@article{macarthur_limiting_1967,
title = {The Limiting Similarity, Convergence, and Divergence of Coexisting Species},
volume = {101},
......@@ -552,6 +563,19 @@
file = {Kursar et al_2009_The evolution of antiherbivore defenses and their contribution to species.pdf:/home/georges/Dropbox/biblio/pdfNEW/Kursar et al_2009_The evolution of antiherbivore defenses and their contribution to species.pdf:application/pdf}
}
@article{graham_predicting_2015,
title = {Predicting climate-driven regime shifts versus rebound potential in coral reefs},
issn = {0028-0836, 1476-4687},
url = {http://www.nature.com/doifinder/10.1038/nature14140},
doi = {10.1038/nature14140},
urldate = {2015-01-21},
journal = {Nature},
author = {Graham, Nicholas A. J. and Jennings, Simon and MacNeil, M. Aaron and Mouillot, David and Wilson, Shaun K.},
month = jan,
year = {2015},
file = {Graham et al_2015_Predicting climate-driven regime shifts versus rebound potential in coral reefs.pdf:/home/georges/Dropbox/biblio/pdfNEW/Graham et al_2015_Predicting climate-driven regime shifts versus rebound potential in coral reefs.pdf:application/pdf}
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title = {Simple means to improve the interpretability of regression coefficients: Interpretation of regression coefficients},
volume = {1},
......@@ -581,6 +605,20 @@
file = {Lasky et al_2014_Trait-mediated assembly processes predict successional changes in community.pdf:/home/georges/Dropbox/biblio/pdfNEW/Lasky et al_2014_Trait-mediated assembly processes predict successional changes in community.pdf:application/pdf}
}
@article{lusk_why_2008,
title = {Why are evergreen leaves so contrary about shade?},
volume = {23},
issn = {0169-5347},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18439708},
doi = {10.1016/j.tree.2008.02.006},
abstract = {Leaf mass per area ({LMA}) is one of the most widely measured of all plant functional traits. In deciduous forests, there is similarity between plastic and evolutionary responses of {LMA} to light gradients. In evergreens, however, {LMA} is lower in shaded than sunlit individuals of the same species, whereas shade-tolerant evergreens have higher {LMA} than light-demanders grown under the same conditions. We suggest that this pattern of 'counter-gradient variation' results from some combination of (i) close evolutionary coordination of {LMA} with leaf lifespan, (ii) selection for different leaf constitutions (relative investment in cell walls versus cell contents) in sun and shade environments and/or (iii) constraints on plasticity as a result of genetic correlations between phenotypes expressed in sun and shade.},
number = {6},
journal = {Trends in Ecology \& Evolution},
author = {Lusk, Christopher H and Reich, Peter B and Montgomery, Rebecca a and Ackerly, David D. and Cavender-Bares, Jeannine},
year = {2008},
pages = {299--303}
}
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title = {Wood density explains architectural differentiation across 145 co-occurring tropical tree species},
volume = {26},
......@@ -610,6 +648,58 @@
file = {Canham et al_2006_Neighborhood analyses of canopy tree competition along environmental gradients.pdf:/home/georges/Dropbox/biblio/pdfNEW/Canham et al_2006_Neighborhood analyses of canopy tree competition along environmental gradients.pdf:application/pdf}
}
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doi = {10.1016/j.tree.2013.07.004},
language = {en},
number = {1},
urldate = {2015-01-06},
journal = {Trends in Ecology \& Evolution},
author = {Pennell, Matthew W. and Harmon, Luke J. and Uyeda, Josef C.},
month = jan,
year = {2014},
pages = {23--32},
file = {Pennell et al_2014_Is there room for punctuated equilibrium in macroevolution.pdf:/home/georges/Dropbox/biblio/pdfNEW/Pennell et al_2014_Is there room for punctuated equilibrium in macroevolution.pdf:application/pdf}
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title = {An integrative view of phylogenetic comparative methods: connections to population genetics, community ecology, and paleobiology: Integrative comparative methods},
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issn = {00778923},
shorttitle = {An integrative view of phylogenetic comparative methods},
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doi = {10.1111/nyas.12157},
language = {en},
number = {1},
urldate = {2015-01-06},
journal = {Annals of the New York Academy of Sciences},
author = {Pennell, Matthew W. and Harmon, Luke J.},
month = jun,
year = {2013},
pages = {90--105},
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url = {http://www.pnas.org/cgi/doi/10.1073/pnas.1308932111},
doi = {10.1073/pnas.1308932111},
language = {en},
number = {22},
urldate = {2015-01-21},
journal = {Proceedings of the National Academy of Sciences},
author = {Kerkhoff, A. J. and Moriarty, P. E. and Weiser, M. D.},
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title = {Phylogenetic and trait similarity to a native species predict herbivory on non-native oaks},
volume = {106},
......@@ -623,6 +713,24 @@
file = {Pearse_Hipp_2009_Phylogenetic and trait similarity to a native species predict herbivory on2.pdf:/home/georges/Dropbox/biblio/pdfNEW/Pearse_Hipp_2009_Phylogenetic and trait similarity to a native species predict herbivory on2.pdf:application/pdf}
}
@article{omeara_evolutionary_2012,
title = {Evolutionary Inferences from Phylogenies: A Review of Methods},
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issn = {1543-592X, 1545-2069},
shorttitle = {Evolutionary Inferences from Phylogenies},
url = {http://www.annualreviews.org/doi/abs/10.1146/annurev-ecolsys-110411-160331},
doi = {10.1146/annurev-ecolsys-110411-160331},
language = {en},
number = {1},
urldate = {2015-01-06},
journal = {Annual Review of Ecology, Evolution, and Systematics},
author = {O'Meara, Brian C.},
month = dec,
year = {2012},
pages = {267--285},
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......@@ -759,7 +867,7 @@ Information about variation in growth between individuals and between census per
month = oct,
year = {2010},
pages = {1262--1269},
file = {j.1461-0248.2010.01520.x.pdf:/home/georges/Dropbox/biblio/zoterofiles/storage/GS3KWSTC/j.1461-0248.2010.01520.x.pdf:application/pdf}