Commit cdf19fdf authored by Georges Kunstler's avatar Georges Kunstler
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Makefile updated for report

parent e3058128
TARGETS = $(subst md,pdf,$(shell ls *.md)) TARGETS = $(subst md,pdf,$(shell ls *.md))
all: $(TARGETS) all: progress.pdf
%.pdf: %.md include.tex progress.pdf: progress.md include.tex biome_ecocode_xy.pdf world_map_all.png traits-XY.pdf R2_boxplot_two.pdf R2_MAP_two.pdf parameters_MAP_2models.pdf parameters_BATOT_MAP.pdf
cp ../../../figs/biome.ecocode.xy.pdf biome_ecocode_xy.pdf
cp ../../../figs/world_map_all.png world_map_all.png
convert world_map_all.png -crop 750x350+125+50 +repage world_map_all.png
cp ../../../figs/test.traits/traits.XY.pdf traits-XY.pdf
cp ../../../figs/R2.boxplot.two.pdf R2_boxplot_two.pdf
cp ../../../figs/R2.MAP.two.pdf R2_MAP_two.pdf
cp ../../../figs/parameters.MAP.2models.pdf parameters_MAP_2models.pdf
cp ../../../figs/parameters.BATOT.MAP.pdf parameters_BATOT_MAP.pdf
pandoc $< --csl=journal-of-applied-ecology.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@ pandoc $< --csl=journal-of-applied-ecology.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
biome_ecocode_xy.pdf: ../../../figs/biome.ecocode.xy.pdf
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traits-XY.pdf: ../../../figs/test.traits/traits.XY.pdf
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R2_boxplot_two.pdf: ../../../figs/R2.boxplot.two.pdf
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R2_MAP_two.pdf: ../../../figs/R2.MAP.two.pdf
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parameters_MAP_2models.pdf: ../../../figs/parameters.MAP.2models.pdf
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parameters_BATOT_MAP.pdf: ../../../figs/parameters.BATOT.MAP.pdf
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% Report from workshop 'How are competitive interactions influenced by traits? A global analysis based on tree radial growth' % Report from workshop 'How are competitive interactions influenced by traits? A global analysis based on tree radial growth'
% Project leader: Georges Kunstler % Project leader: Georges Kunstler
% 16/12/2013 % 18/12/2013
This document gives an update on the analyses completed during and after the workshop held in October 2013 at Macquarie University. This document gives an update on the analyses completed during and after the workshop held in October 2013 at Macquarie University.
**Contact details:** georges.kunstler@gmail.com, Department of Biological Sciences Macquarie University, Sydney, NSW / Irstea EMGR Grenoble France **Contact details:** georges.kunstler@gmail.com, Department of Biological Sciences Macquarie University, Sydney, NSW / Irstea EMGR Grenoble France
**Workshop participants:** David A. Coomes, Daniel Falster, Rob Kooyman, Daniel Laughlin, Lourens Poorter, Mark Vanderwel, Ghislain Vieilledent, Mark Westoby, Joe Wright **Workshop participants:** David A. Coomes, Daniel Falster, Francis Hui, Rob Kooyman, Daniel Laughlin, Lourens Poorter, Mark Vanderwel, Ghislain Vieilledent, Mark Westoby, Joe Wright.
**Other participants and data contributors:** John Caspersen, Hongcheng Zeng, Sylvie Gourlet-Fleury, Bruno Herault, Goran Ståhl, Jill Thompson, Sarah Richardson, Paloma Ruiz, I-Fang Sun, Nathan Swenson, Maria Uriarte, Miguel Zavala, Niklaus E. Zimmermann, Marc Hanewinkel, Jess Zimmerman, Yusuke Onoda, Hiroko Kurokawa, Masahiro Aiba and other.
**Other participants and Data contributors:** J. Caspersen, H. Zeng, S. Gourlet-Fleury, B. Herault, G. Ståhl, J. Thompson, S. Richardson, P. Ruiz, I-F. Sun, N. Swenson, M Uriarte, M. Zavala, N. E. Zimmermann, M. Hanewinkel, J. Zimmerman, Yusuke Onoda, Hiroko Kurokawa, Masahiro Aiba, MRN Québec and other
\newpage \newpage
...@@ -21,7 +22,7 @@ more likely to coexist locally than similar species ...@@ -21,7 +22,7 @@ more likely to coexist locally than similar species
@macarthur_limiting_1967). One way to quantify ecological similarity @macarthur_limiting_1967). One way to quantify ecological similarity
between species is via traits, such as leaf, seed and wood between species is via traits, such as leaf, seed and wood
characteristics [@westoby_plant_2002]. Traits influence many aspects characteristics [@westoby_plant_2002]. Traits influence many aspects
of plant performance, including resource acquisition. Under the *competition-niche similarity hypothesis* higher dissimilarity should results in higher resource partitioning at of plant performance, including resource acquisition. Under the *competition-niche similarity hypothesis* higher trait dissimilarity should results in higher resource partitioning at
local scale and less intense competition. This idea underlies numerous ecological analyses local scale and less intense competition. This idea underlies numerous ecological analyses
[@kraft_functional_2008; @cornwell_community_2009]. However this [@kraft_functional_2008; @cornwell_community_2009]. However this
assumption has rarely been tested against field or experimental assumption has rarely been tested against field or experimental
...@@ -105,7 +106,7 @@ proposed: a multiplicative and an additive ...@@ -105,7 +106,7 @@ proposed: a multiplicative and an additive
model of competitive effect and response[^inter]. model of competitive effect and response[^inter].
Below I consider the Below I consider the
additive effect-response model because it is simpler. However, I have not ruled out to exploring additive effect-response model because it is simpler. However, I have not ruled out exploring
the multiplicative effect-response model[^equmult]. the multiplicative effect-response model[^equmult].
[^compreponse]: Through out the document I will use competitive response as the inverse of competition tolerance. [^compreponse]: Through out the document I will use competitive response as the inverse of competition tolerance.
...@@ -209,8 +210,9 @@ validate the trait extraction (see Figure \ref{trait} for the range of traits va ...@@ -209,8 +210,9 @@ validate the trait extraction (see Figure \ref{trait} for the range of traits va
## Data processing ## Data processing
Next we split each dataset by ecoregion, keeping only Next we split each dataset by ecoregion, keeping only
ecoregions where in average at least three species contributed more than ecoregions where, on average, at least three species contributed more than
5% of the average basal area of the plots, thereby excluding quasi-monospecific stands. 5% of the total basal area of each plots. This had the effect of
excluding quasi-monospecific stands.
First we computed the local basal area ($cm^2/m^2$) of neighborhood First we computed the local basal area ($cm^2/m^2$) of neighborhood
competitor per species for each individual tree. For NFI data the competitor per species for each individual tree. For NFI data the
...@@ -226,8 +228,8 @@ missing value with genus level data when it was possible, or ...@@ -226,8 +228,8 @@ missing value with genus level data when it was possible, or
filling the remaining value with the community mean of the trait. All traits were filling the remaining value with the community mean of the trait. All traits were
centered and standardized per data set (a global traits standardization centered and standardized per data set (a global traits standardization
doesn't seems to provides strikingly different values). We run independent doesn't seems to provides strikingly different values). We run independent
computation of the $t_c$ to validate the processing of the data and inspected computation of the community weight means to validate the processing of the data and inspected
histograms of $t_c$ to identify errors. histograms of $\overline{t_n}$ to identify errors.
We used only individual tree for which 90% of its neighborhood was We used only individual tree for which 90% of its neighborhood was
covered with at least genus level traits in subsequent analysis. The covered with at least genus level traits in subsequent analysis. The
...@@ -240,13 +242,13 @@ taxonomic identification). ...@@ -240,13 +242,13 @@ taxonomic identification).
## Fitting of a mixed linear model ## Fitting of a mixed linear model
During the workshop we ran estimation using a hierarchical Bayesian model During the workshop we ran estimation using a hierarchical Bayesian model
using [JAGS](http://mcmc-jags.sourceforge.net/). In the subsequent analysis I decided to start with a linear mixed model approach (function lmer in using [JAGS](http://mcmc-jags.sourceforge.net/). In the subsequent analysis I decided (with the help of Ghislain to test this approach) to start with a linear mixed model approach (function lmer in
package [lme4](http://cran.r-project.org/web/packages/lme4/index.html) package [lme4](http://cran.r-project.org/web/packages/lme4/index.html)
in R cran). The reasons for the change are in R cran). The reasons for the change are
1. a log-linear function provides a good 1. a log-linear function provides a good
first approximation to the shape of first approximation to the shape of
the functions for the size and competition effect (mainly following the work of C. Canham for instance see more complex non-linear functions for the size and competition effect (mainly followingsuch as the one used in the work of C. Canham see
@uriarte_trait_2010), and @uriarte_trait_2010), and
2. using lmer was much faster than an estimation with JAGS or [Stan](http://mc-stan.org/). 2. using lmer was much faster than an estimation with JAGS or [Stan](http://mc-stan.org/).
...@@ -278,7 +280,7 @@ We compared two alternative models for $\lambda_{n,f}$: ...@@ -278,7 +280,7 @@ We compared two alternative models for $\lambda_{n,f}$:
\times t_{n}$) and \times t_{n}$) and
(ii) $\lambda$ is a (ii) $\lambda$ is a
function the absolute trait distance ($\lambda_{n,f} = a + b \times function the absolute trait distance ($\lambda_{n,f} = a + b \times
$). |t_{n} - t_{f}|$).
These two models can be expressed in terms of community weighted mean trait value as follows. For the trait effect-response model: These two models can be expressed in terms of community weighted mean trait value as follows. For the trait effect-response model:
\begin{equation} \label{logG-ER} \begin{equation} \label{logG-ER}
...@@ -331,6 +333,7 @@ Most of the effect-response models fitted show a competitive effect (negative va ...@@ -331,6 +333,7 @@ Most of the effect-response models fitted show a competitive effect (negative va
- Explore non-linear model for growth and survival using Stan (probably used the models used by Canham and Uriarte). - Explore non-linear model for growth and survival using Stan (probably used the models used by Canham and Uriarte).
- Fit multi-traits models (include multiple traits in effect and response models and either multidimensional distance in the absolute distance model or include all single trait absolute distance). Try to use spike and slab prior for variables selection. - Fit multi-traits models (include multiple traits in effect and response models and either multidimensional distance in the absolute distance model or include all single trait absolute distance). Try to use spike and slab prior for variables selection.
- Try to include traits effect in parameter $Gmax$. This would allows to (1) test if this change the results observed for the traits effect on $\lambda$ (a comment of Maria Uriarte) and (2) test if traits underpin a trade-off between max growth with out competition and competition tolerance. - Try to include traits effect in parameter $Gmax$. This would allows to (1) test if this change the results observed for the traits effect on $\lambda$ (a comment of Maria Uriarte) and (2) test if traits underpin a trade-off between max growth with out competition and competition tolerance.
- Explore if the decrease in the link between trait and competition at high MAP is related in a change in the packing of trait space in this communities.
- Explore the possibility that trait effect may be different for evergreen/deciduous species (leaf traits) or angiosperm/conifer species (wood density). This could be done by fitting different parameters for the trait of evergreen deciduous and conifer in the effect-response model. This is not really possible for the absolute distance model. - Explore the possibility that trait effect may be different for evergreen/deciduous species (leaf traits) or angiosperm/conifer species (wood density). This could be done by fitting different parameters for the trait of evergreen deciduous and conifer in the effect-response model. This is not really possible for the absolute distance model.
- Use an alternative way of dividing the NFI data than the ecoregion (class of MAP and MAT?). - Use an alternative way of dividing the NFI data than the ecoregion (class of MAP and MAT?).
- Try to run a global analysis with all data (memory limit issue to solve). - Try to run a global analysis with all data (memory limit issue to solve).
...@@ -341,7 +344,7 @@ Most of the effect-response models fitted show a competitive effect (negative va ...@@ -341,7 +344,7 @@ Most of the effect-response models fitted show a competitive effect (negative va
\newpage \newpage
# FIGURES # FIGURES & TABLES
![**Positions of the data sets analysed in the climatic biomes of Whittaker.** The coloured polygons represents the biomes. The points represent the mean position of the data set in the mean annual temperature and annual precipitation space. For the national forest inventory the 95% quantile of the climate within the ecoregion is represented by an error bar. The temperature and precipitation are taken from worldclim [@hijmans_very_2005].\label{biomes}](biome_ecocode_xy.pdf) ![**Positions of the data sets analysed in the climatic biomes of Whittaker.** The coloured polygons represents the biomes. The points represent the mean position of the data set in the mean annual temperature and annual precipitation space. For the national forest inventory the 95% quantile of the climate within the ecoregion is represented by an error bar. The temperature and precipitation are taken from worldclim [@hijmans_very_2005].\label{biomes}](biome_ecocode_xy.pdf)
...@@ -354,11 +357,13 @@ Most of the effect-response models fitted show a competitive effect (negative va ...@@ -354,11 +357,13 @@ Most of the effect-response models fitted show a competitive effect (negative va
\newpage \newpage
![**Correlation pairs over all data sets 9in log scale).** Each data set is drawn with a different symbols and colors. Traits SLA ($mm^2/mg$), Leaf N per mass ($mg/g$), wood density ![**Correlation pairs over all data sets (in log scale).** Each data set is drawn with a different symbols and colors. Traits SLA ($mm^2/mg$), Leaf N per mass ($mg/g$), wood density
($mg/mm^3$), maximum height ($m$). \label{trait}](traits-XY.pdf) ($mg/mm^3$), maximum height ($m$). \label{trait}](traits-XY.pdf)
\pagebreak \pagebreak
\pagebreak
\newpage \newpage
![**Effect size of the absolute distance models and the effect-response model over all ecoregion for the four traits.** Effect size is computed as the difference of $R_c^2$ between a constant competition model and the tested model. \label{boxplot-effectsize}](R2_boxplot_two.pdf) ![**Effect size of the absolute distance models and the effect-response model over all ecoregion for the four traits.** Effect size is computed as the difference of $R_c^2$ between a constant competition model and the tested model. \label{boxplot-effectsize}](R2_boxplot_two.pdf)
...@@ -378,7 +383,6 @@ Most of the effect-response models fitted show a competitive effect (negative va ...@@ -378,7 +383,6 @@ Most of the effect-response models fitted show a competitive effect (negative va
\pagebreak \pagebreak
# TABLES
------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------
Data name Demographic data Traits data Availability Abiotic variables Data name Demographic data Traits data Availability Abiotic variables
...@@ -660,7 +664,7 @@ Luquillo 0 0 0 0 1 0 ...@@ -660,7 +664,7 @@ Luquillo 0 0 0 0 1 0
\pagebreak \pagebreak
## Multiplicative model of competitive effect and response # Appendix 1. Multiplicative model of competitive effect and response {#multi}
The general framework for this approach is to consider that $\lambda_{n,f} = r(t_f) \times e(t_n)$ where $r$ and $e$ are respectively function that relate the competitive response and effect to the trait. We can test a series of model with increasing complexity of trait effect. The general framework for this approach is to consider that $\lambda_{n,f} = r(t_f) \times e(t_n)$ where $r$ and $e$ are respectively function that relate the competitive response and effect to the trait. We can test a series of model with increasing complexity of trait effect.
...@@ -682,14 +686,14 @@ The general framework for this approach is to consider that $\lambda_{n,f} = r(t ...@@ -682,14 +686,14 @@ The general framework for this approach is to consider that $\lambda_{n,f} = r(t
\end{equation} \end{equation}
As for the additive model it is then possible to develop the multiplicative model 3 to relate the competition in term of community weighted mean trait of the neighborhood species. As for the additive model it is then possible to develop the multiplicative model 3 to relate the competition in term of community weighted mean trait of the neighborhood species ($\overline{t_{n}}$).
\begin{equation} \begin{equation} \label{multi-er}
\sum_{n=1}^{N_p} \lambda_{n,f} \times B_n = B_\textrm{tot} \times (a +b \times t_{f}) \times (c+ d \times \bar{t_{n}}) \sum_{n=1}^{N_p} \lambda_{n,f} \times B_n = B_\textrm{tot} \times (a +b \times t_{f}) \times (c+ d \times \overline{t_{n}})
\end{equation} \end{equation}
## Appendix 1. Comparison of the multiplicative and additive effect and response model {#multi} ## Comparison of the multiplicative and additive effect and response model
Developing the multiplicative model gives Developing the multiplicative model gives
...@@ -697,19 +701,19 @@ Developing the multiplicative model gives ...@@ -697,19 +701,19 @@ Developing the multiplicative model gives
(a +b \times t_{f}) \times (c +d \times t_{n}) = ac+bc \times t_f +ad \times t_n +bd \times t_f \times t_n (a +b \times t_{f}) \times (c +d \times t_{n}) = ac+bc \times t_f +ad \times t_n +bd \times t_f \times t_n
\end{equation} \end{equation}
In comparison the additive model plus interaction i which is an extension of the model presented above which include an interaction between the traits $t_n$ and $t_f$ is: This equation bears some similarity to the additive model plus interaction Equation \label{add-inter} - which is an extension of the effect/response model presented above (equation \label{response_effect_trait}) - which include an interaction between the traits $t_n$ and $t_f$ is:
\begin{equation} \begin{equation} \label{add-inter}
\lambda_{n,f} = a +b \times t_{f} +c \times t_{n}+d \times t_{n} \times t_{f} \lambda_{n,f} = a' +b' \times t_{f} +c' \times t_{n}+d' \times t_{n} \times t_{f}
\end{equation} \end{equation}
Thus the two models are equal when: The two models are equal when:
\begin{equation} \begin{equation}
a_{add}=ac \mspace{3mu} ;\mspace{3mu} b_{add}=bc\mspace{3mu} ;\mspace{3mu} c_{add}=ad \mspace{5mu} and \mspace{5mu} d_{add}=bd a'=ac \mspace{3mu} ;\mspace{3mu} b'=bc\mspace{3mu} ;\mspace{3mu} c'=ad \mspace{5mu} and \mspace{5mu} d'=bd
\end{equation} \end{equation}
The multiplicative model is more constraining than the additive model plus interaction. In other word the additive model with interaction can be fitted to any multiplicative model but the inverse is not true (This would requires adding an interaction in the multiplicative model). For instance, it is not possible to match the hierarchical distance because if $b_{add}$ and $d_{add} \neq 0$ then $d_{add} \neq = 0$ as well. More generally, if parameters $a$, $b$ , $c$ and $d$ vary between [-max.r, max.r] then $d_{add}>b_{add}*c_{add}/(ma.r^2)$ (or $d_{add}<b_{add}*c_{add}/(-ma.r^2)$). Thus it is not possible to have a strong traits effect on response and effect and no interaction. The multiplicative model is more constraining than the additive model plus interaction. In other word the additive model with interaction can be fitted to any multiplicative model but the inverse is not true (This would requires adding an interaction in the multiplicative model). For instance, it is not possible to match the hierarchical distance because if $b'$ and $d' \neq 0$ then $d' \neq 0$ as well. More generally, if parameters $a$, $b$ , $c$ and $d$ vary between [-max.r, max.r] then $d'>b'*c'/(max.r^2)$ (or $d'<b'*c'/(-max.r^2)$). Thus it is not possible to have a strong traits effect on response and effect and no interaction. From first principle I think it is difficult to decide which model (equation \label{response_effect_trait} or equation \label{multi-er}) is the most likely.
\pagebreak \pagebreak
......
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