Changes in coefficient of determination, efficiency, optimum number of functional groups and Jaccard index in simulated datasets, versus relative error of ecosystem function and number of observed ecosystems.

<p>(A), (C) and (E) Simulated dataset mimicking the microbial experiment of Langenheder et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201135#pone.0201135.ref016" target="_blank">16</a>]. All ecosystems are observed and the mean relative error increases from 0.02 to 1.28. The statistics describe 100 datasets randomly generated. (B), (D) and (F) Simulated dataset mimicking the Biodiversity II experiment of Tilman et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201135#pone.0201135.ref017" target="_blank">17</a>]. The mean relative error is 0.17 and the number of observed ecosystems increases from 32 to 2048. The statistics describe 100 random sampling from a same random dataset. (A) and (B) Tree coefficient of determination (in black) and efficiency (in red). (C) and (D) Optimum number of functional groups indicated by tree <i>AICc</i>. (E) and (F) Jaccard index. In blue, by referring to the number of functional groups a priori defined (3 and 4 in microbial and Biodiversity II experiments, respectively). In red, by referring to 3 functional groups in Biodiversity II experiment, resulting from the clustering of the two largest species functional groups.</p

Species clustering, goodness-of-fit and predictive ability of the whole hierarchical trees of species clustering.

<p>(A), (C) and (E) Microbial experiment of Langenheder et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201135#pone.0201135.ref016" target="_blank">16</a>]. (B), (D) and (F) Biodiversity II experiment of Tilman et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201135#pone.0201135.ref017" target="_blank">17</a>]. (A) and (B) Modelling of ecosystem function based on the hierarchical tree of species clustering, from 1 to 4 functional groups of species in both experiments (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201135#pone.0201135.g002" target="_blank">Fig 2E and 2F</a>). Each bar corresponds to the error induced by leaving out the ecosystem to predict. Solid red line is the 1:1 line. (C) and (D) Hierarchical tree of species clustering. Dotted red line corresponds to the optimum number of functional groups indicated by <i>AICc</i>. Functional groups are noted by italic lowercase letters. (E) and (F) Boxplots of ecosystem functions by assembly motifs.</p

Changes in coefficient of determination, coefficient of efficiency, predicting ratio and Akaïke index versus the number of functional groups.

<p>(A), (C) and (E) Microbial experiment of Langenheder et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201135#pone.0201135.ref016" target="_blank">16</a>]. (B), (D) and (F) Biodiversity II experiment of Tilman et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201135#pone.0201135.ref017" target="_blank">17</a>]. (A) and (B) Coefficient of determination (black circle), coefficient of efficiency (red circle) and predicting ratio (blue square) of each clustering model. The arrow indicates the first local maximum of the coefficient of efficiency, located at σ_<i>max</i> functional groups. (C) and (D) Coefficient of determination (black circle), coefficient of efficiency (red circle) and predicting ratio (blue square) of whole tree of species clustering. (E) and (F) tree Akaïke index corrected for the second order bias (<i>AICc</i>). The arrow indicates the minimum value of Akaïke index, that corresponds to the optimum number σ" of functional groups.</p

Step-by-step process to a posteriori cluster the species in functional groups based on an ecosystem function.

<p>(A) Species are a priori clustered in functional groups (here σ = 3 as an example). (B) Each ecosystem is then described by a combination of functional groups of species, that is an assembly motif (here <i>m =</i> 2^σ-1 = 7 possible assembly motifs). (C) Ecosystems described by the same assembly motif are grouped in a given ecosystem clusters (<i>k</i> = 1 …7). (D) The goodness-of-fit of ecosystem classification is evaluated by its residual sum of squares (<i>RSS</i>_{<i>modelling</i>}), that can be expressed as a coefficient of determination <i>R</i>^<i>2</i>. The ecosystem classification is compared with others, rejected if worse but selected if better than others. (E) The process is iteratively repeated as long as a species clustering can generate an ecosystem classification better than all others. The process a posteriori selects the species clustering that best accounts for the observed ecosystem functioning.</p

Changes in coefficient of determination, efficiency, optimum number of functional groups and Jaccard index in simulated datasets, versus the number of functional groups of functional structure of ecosystems.

<p>The functional structures of ecosystems are those determined by combinatorial analysis of observed datasets (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201135#pone.0201135.g002" target="_blank">Fig 2A and 2B</a>), the number of functional groups increasing from the trunk to the leaves of trees. (A), (C) and (E) Simulated dataset mimicking the microbial experiment of Langenheder et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201135#pone.0201135.ref016" target="_blank">16</a>]. All ecosystems are observed and the mean relative error is 0.08. The statistics describe 100 datasets randomly generated. (B), (D) and (F) Simulated dataset mimicking the Biodiversity II experiment of Tilman et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201135#pone.0201135.ref017" target="_blank">17</a>]. The mean relative error is 0.17. The statistics describe 100 random sampling of 2048 ecosystems. (A) and (B) Tree coefficient of determination (in black) and efficiency (in red). (C) and (D) Optimum number of functional groups indicated by tree <i>AICc</i>. (E) and (F) Jaccard index.</p

R-code and datasets

The datasets were obtained by Tilman et al. (2001: Tilman, D., Knops, J., Wedin, D., Reich, P., Ritchie, M. & Siemann, E. Diversity and productivity in a long-term grassland experiment. Science, 294, 843-846) and Langenheder et al. (2010: Langenheder, S., Bulling, M. T., Solan, M. & Prosser, J. I. Bacterial Biodiversity-Ecosystem functioning Relations Are Modified by Environmental Complexity. PLoS ONE, 5, e10834. doi:10.1371/journal.pone.0010834). The R-files were written by Camille Richon and Benoît Jaillard

FEBuzzardCWVCalculation.R

R-script for calculating the community weighted variance (CWV) for each plot

FEBuzzardSpTraits

Species mean trait data for six traits: SLA (cm2 g-1 ), LDMC, LPC (mg g-1 ), d13C, d15N and CN within each plot across the chronosequence

FEBuzzardCWMCalculations.R

R-script for calculating the community weighted mean (CWM) trait values by plot

Dataset on 10 common alien plants in French grasslands

<div></div><div>Data to build a multi-species hierarchical model of the distribution of the ten most widespread alien plants in French grasslands, based on a subset of the DIVGRASS dataset of more than 50000 plant community plots. It allows testing how plant traits (height, specific leaf area (SLA) and seed mass) affect alien species occurrence along gradients of human pressure, environmental conditions and native community composition.</div><div><br></div><div><div>Dataset from the paper:</div>Carboni, M., Calderon-Sanou, I., Pollock, L., Violle, C., Thuiller, W. 2018. Functional traits modulate alien species response to environmental, biotic and human gradients. Global Ecology and Biogeography<br></div