B Appendix 2: Leaf lifespan model

TROLL model previous implementation encompass Reich’s 1991 and 1997 and Wright’s 2004 allometries to estimate leaf lifespan with (Reich et al. 1991, 1997; Wright et al. 2004). But we have shown that Reich’s allometries are underestimating leaf lifespan for low LMA species. Moreover simulations estimated unrealistically low aboveground biomass for low LMA species. We assumed Reich’s allometries underestimation of leaf lifespan for low LMA species being the source of unrealistically low aboveground biomass inside TROLL simulations. We decided to find a better allometry with Wright et al. (2004) GLOPNET dataset.

B.1 Material and methods

We compiled functional traits from GLOPNET (Wright et al. 2004), TRY (Kattge et al. 2011), and DRYAD (Chave et al. 2009) databases (see B.1). We kept dataset given by GLOPNET as origin dataset for observations. Dataset defined as origin corresponded to leaf lifespan (\(LL\)) and most of the time to leaf mass per area (\(LMA\)) and leaf nitrogen content per leaf dry mass (\(Nmass\)). We measured variable importance in functionnal traits to explain leaf lifespan with an out-of the bag method applied on a random forest. Then, we used a bayesian apporach to test different models with growing level of complexity. We retained the model with the best tradeoff between model complexity (number of parameters \(K\)), convergence, likelihood, and prediction quality (root mean sqaure error of prediciton \(RMSEP\)). We finally tested the new allometry obtained with the selected model with TROLL simulations.

Table B.1: Functional traits gathered with TRY.
Name Trait Unit TRYcode
LL Leaf lifespan (longevity) month 12
SLA Leaf area per leaf dry mass (specific leaf area, SLA) \(m^2.kg^{-1}\) 11
N Leaf nitrogen (N) content per leaf dry mass \(mg.g^{-1}\) 15
P Leaf phosphorus (P) content per leaf dry mass \(mg.g^{-1}\) 14
wsg Stem dry mass per stem fresh volume (stem specific density) \(mg.mm^{-3}\) 4

B.2 Results

Out of the bag method applied on a random forest highlighted the importance of leaf nitrogen content per leaf dry mass (\(N_m\)) to model leaf lifespan (see B.2). \(N_m\) importance was higher than leaf mass per area (158 against 96 percent of mean square error increase) which was used as a proxy for leaf lifespan in previous models. Finally, wood specific gravity (\(wsg\)) add also a significant importance in leaf lifespan estimation.

Table B.2: Variable importance calculated with out-of the bag method applied on a random forest. First column represents the mean decrease in mean square error (%IncMSE) whereas second column represents the total decrease in node impurities, measured by the Gini Index (IncNodePurety). Leaf lifespan (LL) is taken in GLOPNET database from Wright et al. (2004). Leaf mass per area (LMA), and leaf nitrogen content (Nmass) are taken both in TRY (https://www.try-db.org) and GLOPNET databases. Wood specific gravity (wsg) is taken both in TRY and DRYAD databases.
%IncMSE IncNodePurity
LMA 97.18663 2156.576
Nm 157.93939 2561.144
wsg 48.71652 1456.525

The selected model had a maximum likelihood of 13.6 and a RMSEP of 12 months:

\[\begin{equation} LL_{d} \sim log\mathcal{N}({\beta_1}_d*LMA - {\beta_2}_d*N*\beta_3*wsg, \sigma) \tag{1.1} \end{equation}\]

Leaf lifespan \(LL\) follows a lognormal law with location infered from leaf lifespan \(LMA\), nitrogen content \(N\) and wood specific gravity \(wsg\) and a scale \(\sigma\). Each \({\beta_i}_d\) is following a normal law located on \(\beta_i\) with a scale of \(\sigma_i\). All \(\beta_i\), \(\sigma_i\), and \(\sigma\) are assumed without presemption following a gamma law. \(d\) represents the dataset random effects and encompass environmental and protocol variations.

Leaflifespan predictions for the selected model with leaf mass per area (LMA), leaf nitrogen content (Nmass), wood specific gravity (wsg) and predicted versus observed values. Leaf lifespan (LL) is predicted with model M10 fit. Leaf mass per area (LMA) and leaf nitrogen content (Nmass), and wood specific gravity (wsg) are taken in a composite dataset of GLOPNET, TRY and DRYAD datasets.Warning LMA (resp. Nmass and wsg) is not constant and depend on the closest point value for right (resp. center and left) graph.

Figure B.1: Leaflifespan predictions for the selected model with leaf mass per area (LMA), leaf nitrogen content (Nmass), wood specific gravity (wsg) and predicted versus observed values. Leaf lifespan (LL) is predicted with model M10 fit. Leaf mass per area (LMA) and leaf nitrogen content (Nmass), and wood specific gravity (wsg) are taken in a composite dataset of GLOPNET, TRY and DRYAD datasets.Warning LMA (resp. Nmass and wsg) is not constant and depend on the closest point value for right (resp. center and left) graph.

Simulations are validating that this new allometry resolve the issue of unrealistically low aboveground biomass for low LMA species due to an early death of individuals inside simulations. For instance with this allometry Symphonia sp 1 (a low LMA species) is now reaching a realistic aboveground biomass above 400 \(tonC.ha^{-1}\) and realistic diameter and age distribution inside the final population.

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