Supporting information S1
Sakschewski et al (2014): Leaf and stem economics spectra drive functional diversity in a
dynamic global vegetation model
1. Standard LPJmL model description
The standard version of LPJmL is a process-based dynamic global vegetation model
(DGVM) which simulates the land-atmosphere carbon and water exchange influenced by
the growth, production and phenology of 9 generic plant functional types (PFTs
representing natural vegetation at the level of biomes (Gerten et al., 2004; Schaphoff et al.,
2013; Sitch et al., 2003), 12 crop functional types (CFTs) and managed grass (Bondeau et
al., 2007) on a global 0.5°  0.5° spatial grid. For natural vegetation, each grid cell can
contain several PFTs competing for light and water.
Standard LPJmL (Sitch et al., 2003; Bondeau et al., 2007) simulates an average individual
per PFT which is scaled up to grid cell level and competes with average individuals of other
PFTs for the same resource pools within each grid cell. This approach performs well with
only a few PFTs present, but disables to simulate the competitive interactions between tree
individuals with unique properties on smaller spatial scales. We re-implemented LPJmL in
a gap model approach to account for the competitive effects between tree individuals with
unique key trait combinations forming a highly diverse community of possible tree growth
strategies.
2. Trade-offs implemented in LPJmL-FIT
The SLA-LL trade-off and its relation to Narea and tree phenology
Recent studies found global SLA, LL and Narea records of plants approximately log-normal
distributed and significantly correlated (Poorter & Evans, 1998; Reich et al., 1997; Reich et
al., 1999; Wright et al., 2004; Westoby et al., 2000) and identified them as part of the LES
(Wright et al., 2004). Therefore we applied log-log-regressions of LL and Narea over SLA
entries in the TRY database and implemented the corresponding regression functions in
LPJmL-FIT:
LL = 138.35 * SLA-1.128
(1)
with LL in month and SLA in mm² mg-1 (r² = 0.41; N = 517 measurements of 347 species;
P < 0.0001; Fig. S2).
Narea = 6.89 * SLA-0.571
(2)
with Narea in g m-2 and SLA in mm² mg-1 (r² = 0.40; N = 4404 measurements of 1363
species; P <0.0001; Fig. S3).
Standard LPJmL describes two phenology types in the tropics, “evergreen” and
“deciduous”. A fixed LL for evergreen and deciduous trees is accompanied by a PFTspecific minimum water stress scalar wscalmin. This is a constant between 0 and 1
representing the threshold under which the PFT sheds its leaves due to water stress. The
daily water stress is defined by the ratio of transpirational water supply from soil moisture
in the rooting zone and potential demand as a function of potential canopy conductance and
potential evapotranspiration (Sitch et al., 2003). Hence, standard LPJmL prescribes two
different phenologies (evergreen and deciduous) with two different wscalmin.
LPJmL-FIT simulates a large range of LLs as found in nature, and does not prescribe
wscalmin to enforce a specific phenology. Instead, LPJmL-FIT assigns each individual tree a
random wscalmin at establishment. This approach tests all conceivable wscalmin values and
supports individuals with the best adapted wscalmin in a specific simulated environment
(Data S1). Trees with different phenologies adapted to seasonal water stress are realized by
choosing wscalmin values for all plant types from the range between 0 and 1. As a modelspecific parameter, wscalmin cannot be directly calibrated by empirical measurements of LL.
Therefore, LPJmL-FIT assigns each individual tree a random wscalmin at establishment.
This approach tests all conceivable wscalmin values and supports individuals with the best
adapted wscalmin in a specific simulated environment.
The trade-off between SLA and the maximum carboxylation capacity of Rubisco
(Vcmax) mediated by Narea
For the required regression function, we used Vcmaxarea values measured at 25°C and Narea
values from the TRY database:
𝑉𝑐𝑚𝑎𝑥𝑎𝑟𝑒𝑎25° = 31.62 ∗ 𝑁𝑎𝑟𝑒𝑎 0.801
(3)
with VcN in µmol m-2 s-1 (r² = 0.37; N = 501 measurements of 45 species; P<0.0001, Fig.
S4). To apply this function at different simulation temperatures we extended it with a
temperature term derived from (Haxeltine & Prentice, 1996), resulting in a temperatureand Narea- dependent Vcmaxarea which we call VcN:
𝑉𝑐𝑁 = 31.62 ∗ 𝑁𝑎𝑟𝑒𝑎 0.801 ∗
1
𝑒 −0.0693(𝑇−25)
(4)
with T being the temperature in °C. The effect of this trade-off is that leaves with higher
SLA have a lower VcN at a certain temperature and vice versa, although their leaf massbased Vcmax may be higher.
When daily photosynthesis is calculated, LPJmL-FIT chooses the minimum of VcN and the
standardly calculated Vcmaxarea of LPJmL called VcLPJ:
𝑉𝑐𝑚𝑎𝑥𝑎𝑟𝑒𝑎 = min(𝑉𝑐𝑁 , 𝑉𝑐𝐿𝑃𝐽 )
(5)
This way, the effective Vcmaxarea can be limited by each individual’s leaf nitrogen content.
The Narea-Vcmaxarea trade-off only becomes relevant in LPJmL-FIT, if it is limiting
photosynthesis. If other factors such as light, temperature or water are limiting (i.e. VcLPJ
<VcN), either factor may constrain the realized Vcmaxarea.
Trade-off between wood density (WD) and mortality
We incorporate the WD-mortality trade-off using an equation derived by King et al. (2006)
which assigns a WD-dependent annual mortality rate mortWD to each individual:
𝐿𝑜𝑔(𝑚𝑜𝑟𝑡𝑊𝐷 ) = −2.66 +
0.255
𝑊𝐷
(6)
where WD is the wood density (g cm-³). The term mortWD is used as the maximum of the
growth efficiency related mortality of standard LPJmL (Sitch et al., 2003):
𝑚𝑜𝑟𝑡𝑔𝑟𝑒𝑓𝑓 = 1+𝑘
𝑚𝑜𝑟𝑡𝑊𝐷
𝑚𝑜𝑟𝑡2 ∗𝑔𝑟𝑒𝑓𝑓
(7)
where kmort2 = 0.5 is a slope parameter of the relationship between mortality and growth
efficiency and greff is the annual growth efficiency (net annual biomass increase per leaf
area). Whilst in standard LPJmL a low net annual biomass increase per established leaf area
(e.g. due to water stress) would increase mortality, a higher WD decreases this effect in
LPJmL-FIT.
An individual’s total mortality morttotal increases for each individual with tree age
(Smith et al., 2001) and decreases with biomass increment per leaf area and WD (mortgreff,
see Eq. 7-8) according to
𝑚𝑜𝑟𝑡𝑇𝑜𝑡𝑎𝑙 = min(𝑚𝑜𝑟𝑡𝑔𝑟𝑒𝑓𝑓 (𝑊𝐷, 𝑏𝑖𝑜𝑚𝑎𝑠𝑠_𝑖𝑛𝑐) + 𝑚𝑜𝑟𝑡𝑎𝑔𝑒 (𝑡𝑟𝑒𝑒_𝑎𝑔𝑒), 1)
(8)
The age-dependent mortality rate mortage is derived from Hickler et al. (2004) using a
power law with
𝑚𝑜𝑟𝑡𝑎𝑔𝑒 (𝑎𝑔𝑒) =
𝑘
𝑙𝑜𝑛𝑔𝑒𝑣𝑖𝑡𝑦
𝑎𝑔𝑒
2
∗ (𝑙𝑜𝑛𝑔𝑒𝑣𝑖𝑡𝑦)
(9)
with longevity being the maximum longevity of trees (1000 a) and k being a constant
setting the survival rate of individuals at maximum longevity to 0.1.
3. Details of linear regressions
Standard errors for regression coefficients are given in parentheses for the following
regression equations. All coefficients were highly significant (p < 0.0001). r2 values
describe the explanatory power of each model, sample n refers to the number of entries
included in each analysis. Units (prior to log10 transformation): LL (month); SLA (mm² mg1
); Narea (g m-2); Vcmax (µmol m-2 s-1). For the regression of SLA vs. LL, the upper and lower
50% non-simultaneous confidence bounds are used in the trait variability corridor approach
(Fig. S5).
Log (LL) = -1.128(0.02) * log (SLA) + 2.146(0.02); r² = 0.41; n = 517; see figure S2;
lower 50% confidence bound: Log (LL) = -1.128 * log (SLA) + 1.928; see figure S2;
upper 50% confidence bound: Log (LL) = -1.128 * log (SLA) + 2.365; see figure S2;
Log(Narea) = -0.571(0.01) * log (SLA) + 0.838 (0.01); r² = 0.40; n = 4404; see figure S3;
Log(Vcmaxarea25°) = 0.801(0.04) * log(Narea) + 1.506(0.03); r² =0.37; n = 501; see figure
S4;
SLA entries and corresponding LL entries from two locations (latitude = 5.16 and longitude
= 117.90; latitude= -6.75 and longitude= 106.53) in Malaysia (Shiodera et al., 2008) and
Indonesia (Swaine, 2007) reported very high leaf longevities connected to high SLAs for the
majority of recordings. This unique feature stands in contrast to the common observed link
of SLA and LL in all other locations of the data set and former studies (Reich et al., 1997;
Wright et al., 2004). For the two locations, environmental influences or plant specific
features may have led to these observations. For instance, Shiodera et al. (2008) focused on
understory tree saplings only. Tree saplings can show an enhanced LL per given SLA, as an
adaptation to the shaded understory, whilst in a mature state the common pattern is
observed (Rijkers, 2000). A robust regression using the S-estimation approach (Forward
Search for Data Analysis toolbox for MATLAB; Riani et al. 2012) revealed most of the
data points of the two data sets as outliers. To be consistent we removed all measurements
of both data sets for our regression (Fig. S2).
4. Light competition scheme of individual trees in LPJmL-FIT
The basic light competition scheme is adapted from Smith et al. (2001). Within a patch,
light competition occurs in distinct canopy layers each 100m² in size according to the patch
area. The locations of these layers are prescribed starting at the maximum tree height (50m)
followed by additional layers every 2m down to a height specific bole height, but not lower
than 2m. Tree bole height is a yearly calculated variable depending on tree height
(Thonicke et al., 2010). If a tree is smaller than 2m (e.g. true for saplings), a respective
fraction of its leaf mass is transferred to the first leaf layer where photosynthesis is possible
(Fig. 1). An additional bottom layer enables the C3- and C4-grass PFTs of standard LPJmL
to establish. Trees pass through the canopy layers during growth and distribute their leaf
mass equally to the amount of layers they have reached above their bole height. The total
amount of leaf area within each leaf layer determines the fraction of absorbed
photosynthetic active radiation (fAPARLayer) according to the Lambert-Beer’s law adapted
from Smith et al. (2001):
𝐿𝑎𝑦𝑒𝑟−1
𝑓𝐴𝑃𝐴𝑅𝐿𝑎𝑦𝑒𝑟 = exp(−𝑘𝐿 × ∑𝑖=1
𝐿𝐴𝐼𝑖 ) × (1 − exp(−𝑘𝐿 × 𝐿𝐴𝐼𝐿𝑎𝑦𝑒𝑟 ))
(10)
with LAIi as the leaf area index and kL as the extinction coefficient of layer i. Total leaf area
index is the cumulative product of N individuals’ leaf carbon leafCi and their respective
SLA divided by the patch area:
𝐿𝐴𝐼𝑖 =
∑𝑁
𝑖𝑛𝑑=1 𝑙𝑒𝑎𝑓_𝑎𝑟𝑒𝑎 𝑖𝑛𝑑,𝑖
𝑝𝑎𝑡𝑐ℎ_𝑎𝑟𝑒𝑎
=
∑𝑁
𝑖𝑛𝑑=1 𝑙𝑒𝑎𝑓𝐶𝑖𝑛𝑑,𝑖 × 𝑆𝐿𝐴𝑖𝑛𝑑
𝑝𝑎𝑡𝑐ℎ_𝑎𝑟𝑒𝑎
(11)
The fraction of light reaching the bottom layer is calculated as a function of the leaf area
index (LAI):
𝑁
𝐿𝑎𝑦𝑒𝑟
𝑓𝑃𝐴𝑅𝑏𝑜𝑡𝑡𝑜𝑚 = exp (−𝑘𝐿 × ∑𝐿𝑎𝑦𝑒𝑟=1
𝐿𝐴𝐼𝐿𝑎𝑦𝑒𝑟 )
(12)
The absorbed radiation in each layer is distributed to N individual trees weighted by their
leaf area with respect to the total leaf area in this layer:
𝑙𝑒𝑎𝑓𝐶𝑖𝑛𝑑,𝐿𝑎𝑦𝑒𝑟 × 𝑆𝐿𝐴𝑖𝑛𝑑
𝑓𝐴𝑃𝐴𝑅𝑖𝑛𝑑,𝑙𝑎𝑦𝑒𝑟 = 𝑓𝐴𝑃𝐴𝑅𝐿𝑎𝑦𝑒𝑟 × ∑𝑁
𝑖=1 𝑙𝑒𝑎𝑓𝐶𝑖,𝐿𝑎𝑦𝑒𝑟 ×𝑆𝐿𝐴𝑖
(13)
The amount of absorbed photosynthetic active radiation by an individual APARind:
𝑁
𝐿𝑎𝑦𝑒𝑟
𝐴𝑃𝐴𝑅𝑖𝑛𝑑 = 𝑃𝐴𝑅 × ∑𝐿𝑎𝑦𝑒𝑟=1
𝑓𝐴𝑃𝐴𝑅𝑖𝑛𝑑,𝐿𝑎𝑦𝑒𝑟
(14)
is used for the calculation of photosynthesis according to Sitch et al. (Sitch et al., 2003).
5. Distribution fitting
Log-normal probability density functions (PDFs) with parameters µ and σ were fitted plant
trait data and LPJmL-FIT output in the form:
𝑓(𝑥) =
1
𝑥𝜎√2𝜋
𝑒
−(ln(𝑥)−µ)²
2𝜎²
(15)
Distribution fitting was applied using the maximum likelihood method. The location
parameter µ and the scale parameter σ of the log-normal distribution are the mean and
standard deviation of the associated normal distribution and relate to the expectation value
E and the variance as follows:
𝐸=𝑒
(𝜇+
𝜎2
)
2
(16)
2
2
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝑒 (2𝜇+𝜎 ) (𝑒 𝜎 − 1)
(17)
Trait distributions of experiment C did not follow a log-normal distribution. Therefore we
fitted an exponential function of the form:
pdf(𝑆𝐿𝐴) = 𝑐1 ∗ 𝑒 𝑐2 (𝑆𝐿𝐴−𝑆𝐿𝐴𝑚𝑎𝑥 )
(18)
6. Calculation of probability density function overlap
To quantify how much the empirically-derived vs. modeled probability density functions
deviate from each other within the investigated SLA range, we calculate the percentage
overlap (ov) of the two functions:
1
𝑜𝑣 = (1 − 2 ∫| pdf𝑚 (𝑆𝐿𝐴) − pdf𝑜 (𝑆𝐿𝐴)| 𝑑𝑆𝐿𝐴) × 100
(19)
where pdfo and pdfm are the corresponding probability functions from TRY data and
LPJmL-FIT, respectively.
Table S1. Comparison of modeled vs. observed expected values E and scale parameter σ
based on probability density functions of SLA (mm² mg-1) trait distributions across the
Amazon region.
Exp. A
Location1
1See
Exp. B
σ
E
TRY data
σ
E
σ
E
1
12.39
0.31
8.06
0.22
12.42
0.30
2
11.2
0.22
8.31
0.14
10.70
0.27
3
10.35
0.23
8.44
0.16
11.84
0.34
4
10.37
0.28
9.93
0.23
10.55
0.23
5
9.46
0.26
9.08
0.20
10.95
0.32
6
9.83
0.25
10.84
0.18
8.02
0.36
7
11.91
0.27
10.67
0.17
12.91
0.22
8
12.29
0.27
9.08
0.21
12.83
0.32
9
11.28
0.27
9.51
0.20
12.93
0.28
10
10.17
0.23
8.46
0.16
10.28
0.29
11
8.85
0.30
7.83
0.24
8.93
0.42
12
12.23
0.29
10.74
0.22
16.03
0.38
Fig. S8 for coordinates of locations L1-L12.
Table S2. Percentage overlap (ov) between probability density functions of modeled vs.
observed SLA.
Exp. A vs.
TRY
Location1
Exp. B vs.
TRY
Exp. C vs.
TRY
1
98.6
78.8
5.8
2
86.7
62.3
2.7
3
78.6
48.7
6.1
4
89.3
74.4
1.5
5
80.7
56.0
4.1
6
66.4
65.6
1.7
7
83.1
51.1
3.7
8
92.1
71.4
7.1
9
80.5
53.5
5.7
10
88.0
62.8
2.6
11
83.3
72.1
3.3
12
71.6
53.1
17.4
mean
83.3
62.5
5.1
mean L1-L4
88.3
66.1
4.0
7. Supporting information figure captions
Fig. S1. Geographical origin of TRY data used to derive the tradeoffs of this study (eq. 1, 2,
3). Blue circles indicate data of the SLA-LL regression (eq. 1). Orange circles indicate the
data of the SLA-Narea regression (eq. 2). Cyan circles indicate data of the Narea-Vcmaxarea
regression (eq. 3).
Fig. S2. Regression of leaf longevity (LL) against specific leaf area (SLA). Solid line:
Regression line (r²=0.41; n=517). Dashed lines: 50% non-simultaneous confidence bounds.
Data from two geographic regions (see 3. Details of linear regressions in SI) were not
considered for the regression and are marked as red dots.
Fig. S3. Regression of leaf nitrogen per leaf area (Narea) against specific leaf area (SLA).
Solid line: Regression line (r²=0.40; n=4404).
Fig. S4. Regression of maximum carboxylation rate of RUBISCO enzyme per area
measured at 25°C (Vcmaxarea25°) against leaf nitrogen per leaf area (Narea). Solid line:
Regression line (r² =0.37; n=501).
Fig. S5. Trait variability corridor of a regression between two exemplary traits. If the value
of trait 2 is derived from a given value of trait 1 by strictly sticking to the regression line,
the result is a 1:1 assignment between the traits 1 and 2. In LPJmL-FIT the regression
function (red solid line) and 50% non-simultaneous confidence bounds (red dashed lines)
indicate the mean µ and double the variance σ of normal distributions spanning an unimodal
trait variability corridor. Each value of trait 1 can now yield a range of values for trait 2,
and within this range each value is assigned a certain probability. This approach keeps the
trend of the regression and conserves the natural variability of the underlying data set.
Fig. S6. Sampling of SLA input values. The distribution of globally observed SLA values
(broadleaved trees) from the TRY database (Kattge et al., 2011) was fitted with a lognormal probability density function (see 5. Distribution fitting). The range between the 1
and 99% percentiles of this probability density function was declared as the range of
possible SLA values to be tested in LPJmL-FIT. Within this range 100 uniformly spaced
SLA values determine the spectrum of 100 possible plant types regarding SLA. These trees
were set as saplings at establishment time within a given patch in LPJmL-FIT (cf. Fig. S7).
Fig. S7. LPJmL-FIT is implemented as a gap model with individual trees growing on
100m2 patches within a particular grid cell. Trees with unique trait combinations compete
for light and water. Several trees with different trait combinations may coexist within a
patch. Canopy colors: SLA range. Stem colors: wood density range. The size of the green
squares represents the biomass of the C3- and/or C4-grass PFTs within a patch (see video
visualization of model output under: http://www.pik-potsdam.de/~borissa/video).
Fig. S8. Test locations L1-L12 where sufficient TRY data were available for fitting
empirical SLA distributions with probability density functions. The sites are located along a
climatic gradient (e.g. precipitation in Fig. S9) of a wetter and less seasonal climate which
sustains tropical rainforests to a drier and more seasonal climate which sustains closed and
open dry deciduous forests. Coordinates of sites (longitude, latitude): L1 (-60.75, -14.75);
L2 (-60.25, -2.75); L3 (-76.25, -0.75); L4 (-69.25, -12.75); L5 (-77.75, -1.25); L6 (-67.26,
1.75); L7 (-51.25, -1.75); L8 (-61.25, -14.25); L9 (-68.25, -10.75); L10 (-72.75, -3.25); L11
(-44.75, -23.25); L12 (-79.75, 8.75).
Fig. S9. Precipitation patterns of input data used for all simulations in the Amazon region.
a) Annual mean of the precipitation data. b) Mean annual standard deviation of the
precipitation data.
Fig. S10. Histograms of SLA values from the TRY database at the 12 test locations L1-L12
(cf. Fig. S8).
Fig. S11. Histograms of SLA values simulated in experiment A in LPJmL-FIT at the 12
selected test locations L1-L12 (cf. Fig. S8).
Fig. S12. Probability density functions fitted to the SLA distributions from the TRY
database (red; cf. Fig. S10) and LPJmL-FIT (black; cf. Fig. S11) in simulated experiment A
at the 12 test locations L1-L12 (cf. Fig. S8).
Fig. S13. Comparison between the probability density functions for the SLA distributions
derived from simulated experiments A (black solid), B (dashed), and C (dashed-dotted),
and the TRY database (red).
Fig. S14. Modeled vs. observed mean vegetation carbon (vegC) across the Amazon region.
Modeled vegC was averaged over the last 600 years of the simulation. (a) vegC from
(Saatchi et al., 2011). (b) Difference map between vegC from experiment A and Saatchi
(2011). (c) vegC from experiment A. (d) Yes/No indicates whether modeled vegC in
experiment A falls within the 5-95% percentile of the uncertainty range of the Saatchi
(2011) map. (e) vegC from experiment B. (f) Same as (d), but for experiment B.
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