Forest production efﬁciency increases with
A. Collalti 1,2, A. Ibrom 3✉, A. Stockmarr4, A. Cescatti5, R. Alkama 5, M. Fernández-Martínez 6,
G. Matteucci 7, S. Sitch 8, P. Friedlingstein 9, P. Ciais 10, D. S. Goll 11, J. E. M. S. Nabel 12,
J. Pongratz12,13, A. Arneth14, V. Haverd15 & I. C. Prentice16,17,18
Forest production efﬁciency (FPE) metric describes how efﬁciently the assimilated carbon is
partitioned into plants organs (biomass production, BP) or—more generally—for the pro-
duction of organic matter (net primary production, NPP). We present a global analysis of the
relationship of FPE to stand-age and climate, based on a large compilation of data on gross
primary production and either BP or NPP. FPE is important for both forest production and
atmospheric carbon dioxide uptake. We ﬁnd that FPE increases with absolute latitude, pre-
cipitation and (all else equal) with temperature. Earlier ﬁndings—FPE declining with age—are
also supported by this analysis. However, the temperature effect is opposite to what would be
expected based on the short-term physiological response of respiration rates to temperature,
implying a top-down regulation of carbon loss, perhaps reﬂecting the higher carbon costs of
nutrient acquisition in colder climates. Current ecosystem models do not reproduce this
phenomenon. They consistently predict lower FPE in warmer climates, and are therefore likely
to overestimate carbon losses in a warming climate.
1National Research Council of Italy, Institute for Agriculture and Forestry Systems in the Mediterranean (ISAFOM), 06128 Perugia (PG), Italy. 2University of
Tuscia, Department of Innovation in Biological, Agro-food and Forest Systems (DIBAF), 01100 Viterbo, Italy. 3Technical University of Denmark (DTU),
Department of Environmental Engineering, Lyngby, Denmark. 4Technical University of Denmark (DTU), Department of Applied Mathematics and Computer
Science, Lyngby, Denmark. 5European Commission, Joint Research Centre, Directorate for Sustainable Resources, Ispra, Italy. 6Research group PLECO
(Plants and Ecosystems), Department of Biology, University of Antwerp, 2610 Wilrijk, Belgium. 7National Research Council of Italy, Institute for BioEconomy
(IBE), 50019 Sesto Fiorentino, FI, Italy. 8College of Life and Environmental Sciences, University of Exeter, Exeter EX4 4RJ, UK. 9College of Engineering,
Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK. 10 Laboratoire des Sciences du Climat et del’Environnement, CEA CNRS
UVSQ, Gif-sur-Yvette 91191, France. 11 Department of Geography, University of Augsburg, Augsburg, Germany. 12 Max Planck Institute for Meteorology,
Hamburg, Germany. 13 Ludwig-Maximilians-Universität München, Luisenstr 37, 80333 Munich, Germany. 14 Karlsruhe Institute of Technology, Institute of
Meteorology and Climate Research/Atmospheric Environmental Research, 82467 Garmisch-Partenkirchen, Germany. 15 CSIRO Oceans and Atmosphere,
Canberra, ACT 2601, Australia. 16 Department of Life Sciences, Imperial College London, Silwood Park Campus, London Ascot SL5 7PY, UK. 17 Department of
Biological Sciences, Macquarie University, North Ryde, NSW 2109, Australia. 18 Department of Earth System Science, Tsinghua University, 100084
Beijing, China. ✉email: email@example.com
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Autotrophic respiration releases to the atmosphere about
half (∼60 PgC yr−1) of the carbon ﬁxed annually by
photosynthesis1. Forest ecosystems are the largest carbon
sink on land, taking up about 3.5 ± 1.0 PgC yr−1(2008–2017) on
average2. A small change in the proportion of carbon losses, for
example due to climate change, would strongly affect the net
carbon balance of the biosphere. Predicting the autotrophic
component of the carbon balance of forests under changing cli-
mate requires understanding of how much atmospheric CO
assimilated through photosynthesis (gross primary production,
GPP), how much is released due to plant metabolism (auto-
trophic respiration, R
), how efﬁciently plants use assimilated
carbon for the production of organic matter (net primary pro-
duction, NPP), and how organic carbon is partitioned into plant
organs (biomass production, BP) versus other less stable forms—
which include soluble organic compounds exuded to the rhizo-
sphere or stored as reserves, and biogenic volatile organic com-
pounds (BVOCs) emitted to the atmosphere3.
The climate sensitivity of the terrestrial carbon cycle can be
benchmarked using ratios between these ﬂuxes across a range of
climates. We focus here on the ratio of NPP to GPP, the so called
carbon use efﬁciency (CUE =NPP/GPP) and of BP to GPP,
called biomass production efﬁciency (BPE =BP/GPP). The two
concepts are close, but not identical4,5. BPE is substantially easier
to obtain, because the additional ﬂuxes that constitute NPP are
notoriously difﬁcult to measure. For this reason, there are far
more data available on BPE, while uncertainties associated with
both BP and NPP measurement make it impossible to distinguish
them in large data compilations. Therefore, we assessed estimates
of both BPE and CUE as a single metric, hereafter called forest
production efﬁciency (FPE), but making distinctions between
them when needed and when possible.
Over 20 years ago, the debate about spatial gradients of forest
CUE seemed to be resolved by Waring et al.6, who found CUE to
be nearly constant (0.47 ± 0.04: here and elsewhere, ± denotes one
standard deviation) across temperate and boreal forest stands
(n=12). The assumption of a universal value for CUE—implying
a tight coupling of whole-plant respiration to photosynthesis—
has obvious practical convenience, and numerous vegetation
models have adopted it5. Many complex process-based vegetation
models, however, assume decoupling of photosynthesis and
respiration, with the latter driven by temperature7and biomass8
—implying that CUE must vary with changing environmental
conditions. There is no general, observationally based consensus
as to which of these two (mutually incompatible) model
assumptions is nearer to the truth. One study found that BPE is
greater at higher soil fertility4, perhaps because less carbon needs
to be allocated for nutrient acquisition. Forest management9,
stand age10 and climate11,12 have also been reported to inﬂuence
CUE and BPE.
Here we revisit the global patterns of forest CUE and BPE
considering multiple controls and the potential effects of meth-
odological uncertainty, based on a large global set of data on
forest CUE and/or BPE (n=244), spanning environments ran-
ging from the tropical lowlands to high latitudes and high alti-
tudes (Supplementary Fig. 1).
Overall, we ﬁnd that FPE decreases with age and increases with
site factors such as annual air temperature, total annual pre-
cipitation and absolute latitude.
FPE is not a universal constant. Results show that both CUE
(0.47 ± 0.13; range 0.24–0.71; n=47) and BPE (0.46 ± 0.12; range
0.22–0.79; n=197) have large variability; therefore, neither can be
assumed to be uniform (Fig. 1and Supplementary Fig. 2). CUE
and BPE are statistically indistinguishable in our dataset because
of uncertainties associated with both quantities (±0.39 for CUE
and ±0.16 for BPE: see Methods). Overall, the average FPE in our
dataset (0.46 ± 0.12; range 0.22–0.79; n=244) is statistically
indistinguishable from that provided by Waring et al.6, but its
standard deviation is three times larger (Methods and ref. 5).
Different GPP estimation methods produced slightly different
distributions (Fig. 2a), with median values ranging from 0.42
(scaling; upscaling of chamber-based measurements) through 0.48
(micrometeorological; ecosystem-scale CO
ﬂux measurements) to
0.48 (model; process-based models) (see Methods for deﬁnitions).
Stand age had a further effect on FPE, as shown by the differing
median CUE and BPE values of stands in intermediate (in the
forestry sense, i.e. 20–60 years) and younger age classes, with FPE
varying from 0.52 (age class <20 years) to 0.42 (age class >60
years) (Fig. 2b). Figure 3shows how the data compare to those
published by Waring et al.6. The small variability of CUE reported
by Waring et al.6was already noted by Medlyn & Dewar13 as
untypical, and artiﬁcially constrained by the method used to cal-
culate CUE. Medlyn & Dewar13 suggested a 0.31–0.59 range as
being realistic. Figure 3also indicates systematically lower CUE
than Waring et al.6for forests with GPP < ∼2000 gC m−2yr−1,
especially in forests in the old age class; and a tendency to higher
values for forests with GPP> ∼2000 gC m−2yr−1and in the
young age class.
Factors controlling FPE variability. We used mixed-effects
multiple linear regression to infer the multiple drivers of the
spatial pattern of FPE. This method separates the contribution of
every predictor variable included in the analysis, even if they are
correlated to some degree (Methods). Four predictors—out of an
initial selection of eleven (listed in Methods)—proved to be
important: stand age (age, years), mean annual temperature
(MAT, °C), total annual precipitation (TAP, mm year−1) and
absolute latitude (|lat|, °), all included as ﬁxed effects (Fig. 4). The
method used to measure GPP (GPP method)—was included as a
random effect (Table 1, Eq. (1)).
The use of multiple regression was essential for this analysis.
Simple correlations between FPE and individual predictors
showed no signiﬁcant effects, while there were signiﬁcant
correlations among the predictors (Supplementary Table 1).
CUE, n = 47
BPE, n = 197
Forest production efficiency
Fig. 1 Carbon use efﬁciency vs. biomass production efﬁciency. Density
plot of carbon use efﬁciency (CUE, red line, n=47) and biomass
production efﬁciency (BPE, blue line, n=197) data from all available data.
The vertical lines are medians.
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The ﬁnal model with four ﬁxed effects is:
FPE ¼β0þβ1MAT þβ2age þβ3TAP þβ4lat
is the intercept, β
are the estimated sensitivities of
FPE to MAT, stand age, TAP and |lat|; ηZ
is a random
intercept for two distinguishable ‘GPPmethod’classes and εis the
residual (Table 1). The model could not be further reduced at a
5% test level, i.e. omitting any one of these predictors yielded a
signiﬁcantly different model. Supplementary Table 2 lists the
combinations that were tried.
We examined random effects from three methods to estimate
GPP (Methods). The methods biometric and scaling constituted a
single class, while GPP values determined from micrometeor-
ological measurements were systematically higher (thus FPE was
systematically lower). The multiple regression model explained
30% of the variance in the observed FPE values. Given the large
uncertainty in the estimation of NPP and GPP values, and the
structural and physiological diversity of the forests, this value was
We could not ﬁt an independent statistical model for CUE,
because there were too few sites with NPP (n=31) measure-
ments. Furthermore, adding a random intercept for the two
categories (CUE or BPE) to Eq. (1) yielded almost identical
values, of 0.47 for CUE and 0.46 for BPE.
We also applied the mixed-effects multiple regression model to
the TRENDY v.7 outputs of eight Dynamic Global Vegetation
Models (DGVMs) to examine whether the multivariate relation-
ships shown for the FPE data could also be seen in the model
simulations, in order to test whether the observed pattern would
also emerge from the processes representations in the models. We
originally aimed to use the same mixed-effects linear model, at
the locations of the data points to ﬁt the simulated FPE. However,
because these DGVMs do not consider forest age, we had to alter
the model equation to:
FPE ¼μ0þμ1MAT þμ2TAP þμ3latjjþηZModel þεð2Þ
Neither this model, nor any model that could be derived from
it, fulﬁlled the conditions of normally distributed residuals. In
other words, the simulations did not represent a common
emergent relationship consistent with the data. The most likely
explanation is that the models use different parameters (and even
sometimes different functional relationships) for different biomes,
so that no general relationship applying across all forest types can
be expected to emerge. This phenomenon is evident from Fig. 5
where many models show discontinuities in CUE.
CUE outputs from the TRENDY v.7 model ensemble,
produced by the eight DGVMs, consistently showed a negative
relationship with MAT—opposite to that shown by our analysis.
The slope (∂CUE/∂MAT) estimated from data was +0.006 °C−1
(see Table 1); the slopes from models ranged from –0.0025 °C−1
for LPJ-GUESS to –0.0098 °C−1for SDGVM (Fig. 5). The average
slope across the eight models was –0.005 °C−1. All models
showed high CUE for boreal forests and low CUE for tropical
forests, but with considerable variation among models (Supple-
mentary Fig. 4). The modelled CUE values agree well with the
data only in temperate regions (MAT 5–15 °C, n=156), but
differ greatly in boreal (MAT < 5 °C, n=35) and tropical (MAT
> 15 °C, n=40) regions.
Micromet <20 yr
0.6 0.8 0.2 0.4
Fig. 2 Effects of GPP method and age on FPE variability. a Forest production efﬁciency (FPE) density plots for three subsets of data where the GPP was
estimated with three different methods (micrometeorological, red line, n=98; scaling, blue line, n=73; and models, green line, n=53). The vertical lines
are medians. bDensity plots for different age classes (age < 20 years, light brown line, n=47; 20–60 years, green line, n=49; and age > 60 years, blue
2000 <20 yr
NPP or BP in g C m–2 yr–1
GPP in g C m–2 yr–1
1000 2000 3000 4000 5000
n = 228
Fig. 3 Comparison of the present work dataset vs. Waring et al.6.Scatter
plot of net primary production (NPP, gC m−2yr−1) or biomass production
(BP, gC m−2yr−1) versus gross primary production (GPP, gC m−2yr−1)
(n=228). Open circles: BP, ﬁlled circles: NPP. Stars represent data points
from Waring et al.6. The line marked with W98 represents a CUE (i.e. NPP/
GPP) of 0.47. Age classes are marked by colours (see top left of the ﬁgure);
NA stands for ‘age not available’. The uncertainty (gC m−2yr−1) of the data
points is indicated by bars (for data uncertainty see Methods).
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The empirical ranges of CUE and BPE and age effects on FPE.
Under some extreme circumstances, the carbon ﬂux to mycor-
rhizae and root exudates can constitute as much as 50% of daily
assimilation14 or as much as 30% of annual NPP15,16. While in
nonstressed conditions BVOCs consume a small fraction (∼5% or
less) of annual NPP, under stressed conditions and in hot cli-
mates, BVOC emissions can consume 15–50% of annual
NPP17,18. Thus CUE–if not equal to BPE –, should always be
larger than BPE. In our dataset, in those cases where both could
be estimated, CUE was larger than the estimated BPE in seven out
of thirteen cases (Supplementary Information, Supplementary
Table 3). In the remaining cases, the estimated CUE was statis-
tically indistinguishable from BPE. This ﬁnding suggests that the
fraction of these unaccounted organic carbon ﬂows varies sub-
stantially among forests.
Statistically ﬁtted values of BPE and CUE ranged between 0.27
(−0.04) and 0.58 (+0.04). The numbers in parentheses for CUE
and BPE reﬂect our estimates of methodological bias (random
intercepts, see Table 1). Ninety-two percent of BPE and CUE
0 0 10 20 30
|lat| in °
40 50 60500 1000 1500
TAP in mm per year
2000 2500 3000 3500
–5 0 100 200 300 400 500
MAT in °C Age in years
Fig. 4 Predicted FPE vs. single effects of environmental and structural variables. Predictions of the mixed linear model for single ﬁxed effects (Eq. (1)),
given the other independent variables constant at their average values for that GPP method category. The dashed lines represent conﬁdence intervals at
the 0.05 and 0.95 levels calculated with the function ‘predict Interval’of the R-package ‘merTools’.
Table 1 Parameters of the mixed-effects multiple regression model (Eq. (1)).
Estimate Std Error df t value pvalue Signiﬁcance
) Slopes: 0.19 0.106 24 1.77 0.09 n.s.
) 0.0060 0.0025 136 2.45 0.016 *
)−0.00038 0.000116 136 −3.28 0.0013 **
) 6.8E–5 2.07E–05 136 3.28 0.0014 **
) 0.0039 0.0016 136 2.45 0.016 *
Parameter estimate of coefﬁcients in Eq. (1) and their standard errors (Std. Error), degrees of freedoms (df), t- and pvalues of the two-sided t-test and the ANOVA (*p< 0.05, **p< 0.01, ***p< 0.001).
The squared Pearson’s correlation coefﬁcient and the squared Spearman’s correlation values are both equal to 0.31.
MAT mean annual temperature, age stand age, TAP total annual precipitation, |lat| absolute latitude.
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values in the dataset lie within the allowable range according to
Amthor19,reﬂecting maximum growth with minimum expendi-
ture (0.65) and minimum growth with maximum maintenance
costs (0.2). The remaining 8% of the data exceed the upper bound
given in ref. 19. However, no values below 0.2 were found, and it
seems likely such values cannot be physiologically sustained by
plants for long periods8. They might be encountered in moribund
stands, unlikely to be sampled (perhaps an example of survivor-
ship bias, or the desk drawer problem’20). However, values >0.65
apparently can (temporarily) occur in young, actively growing
Age- or size-related declines in both GPP, NPP and FPE (as
CUE or BPE) have been reported in earlier studies9,11,21,22 but a
decline in FPE is shown unequivocally here (slope ∂FPE/∂age =
−0.0004 yr−1), based on a larger dataset than previously
analysed23–25 (Fig. 4and Table 1). This decline could have
several contributory causes. First, the longer transport pathway
for water in taller trees can result in more closed stomata (to
avoid xylem cavitation) and therefore reduced GPP26, with no
corresponding reduction in R
, at least in the short-term27.
Second, larger trees may respire more because of their greater
sapwood volume and mass per unit leaf area8,28,29, leading to
(for the maintenance of living sapwood tissues) and
reduced NPP relative to GPP. Third, soil fertility declines due to
nutrient immobilization as stands age30; this is consistent with
observations of an increased ratio of ﬁne-root-to-leaf-carbon, and
reduced nitrogen concentration in soils10,31. Ontogenetic shifts
from structural biomass to reserve allocation, and structural and
resource limitations in older stands, are also all expected to
decrease production efﬁciency32. Conversely, reducing plant
competition and rejuvenating stands through forest management
should tend to increase both CUE and BPE9,33. At the stand scale,
closing canopies may contribute further to reducing or stabilizing
the GPP34 of individual trees. It is also likely that young trees
allocate more carbon to biomass growth as they compete for light
and nutrients; while older trees invest more in maintenance of
their existing biomass, and prioritize the chemical defence of that
biomass, relative to acquisition of new biomass35,36.
An additional hypothesis37 invokes an increase in nonstruc-
tural carbohydrates (NSC) allocation as trees grow. NSC is a
substantial carbon pool, containing in some cases up to four times
the carbon content of leaves in the canopy and increasing as trees
increase in size38. An increased ﬂux to NSC however would imply
a reduced BPE, but not a reduced CUE.
Environmental effects on FPE. The increase in FPE with
increasing annual precipitation, to our knowledge, has not been
noted previously. Higher TAP results in increasing soil water
availability and greater stomatal openness, which might imply
increased photosynthesis. There is no direct evidence that water
availability inﬂuences autotrophic respiration; on the other
hand, respiration has been found to increase with drought39.
0.9 Slope=–0.0037 ± 0.0 Pvalue=0.0
JSBACH SDGVM Site level
Slope=–0.0063 ± 0.0001 Pvalue=0.0 Slope=–0.0025 ± 0.0 Pvalue=0.0
Slope=–0.005 ± 0.0001 Pvalue=0.0
Slope=–0.005 ± 0.0004 Pvalue=0.0
Slope=–0.005 ± 0.0001 Pvalue=0.0
Slope=–0.0098 ± 0.0 Pvalue=0.0
Slope=–0.004 ± 0.0 Pvalue=0.0
Slope=–0.0044 ± 0.0001 Pvalue=0.0
10 20 30 –10 0 10 20 30 –10 0 10 20 30
0.05 0.10 0.15
0.20 0.25 0.30
MAT (°C) MAT (°C)
Fig. 5 Modelled TRENDY v.7 CUE and growth temperature patterns. Density plots (i.e. frequency of forest carbon use efﬁciency (CUE) value divided by
the total number of grid cells of simulated CUE derived from the following TRENDY v.7 process-based models: ISAM, JULES, LPJ-GUESS, CABLE-POP,
ORCHIDEE, ORCHIDEE-CNP, JSBACH and SDGVM, averaged from 1995 to 2015 as function of MAT (°C). In the last (right bottom) density plot, data
points extracted from coordinates and times of observed sites and used to plot the simulated CUE as function of MAT from the eight TRENDY v.7 models.
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With increasing TAP, photosynthesis might be expected to
increase faster than plant respiration, leading to higher CUE
The increase of FPE with absolute latitude has also, to our
knowledge, not been described before. Higher latitudes experi-
ence longer days in summer. The diffuse fraction also increases
with the path-length of radiation through the atmosphere. Both
effects might be expected to increase the radiation use efﬁciency
of GPP. While high irradiances in the tropics leads to saturation
of photosynthesis in the uppermost leaf layers40, they also allow
for higher leaf area to utilize the transmitted radiation in the
relatively short daylight hours. Higher leaf area also implies
and lower FPE. The latitude effect compensates for the
MAT effect, because these two variables are negatively correlated.
Despite the correlation, the linear mixed model is able to
distinguish between the individual effects of MAT and |lat|. This
can be demonstrated by comparison of high-latitude with high-
elevation sites at the same MAT. The effects of radiation are
incorporated in vegetation models which, therefore, could in
principle represent radiation regime effects on FPE.
Moreover, as far as we know, the observed increase in FPE with
mean annual temperature has not previously reported. This
increase is opposite to what would be expected based on the
instantaneous responses of photosynthesis and plant maintenance
respiration as described in textbooks41 and assumed in many
process-based models (Fig. 5). The instantaneous response of
maintenance respiration to a temperature change is steeper than
that of photosynthesis42. Moreover, under natural conditions
photosynthesis is commonly limited by light, while respiration is
not. However, the instantaneous response of autotrophic
respiration rate is largely irrelevant here because of the longer
time scale. A long line of investigations, starting with Gifford43,
has shown the ubiquity of respiratory thermal acclimation,
whereby the effect of increased growth temperature on enzyme
kinetics is offset by a lowering of the base rate44. This acclimation
takes place on a time scale of days to weeks1. Genetic adaptation
throughout multiple generations is expected to proceed in the
same direction (for deﬁnitions and distinctions between acclima-
tion and adaptation see ref. 45). One consequence of these
processes is that observed rates of maintenance respiration vary
with temperature (in both space and time) far less steeply than
would be expected based on the instantaneous response of
enzyme kinetics46. This has been shown comprehensively in
leaves, and is likely to apply to all plant tissues1. Moreover, the
ratio of respiration to carboxylation capacity, assessed at growth
temperature, is slightly but signiﬁcantly larger in colder
He et al.47 found—in contrast to our results—a latitudinal
pattern with higher CUE at high latitudes declining nonlinearly
with increasing MAT and stabilizing at increasing TAP. These
results were obtained using an ‘emergent constraint’method to
narrow the range of global mean carbon use efﬁciency values
produced by an ensemble of ecosystem models. The observed
correlation between simulated global and site-speciﬁc CUE was
used to translate the probability distribution of observed site CUE
into a distribution of global CUE. This method’s validity,
however, depends on the models correctly representing the
relationship between site-speciﬁc and global CUE. Thus, the
ﬁndings of ref. 47 could simply reﬂect the standard assumption of
models that R
increases with temperature more steeply than
GPP42. We have shown the same patterns here in all of the
TRENDY v.7 ensemble simulations (Fig. 5) but our analysis
shows that the underlying assumption is incorrect.
Adaptive mechanisms, potentially contributing to respiratory
thermal acclimation, include changes in the physiology and
growth of active tissues (i.e. the relation between assimilating and
non-assimilating tissues) and changes in the amount of enzymes
and their activation states to match substrate availability42,48.
Heat tolerance in leaves has also been found to increase linearly
with temperature and to decrease with absolute latitude49.
Therefore, a simple explanation for the increase of FPE with
temperature might be that plants can achieve the same function at
a higher temperature with smaller amounts of enzymes, thereby
decreasing the respiratory losses incurred during the maintenance
of catalytic capacity. Especially low FPE in boreal forests could be
the consequence of greater allocation of assimilates to nutrient
acquisition (via root exudation and exports to mycorrhizae) in
cold soils where microbial activity is much lower than in tropical
forests31,50. Low FPE in cold climates may also reﬂect the need to
repair tissues affected by frost damage51.
Whole-plant constraints and consequences for modelling.
Amthor19 derived an upper bound of 0.65 for CUE, based on a
rough quantiﬁcation of the minimum respiratory costs for plants
to function. His lower bound of 0.2 was based on the need for a
sufﬁciently positive carbon balance to have minimum photo-
synthesis to survive and to allow trees to compensate for tissue
turnover, reproduction and mortality. However, most CUE values
lie within narrower bounds, suggesting the existence of additional
regulatory mechanisms at the whole-plant scale. Gifford43 noted
that autotrophic respiration and primary production are inter-
dependent, because carbon must be assimilated before it is
respired, while respiration is required for the growth and main-
tenance of tissues. He opined that: ‘Plant respiratory regulation is
too complex for a mechanistic representation in current terres-
trial productivity models for carbon accounting and global
change research’and indicated a preference for simpler approa-
ches that capture the essence of the process. The opposite view
was expressed by Thornley52, who argued that: ‘attempting to
grasp and pin down complexity is often the ﬁrst step to ﬁnding a
way through a labyrinth’. Without taking a position on this
controversy, we note that the standard approach in most of
today’s land ecosystem models, or more generally in vegetation
models—where maintenance respiration per unit of respiring
tissue is typically determined as a ﬁxed basal rate at a standard
temperature (commonly 15 or 20 C°), increasing with the sub-
strate and temperature according to a ﬁxed Q
Arrhenius-type equation—cannot generate the positive response
of CUE or BPE to growth temperature observed in our study.
Moreover, as shown in Fig. 5, the presence of discontinuities in
CUE probably represents an attempt to sidestep an inevitable
consequence of this incorrect approach. Unless plant functional
types from warmer environments are assigned lower basal
maintenance respiration rates, modelled CUE becomes implau-
sibly low in warm climates. However, the idea of assigning ﬁxed
basal maintenance respiration rates to plant types has no obser-
vational or experimental basis.
In contrast, the use of production efﬁciency concepts in
models seems well motivated53, provided they are not assumed
to be constant across different stands and environments.
Production efﬁciency is a valuable unifying concept for the
analysis of forest carbon budgets. Although more variable than
was once thought, FPE appears to be a relatively conservative
quantity, subject to inherent biological constraints, that has
demonstrable relationships to stand development, latitude and
climate. The possible explanations for the observed global multi-
factorial pattern in FPE give rise to hypotheses on how
vegetation models might incorporate whole-plant regulation
mechanisms of the carbon losses for a given stand. The
demonstrated empirical pattern should then be used to constrain
new model developments.
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Deﬁnitions of terms. GPP is deﬁned here as ‘the sum of gross carbon ﬁxation
(carboxylation minus photorespiration) by autotrophic carbon-ﬁxing tissues per
unit area and time54. GPP is expressed as mass of organic carbon produced per unit
area and time, over at least one year. NPP consists of all organic carbon that is
ﬁxed, but not respired over a given time period54:
NPP ¼GPP Ra¼ΔBþLþFþHþO¼BP þOð3Þ
with all terms expressed in unit of mass of carbon per unit area and time. R
autotrophic respiration (composed of growth and maintenance respiration com-
ponents); ΔBis the annual change in standing biomass carbon; litter production
(roots, leaves and woody debris) is L; fruit production is F; the loss to herbivores is
H, which was not accounted here because of the very limited number of obser-
vations available. BP is biomass production4. Symbol Orepresents occult, carbon
ﬂows, i.e. all other allocations of assimilated carbon, including changes in the
nonstructural carbohydrate pool, root exudates, carbon subsidies to symbiotic
fungi (mycorrhizae) or bacteria (e.g. nitrogen ﬁxers), and BVOCs emissions
(Supplementary Fig. 1). These ‘occult’components are often ignored or unac-
counted when estimating NPP, hence this bias is necessarily propagated into the R
estimate when R
is calculated as the difference between GPP and NPP55.
Estimation methods. We grouped the ‘methods’into four categories:
●biometric: direct tree stock measurements, or proxy data together with
biomass expansion factors, allometric equations and the stock change as a BP
component. If not otherwise stated, we assumed that the values included both
above- and below-ground plant parts (n=13 for GPP; n=200 for NPP
●micrometeorological: micrometeorological ﬂux measurements using the eddy-
covariance technique to measure CO
ﬂux and partitioning methods to
estimate ecosystem respiration and GPP (n=98 for GPP; n=4 for NPP
●model: model applications ranging from single mathematical equations (for
canopy photosynthesis and whole-tree respiration) to more complex
mechanistic process-based models to estimate GPP and R
, with NPP as the
net difference between them (n=53 for GPP; n=24 for NPP or BP).
●scaling: upscaling of chamber-based measurements of assimilation and
respiration (GPP and R
)ﬂuxes at the organ scale, or the entire stand (n=
73 for GPP; n=9 for NPP or BP).
The difference between ‘scaling’and ‘modelling’lies in the data used. In the case
of ‘scaling’the data were derived from measurements at the site. ‘Model’means
that a dynamic process-based model was used, but with parameters calibrated and
optimized at the site, based on either biometric or micrometeorological
Data selection. The data were obtained from more than 300 peer-reviewed articles
(see also ref. 5), adding, merging and extending published works worldwide on
CUE or BPE4,9,11,23,25,56,57. Data were extracted from the text, Tables or directly
from Figures using the Unix software g3data (version 1.5.2, Jonas Frantz). In most
studies, NPP, BP and GPP were estimated for the tree stand only. However, GPP
estimated from CO
ﬂux by micrometeorological methods applies to the entire
stand including ground vegetation. We therefore included only those micro-
meteorological studies where the forest stand was the dominant primary producer.
The database contains 244 records (197 for BPE and 47 for CUE) from >100 forest
sites (including planted, managed, recently burned, N-fertilized, irrigated and
-fertilized forests; Supplementary Information, Supplementary Fig. 3
and online Materials; https://doi.org/10.5281/zenodo.3953478), representing 89
different tree species. Globally, 170 records out of the total data are from temperate
sites, 51 from boreal, and 23 for tropical sites, corresponding to 79 deciduous
broad-leaf (DBF), 14 evergreen broad-leaf (EBF), 132 evergreen needle-leaf (ENF)
and 19 mixed-forests records (MX). The majority of the data (∼93%) cover the
time-span from 1995 to 2015. We assume that when productivity data came from
biometric measurements the reported NPP would have to be considered as BP
because ‘occult’, nonstructural and secondary carbon compounds (e.g. BVOCs or
exudates) are not included. In some cases, multiple datasets from the same site
were included, covering different years or published by different authors. We
considered only those values where either NPP (or BP) and GPP referred to the
same year. From studies where data were available from more than 1 year, mean
values across years were calculated. When the same reference for data was found in
different papers or collected in different databases, where possible, we used data
from the original source. When different authors described the same values for the
same site, one single reference (and value) was used (in principle the oldest one).
By using only commonly available environmental drivers to analyse the spatial
variability in CUE and BPE, we were able to include almost all of the data that we
found in the literature. We examined as potential predictors site-level effects of:
average stand age (n=204; range from 5 to ∼500 years), mean annual temperature
(MAT; n=230; range −6.5 to 27.1 °C) and total annual precipitation (TAP; n=
232; range from ∼125 to ∼3500 mm yr−1), method of determination (n=237),
geographic location (latitude and longitude; n=241, 64°07′Nto−42°52′S and 155°
70′Wto−173°28′E), elevation (n=217; 5–2800 m, above sea level), leaf area index
(LAI, n=117; range from 0.4 to 13 m2m−2), treatment (e.g.: ambient or artiﬁcially
increased atmospheric CO
concentration; n=34), disturbance type (e.g.: ﬁre n=
6; management n=55), and the International Geosphere-Biosphere Programme
(IGBP) vegetation classiﬁcation and biomes (n=244), as reported in the published
articles (online Materials). The methods by which GPP, NPP, BP (and R
determined were included as random effects in a number of possible mixed-effects
linear regression models (Supplementary Table 4).
We excluded from statistical analysis all data where GPP and NPP were
determined based on assumptions (e.g. data obtained using ﬁxed fractions of NPP
of GPP). In just one case GPP was estimated as the sum of upscaled R
NPP58; however, this study was excluded from the statistical analysis. NPP or R
estimates obtained by process-based models (n=23) were also not included in the
statistical analysis. No information was available on prior natural disturbance
events (biotic and abiotic, e.g. insect herbivore and pathogen outbreaks, and
drought) that could in principle modify production efﬁciency, apart from ﬁre. The
occurrence of ﬁre was reported by only a few studies59–61. These data were
included in the database but ﬁre, as an explanatory factor, was not considered due
to the small number of samples in which it was reported (n=6).
Data uncertainty. Uncertainties of GPP, NPP and BP data were all computed
following the method based on expert judgment as described in Luyssaert et al.55.
First, ‘gross’uncertainty in GPP (gC m−2yr−1) was calculated as 500 +7.1 × (70−|
lat|) gC m−2yr−1and gross uncertainties in NPP and BP (gC m−2yr−1) were
calculated as 350 +2.9 × (70−|lat|). The absolute value of uncertainty thus
decreases linearly with increasing latitude for GPP and for NPP and BP, because we
assumed that the uncertainty is relative to the magnitude of the ﬂux, which also
decreases with increasing |lat|. Subsequently, as in Luyssaert et al.55, uncertainty
was further reduced considering the methodology used to obtain each variable, by a
method-speciﬁc factor (from 0 to 1, ﬁnal uncertainty (δ)=gross uncertainty ×
method-speciﬁc factor). Luyssaert et al.55 reported for GPP-Micromet a method-
speciﬁc factor of 0.3 (i.e. gross uncertainty is reduced by 70% for micro-
meteorological measurements); and for GPP-Model, 0.6. GPP-Scaling and GPP-
Biometric were not explicitly considered in ref. 55 for GPP. We we used values of
0.8 and 0.3, respectively. For BP-Biometric and NPP-Micromet we used a reduc-
tion factor of 0.3; for NPP-Model, 0.6; and for NPP-Scaling (as obtained from
measurements), 0.8. When GPP and/or NPP or BP methods
were not known (n=7), a factor of 1 (i.e. no reduction of uncertainty for methods
used, hence maximum uncertainty) was used. The absolute uncertainties on CUE
(δCUE) and BPE (δBPE) were considered as the weighted means62 by error pro-
pagation of each single variable (δNPP or δBP and δGPP) as follows:
and similarly for δBPE, by substituting NPP with BP and CUE with BPE.
Data and model selection. The CUE and BPE data were combined into a single
variable, as sites for which both types of estimates existed did not show any
signiﬁcant differences between these entities (Supplementary Fig. 2). CUE values
based on modelling were excluded (in our database we do not have BPE data from
modelling). Tests showed that the CUE value was systematically higher when GPP
was estimated with micrometeorological methods, compared to values based on
biometric or scaling methods. Only data with complete information on CUE,
MAT, age, TAP, and latitude were used. Altogether, 142 observations were selected.
In order to use the most complete information possible, a full additive model
was constructed ﬁrst (Eq. (1)). The method used for estimation of GPP (GPPmeth)
was speciﬁed as a random effect on the intercept, as visual inspection suggested
that CUE values were smaller where ‘scaling’was used to estimate GPP compared
to cases where ‘micromet’was used to estimate GPP.
In Eq. (1) the variable ‘age’represents the development status of the vegetation,
i.e. either average age of the canopy forming trees or the period since the last major
disturbance. The other three parameters represent different aspects of the climate.
The absolute latitude, |lat|, was chosen as a proxy of radiation climate, i.e. day
length and the seasonality of daily radiation. The term ηZ
random effect on the intercept due to the different methods of estimating GPP.
These variables were not independent (Supplementary Table 1). If the different
driver variables contain information that is not included in any of the other driver
variables, multiple linear regression is nonetheless able to separate the individual
effects. If, on the contrary, two variables exert essentially the same effect on the
response variable (CUE) this can be seen in an ANOVA based model comparison.
These considerations led us to the selection procedure in which we started with the
full model (Eq. (1)) and compared it with all possible reduced models
(Supplementary Table 2). The result of this analysis is the model with the smallest
number of parameters that does not signiﬁcantly differ from the full model.
We also examined, whether there were any signiﬁcant interactions of predictor
variables. There were not.
We used the Rfunction lmer from the R-package lme463 to ﬁt the mixed and
ordinary multiple linear models to the data. We checked for potential problems of
multicollinearity using the variance inﬂation factor (VIF)64. All predictors had VIF
< 5 (between 1.1 and 3.8).The model residuals were also tested for normality (using
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the Anderson-Darling test of non-normality, in the R-package nortest65). For
models that did not take a random intercept regarding ‘GPPmeth’into account
(16–30 in Supplementary Table 2) the Anderson-Darling test found signiﬁcant
deviation from normality of the model residuals, hence these models were excluded
from the analysis. The remaining models were compared with one another using
the function ANOVA of the R-package lmerTest66. This resulted in a 15 × 15
matrix of model comparisons in which the full model turned out to be signiﬁcantly
different from all other models.
The same analysis was also performed with a log-transformed version of Eq. (1):
1ln MAT þ7:5ðÞþβ0
where 7.5 °C was added to MAT in order to make its minimum 1 °C. Note that the
linear model from the log-transformed variables differs from the untransformed
linear model. The coefﬁcients, here noted with a prime, can be interpreted on the
basis of the back-transformed model. Contrary to the untransformed linear model
where effects are additive, the back-transformed model is a multiplicative effect
model, with the slope parameters as exponents for each variable and the intercept
0as power of e). As with the untransformed model, negative slope parameter
values lower CUE, positive increase it with increasing driver variable values.
The results from this analysis were, as with the original additive model (Eq. (1)),
(i) the full model could not be reduced any further and (ii) the directions of the
effects were the same as with the additive model, i.e. the predicted CUE increased
with increasing MAT, TAP and |lat| but decreased with increasing age.
The AIC and BIC values were lower for the log-transformed model compared to
the untransformed model, with AIC values of −169.7 and −157.2 and BIC values
of −149.0 and −136.5 for the log-transformed and untransformed models,
respectively. The coefﬁcients and model performance parameters of the
untransformed and the log-transformed models are shown in Table 1and
Supplementary Table 4. The adjusted squared correlation coefﬁcients were similar:
0.306 for the untransformed and 0.321 for the log-transformed model. Despite
considerable uncertainty of the CUE values, it was possible to derive signiﬁcant,
systematic, linear relationships between the four driver variables and CUE or ln
(CUE). Both model variants showed the same direction and similar magnitudes of
the effects. It can be concluded that CUE (or ln (CUE)) from a global dataset of a
large variety of forests is signiﬁcantly positively affected by MAT, TAP and |lat|,
and signiﬁcantly negatively affected by age. Even excluding from the analysis the
ﬁve tropical forest data with |lat| < 20 degrees did not alter signiﬁcantly the
empirical relationship (Supplementary Table 5).
Because the parameters of the untransformed, additive model are much easier
to interpret, we use the additive model in the main text and use the log-
transformed model only as a conﬁrmation of trends found in the additive model.
Outputs from TRENDY v.7. We used the simulations from eight Dynamic Global
Vegetation Models (DGVMs) performed in the framework of the TRENDY v.7
project2,67 (http://dgvm.ceh.ac.uk/node/9; data downloaded 27 November 2019).
Models that did not provide NPP and GPP at plant functional type level were
excluded because of the need to analyse CUE in forests without signiﬁcant con-
tributions from shrubs, grassland or crops. The selection comprises the following
models: ISAM, JULES, LPJ-GUESS, CABLE-POP, ORCHIDEE, ORCHIDE-CNP,
JSBACH and SDGVM (for references on models see refs. 2,67 and Supplementary
Table 6). All the models represent the surface ﬂuxes of CO
, water and the
dynamics of carbon pools in response to changes in climate, atmospheric CO
concentration, and land-use change across a global grid. However, processes
underlying the exchanges of water and carbon are based on different formulations
in different models.
In the TRENDY protocol all DGVMs were forced with common historical
climate ﬁelds and atmospheric CO
concentrations over the period from 1700 to
2017. Climate ﬁelds were taken from the CRU-JRA55 dataset2, whereas the time
series of atmospheric CO
concentrations were derived from the combination of ice
core records and atmospheric observations. Land-use change was taken into
account in the simulations (S3). However, similar simulations without land-use
change (S2) were also tested, showing no differences. CUE was estimated as NPP/
GPP (where NPP is commonly obtained in models by subtracting R
for the forest plant functional types simulated to be present in each grid cell. The
model outputs refer to the mean from 1995 to 2015 for comparability with the
records used when showing global land analysis (Fig. 5and Supplementary Fig. 4).
At site level, the same dates as the observations were chosen from the model
Reporting summary. Further information on research design is available in the Nature
Research Reporting Summary linked to this article.
All data supporting this study are available in the supplementary materials and are
publicly available at theZenodo repository (https://doi.org/10.5281/zenodo.3953478).
Correspondence and requests for additional materials should be addressed to A.C. and A.
I. Source data are provided with this paper.
There is no particular custom code or mathematical algorithm that is deemed central to
the conclusions. All relevant R-functions that were used are referred to in the method
section (see package vignettes for details).
Received: 4 April 2020; Accepted: 18 September 2020;
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We thank R.H. Waring, S. Vicca, M. Campioli, F. Pagani and E. Grieco for early con-
structive comments and thoughtful suggestions; S. Noce for the map of data points. We
thank efforts from all site investigators and their funding agencies. This paper contributes
to the AXA Chair Programme in Biosphere and Climate Impacts and the Imperial
College initiative Grand Challenges in Ecosystems and the Environment. A.C. and G.M.
are partially supported by resources available from the Ministry of University and
Research (FOE-2019), under the project “Climate Change”(CNR DTA.AD003.474);
M.F.-M. is a postdoctoral fellow of the Research Foundation—Flanders (FWO);
A.C., A.I. and I.C.P. conceived the paper. A.Co., A.S., A.I., A.Ce. and R.A. analysed data.
A.Co., A.I., A.Ce., R.A., M.F.-M. and I.C.P. wrote the manuscript. All authors contributed
substantially to discussions and revisions.
The authors declare no competing interests.
Supplementary information is available for this paper at https://doi.org/10.1038/s41467-
Correspondence and requests for materials should be addressed to A.I.
Peer review information Nature Communications thanks Creighton Litton, Akihiko Ito
and the other, anonymous, reviewer for their contribution to the peer review of this
work. Peer reviewer reports are available.
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