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Carbon allocation plays a key role in ecosystem dynamics and plant adaptation to changing environmental conditions. Hence, proper description of this process in vegetation models is crucial for the simulations of the impact of climate change on carbon cycling in forests. Here we review how carbon allocation modelling is currently implemented in 31 contrasting models to identify the main gaps compared with our theoretical and empirical understanding of carbon allocation. A hybrid approach based on combining several principles and/or types of carbon allocation modelling prevailed in the examined models, while physiologically more sophisticated approaches were used less often than empirical ones. The analysis revealed that, although the number of carbon allocation studies over the past 10 years has substantially increased, some background processes are still insufficiently understood and some issues in models are frequently poorly represented, oversimplified or even omitted. Hence, current challenges for carbon allocation modelling in forest ecosystems are (i) to overcome remaining limits in process understanding, particularly regarding the impact of disturbances on carbon allocation, accumulation and utilization of nonstructural carbohydrates, and carbon use by symbionts, and (ii) to implement existing knowledge of carbon allocation into defence, regeneration and improved resource uptake in order to better account for changing environmental conditions.
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Tree Physiology 00, 1–24
Forest carbon allocation modelling under climate change
Katarína Merganiˇ
cová 1,2,13, Ján Merganiˇ
c2, Aleksi Lehtonen 3, Giorgio Vacchiano4,
sa Zorana Ostrogovi´
5, Andrey L.D. Augustynczik6, Rüdiger Grote7, Ina Kyselová8,
Annikki Mäkelä9, Rasoul Yousefpour6, Jan Krejza 8, Alessio Collalti 10,11 and
Christopher P.O. Reyer12
1Czech University of Life Sciences, Prague, Faculty of Forestry and Wood Sciences, Kamýcká 129, 16500 Praha-Suchdol, Czech Republic; 2Technical University Zvolen,
Forestry Faculty, T. G. Masaryka 24, 96053 Zvolen, Slovakia; 3The Finnish Forest Research Institute - Luke, PO Box 18 (Jokiniemenkuja 1), FI-01301 Vantaa, Finland;
4Università degli Studi di Milano, DISAA. Via Celoria 2, 20132 Milano, Italy; 5Croatian Forest Research Institute, Department for forest management and forestry economics,
Cvjetno naselje 41, 10450 Jastrebarsko, Croatia; 6University of Freiburg, Tennenbacher Str. 4 (2. OG), D-79106 Freiburg, Germany; 7Institute of Meteorology and Climate
Research (IMK-IFU), Karlsruhe Institute of Technology, Garmisch-Par tenkirchen, Germany; 8Global Change Research Institute CAS, Bˇ
elidla 986/4a, 603 00 Brno, Czech
Republic; 9University of Helsinki, Depar tment of Forest Science, Latokartanonkaari 7, P.O. Box 27, 00014 Helsinki, Finland; 10 National Research Council of Italy, Institute for
Agriculture and Forestry Systems in the Mediterranean (CNR-ISAFOM), 87036 Rende, Italy; 11 Department of Innovation in Biological, Agro-food and Forest Systems,
University of Tuscia, 01100 Viterbo, Italy; 12 Potsdam Institute for Climate Impact Research, Telegraphenberg, PO Box 601203, D-14473 Potsdam, Germany;
13Corresponding author (
Received December 14, 2018; accepted September 24, 2019; handling Editor Andrea Polle
Carbon allocation plays a key role in ecosystem dynamics and plant adaptation to changing environmental conditions.
Hence, proper description of this process in vegetation models is crucial for the simulations of the impact of climate
change on carbon cycling in forests. Here we review how carbon allocation modelling is currently implemented in 31
contrasting models to identify the main gaps compared with our theoretical and empirical understanding of carbon
allocation. A hybrid approach based on combining several principles and/or types of carbon allocation modelling
prevailed in the examined models, while physiologically more sophisticated approaches were used less often than
empirical ones. The analysis revealed that, although the number of carbon allocation studies over the past 10 years has
substantially increased, some background processes are still insuciently understood and some issues in models are
frequently poorly represented, oversimplied or even omitted. Hence, current challenges for carbon allocation modelling
in forest ecosystems are (i) to overcome remaining limits in process understanding, particularly regarding the impact
of disturbances on carbon allocation, accumulation and utilization of nonstructural carbohydrates, and carbon use by
symbionts, and (ii) to implement existing knowledge of carbon allocation into defence, regeneration and improved
resource uptake in order to better account for changing environmental conditions.
Keywords: carbon partitioning, xed ratio, model calibration, mycorrhiza, natural disturbances, natural resources, nonstruc-
tural carbohydrates, repair and defence function, reproduction, temporal resolution.
Process-based models are widely and intensively used for
simulating long-term tree and/orforest stand growth (Bohn et al.
2014,Lonsdale et al. 2015), as well as for forecasting carbon
(C) and vegetation dynamics using dierent climate scenarios
(Peters et al. 2013,Gutiérrez et al. 2014,Sánchez-Salguero
et al. 2016,Collalti et al. 2018), because they can predict
water, C and nutrient ow within ecosystems. However, our
understanding of the processes governing these ows is patchy
(Garcia et al. 2016), with some being understood in much
more detail than others. Carbon accumulation in structural and
nonstructural components of forests depends on a variety
of linked processes such as photosynthesis, respiration and
C allocation into dierent compartments, including those for
defence and reproduction (Xia et al. 2017). In particular, C
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cová et al.
allocation is, due to the incomplete knowledge of the underlying
mechanisms that lead plants to steer C to one pool rather than
to another, often oversimplied (Franklin et al. 2012,Mäkelä
2012), and considered as a major weakness of models (Le
Roux et al. 2001,Richardson et al. 2015).
Carbon allocation of forest ecosystems has a critical role in
the C exchange between the atmosphere and biosphere (Litton
et al. 2007), and it is regarded as one of the most important
plant adaptation mechanisms to environmental changes (Yan
et al. 2016). Although the processes driving C partitioning
to individual tree organs are still not thoroughly understood,
experimental results suggest that C allocation depends on
species, environmental conditions, stand structure, phenology,
ontogeny and many other factors (Litton et al. 2007,Ryan et al.
2010,Poorter et al. 2011,Franklin et al. 2012,Vicca et al.
2012,de Kauwe et al. 2014,Li et al. 2016,Collalti and
Prentice 2019). The C that trees allocate to woody structural
components has longer residence time compared with what is
allocated to leaves and ne roots (Campioli et al. 2008). Hence,
if the ratio between fast and slow turnover compartments
changes in response to altered resource availability and stress
intensity, future predictions of C feedbacks between biosphere
and atmosphere that do not account for this change may be
biased (Friend et al. 2013,Lehtonen and Heikkinen 2015).
Therefore, sophisticated C allocation modelling approaches are
required to better understand the eects of changes in climate,
air chemistry and forest management on terrestrial ecosystems.
It should be noted, however, that the degree to which allocation
processes need to be accounted for depends on the scope of
the model application. For some particular research questions
addressing only forests under steady state, modelling allocation
shifts might not be a priority.
In the presented study we analyse the results from a
questionnaire-based survey of 31 models operating from forest
stand-scale to global levels. Our specic objectives are (i) to
identify the dominant forest C allocation modelling approaches
currently used in models simulating forest dynamics and (ii)
to highlight identied gaps and provide examples on how to
improve C allocation modelling in the context of climate change.
The information should primarily help not only modellers to
identify decits and improve C allocation modules responsive to
changing environmental conditions but also researchers involved
in interpreting and using model results to better understand
which models are useful for a particular purpose.
Materials and methods
In our study, we adopted a broad denition of the term C
allocation presented by Litton et al. (2007) encompassing
both the pattern of biomass distribution among individual tree
components and the process of C partitioning, i.e., the ux of C
to a particular tree component per unit time dened as biomass
or pool increment.
Questionnaire survey and database creation
The questionnaire (see Supplementary A available as Supple-
mentary Data at Tree Physiology Online) was prepared by the
working group ‘Carbon allocation’ within the European Cooper-
ation in Science and Technology (COST) Action network project
‘Towards robust PROjections of European FOrests UNDer cli-
mate change’ (PROFOUND FP1304) as a web-based survey. It
consisted of both open-ended and closed-ended questions (Q)
divided into three main parts focusing on the general description
of the whole modelling system (14 questions), C allocation
model implemented in the modelling system (25 questions) and
reference sources (11 questions). The principles and the types of
C allocation models were taken from the previous works dealing
with C allocation modelling in forests (Lacointe 2000,Fabrikaand
Pretzsch 2011,Franklin et al. 2012,de Kauwe et al. 2014).
The survey was distributed by email to the participants of
PROFOUND as well asa related COST Action networking project
called ‘Climate Change Manipulation Experiments in Terrestrial
Ecosystems—Networking and Outreach’ (ClimMani), the INTER-
FACE research coordination network, and further forwarded to
relevant model developers and model users based on personal
contacts of participants. In total, we invited approximately 260
scientists worldwide. Participation in the survey was voluntary.
The survey was open from 11 November 2016, to 31 January
2017. Since non-European researchers were not present during
the meetings of the COST Actions, during which the question-
naire was developed and presented, the response rate from
those regions was lower.
In total, we gathered 40 responses with information about
C allocation modelling approaches implemented in 31 dierent
models (Table 1) from 16 countries (see Figure S1 available as
Supplementary Data at Tree Physiology Online). This number
of models reects the number of complex vegetation based
models found in preceding studies focusing on a similar pool of
models (Fontes et al. 2010). The applied modelling approaches
varied from the viewpoint of temporal, spatial and modelled
units as dened by Fabrika and Pretzsch (2011) (see Figure S2
available as Supplementary Data at Tree Physiology Online).
The collected responses were checked for consistency and
stored in a Microsoft Access database. In the case of ambiguous
replies, these were cross-checked with references and model
developers and/or users who had lled in the questionnaire.
Model complexity ranking
To perform a quantitative model intercomparison, we analysed
the complexity of C allocation models based on individual
questions presented in the second part of the questionnaire
(see Supplementary A available as Supplementary Data at Tr ee
Physiology Online). Under the term ‘complexity’, we understand
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Forest carbon allocation modelling under climate change 3
Table 1. List of examined vegetation models in this study. Modelling approach refers to a broad specication of how processes are modelled by
the whole modelling system; in the case of a hybrid approach, several modelling concepts are combined, while the dominant modelling concept is
presented in table. Carbon allocation types are dened in Table 2.
Name of the model Whole modelling system Applied types of carbon allocation References
Modelling approach Dominant modelling
3D-CMCC FEM Hybrid Process-based Allometry and resource limitation Lüdeke et al. (1994),Arora and
Boer (2005),Collalti et al. (2014,
2016,2018,2019a)and Marconi
et al. (2017)
3PG-BW Hybrid Process-based Allometry and resource limitation Landsberg and Waring (1997)
ANAFORE Hybrid Process-based Pipe model, resource limitation and
source–sink model Deckmyn et al. (2008)
BALANCE Hybrid Process-based Pipe model, source–sink model and
root–shoot functional balance Rötzer et al. (2010,2012),Grote
and Pretzsch 2002
BASFOR Hybrid Process-based Fixed ratios, resource limitation,
source–sink model and root–shoot
functional balance
Van Oijen et al. (2005)
Biome-BGC Process-based Process-based Fixed ratios Thornton et al. (2005)
Biome-BGCMuSo Process-based Process-based Fixed ratios Running and Hunt (1993) and
Hidy et al. (2016)
CARAIB Process-based Process-based Fixed ratios Warnant et al. (1994)
CASTANEA Process-based Process-based Allometry, pipe model and resource
Dufrêne et al. (2005) and Guillemot
et al. (2016)
CENTURY Process-based Process-based Fixed ratios and resource limitation Parton et al. (1987) and Allister
et al. (1993)
Community Land Model
Hybrid Process-based Allometry and resource limitation Oleson et al. (2013) and Fan et al.
CoupModel Hybrid Process-based Allometry, xed ratios, optimal
response, resource limitation and
transport resistance
Eckersten and Jansson (1991),de
Willigen (1991),Jansson and
Karlberg (2004) and Svensson
et al. (2008)
ED2 Hybrid Process-based Allometry, xed ratios and pipe
Medvigy et al. (2009) and Hurtt
et al. (2013)
FORESEE (4C) Hybrid Process-based Allometry and pipe model Bugmann et al. (1997) and
Lasch-Born et al. (2019)
ForGEM Empirical Empirical Allometry Kramer et al. (2008),Kramer and
van der Werf (2010) and Kramer et
al. (2015),
FORMIND Process-based Process-based Allometry Bohn et al. (2014)
GO+Hybrid Process-based Allometry, optimal response and
resource limitation
Loustau (2010)
GO+TreeStabd Hybrid Structural Allometry Loustau et al. (2005)
GOTILWA+Process-based Process-based Pipe model and source–sink model Shinozaki et al. (1964) and Keenan
et al. (2009)
Heterofor Hybrid Empirical Allometry and root–shoot functional
Jonard and André (2018)
iLand Hybrid Process-based Allometry and root–shoot functional
Seidl et al. (2012)
Klein & Hoch Process-based Process-based Source–sink model Klein and Hoch (2014)
LANDIS-II Hybrid Process-based Allometry, xed ratios and resource
Scheller et al. (2011)
LandscapeDNDC Hybrid Process-based Pipe model and source–sink model Grote (1998),Grote and Reiter
(2004) and Grote et al. (2011)
LIGNUM Hybrid Process-based Allometry, pipe model and
source–sink model
Sievänen et al. (2008) and
Perttunen et al. (1998)
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Table 1. Continued
Name of the model Whole modelling system Applied types of carbon allocation References
Modelling approach Dominant modelling
LPJ-GUESS Hybrid Process-based Allometry, xed ratios, pipe model,
resource limitation and root–shoot
functional balance
Smith et al. (2001),Sitch et al.
(2003) and Smith et al. (2014)
ORCHIDEE-CAN Hybrid Process-based Allometry, pipe model and
source–sink model
Naudts et al. (2015)
PICUS Hybrid Process-based Allometry, pipe model and
source–sink model
Lexer and Hönninger (2001),Seidl
et al. (2005),Seidl et al. (2007)
and Seidl et al. (2009)
PnET Hybrid Empirical Fixed ratios and pipe model Aber and Federer (1992)
SIBYLA Empirical Empirical Allometry Fabrika (2005),Fabrika and ˇ
(2006) Fabrika and Pretzsch
TreeMig Hybrid Process-based Fixed ratios Bugmann (1994) and Lischke et al.
the level of detail applied within a model to describe the
behaviour of the system including its inter-dependencies. Com-
plexity was quantied in four dierent ways depending on the
underlying question: (i) the principles and types of allocation
modelling (Q 2.1 and 2.2, see Supplementary A available
as Supplementary Data at Tree Physiology Online) and their
temporal and spatial scales (Q 2.3 and 2.4) were rated starting
from 1, which indicated the simplest approaches and the largest
scales of time and space, to the question-specic maximum
(5 for principles and a spatial scale, 7 for a temporal scale
and 10 for types of C allocation modelling), which represented
the most complex approaches and the nest temporal and
spatial scales; (ii) each individual answer on the presence of
variables aecting C allocation (Q 2.5), compartments (Q 2.6),
priority of C allocation (Q 2.8.1–2.8.5), model sensitivity (Q
2.9; see Supplementary A available as Supplementary Data at
Tree Physiology Online) was rated with a value of 1; (iii) each
answer on the presence of constant parameters (Q 2.7) was
rated with a value of 1; and (iv) yes/no answers (Q 2.8,
2.10, 2.13) were rated with 1 or 0, respectively. In the case
of multiple questions (e.g., Q 2.5 or Q 2.7), the score for the
question was calculated by summing up the values for all the
entries of the particular question. Afterwards, to ensure the
same scale of the complexity measure for all questions the total
score of each question was rescaled in the range 0–1, with
1 representing the maximum attainable score. Hence, values
close to 0 suggest low complexity of C allocation modelling
and values close to 1 indicate high complexity. This is in line
with Jin et al. (2016), who stated that complex models closely
couple environmental conditions and physiological processes,
involve more variables than simpler models and operate at ner
temporal scales. The obtained complexity values were then
further used in the analysis of gaps in C allocation modelling.
Analysis of the gaps in carbon allocation modelling
Most frequent gaps in the representation of C allocation in
forest growth models identied by the respondents (Q 2.13.1
in Supplementary A) were analysed in three steps:
(i) Identication of the gap
(ii) Evidence to prove the gap
(iii) Approaches and examples to overcome the gap
The existence of the gap was further examined using the
responses on related questions from the second part of the
questionnaire (Q 2.1 to 2.12). We were primarily concerned
with the frequency of the gap, i.e., in how many models
the identied problem may potentially occur. The evidence
of the identied gaps was justied by a literature review to
independently conrm the relevance of each gap for accurate
modelling of C allocation using published empirical evidence.
Finally, we examined possible modelling approaches to over-
come the identied gaps, either from the models specied in
the questionnaire or from other existing modelling approaches
in the literature. For the literature review, we used the databases
of Elsevier Scopus©, ISI Web of Knowledge©, CAB Abstract©
and Google Scholar©. The material was selected by searching
for the term ‘carbon allocation’ and its synonyms identied by
Litton et al. (2007) in combination with the terms ‘model’ or
‘modelling’ in the title, abstract and/or keywords of published
papers in English.
As Franklin et al. (2012) pointed out, C allocation is not a
process but an outcome of several dierent processes. Pho-
tosynthates produced by plants are allocated to physiologically
dierent parts of plant functioning (Figure 1). The C assigned
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Forest carbon allocation modelling under climate change 5
Figure 1. Scheme of carbon allocation in plants. Black arrows inside
the box represent carbon pathways; red arrows outside the box show
the directions of impacts. Thick arrows indicate that all examined
models simulate the particular pathway; moderately thick arrows show
that only a part of models account for the movement, and dashed
arrows represent the links that were experimentally proven, but were
not explicitly simulated by any of the models included in the analysis.
The numbers in small boxes indicate which carbon allocation principle is
able to account for this inuence (2, functional relationship; 3, functional
balance; 4, eco-evolutionarily-based; 5, thermodynamic principle).
to plant structures is used for the production of new structural
tissues of both vegetative and generative plant organs to ensure
resource uptake (leaves and ne roots), plant functionality and
support (stem, branches and coarse roots), and reproduction
(owers, fruits and seeds). In order to keep the plant functioning,
some portion of available C is respired. For the protection
of already captured resources, some carbohydrates are used
as mechanical or chemical defence. Plants also export some
portion of xed C into mycorrhiza or into the soil in the form of
root exudates to increase their nutrient uptake. A portion of pho-
tosynthates is stored as nonstructural compounds, mainly starch
and sugars, which represent plant reserves that can be used in
future for any of the above-mentioned reasons. Plant allocation
strategy determines which C allocation pool is favoured at
a particular point in time. The choice of the strategy and
subsequently the proportions of C allocated to individual parts
are inuenced by the actual state of the plant (age, size, etc.),
by the surrounding environment (water, nutrients, temperature,
etc.) and by disturbances including management. From the point
of plant survival, all pathways are indispensable. However, in the
models they are unequally represented (Figure 1). In the context
of climate change, under which disturbances and/or adverse
environmental conditions have become more frequent (Seidl
et al. 2017), causing shifts in allocation patterns (Litton and
Giardina 2008), accounting for underrepresented C pathways
in models may be crucial.
Approaches to carbon allocation modelling
Investigated models diered in applied C allocation modelling
approaches. Fifteen models used a single principle of C alloca-
tion modelling as dened by Franklin et al. (2012) (Table 2),
while 16 were based on a combination of at least two prin-
ciples. Out of these, 11 models combined two principles, 4
models combined three principles and CoupModel combined
four dierent principles of C allocation modelling (Figure 2).
The frequency of applying individual principles and/or types
decreased with their complexity (Table 2;Figure 3). Empirically
dened C allocation was most commonly used (61% of mod-
els), followed by the principles of functional relationship and
functional balance (Table 2). Eco-evolutionary-based types of
C allocation modelling were used in three models (CLM 4.5,
CoupModel and GO+), while the thermodynamic principle was
not used in any (Table 2).
Identied gaps in carbon allocation modelling
Model developers and users identied 24 specic problems
related to C allocation modelling. The most commonly identied
problems were (i) usage of xed ratios despite known natural
dynamics of C allocation, lack of direct sensitivity of C allocation
modelling (ii) to environmental conditions and (iii) to natural
disturbances, (iv) missing pools that may trigger C losses under
environmental changes or function as a buer to withstand
stress conditions, (v) allocation time steps that are too large
to model the dynamics of resource acquisition and (vi) lack of
data for calibration and validation of C allocation procedures.
These issues are of particular importance in the context of
ongoing climate change, which may cause unprecedented shifts
in environmental conditions that drive ecosystem and plant pro-
cesses including C allocation (DeLucia et al. 2000). Below we
specically analyse each gap using the two rst steps dened in
the section Analysis of the gaps in carbon allocation modelling.
The approaches to overcome the gaps are summarized at the
end of the results.
To analyse model complexity from the viewpoint of the gaps
identied by model respondents, we visualized the values of
relative complexity for each model that were derived from
the responses to those questions related to the analysed
gaps (ve questions) following the methodology in the section
Model complexity ranking. The results indicate that few models
are complex in all ve characteristics tested here, i.e., some
models use more complex principles of C allocation modelling,
while other models operate at a ner temporal scale, and some
others account for the impact of disturbance factors in greater
detail (Figure 4).
The use of xed ratios for carbon allocation modelling
Identication of the gap Modelling C allocation using ‘xed
ratios’ assumes that compartment fractions, C allocation ratios
and/orgrowthproportions areheldconstant(Franklinetal.2012).
These parameters may be set depending on specic environ-
mental conditions, e.g., vegetation group/biome/plant functional
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Table 2. Description of principles and types of carbon allocation modelling and the frequency of their usage in examined vegetation models.
ID of carbon
Principle of carbon
allocation modelling
Basic description Computation
Variation of
allocation with
Variation of
allocation with
between plant’s
strategy and
of models
1 Empirical Carbon allocation is based
on constant statistical
relationships among
individual organs.
High No No No 19
Carbon allocation is
dened by allometric
functions describing
relationships among plant
3 Functional balance Carbon is allocated to
maintain internal balance
between organs according
to an optimum internal status
of resource or element ratio.
Moderate Yes Yes No 16
4 Eco-evolutionarily-
Carbon is allocated in
order to maximize a
tness proxy.
Low Yes Yes Yes 3
5 Thermodynamic Carbon is allocated in
order to maximize entropy
or entropy production.
Moderate Yes Yes Yes 0
Type of carbon
allocation modelling
1 Fixed ratios Fixed fractions of
assimilated carbon are
allocated to individual
High No No No 10
1 (2) Allometry Carbon is allocated to a
particular organ according
to mass and size
2 (3) Pipe model Carbon is allocated in
order to provide the
(sapwood) conductance
necessary to support
High Yes No/yes No 12
3 Root–shoot
functional balance
Carbon is allocated to
individual organs to ensure
a balanced supply of
resources from foliage and
ne roots.
Moderate Yes Yes No 6
3 Resource limitation Allocation of assimilated
carbon to individual organs
is driven by the most
limiting source to growth.
Moderate No/yes Yes No 12
3 Source–sink model Allocation of assimilated
carbon to individual organs
is driven by the demands of
individual organs and the
availability of assimilates.
Moderate Yes Yes No 9
3 Transport resistance Allocation of assimilated
carbon is controlled by
concentration gradients of
between plant parts.
Low Yes Yes No 1
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Forest carbon allocation modelling under climate change 7
Table 2. Continued
ID of carbon
Principle of carbon
allocation modelling
Basic description Computation
Variation of
allocation with
Variation of
allocation with
between plant’s
strategy and
of models
4 Optimal response Selects an optimal
allocation strategy that
maximizes a predened
goal (tness proxy) when
there is a signicant
competition only for one
Low Yes Yes No 2
4 Game-theoretic
Selects an optimal
allocation strategy that
maximizes a predened
goal (tness proxy) when
there is a signicant
competition for more than
one resource.
Low Yes Yes Yes 0
4 Adaptive dynamics Selects an optimal
allocation strategy that
maximizes a goal (tness
proxy), which is
dynamically selected.
Low Yes Yes Yes 0
5 Maximum entropy
Selects the most probable
allocation strategy that
maximizes entropy under
given environmental and
internal constraints.
Moderate Yes Yes Yes 0
5 Maximum entropy Predicts the most probable
allocation strategy and the
frequency distribution of
dierent strategies
(allocation patterns) around
the most probable strategy
under given environmental
and internal constraints.
Moderate Yes Yes Yes 0
types/tree species, soil water and nutrient status, etc., but they
do not change in response to phenology, stand development or
varying environmental conditions and natural disturbances.
More than a half of the investigated models (18 models,
58%) applied xed C allocation to a certain extent (Q 2.2
and Q 2.7, see Supplementary A available as Supplementary
Data at Tree Physiology Online). Carbon allocation based solely
on xed ratios was used in four models, while others used a
hybrid modelling approach that combined xed allocation with
one or more other modelling types, usually allometry, resource
limitation or pipe model (Figures 2 and 3). Models with xed
ratios represent an oversimplication of the underlying mecha-
nisms (Figure 1;Collalti et al. 2019a). Since climate change is
expected to induce changes in forests, using xed coecients
is evidently a shortcoming when modelling forest development
(Litton et al. 2007,Ostrogovi´c Sever et al. 2017,Collalti et al.
2019b) even with the models combining xed ratios with more
sophisticated approaches (de Kauwe et al. 2014).
Evidence to prove the gap Although xed C allocation ratios
could be applicable in special cases, such as large-scale mod-
elling of forests in a steady state (see CLM 4.5), for most
purposes C allocation appears dynamic, involving dierent plant
processes driven by a variety of environmental factors (Wardlaw
1990). Its dynamics can be synthesized into: (i) seasonal—
due to phenology (White et al. 1997,Caldararu et al. 2014,
Collalti et al., 2014,Delpierre et al. 2015,Schiestl-Aalto et
al. 2015,Collalti et al., 2016,Marconi et al. 2017); (ii)
periodical—during stand development due to age- or size-
related parameters or processes (Franklin et al. 2012), e.g.,
age-dependent root-to-shoot ratio (Genet et al. 2009), age-
dependent partitioning of C into foliage and wood (Litton et al.
2007,Valentine and Mäkelä 2012), tree height-related dynamic
of nonstructural carbohydrates (NSC) (Sala and Hoch 2009),
masting dynamics (Vacchiano et al. 2018; see Chapter Missing
pools and repair functions), stand density (Poorter et al. 2011,
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Figure 2. Examples of approaches applied in vegetation models using
dierent principles and types of carbon allocation modelling: Approach
1 applied in SIBYLA, Approach 2 in LANDSCAPE DNDC and Approach
3 in CoupModel. Approaches 2 and 3 are examples of combinations of
several carbon allocation types.
Krejza et al. 2013), competition (Vanninen and Mäkelä 2005);
and (iii) long term—due to direct sensitivity of C allocation
processes to environmental conditions (Poorter et al. 2011,
Chapter Direct sensitivity of carbon allocation to environmental
conditions) and natural disturbances (Running 2008, Chapter
Missing pools and repair functions).
The most pronounced eect of climate change on C allocation
is expected to be evident in its long-term dynamics due to
direct sensitivity of C allocation to environmental conditions.
Nevertheless, climate change can also indirectly alter seasonal
C allocation dynamics through shifts in plant phenology (Cleland
et al. 2007). Moreover, under climate change, increasing plant
respiration may push plants to allocate more C to reserves
than to structural growth (Collalti et al. 2018), aecting also
periodical NSC dynamics.
The problem of ‘xed ratios’ is also evident through xed
growth proportions, i.e., growth derived from C assimilation,
an approach that is commonly used in process-based models
(White et al. 1997,Mäkelä et al. 2000,Caldararu et al. 2014).
Nevertheless, it is known that growth may be uncoupled from
net photosynthesis (Fatichi et al. 2014,Körner 2015), relying
more on C storage and being more sensitive to temperature,
nutrient and water limitation than photosynthesis (Muller et al.
2011,Schiestl-Aalto and Mäkelä 2017).
Direct sensitivity of carbon allocation to environmental
Identication of the gap Including direct environmental con-
trols of C allocation in models is fundamental if the aim is
to simulate ecosystem dynamics under the ongoing climate
change. We identied 17 factors that inuence simulated C
allocation in the examined models, out of which 8 represented
environment, i.e., climate and soil (Q 2.9, see Supplementary
A available as Supplementary Data at Tree Physiology Online)
(Figure 5). The factors aect the dynamics of tree growth, the
contribution of each tree component to autotrophic respiration
and the C transfer to the rhizosphere. In particular, the latter point
Figure 3. Combinations of dierent types of carbon allocation modelling
in the investigated vegetation models. Numbers on axes represent
individual types of carbon allocation modelling as follows: 1, xed ratios;
2, allometry; 3, root–shoot functional balance; 4, resource limitation; 5,
pipe model; 6, transport resistance; 7, source–sink model; 8, optimal
response. The size of the bubble indicates the number of models from
our database that use a particular type or a combination of types
for modelling carbon allocation, with the smallest size representing
one model and the biggest size representing four models. Red colour
indicates that only one type of carbon allocation modelling has been
applied, green colour indicates the combination of two types, blue colour
stands for the combination of three types and purple colour for four or
ve types of carbon allocation modelling, while only the rst three types
are explicitly presented on the axes.
has been highlighted since it is driven by changes in the root–
shoot ratio (e.g., Litton and Giardina 2008) and in lifespan and
decomposition rates of tree components (Körner 2003,Epron
et al. 2012b).
The analysis revealed that in 11 models no climatic or
soil conditions directly aected simulated C allocation (see
Figure S3B available as Supplementary Data at Tree Physiology
Online). From the models that accounted for at least one of iden-
tied environmental conditions, most (14 models) considered
air temperature, while precipitation aected C allocation only
in 4 models (Figure 5). Only ANAFORE included the impact of
three identied soil characteristics (soil water, nitrogen and other
nutrients). Although nitrogen was the most frequently included
nutrient in models, still 12 models do not simulate nitrogen
cycling in ecosystems (Figure 5).
Evidence to prove the gap Increasing temperature has
the potential to increase C accumulation in aboveground
biomass, meaning stimulation of the height growth more than
the growth of stem diameter (Way and Oren 2010), while
temperatures below 18 C signicantly increased the fraction
of roots at the expense of stems and leaves (Usami et al.
2001,Overdieck et al. 2007,Kasurinen et al. 2012). Faster
decomposition at higher temperatures releases more nutrients
from the soil organic nitrogen pool, which could result in an
increase of gross primary productivity caused by higher needle
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Forest carbon allocation modelling under climate change 9
Figure 4. Relative complexity of the models reviewed in this study. Values close to 1 indicate high complexity of the model, while values close to 0
indicate low complexity. The ve dimensions of the spider plot refer to individual questions on carbon allocation modelling posed in the questionnaire
(A, Q 2.1 principle of carbon allocation modelling; B, Q 2.3 time step of the carbon allocation model; C, Q 2.5.2 disturbances that aect carbon
allocation; D, Q 2.6 individual compartments for carbon allocation; F, Q 2.9 sensitivity of carbon allocation algorithm to individual factors). The colours
indicate the modelling approach of the whole modelling system (orange, hybrid; green, process-based; purple, empirical).
Figure 5. Percentage of models that account for the impact of dierent
factors on carbon allocation (dashed line represents 50% of models).
biomass production (Pumpanen et al. 2012). Increased nutrient
availability leads to increased partitioning to aboveground
parts of the tree and decreased partitioning to belowground
tree parts (Litton et al. 2007,Repola 2008,Poorter et al.
2011), whereas reduced nutrient availability or drought
generally favour C allocation to the root system, especially in
the humid soil horizons (Friedlingstein et al. 1999,Konôpka
and Lukac 2012,Hommel et al. 2016). Waterlogging also
aects biomass fractions of leaves and roots, though in the
opposite direction to water shortage, e.g., by favouring leaves
(Poorter et al. 2011). Tree seedlings limited by magnesium
reduced C allocation to roots, while phosphorus limitation
favoured C allocation to roots (Ericsson 1995)ormycorrhizal
symbionts (Ekblad et al. 1995). Potassium fertilization had a
signicant eect on C allocation favouring aboveground tree
parts (Epron et al. 2011), and adding calcium resulted in
higher C allocation to radial growth and reproductive processes
(Halman et al. 2013). The elements of phosphorus, potassium
and magnesium were found to be limiting for the production of
late-successional ecosystems (Körner 2015).
Water and nutrient demands are closely connected with
elevated atmospheric CO2, because increased photosynthetic
rates in response to elevated atmospheric CO2do not always
enhance stem growth (Fatichi et al. 2014) but rather increase
fruit production, C release into the soil (de Kauwe et al. 2014)
or the amount of C allocated to NSC (Collalti et al. 2018).
An increase in biomass accumulation as a result of higher
atmospheric CO2was observed only when sucient nutrients
were supplied (Murray et al. 2000,Franklin et al. 2012). The
process of downward regulation may be accompanied by higher
C sequestration into structural and conducting tissues as well as
by reduction of photosynthetically active tissues (Murray et al.
2000,Rolo et al. 2015). The study on European beech and
Norway spruce showed lower values of specic leaf areas when
growing under enhanced levels of atmospheric CO2(Rolo et al.
Impact of disturbances on carbon allocation
Identication of the gap Climate change is a prominent
reason for the observed and projected increasing frequency
and intensity of disturbances (Seidl et al. 2014), which have
signicant impacts on forest C cycling (Hicke et al. 2012,
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Figure 6. Number of natural disturbance factors (drought, re, insects,
wind or generic disturbance) aecting carbon allocation in examined
Running 2008). Hence, modelling disturbances and the
response of forest ecosystems is becoming crucial for future
projections of forest dynamics. In spite of that, out of 31 models
in our database, only 15 included the inuence of one or
several disturbances on C allocation (excluding management as
a disturbance). Most of the models (10 out of 15) included one
or two disturbances. The models with the highest complexity
values from the viewpoint of disturbances (iLand, LANDIS-
II, CENTURY and ORCHIDEE-CAN; Figure 4, C) included four
dierent disturbance types (Figure 6).
The most commonly included disturbance eect was drought,
covered by 13 models, followed by re (6 models), wind (6
models) and insects (5 models). Two models also included
‘generic’ disturbance not associated with any specic distur-
bance agent (LPJ-GUESS and TreeMig). While this possibly
reects the dominance of individual disturbance agents in
the dierent regions and forest types the models have been
designed for (c.f. Reyer et al. 2017), there is increasing evi-
dence that the interactions of disturbances are actually crucial
to assess disturbance impacts under climate change (Seidl et
al. 2017). No model covered the eects of other regionally
important disturbances such as ice storms and pathogens.
It should be noted that many models explored here consider
the eect of disturbances only indirectly, i.e., as responses of
C allocation to disturbance-induced changes in light, nutrient
and water availability. However, there is evidence of additional
eects of drought, insect and wind damage on allocation, which
are not covered by models yet. This includes a reduced hydraulic
conductivity that may persist throughout years or a change in
root to shoot ratios (e.g., Bansal et al. 2013). In general, even
though the number of forest models that include disturbances
are increasing, the disturbances are often represented by sta-
tistical approaches (Seidl et al. 2011), which complicates their
integration into complex process-based models that deal with
allocation mechanistically.
Evidence to prove the gap Drought, insect and wind damage
have direct eects on C allocation in trees. Although the reac-
tions may be species specic, a recent meta-analysis by Eziz et
al. (2017) revealed that under drought conditions the fraction
of plant root mass and reserves generally increased, while the
fraction of stem, leaf and reproductive biomass decreased. The
process is enhanced by increasing ne root mortality under dry
conditions although, at a certain threshold, ne root production
decreases again (Meier and Leuschner 2008,Nikolova et al.
2010). According to Galvez et al. (2011), severe drought stress
promotes the accumulation of carbohydrate reserves in roots at
the expense of growth. Similarly, Liu et al. (2017) indicated
an accumulation of NSC in leaves and reduced shoot and stem
growth under severe summer drought conditions. However, as
Hartmann and Trumbore (2016) pointed out, the accumulation
of NSC occurs only in the case of short-term drought events.
After the drought, plants favour root growth as a recovery
strategy in order to restore root functions (Hagedorn et al.
2016). Seidl and Blennow (2012) hypothesized that post-
storm stem growth reductions of the remaining trees in Sweden
might be caused by allocation changes to repair root damages
and produce insect defence compounds. The former mechanism
has been found both in tree-pulling experiments (Nielsen and
Knudsen 2004) and eld data analysis (Vargas et al. 2009).
Also, analyses on seedlings have shown that mechanical stimuli
mimicking natural wind sways increase biomass allocation to
roots (Coutand et al. 2008). Investment in insect defense
compounds has been shown for mildly drought-aected trees
(McDowell 2011). Defoliation is also known to cause shifts in
C allocation towards new leaf production (Mayeld et al. 2005,
Eyles et al. 2009,Pinkard et al. 2011,Jacquet et al. 2012)
and accumulation of reserves at the expense of stem growth
(Wiley et al. 2013,Piper et al. 2015). Saell et al. (2014)
showed that trees suering from a chronic fungal disease of
leaves changed their C allocation in favour of NSCs in crowns
to maintain foliage growth and shoot extension in the spring.
Browsing was also found to have an eect on C allocation in
trees, particularly in the short term (Palacio et al. 2008,2011,
Endrulat et al. 2016).
Missing pools and repair functions
Identication of the gap Pathways of C within a plant are
unequally considered in models (Figure 1). Under climate
change, characterized by shifts in environmental conditions and
more frequent extreme events, C allocation in under-represented
plant parts or processes may be favoured to ensure the survival
of an individual or population. Thus, models omitting these
pathways may become incapable of providing the complete
picture of C cycling in forests under novel conditions. On
average the models allocated C to 6 (calculated mean of 5.8)
dierent biomass compartments. Two models (TreeMig and
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Forest carbon allocation modelling under climate change 11
Figure 7. Frequency of tree compartments used in models.
FORMIND) distinguished only two compartments, while the
most complex representation of biomass pools with a maximum
of nine dierent compartments was implemented in CoupModel
and 3D-CMCC FEM (Figure 4, D). The leaf compartment was
included in all but one model, followed by ne roots used in 22
models and sapwood used in 19 models (Figure 7). Although
the average number of compartments coincides with the number
of main plant parts according to Cannell and Dewar (1994),
reproductive and storage sinks were not frequently represented
in the models (Figures 1 and 7).
A storage/reserve pool that represents nonstructural C is
included in a half of the models; one model (LPJ-GUESS)
includes a C pool for vegetative reproduction and six for sexual
reproduction (Figure 7). Of these, two activate such a pool only
for crops (CoupModel and CLM 4.5), one uses xed allocation
fractions for fruit production (Biome-BGCMuSo), while three use
xed fractions during dened periods (ANAFORE, ORCHIDEE-
Aside from missing pools, two more decits regarding C
allocation pools were identied: C available for defence and
repair and C export, particularly the C that is provided to
symbionts, i.e., mycorrhiza, which can account up to 30% of
annual net primary production (NPP; Hobbie 2006,Courty
et al. 2010). Defence and repair processes are important under
stressful conditions and are particularly relevant for determining
tree mortality. Allocated C to mycorrhiza might be seen as a
part of the investment into resource acquisition by roots and are
thus implicitly considered in root turnover and specic uptake
parameters. However, this implicit consideration assumes that
the relationship between plant and symbiont stays constant,
which is not the case in a changing environment (Vargas 2009).
Nevertheless, none of the models explicitly accounted either
for C export to mycorrhiza or for defence and repair processes
(Figures 1 and 7).
Evidence to prove the gap Seed production can consume
between 3% and 20% of annual gross primary production
(GPP; Schaefer et al. 2008), depending on species and on
interannual variability in reproductive output. In tree species
with irregular fruiting patterns, peak seed years (‘masting’:
Ascoli et al. 2017) may result in reductions of 40% in woody
growth (Holmsgaard 1955,Eis et al. 1965,Selås et al. 2002,
Monks and Kelly 2006,Drobyshev et al. 2010). This indicates
that large resources are invested into the reproductive pool,
governed by resource accumulation and depletion mechanisms
and growth reproduction trade-os (Hacket-Pain et al. 2015).
Moreover, although masting can synchronize over large areas in
response to weather-related drivers (Vacchiano et al. 2017),
a huge variability in seed output and its response to the
environment exists at the individual tree level (van der Meer et
al. 2002,Vilà-Cabrera et al. 2014). In general, the results indi-
cate that resource accumulation in cooler years triggers larger
fruiting/masting events later on, with later warm temperatures
inducing mast owering (Sala et al. 2012b,Müller-Haubold
et al. 2015,Abe et al. 2016,Monks et al. 2016,Pearse
et al. 2016). Interestingly, it is nevertheless not the stored C but
the newly produced C that is actually used for fruits and seeds
(Hoch et al. 2003,2013), which is corroborated by a frequent
decline of wood growth in a masting year (e.g., Drobyshev
et al. 2010,Martín et al. 2015). This indicates that full resource
pools are a trigger for allocation changes rather than the source
of masting. In addition, stress has been suggested to trigger
seed production based on the theory that mortality-inducing
events create favourable conditions for regeneration (Piovesan
and Adams 2001,2005), which however, has not always been
supported by measurements (Müller-Haubold et al. 2015).
Under climate change, storage represents an important
pool as it facilitates recovery processes (Hartmann 2015)after
environmental disturbances (e.g., drought, re, pathogen attacks
and defoliation by insect; Barigah et al. 2013). Temperate
deciduous tree species store a large amount of NSC in their
stems, which could be used for stem growth for a period of
7to30years(Klein et al. 2016a). For modelling purposes,
NSCs are important as reserves are used not only to control
their overall annual C cycle and the NPP/GPP ratio (Collalti
et al. 2019b,Collalti and Prentice 2019), but also to repair
or replace stress-related damages. This is a prerequisite to
mortality estimates and also aects long-term development
including delayed recovery and carry-over eects.
Similar to seed production, plants can invest up to 22%
of their GPP to their fungal symbionts (Vargas 2009). The
dierentiation of C allocated to mycorrhiza is mainly required
under changing environmental conditions (Hasselquist et al.
2016,Schiestl-Aalto et al. 2019), since climate change will
signicantly modify mycorrhizal diversity (Bellgard and Williams
2011), which will subsequently aect plant growth and survival.
In particular, nitrogen addition, and also higher temperatures
that lead to higher decomposition rates, requires dierenti-
ation between roots and fungal biomass. In contrast to the
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Table 3. Comparison of time step of the allocation model and the whole modelling system. Numbers indicate the number of models with the
respective combination of time steps. Red colour indicates the same time step at both modelling levels; green colour indicates that the carbon
allocation module operates at coarser temporal resolution than the whole modelling system, while blue colour indicates the opposite.
reproductive pool, which is separated from other tissues and
develops under specic environmental conditions, pools for
defence and repair are constitutively present and therefore need
to be an integrated part of other biomass fractions (Dietze
et al. 2014). Defence and repair processes are important under
stressful conditions and are particularly relevant for determining
tree mortality. For example, the immediate cause of death due to
drought stress might be hydraulic failure (i.e., xylem cavitation)
but the ability to postpone this failure may depend on the
ability of the tree stabilize water conductivity, repair previous
damages or build on new vessels that all depend on C supply
(Sala et al. 2012a). Failure to represent this process leads
to over- or underestimation of mortality, and carry-over eects
of decreased growth long after the stress has ceased will be
missed (Thomas et al. 2009). Similarly, air pollution leads to
considerably higher damages if the constitutive defences of a
leaf are exhausted (Wieser and Matyssek 2007).
Time step of carbon allocation
Identication of the gap The allocation of C in plants occurs
at short time scales of hours and weeks (Ulrich 1993)and
quickly responds to environmental changes and/or disturbances
(Ferrieri et al. 2013). The results of the questionnaire revealed
that C allocation models in our database worked with six
dierent time intervals, with a year being the largest and
30 min being the smallest time step (Table 3). The daily time
step was the most frequently used (45.2% models) followed
by the yearly, applied in one-third of the models (Table 3).
The smallest time step of 30 min was used in CLM 4.5
(Figure 4, B), as it accounts for the close linkage with highly
variable atmospheric processes. Three models (CoupModel,
GOTILWA+and GO+) used a time step of 1 h. BALANCE
operated at a time step of 10 days, and three models used
atimestepofamonth(Ta ble 3). Comparing the time step
of the whole modelling system with the time step of the C
allocation module, we found that 17 models used the same time
steps at both modelling levels, while in 13 models the allocation
Figure 8. Data sources used to test the carbon allocation submodules
in 24 examined models (for some models more sources of data were
used). LAI, leaf area index; DBH, diameter at breast height.
module operated at a larger time step than the whole modelling
system, and only in 1 model it was the other way round
(Figure 8).
Models with an annual time scale (used in 29% of models)
do not explicitly handle seasonal changes in C allocation due to
intra-annual variations of phenology and environmental condi-
tions, which can lead to poorly simulated uxes also at an inter-
annual scale (Vermeulen et al. 2015). In addition, most models
(87%) currently do not include seasonal changes in C allocation,
although the majority consider on/o of leaves for deciduous
tree species. Those models that do include seasonality suer
from our general gaps of understanding of C allocation, also
related to the role of C allocation to NSC.
Evidence to prove the gap Formorethanacentury,growth
and biomass production have been the processes of the primary
interest of foresters, while modellers have only considered
growth as a result of C acquisition and allocation since the
1970s, and in particular the allocation component has not yet
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Forest carbon allocation modelling under climate change 13
been thoroughly understood from physiological principles. This
may be the reason why more than one-third of the models in
this study use a so-called ‘top-down’ approach when simulating
C allocation in ecosystems. Models operating at coarser time
scales either are based on empirical relationships or use an
‘average day’ approximation (Hastings and Gross 2012). Such
an approach is suitable for modelling stable systems, where slow
processes at a lower temporal resolution regulate processes at
higher scales (Pretzsch 2009).
Changing environmental conditions cause system instability
(Scheer et al. 2001), due to which signals from faster pro-
cesses varying at higher temporal scales may become dom-
inant and force slow processes to change (Robinson and Ek
2000,Pretzsch 2009). Models working at an annual temporal
resolution often fail to capture these changes caused by novel
environmental conditions (Hastings and Gross 2012 Lasch-Born
et al. 2019). Finer temporal resolution enables us to examine
the impact of the particular change on the analysed system
(Pretzsch et al. 2015). As has already been shown above, C
allocation depends on the instantaneous values of the environ-
mental variables and their combinations (Da Silva et al. 2011).
Hence, mechanistic models operating at shorter time scales are,
in principle, able to provide more robust extrapolation of system
behaviour under climate change (Hastings and Gross 2012).
They usually include the impact of atmospheric and hydrological
conditions, which are most frequently readily available at a daily
resolution (Gea-Izquierdo et al. 2015). Models with seasonality
often assume that the growth of a certain component is com-
pleted when its potential demand has been satised (Running
and Gower 1991,Drouet and Pagès 2007,Gayler et al. 2007,
Schippers et al. 2015), and if anything is left over, that is
allocated to NSC and can be used for growth in consecutive
years (i.e., ‘passive’ storage; Kozlowski 1992). However, this
approach is sensitive to how the demand is determined and
assumes that NSC is a passive pool, although several recent
studies have demonstrated that in many cases the accumulation
of NSC competes actively with growth (McDowell 2011,Sala
et al. 2012;Saell et al. 2014). Unfortunately, we still do
not understand the interactions between the timing of growth,
predetermined ‘growth potential’ and the environment, in order
to solve these questions strictly on a physiological basis.
Lack of data for calibration and validation of carbon
allocation models
Identication of the gap Arguably, the biggest challenge for
modelling C allocation in forest ecosystems is data acquisition
and availability. Direct measurements for the allocation of C
to various tree compartments are typically resource-intensive
and hard to acquire. To overcome this issue, modelling studies
rely on indirect measurements of C allocation with the help of
allometric relationships (e.g., Wolf et al. 2011). Despite data
scarcity regarding the allocation of C in forest ecosystems, 24
out of 31 models (77%) reported in our questionnaire that their
allocation modules were tested against some data. The data
source used to parametrize allocation modules, however, was
often not well suited to describe the underlying processes and
C pools (Figure 8).
Allometric studies are dominant sources of C allocation data,
especially for the stem and root pools (Figure 8). Other direct
measurements of the allocation mechanism, e.g., the samples
of root cores for dening ne root biomass, were reported
in 2 studies out of the 24 models, indicating the need for
data sources that provide a better description of below ground
biomass. The accurate evaluation of the ne root compartment
is critical, especially when considering the functional balance
between leaves and ne roots. Moreover, only a few studies
reported that the derivation of allometric relationships between
tree compartments was carried out at the same sites used for
calibrating and validating the C allocation models (biomass on
site), whereas for the majority of studies the sources of the
allometric relationships were unclear.
The use of allometric relationships based on tree height
and diameter at breast height for modelling allocation into
nonstructural C, reproductive structures and foliage biomass,
as displayed in our results (Figure 8), may not be particularly
appropriate. Traditional forest inventory collecting information
on tree height and diameter is usually carried out in 1- to 5-
year long intervals, and thus the data are unable to capture
the short-term dynamics of the pools. For such purposes, data
sources with a ner temporal scale, such as from experiments
using dendrometers and microcores, are required.
Evidence to prove the gap The data constraints for modelling
C allocation have been widely recognized in the literature (e.g.,
Litton et al. 2007,Franklin et al. 2012,de Kauwe et al. 2014).
While the allocation of aboveground C is fairly well understood
and evaluated with allometric relationships, from which data are
readily available, the dynamics of internal C allocation and the
representation of belowground biomass patterns still demand
investigation, as such uxes require more detailed experiments
and resource-intensive methods (Litton and Giardina 2008,
Warren et al. 2011,Mildner et al. 2014). Similarly, as evidenced
in our results, modelling the dynamics of NSC in reserve
pools remains a major challenge. Traditionally, the evaluation of
nonstructural C has been carried out through the analysis of NSC
concentration in plant tissues. However, the accurate evaluation
of NSC in plant tissues is a dicult task and the uncertainty
related to such quantications may be substantial (Hartmann
and Trumbore 2016,Collalti et al. 2019b). The same caveat is
highlighted by Fatichi and Leuzinger (2013), recognizing the
inaccuracy of C pools and ux data as a major constraint for
selecting suitable C allocation schemes and suggesting that eld
data collection and laboratory experiments with higher precision
are key for improving C allocation modelling.
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The inconsistency between datasets for evaluating C allo-
cation patterns has also been acknowledged as an important
limitation of C allocation modelling, and the harmonization of
data from various sources, such as eddy covariance and forest
growth data, is key for a comprehensive understanding of C
allocation processes (Guillemot et al. 2015). Comparison of
eddy covariance and biometric measurements data is chal-
lenging (Campioli et al. 2016,Ani´c et al. 2018), due to the
fact that the eddy covariance method is primarily driven by
canopy photosynthesis and it reects current accumulation of
atmospheric C, while biometric data represent biomass growth
that uses carbohydrates from current assimilation as well as
previously stored NSC (Gough et al. 2008). Linking these
two datasets seems to be a promising approach for tackling
the question of whole-ecosystem NSC dynamics (Gough et al.
2009). Such a link might provide valuable information on the
responses of allocation patterns to environmental drivers and
improve model performance.
Approaches and examples to overcome the gaps in carbon
allocation modelling
The above-discussed gaps in C allocation modelling can be
solved by (i) changing and/or modifying the applied modelling
approaches, (ii) integrating new components into models and
(iii) direct empirical studies of C allocation. The choice of
the C allocation principle/type (Table 2) predetermines the
magnitude of C sequestration (e.g., Montané et al. 2017),
the sensitivity to possible environmental changes (Figure 1)
and model time resolution. Under climate change conditions,
more complex modelling approaches would outperform simpler
approaches (Ta ble 2), since their intrinsic structure allows them
to adjust in response to external impacts (Figure 1). Empirical
approaches as well as a general pipe model theory assume
that partitioning is in a steady state, thus they usually lack
responses to environmental changes (Bugmann 1994,Franklin
et al. 2012) and can be used only for a limited range of
conditions (Lacointe 2000). However, in some applications of
the pipe model theory, C allocation is responsive to environ-
mental conditions, albeit just those caused by competition/stand
density (Valentine and Mäkelä 2005,Mäkelä et al. 2016).
Source–sink approaches (e.g., BALANCE, BASFOR and Lan-
scapeDNDC) calculate C allocation from the actual biomass of a
specic compartment. Since the compartment size is inuenced
by senescence (included in e.g., CASTANEA, 3D-CMCC FEM
and GOTILWA), all environmental conditions that inuence this
process also aect allocation.
In the models that rely on functional balance principles,
availability of soil nutrients, primarily nitrogen (e.g., BALANCE,
BASFOR, Heterofor and iLand), can be used as a main driver for
distributing C into tree compartments. The impact of drought
can be simulated using an optimal partitioning theory since C
allocation is dynamic with regard to the limiting source, e.g., in
water limiting conditions more C is allocated to roots (Ostle et al.
2009,Pezzatti 2011). Farrior et al. (2013,2015) applied an
evolutionarily stable strategy to simulate the inuence of water
limitation on the C allocation of individual trees in a closed-
canopy equilibrium forest. The most theoretically comprehensive
approach from an evolutionary perspective is modelling on the
base of adaptive dynamics (Franklin et al. 2012), which has
however not been applied in any of the models studied here
(Table 2).
Another approach on how to include direct environmental
eects on C allocation in models is to modify allocation coef-
cients with regard to simulated resources, most commonly
water (ANAFORE) and light (3D-CMCC FEM) or nitrogen (Xia
et al. 2017) following, e.g., the work by Friedlingstein et al.
(1999) or using dose–response curves for the responses of
main plant fractions (i.e., leaf, stem and root) to environmental
factors (Poorter et al. 2011). Drought disturbance eects on
allocation are incorporated in models via altered respiration
needs of each organ, altered order of preference for allocation,
changed allocation ratios and/or applying the pipe model theory
(Grote and Pretzsch 2002,Lasch et al. 2005,Van Oijen et al.
2005,Deckmyn et al. 2008,Rötzer et al. 2010,Jansson
2012). A model that includes a C allocation modier, which
responds to light, water availability or competition (e.g., 3D-
CMCC FEM, ORCHIDEE-CAN) and is able to simulate particular
disturbances, accounts for the impact of tree mortality triggered
by windstorms, insect outbreaks or re (e.g., iLand). Recently,
frameworks on how to model insect and pathogen damage
to aect the allocation, especially NSC, have been published
(Dietze and Matthes 2014). An active role of NSC in C allocation
(Martinez-Vilalta 2014) is considered in several models (e.g.,
3D-CMCC FEM), which prioritize C allocation to reserves over
biomass growth and use the reserve pool, e.g., for the produc-
tion of leaves and ne roots at the beginning of the growing
Including seasonality in models of C allocation has been con-
sidered as a means of making the models capable of reecting
intra-annual environmental changes (Pretzsch 2009). At the
sub-annual scale, growth and hence C allocation to dierent
tissues varies following a seasonal pattern where the growth
of dierent organs adheres to a species-specic sequence.
For example, in oak species, cambial growth starts before the
growth of foliage and primary wood, whereas in many conifers,
it is the other way round (Michelot et al. 2012,Griˇ
car et
al. 2017,Schiestl-Aalto and Mäkelä 2017). The treatment of
allocation can only be genuinely regarded as sub-annual if this
seasonal rhythm is considered. The response of C allocation
to various environmental factors incorporated using principles
and/or types sensitive to environmental conditions (see Table 2)
may be interpreted as a representation of seasonality in models.
For, example a source–sink type of modelling C allocation
implies that sink demand of all plant compartments changes
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Forest carbon allocation modelling under climate change 15
dynamically throughout phenological stages (e.g., LANDSCAPE
Another option is to dene seasons a priori using, e.g., a growing
degree day threshold, which controls fruit formation (e.g., CLM-
Palm and Biome-BGCMuSo). However, if such an approach is
applied with allometric allocation, it should be regarded as
a technical solution rather than trying to realistically mimic
intra-annual C allocation patterns (‘average-day approximation’;
Hastings and Gross 2012), since allometric relationships cannot
be determined at a shorter time resolution than 1 year by any
reasonable accuracy. During stand development, C allocation
can be modied by implementing size-related allocation ratios,
often based on the notion that dierent compartments try to
maintain a particular balance (e.g., 3PG, ForGEM, CoupModel
To overcome the gap in considering reproduction, algorithms
have been ‘borrowed’ from crop simulators (e.g., Pavlick et al.
2013). The onset and/or relative magnitude of allocation to
fruits have been related to temperature, growing degree days,
heat thresholds or day length (Oleson et al. 2013), and addi-
tional impacts of available water (Berg et al. 2010) and nitrogen
(Hidy et al. 2016) have been considered. These models work
for regularly fruiting trees or if only average allocation values
throughout longer than annual time scales are required. Some
examples also exist for introducing labile or NSC pools that
distribute over other compartments in highly process-oriented
forest growth models (Grote 1998,Deckmyn et al. 2008,
Collalti et al. 2016). In resource budget models (Isagi et al.
1997,Crone and Rapp 2014), fruiting uctuates from one year
to the next when the tree produces seeds that subsequently
deplete resource reserves. Pollination is considered as a limiting
factor that may lead to fruiting failure and resource savings,
which may be invested in owering the following year (Satake
and Iwasa 2000,Venner et al. 2016). In some models, owering
is inhibited in response to weather conditions of the same year
(Abe et al. 2016).
Regarding other C pools considered for allocation, some
specic approaches have been suggested that might be further
elaborated or simplied. Models considering mycorrhiza have
been reviewed by Deckmyn et al. (2014) and He et al. (2016),
demonstrating the importance of considering plant–fungi feed-
back relations. An explicit dependence on root growth and soil
nitrogen availability has been presented by Ruotsalainen et al.
(2002) and Meyer et al. (2009,2012).Moore et al. (2015)
also included a dynamic switch of the role from plant symbiont to
decomposer. Damage repair mechanisms have been considered
in models describing the impact of air pollution (Van Oijen et
al. 2005,Deckmyn et al. 2007), requiring a dynamic pool of C
that might be linked to a general pool of free available C.
Data collection should aim for methods of direct quan-
tication of C allocation enabling tracing of the path of C
from the assimilation to formation of new structures. Sap ow
measurements and labelling C isotopes appear to be promising
methodologies for a better understanding of tree C dynamics
(e.g., Kuptz et al. 2011,Klein et al. 2016a;McCarroll et al.
2017). Recent developments in tools to trace C isotopes, e.g.,
isotope ratio infrared spectroscopy, has contributed to a sub-
stantial increase in accuracy for the evaluation of C in ephemeral
pools and transport rates, providing an important step towards
a better understanding of C allocation processes (Epron et al.
2012a). For the evaluation of NSC, bomb radiocarbon mea-
surements have been proposed (Carbone et al. 2013), as
this method allows deriving the average time since the NSC
was initially assimilated from the atmosphere (Hartmann and
Trumbore 2016). When the use of allometric relationships is
necessary, applying site and species-specic biomass measure-
ments are warranted for evaluating and calibrating allocation
models. Moreover, combining multiple data sources may over-
come limitations on the temporal resolution required for the
growth patterns of each C pool (Gea-Izquierdo et al. 2015).
Luyssaert et al. (2007) collected results from multiple exper-
iments describing C budget variables, ecosystem traits, man-
agement history and environmental variables, such as climate
and soil characteristics. In a similar fashion, Bond-Lamberty and
Thomson (2010) compiled a global dataset with soil respiration
experiments, providing a basis for a better understanding of soil
respiration dynamics, which usually require resource intensive
experiments. Eorts for harmonizing and standardizing the
datasets will be crucial for a better description of C allocation
Discussion and conclusions
Since the rst study about C allocation (Hartig 1878), this
plant function has gained recognition both in experimental as
well as in modelling studies, especially over the past 20 years
(seeFigureS4available as Supplementary Data at Tree Phys-
iology Online). This increasing attention results from ongoing
climate change aecting the functioning of ecosystems both
directly and indirectly (Charru et al. 2017). Based on our
review and synthesis of experimental knowledge and modelling
approaches, we suggest that the major challenge is to overcome
key limitations in understanding of C allocation fundamentals,
which can subsequently enhance its description in models, as
already outlined by others (de Kauwe et al. 2014,Garcia et al.
Challenges to ll the knowledge gaps in carbon allocation
Despite considerable progress, a comprehensive picture of C
allocation in trees is still missing. Improved empirical knowl-
edge about C allocation in trees is of particular importance
under changing environmental conditions because a realistic
representation of processes in models may enhance their appli-
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16 Merganiˇ
cová et al.
cability in diverse situations (Seidl et al. 2011). There are
several methodological issues to be solved, particularly those
focusing on measuring carbohydrates in plant tissues and
the accurate determination of their absolute concentrations
(Quentin et al. 2015) and explaining the role of NSC in
plant tissues (Carbone et al. 2013,Collalti et al. 2019b). The
increased knowledge on the NSC accumulation and mobilization
for metabolic activities would enhance not only our understand-
ing of tree recovery and resilience adaptation mechanisms, but
also the estimates of both aboveground and belowground NPP
provided by models (Langley et al. 2002). The other areas of
as yet limited scientic understanding in this eld, which are
likely to become more pressing issues with ongoing climate
change, are the impact of disturbances on C allocation in trees,
the production of seeds and fruit by trees and the C use
by tree symbionts and/or for defense or repair. For a better
understanding and mechanistic description of C allocation in
models, more empirical studies dealing with these issues under
changing environmental conditions are required (Guillemot et al.
2015,Sevanto and Dickman 2015).
Carbon allocation modelling concepts in the view of climate
Our analysis revealed that simpler empirical approaches of C
allocation modelling prevail (Table 2), although they are not
always able to capture the impact of environmental changes on
C allocation. In general, dynamic C allocation schemes respon-
sive to limiting factors aboveground and belowground should
be favoured when modelling C allocation, because they can at
least principally respond to new combinations of environmental
conditions expected under climate change (Campioli et al.
2008). The most robust approach for modelling C allocation
is a top-down evolutionary-based principle (Drewniak and Gon-
zalez-Meler 2017). Bottom-up approaches are apparently not
able to capture complex allocation patterns controlled by the
environment (Chen et al. 2013), although allocation schemes
based on functional relationships and optimization theory are
more robust than those based on xed allocation or resource
limitation principles (de Kauwe et al. 2014).
Challenges for carbon allocation modelling under climate
In the future, ensemble tests considering a number of modelling
concepts on dierent spatial scales should be performed to
nd the principle that best meets observed responses as has
been suggested by Cariboni et al. (2007) and Pianosi et al.
(2016). Examples of such exercises can be found in Fischlin
et al. (1995),Alvenäs and Jansson (1997),White et al. (2000),
Pappas et al. (2013) and Montané et al. (2017). Such studies
may clarify the eect of combining several principles/types of
C allocation modelling, the approach that has been applied in
the majority of investigated models (Figure 3). The results of
ensemble simulations may also specify which parts of the model
need improvements.
While there are several approaches for how to deal with
the lack of sensitivity of C allocation models to environmental
conditions either by using more sophisticated modelling prin-
ciples or by implementing allocation modiers (see Chapter
Approaches and examples to overcome the gaps in carbon
allocation modelling for more details), the impact of distur-
bances on C allocation cannot be simulated if the model
does not account for them. Hence, the key step is to actually
include disturbances and their impacts on forests in models
(Seidl et al. 2011). Subsequently, the disturbances can be
linked to the processes governing C allocation in models, while
experimental studies should be used as a platform for model
Implementing new features in the model to improve simulated
C allocation processes should be performed with regard to the
research question and study location. Including specic nutrient
dynamics in models may be important for future projections
of the C cycle in regions where the particular nutrient is
limited (Zaehle 2013). In nitrogen-limited forests, implementing
nitrogen dynamics and/or C allocation to symbionts signicantly
enhance the predictive power of models (de Kauwe et al. 2014,
Wårlind et al. 2014,He et al. 2018). In the future, other nutrients
may constrain forest productivity. The modelling approach of
phosphorus cycling in ecosystems implemented in ANAFORE
may serve as an example how to account for the eects of its
deciency on C allocation (Bortier et al. 2018).
From the viewpoint of long-term plant strategy, successful
reproduction is a major evolutionary goal of C allocation (Agren
and Wikstrom 1993). Hence, omitting to allocate C into repro-
ductive organs, particularly during masting years, may be a
cause of low prediction accuracy of forest models (Vacchiano
et al. 2018). If variable allocation across years is aimed for, then
the NSC dynamics need to be included in the allocation pattern,
and the interaction of inter- and intra-annual C allocation must be
considered. The size of the NSC pool might be used to dene
feedback to photosynthesis, thus decreasing the atmospheric
CO2eect. The question of time steps is crucial when dening
the role of C in stress responses and tree mortality, where
the availabilty of reserves may be the decisive determinant of
survival (Dietze et al. 2014). By uncoupling photosynthesis and
growth under stress conditions, e.g., drought, a more realistic
representation of the carry-over eect of stress periods on
growth can be obtained due to buering power of the C
storage/reserve pool. This pool needs to be dynamic and may
change size based on short-term stress occurrence (induced
defences) or long-term stress intensity (acclimation) (Hartmann
and Trumbore 2016).
We conclude that to obtain reliable output from models under
climate change, modellers should consider: (i) using more
sensitive to changing environmental conditions C allocation
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