Plant, Cell and Environment (2013)
doi: 10.1111/pce.12123
Physiological mechanisms in plant growth models: do we
need a supra-cellular systems biology approach?
HENDRIK POORTER1, NIELS P. R. ANTEN2 & LEO F. M. MARCELIS3,4
1
IBG-2 Plant Sciences, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany, 2Centre for Crop Systems Analysis,
Wageningen University, P.O. Box 430, 6700 AK Wageningen, The Netherlands, 3Wageningen UR Greenhouse Horticulture, P.O.
Box 644, 6700 AP Wageningen, The Netherlands and 4Horticultural Supply Chains, Wageningen University, P.O. Box 630, 6700
AP Wageningen, The Netherlands
ABSTRACT
In the first part of this paper, we review the extent to which
various types of plant growth models incorporate ecophysiological mechanisms. Many growth models have a central
role for the process of photosynthesis; and often implicitly
assume C-gain to be the rate-limiting step for biomass accumulation. We subsequently explore the extent to which this
assumption actually holds and under what condition constraints on growth due to a limited sink strength are likely to
occur. By using generalized dose–response curves for growth
with respect to light and CO2, models can be tested against
a benchmark for their overall performance. In the final part,
a call for a systems approach at the supra-cellular level is
made. This will enable a better understanding of feedbacks
and trade-offs acting on plant growth and its component
processes. Mechanistic growth models form an indispensable element of such an approach and will, in the end,
provide the link with the (sub-)cellular approaches that are
yet developing. Improved insight will be gained if model
output for the various physiological processes and morphological variables (‘virtual profiling’) is compared with measured correlation networks among these processes and
variables. Two examples of these correlation networks are
presented.
Key-words: dose–response curves; evolutionary stable strategy; photosynthesis; plant growth; simulation; source–sink
interaction.
INTRODUCTION
Plant growth is a process that is highly relevant in a range of
contexts. From an evolutionary viewpoint, the ability of an
individual to grow and achieve a certain size in a given environment is one of the prerequisites to reproduce successfully
and achieve an adequate fitness. In an ecological context,
growth and the physiological processes required for that
have a profound impact on the various biogeochemical cycles
in basically all ecosystems of the world, and thereby also on
system earth as a whole. Finally, from a human perspective,
plant growth is of fundamental importance as it forms the
basis of all agricultural productivity. It is therefore not surprising that the processes underlying plant growth are the
Correspondence: H. Poorter. e-mail: [email protected]
© 2013 John Wiley & Sons Ltd
focus of significant research efforts. There is a large research
community investigating the biophysical and biochemical
limitations on photosynthesis and the way(s) by which possible inefficiencies in light and/or dark reactions could be
alleviated (Zhu, Long & Ort 2010). Others study the way
respiration could be reduced or, at least, could be made less
‘wasteful’ in order to have more photosynthates available for
growth (Affourtit et al. 1999).Yet others work on the efficient
uptake or use of nutrients (Lynch 2011) and water (Blum
2009) or study the molecular mechanisms that determine cell
division (De Veylder, Beeckman & Inzé 2007). The ultimate
goal is often to change or affect these processes in a way that
will positively shape the growth and productivity of plants.
An alternative approach with a top-down direction is followed by geneticists. They take genotypes with contrasting
growth rates or yield and try to link this variation directly to
specific genomic regions, and ultimately genes by means of
quantitative trait loci (QTL) approaches or genome-wide
association mapping. As can be expected from quantitative
traits, such approaches generally show that many loci are
involved, of which few or none exert strong dominance
(Poorter et al. 2005; Bouteillé et al. 2012). In a recent genomewide association study with rice, for example, the total
explained phenotypic variance for a wide variety of growthrelated traits ranged from 5 to 50%, with up to 16 loci
involved per trait (Zhao et al. 2011).
Understanding plant growth becomes even more challenging because of the strong effect of the environment, which
may modulate the various components of the growth processes in different, sometimes contrasting, ways. For example,
plants grown at high light intensities generally have higher
rates of photosynthesis and thereby a higher rate of biomass
production per unit leaf area than low-light grown plants.
However, plants grown at high light at the same time have a
reduced amount of leaf area per unit plant mass. At light
levels higher than 25 mol m-2 day-1, this may lead to a situation where, for quite some species, the growth rate is not
stimulated anymore although the rate of photosynthesis per
unit leaf area is still increasing (Poorter & Van der Werf 1998;
see also section 5). Physiological interactions may become
even more complex when two or more environmental factors
interact.
Studying the genetic and cellular regulation of the various
physiological processes that take place within the plant will
undoubtedly improve our understanding of plant functioning. However, the most relevant issue in the end is how these
1
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H. Poorter et al.
different processes interact with each other and with the
environment, and what the implications are for plant growth
as a whole. It has long been recognized that modelling could
be very helpful here (De Wit & Brouwer 1968). Plant growth
models as a simplification of complex systems have tremendous value as a way to structure and integrate available
knowledge, test hypotheses and come up with quantitative
estimates of total plant mass, above-ground mass and/or
yield.
Plant growth models come in a wide variety, ranging from
simple formulas that mathematically capture plant size over
time with just two or three parameters (Blackman 1919) up
to highly complicated simulation models that evaluate global
change effects on the performance of vegetation worldwide
(Haxeltine & Prentice 1996). They apply an array of conceptual approaches and incorporate a range of more-or-less
detailed (eco-)physiological processes, mostly centred
around the carbon economy of the plant, as this provides the
backbone for all growth. The main focus of the present paper
will be on the physiology and modelling of whole-plant
growth for individual plants grown in the absence of competitors. However, we will also discuss some models where
plants do grow in stands, as the guiding principles are overlapping to a large extent. Firstly, we pay attention to the type
and amount of mechanism incorporated in the various
groups of plant growth models to date, discussing the strong
and weak points of each of them. Secondly, we focus on the
conditions where C may not be the limiting factor for growth
and the extent to which so called source–sink feedbacks are
incorporated in the mechanistic models. The final part of the
paper discusses the need for a supra-cellular systems
approach to growth. It shows, with two extensive datasets,
how possible trade-offs within the plant could be elucidated
and discusses how mechanistic models could be of help here
to understand these trade-offs within the context of wholeplant functioning.
1. MECHANISMS IN BOTTOM-UP MODELS
Mechanistic models of plant growth – also called processbased models – are models where some form of physiological
mechanism is employed. Generally, processes at one integration level are used to simulate plant performance or another
rate or state variable at a higher integration level. The extent
of mechanistic detail of these so-called bottom-up models
varies strongly.
A. Empirical models
The simplest models of plant mass or productivity are
empirical models, also denoted as ‘statistical’ models. Empirical models are frequently used in such different fields as
agriculture, horticulture and forestry to describe and/or forecast the productivity in monocultures of economically interesting plant species. In terms of mechanism, they can be
considered as a ‘null-model’, as they do not contain any
physiological processes at all. Rather, they can be seen as
dose–response curves (DRCs; see Table 1 for an explanation
of all abbreviations used), which relate biomass or yield
observations in a given geographic location or climatic zone
to one climatic or edaphic variable of interest. They can also
be extended to include several independent factors. Simple
or multiple regression techniques then provide an equation
that can be used as a predictor for biomass (Aylott et al.
2008; Wullschleger et al. 2010). In plant biology, the basic
concepts of DRCs have been placed in a mathematical
framework by Mitscherlich (1909).
Empirical models are extremely simple yet effective in
their ability to predict the productivity of natural and crop
stands with one notable exception: they perform badly if they
are to predict yield outside the boundaries where data have
been collected (Dourado-Neto et al. 1998). One example
where extrapolation may lead to erroneous estimates is the
case of temperature. Generally crops like rice and maize are
relatively cold-sensitive and grow and produce better at
warmer temperatures. However, this may not be extrapolated to too high night temperatures, as quite some species
become sterile under those conditions, with yield plummeting (Cheng et al. 2009). DRCs of biomass will be further
discussed in section 5.
B. Models that apply the radiation use efficiency
(RUE) concept
A popular group of models, which include some degree of
mechanistic detail, make use of the ‘RUE’ concept, which is
also referred to as ‘light use efficiency’ (LUE). These models
take light availability as an external input and calculate light
interception by the vegetation, for example based on the leaf
area index (LAI). Rather than precisely modelling photosynthesis and respiration, they then use an empirical conversion
factor to describe the relation between intercepted light
and the biomass increase of the plant or vegetation
(Arkebauer et al. 1994). The growth rate is calculated with a
simple ordinary differential equation:
dM dt = LUE ⋅ (1 − exp− k⋅LAI ) ⋅ I
(1)
where dm / dt is the growth rate of crop or stand, k is the light
extinction coefficient and I is the photosynthetic active radiation (PAR) incident on the crop. Applications can be found
in, for example, Spitters (1990) and Jones et al. (2003). RUE
can be adjusted downward with an empirical formula if
drought, nitrogen shortage or temperature stress limit plant
growth (Yuan et al. 2007; Kergoat et al. 2008). The advantage
of this approach is that the time step in dynamic models can
be large (days, seasons), which considerably simplifies the
simulations. Drawback is that the physiology of the plant
essentially remains a black box and no mechanistic connection to, for example, the water or nutrient economy of the
plant can be made.
C. Photosynthesis – respiration models
The next level of complexity is formed by models that explicitly simulate photosynthesis and respiration. These models
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
Physiological mechanisms in plant growth models
3
Table 1. Abbreviations used in this paper, along with a definition and the units applied here
Abbreviation
Variable
Definition
Units
Aa
Rate of photosynthesis
Net CO2 uptake / leaf area / time
Abs
Am
Ams
Absorptance
Rate of photosynthesis
Rate of photosynthesis at light saturation
CP
CY
C#T
CST
CUE
[C]
[Chl]
DMC
DPI
DRC
Carbon concentration of a plant
Carbon concentration of constituent Y
Cell number
Cell size
Carbon use efficiency
Carbon concentration per leaf mass
Chlorophyll concentration
Dry matter content
Daily photosynthetic photon irradiance
Dose-response curve
Ea
gs
HI
I
Rate of transpiration
Stomatal conductance
Harvest index
Incident light
Fraction of I absorbed by the leaf
Net CO2 uptake / leaf mass / time
Net CO2 uptake / leaf mass / time, measured at
saturating light
Carbon / total plant dry mass
Carbon concentration of constituent class Y
Cell number of tissue T per unit leaf area
Volume of the cells in tissue T
Fraction of daily fixed C which is used for growth
Carbon / leaf dry mass
Chlorophyll / leaf dry mass
Total plant dry mass / total plant fresh mass
Flux of quanta in the 400–700 nm range / area / time
Relationship between a plant variable and a range of
a given environmental factor
Transpiration / leaf area / time
mol m-2 s-1
or
mol m-2 day-1
mol mol-1
nmol g-1 s-1
nmol g-1 s-1
J
Electron transport capacity
k
LAI
Extinction coefficient
Leaf area index
LAR
LD
LMA
LMF
LNC
LVA
MS
Mt
MINp
NIR
[NO3]
pi / pa
PNC
PNUE
QY
Rm
RGR
RUE
RMF
[Rub]
SLA
SMF
TDM
ULR
Vc
Leaf area ratio
Leaf density
Leaf mass per area
Leaf mass fraction
Leaf nitrogen concentration
Leaf volume per area
Seed mass
Total plant mass
Mineral concentration of a plant
Nitrogen intake rate
Nitrate concentration of the leaves
Intercellular CO2 partial pressure relative to
outside
Plant nitrogen concentration
Photosynthetic nitrogen use efficiency
Concentration of constituent Y
Respiration rate
Relative growth rate
Radiation use efficiency
Root mass fraction
Rubisco concentration
Specific leaf area
Stem mass fraction
Total dry mass
Unit leaf rate
Rubisco activity
VAT
Volume per area
Reproductive dry mass / total plant dry mass
Photosynthetic irradiance (400–700 nm) / ground area
/ time
Photosynthetic electron transport capacity at light
saturation / leaf area / time
Extinction coefficient for light in a stand
total amount of leaf area in crop or vegetation /
ground area
Leaf area / total plant dry mass
Leaf dry mass / leaf volume
Leaf dry mass / leaf area
Leaf dry mass / total plant dry mass
Leaf Nitrogen / leaf area
Leaf volume / leaf area (equivalent to leaf thickness)
Mass of the seed
Total plant mass at time t
Mineral mass / total plant dry mass
Nitrogen uptake / root dry mass / time
Nitrate / leaf dry mass
Nitrogen / total plant dry mass
Photosynthesis / leaf organic nitrogen / time
mass of constituent Y / total plant dry mass
Respiration / leaf dry mass / time
Increase in plant mass / total plant dry mass / time
dry matter increase / amount of light intercepted
Root dry mass / total plant dry mass
Rubisco / leaf dry mass
Leaf area / leaf dry mass
Stem dry mass / total plant dry mass
Dry mass of leaves, stems plus roots
Increase in total plant dry mass / leaf area / time
Number of carboxylations at light saturation / leaf
area / time
Volume of tissue T per unit leaf area (= tissue
thickness)
mmol C g-1
mmol C g-1
m-2
ml
mol mol-1
mmol C g-1
g g-1
mol m-2 day-1
mmol m-2 s-1
mmol m-2 s-1
g g-1
mol m-2 day-1 or mmol m-2 s-1
mmol e- m-2 s-1
–
m2 m-2
m2 kg-1
g ml-1
g m-2
g g-1
mol N m-2
ml m-2 (= mm)
g
g
g g-1
mmol N g-1 day-1
mg g-1
Pa Pa-1
mmol N g-1
mol CO2 mol-1 N s-1
g g-1
nmol g-1 s-1
mg g-1 day-1
g (mol quanta)-1
g g-1
g g-1
m2 kg-1
g g-1
g
g m-2 day-1
mmol m-2 s-1
ml m-2 (= mm)
Note that mass fractions also appear in the literature as weight ratios (e.g. LWR), mass ratios (LMR) or weight fractions (LWF).
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
4 H. Poorter et al.
commonly use the Farquhar-Von Caemmerer-Berry equations as a basis for leaf photosynthesis (Lloyd & Farquhar
1996; Mäkelä et al. 2000). Employing the dependencies of
photosynthesis for light, CO2 and temperature, as well as the
amount of leaf area present for a given plant or canopy, such
models calculate the total carbon fixation of a plant or vegetation over a given time step (Goudriaan & Van Laar 1994;
Le Roux et al. 2001; Jones et al. 2003). Subsequently sugars
required for maintenance respiration are subtracted from the
total amount of produced photosynthates, and the remaining
sugars are then distributed with some rule over the various
vegetative and generative compartments of the plant. In a
final step, these sugars are converted to biomass, after which
the whole calculation repeats again for the next iteration.The
mechanism can be more or less refined by taking into account
the amount of N in the leaves available for the photosynthetic machinery (Niinemets & Tenhunen 1997; Müller,
Wernecke & Diepenbrock 2005), the extent to which a plant
canopy is approached as one big leaf or as different leaf
layers (Goudriaan & Van Laar 1994; De Pury & Farquhar,
1997) and any dynamic restriction due to limited water or
nutrient availability or because of temperature constraints
(Jones et al. 2003; Hammer et al. 2009).
The physiological limitations of leaf photosynthesis are
reasonably well understood and relatively easily incorporated. Other aspects, such as the allocation of C over the
various plant compartments are less well apprehended. Consequently, C-allocation is one of the weaker features of plant
models (Marcelis & Heuvelink 2007). A range of models
therefore simply simulate allocation using empirical look-up
tables in the simulation programmes (Mäkelä et al. 2000).
Further challenges arise if mechanistic models need to deal
with perennial systems such as forest plantations. Dynamic
simulations now have to take into account conversion from
sapwood to heartwood, the turnover of the various organs
and decomposition of plant material and associated release
of nutrients (Lo et al. 2011). The ultimate challenge in modelling is probably the realm of ecosystem and global biome
functioning, where ecophysiological processes at the cellular
level have to be combined with soil and climate properties
over a time frame of centuries and for a wider range of plant
functional types that may compete with each other, while
allowing for acclimation of plants to changing environmental
conditions (Medlyn, Duursma & Zeppel 2011; Van Bodegom
et al. 2012).
D. Functional–structural plant models (FSPMs)
Most of the older mechanistic crop or vegetation models
consider the structure of the vegetation in terms of one
descriptor, for which the LAI is the most frequently used
variable. Consequently, they do not include detail on plant
architectural traits, which actually may have important
impacts on the resource acquisition of plants (Pearcy & Yang
1996; Rubio et al. 2001). A development of the last decade
are the FSPMs (Pearcy & Yang 1996; Vos, Marcelis & Evers
2007; DeJong et al. 2011) that combine the C-based
approaches described earlier with a more precise structural
description of how the leaves, stems and roots of individual
plants are positioned in space and what consequence this will
have for the capture of light and nutrients. These models are
now widely used, especially in relatively detailed analyses.
Applications include studies on the physiological regulation
of branching patterns (Evers et al. 2011), the morphological
consequences of neighbour plant detection (de Wit et al.
2012) and the interplay between plant structure and spatial
distribution of diseases (Baccar et al. 2011).
E. Explanatory power of bottom-up models
The mechanistic simulation models of plant growth encapsulate a considerable amount of ecophysiological knowledge
and can be used to predict the growth rate or productivity in
a variety of climatic scenarios. They also form an indispensable help in decision management (Boote, Jones & Pickering
1996). More than empirical models, they are able to predict
growth outside the strict boundaries where conditions for
plant performance have been tested experimentally. The reasoning behind these models is that if we understand the
component processes that underlie growth and study them
over a wider range of environmental factors, we will come
sufficiently close to an accurate prediction of growth when
we combine all these processes. These models clearly have
some kind of limitation as well (Marcelis, Heuvelink &
Goudriaan 1998; Dewar et al. 2009). For example, as much as
empirical models do not include temperature effects on sterility, if this is outside the tested range (section 1A), most
mechanistic models do not include this sterility effect either.
Moreover, uncritical implementation of short-term physiological mechanism in a model that aims to simulate longterm acclimation may in the end lead to model results that do
not properly represent plant performance. For example, quite
some models include a Q10 of two or more for the temperature effect on respiration, which is reasonable for short-term
temperature fluctuations, but is unrealistic over longer time
frames (Atkin & Tjoelker 2003).
How well do mechanistic models perform in the prediction
of crop or timber yield in a given area, and how does that
compare with empirical models? Although an exact tolerance limit is generally not stated, crop modellers often seem
to accept differences between observed and predicted
growth of 10–15% as being reasonably good. A preliminary
survey across a range of papers that explicitly compared
measured growth or yield data with simulated values (Porter,
Jamieson & Wilson 1993; Jamieson et al. 1998; Marcelis &
Gijzen 1998; Jones et al. 2003; Aylott et al. 2008; Palosuo et al.
2011; Rötter et al. 2012) showed that the median value for the
deviation of the simulation from the observed field data was
17%. The ranges were wide, though, with a 10th and 90th
percentile of 3 and 38%, respectively. Even if these values
would have been much lower, this does not necessarily imply
that from a scientific perspective our knowledge about the
mechanisms is sufficiently represented. Wheat crop models
may serve as an example here. They probably rank among
the best designed and validated models for a system, which
is relatively simple because of the annual character of the
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
Physiological mechanisms in plant growth models
plants. Different wheat models, developed by research
groups based on different continents, are generally performing very well at the geographic location they were developed
for. However, comparative test runs show that each of
these models performs less when fed with weather data
characteristic of wheat-growing regions on other continents
(Goudriaan 1996). Apparently, each model still includes a
range of ‘tweaks and adaptations’ that may make them
perform well for the local soil and climate, but render them
less generic as was originally anticipated. Similar blind tests,
where different models forecasted the production of wheat
or barley grown at a range of latitudes in Europe, show pretty
large variation in outcome as well (Palosuo et al. 2011; Rötter
et al. 2012). Our conclusion is that these models clearly function well when it comes to accommodating year-to-year variation in local climate with the purpose to forecast yield, but
that the mechanisms are still too limited to make them really
generic. Care should therefore be exercised when they are
used to investigate global change effects or where other
forms of hypothesis testing are applied.
Another issue is whether mechanistic models outperform
empirical models. When it comes to prediction of growth or
yield, this is not necessarily the case (Alscher, Krug & Liebig
2001).This poses an additional challenge for incorporating an
adequate amount of physiological mechanism into mechanistic models. There is no doubt, however, that mechanistic
models will provide us with physiological insights that we
otherwise would not be able to obtain.
2. BOTTOM-UP APPROACHES WITH
GOAL-SEEKING FEATURES
In a number of cases, bottom-up models are combined with
special algorithms that enable modelling shortcuts in physiological processes that are not well understood or that shed
light on evolutionary questions that go beyond the simulation of plant growth per se.
A. Teleonomic models
Teleonomic models apply for at least part of the simulations’
so-called ‘goal-seeking’ algorithms. That is, they calculate a
range of options or parameter values, which are then evaluated with a specified target in mind. Goal-seeking algorithms
are especially popular where insights into the mechanism are
scanty or simulation becomes too time-consuming and cumbersome (Dewar et al. 2009). A good example at the individual plant level is the regulation of sugar allocation to the
different organs of the plant (Thornley 1995). Rather than
trying to simulate the actual physiological details of the transport process, algorithms are applied that computationally
seek at which partitioning of sugars the plants will grow best.
In ecology, teleonomic algorithms are applied to model, for
example, the N-distribution within a canopy (Field 1983;
Leuning 1995). The nitrogen profile is then not simulated as
the outcome of (re)translocation processes, but rather distributed a priori over the various leaf layers in a way that
maximizes canopy photosynthesis. In both examples, the
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
5
rates of photosynthesis, respiration, etc. are modelled mechanistically in a similar way as in other bottom-up models.
B. Evolutionary algorithms
Another approach is the application of so-called ‘evolutionary algorithms’. In this case, the maximum value for a targeted process of interest in the model is sought by evaluating
in a reiterative way the combination of parameters that gives
the best model performance. Zhu, De Sturler & Long (2007),
for example, used such an approach in a model that incorporated a wide range of components of the photosynthesis
process. Under the usual assumption that the model was right
and correctly parameterized, they could show that the
N-investment in enzymes of the Calvin cycle was suboptimal
and could be improved by increasing the amount of Rubisco,
sedoheptulose-1,7-bisphosphatase (SBP) and fructose-1,6bisphosphate-aldolase (FBP)-aldolase at the expense of
some other proteins. With adequate knowledge, evolutionary
algorithms could in principle also be used to study processes
at a higher integration level, such as growth.
C. Game theory
Another branch of models mimics the evolutionary processes
a step further by involving the response to other plants into
the system. Like functional-structural models (section 1D)
they consider a vegetation stand as an assemblage of individual plants. The difference with most other models discussed here is that they allow the ‘evolution’ of different
strategies in which the individual of interest may unilaterally
alter its morpho-physiological properties or growth patterns
relative to that of neighbouring plants. By doing so, such a
plant may gain additional resources it would not have
acquired if it had not adopted its growth ‘strategy’ by taking
into account the behaviour of neighbouring plants (Anten
2005). A good example is the competition for a unidirectional
resource such as light. When an individual becomes taller
than its neighbours, it can intercept relatively more of the
incoming radiation than its competitors (Weiner 1990).
Therefore, it may pay off for an individual plant to initially
invest more of its resources into height growth, even if this
would be at the expense of stem stability or investment in leaf
biomass (Givnish 1982; Falster & Westoby 2003). In this
manner, a so-called evolutionarily stable strategy (ESS) can
be calculated, which is a strategy such that no alternative
strategy can provide an individual with a higher fitness within
a given population of plants.
Intriguingly, a vegetation stand that has achieved an evolutionary stable situation for height will be taller than a stand
where maximum biomass is achieved (Givnish 1982). This
phenomenon of supra-optimal behaviour with respect to
growth seems more general: game theoretical models have
suggested that plants produce more leaf area (Schieving &
Poorter 1999; Anten 2002), grow more roots (Gersani et al.
2001), have a faster leaf turnover (Boonman et al. 2006;
Hikosaka & Anten 2012) and have more horizontally projected leaves (Hikosaka & Hirose 1997) than would be
6
H. Poorter et al.
optimal with respect to maximum whole stand growth. These
game theoretical models are particularly useful in determining how evolution drives the structure and functioning of
natural vegetation. However, this issue may also be relevant
in an agricultural setting. If plant breeders select the bestperforming plants from a mixture of competing individuals,
they may unwittingly select for traits that favour competitive
ability. If the models mentioned earlier are right, the consequence could be that this comes at a cost of decreased yield.
Breeding against these mechanisms could then favourably
increase productivity (Zhang, Sun & Jiang 1999), although it
could also imply that such plants are less competitive against
weeds.
Seed size
Seed #
Yield
Mt
MS
RGR
An alternative way to analyse growth is a top-down
approach. Starting with the total biomass of the plant, one
can dig down and factorize the underlying parameters and
processes into increasingly more detailed components. This
approach is often applied to analyse experimental data in a
systematic framework based on C-economy principles. Aim
of such an analysis is to examine which of the underlying
processes vary between treatments, genotypes or species and
which ones remain relatively constant.
A. Relative growth rate (RGR)
The most basic expression of growth is the so-called ‘absolute
growth rate’ (AGR), which is the change in size of the plant
per unit of time. If AGR is constant, plant mass will increase
linearly over time.This variable does not well encapsulate the
changes in size of young plants, as they will often increase
biomass in a way that is approximately proportional to the
biomass of the plant already present. The principle of proportional growth is engrained in the concept of ‘relative
growth rate’, as proposed by Blackman (1919). If RGR would
be strictly constant, then plant mass will follow an exponential trajectory over time:
AA
CUE
Germ. rate
LAR
ULR
3. MECHANISTIC TOP-DOWN MODELS
M2 = M1 ⋅ e RGR⋅( t2 − t1 )
HI
CP
SLA
LMF
*
PNUE
LVA
LNC
S (QY . CY)
LD
S VAT
S (CST .C#T)
Figure 1. General scheme with a top-down analysis of total plant
mass (Mt) into component variables. The breakdown analysis is
shown for the growth of the vegetative plant (down) or for the
generative plant (up, shaded). Abbreviations are listed in Table 1.
Green ellipsoids represent rates, red boxes ratios, blue boxes
chemical composition, black boxes finer chemical or anatomical
detail. Note that the factorization indicated by * actually pertains
to the inverse of SLA, that is leaf mass per area.
(2)
where M2 and M1 represent the mass of the plants at time t2
and t1, respectively. Strict exponential growth, however, is not
common either for plants. Not only do they show diel fluctuations in growth, with a positive RGR during the day and
negative growth during the night period, plants also often
decrease RGR during ontogeny, because of increased selfshading or larger structural demands. However, an average
RGR over a certain time period may still serve as an
adequate description of growth, as long as the newly formed
mass is more or less proportional to the plant mass already
present (Causton & Venus 1981).
At some stage during the growth period, the exponential
phase may linearize (Goudriaan & Monteith 1990) as selfshading increases and plants invest more in stems and other
non-leaf structures. At the fruit-ripening stage, many annual
species will not only show a decline in RGR, but also in AGR,
resulting in an overall S-shaped curve of total plant mass over
time. This can be well described by sigmoidal functions like
the logistic, Gompertz, Richards or b functions (Yin et al.
2003). The S-shaped pattern is strongly intensified in competition, where mutual shading and intensified depletion of soil
resources hamper growth.
In the comparison of growth of widely spaced plants of
different genotypes or mutants, Eqn 2 may provide important clues on how to explain observed differences in size. In
its most basic form, this equation can already capture part of
the growth cycle from seed to vegetative plant, where the
mass M1 equates seed mass, time t1 represents the day of
germination and time t2 represents the time at which the
biomass is evaluated (see middle part of Fig. 1). In an analysis
of ethylene-insensitive Arabidopsis plants, for example, a
consistent difference in biomass was found at the end of
the experiment, with mutants being ~50% smaller than the
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
Physiological mechanisms in plant growth models
7
wild-type plants. Interestingly, the mutants were found to
have exactly the same RGR as the wild type. A possible
difference in germination time could be excluded as well. The
lower dry mass of the mutant was therefore almost completely due to a pleiotropic effect on seed mass, which turned
out to be 40% lower than for the wild type (Tholen,
Voesenek & Poorter 2004). In genotypic comparisons of final
biomass, this seed size effect should always be considered,
particularly in interspecific comparisons where seed mass
may vary over up to seven orders of magnitude (Moles et al.
2007).
constituents vary widely in their C-concentration, ranging
from 0% for minerals up to 70% for highly reduced compounds like lignin and lipids. Similarly, the rate of photosynthesis can be broken down in the photosynthetic
nitrogen-use efficiency (PNUE, the photosynthetic rate per
unit leaf nitrogen) and the amount of nitrogen per unit leaf
area, or in even further fractions (Evans 1996). Note that a
similar type of factorization can also be made for reproductive plants, where total mass can be factorized into yield and
harvest index, with the first being separated further into seed
number and size (top part of Fig. 1).
B. Factorizing RGR in underlying components
C. Explanatory power of top-down models
Following not only the progression in plant mass, but also in
leaf area allows RGR to be factorized into two underlying
components, one representing the total amount of leaf area
per unit plant mass (leaf area ratio; LAR), the other the
increase in biomass per unit leaf area [unit leaf rate (ULR);
an alternative term is net assimilation rate; see Fig. 1 and
Evans 1972]. The power of this simple factorization cannot
be overestimated because ULR is often strongly correlated
with photosynthesis (Poorter & van der Werf 1998). Hence,
without doing more than weighing plants and measuring leaf
area, already a fairly good indication can be obtained
whether observed differences in RGR are due to the structural component (LAR) or to the gas exchange, as characterized by the ULR. This then is achieved without any
measurements of photosynthesis or respiration, with all their
problems of scaling up from leaf to whole plant and from the
short term (with measurements mostly carried out over
minutes or, at best, hours) to the full day or growth season.
LAR can be factorized further into two components, the
fraction of the total biomass allocated to leaves (leaf mass
fraction; LMF) and the amount of leaf area that is realized
per unit biomass invested in leaves, which is termed specific
leaf area (SLA; Fig. 1). RGR, ULR, LAR, SLA and LMF are
the classical parameters used in growth analysis (Evans
1972). However the analysis does not need to stop here. ULR
can subsequently be factorized into three components: (1)
the daily rate of photosynthesis per unit leaf area (Aa); (2) the
fraction of daily fixed C that is not respired or lost by other
processes such as exudation and volatilization, but that is
used for the building blocks of new biomass (CUE); and – to
link C at the one hand and biomass at the other hand – (3) the
C-concentration (Cp) of the newly build material. This equation then becomes (Poorter 2002):
In the top-down mechanistic model discussed earlier, measured RGR values are taken and broken down into underlying components (see Eqn 3). As such, the focus cannot be on
how well the model forecasts final biomass or growth rates, as
calculated growth rates form the start of the analysis. The
main question that can be answered with this type of analysis
is how strongly variation in RGR scales with variation in
each of the underlying parameters. As far as such factorizations are multiplicative by nature, there are simple techniques available, such as scaling slopes analysis (Renton &
Poorter 2011), that can estimate to what extent variation in
RGR and underlying components are linked. Applying such
a top-down analysis provides good insight in where the main
differences in growth rate between genotypes, species or
environments come from. Additionally, as many scientists
follow this model in their data analysis, opportunities for
well-founded generalizations from meta-analyses are much
better than when all papers followed their idiosyncratic type
of analysis.
There are, however, at least three reasons why this cannot
be the last step in the analysis of plant growth. Firstly, the
scheme shown in Fig. 1 tacitly assumes that all the parameters are independent from each other. However, that is
rarely the case, as generally a certain amount of covariance
is present between the various growth traits (Renton &
Poorter 2011). The second reason why it is wise to be cautious with such an analysis is that it still provides an incomplete picture of the actual growth process. As will be
discussed in section 4B, there are various cases where
growth is not limited by the process of photosynthesis and
the availability of photosynthates. Feedback mechanisms
will cause photosynthesis to decrease, but well after the
growth process itself is inhibited. Analysing these growth
patterns using the scaling-slope technique mentioned
earlier, would still indicate that RGR and ULR are both
inhibited, and that the change in ULR scales for at least a
certain fraction with the decrease in RGR even though the
actual cause of the RGR-decrease is not likely to be related
to sugar availability at all.
The third caution comes from the fact that this analysis
only shows the C-economy perspective of growth. This could
be problematic as growth is a multidimensional phenomenon, in which a range of processes interact. In principle,
RGR can be factorized relative to different factors (e.g. C, N,
RGR =
Aa ⋅ CUE
⋅ SLA ⋅ LMF
Cp
(3)
Further factorization is possible, as shown in Fig. 1. The
inverse of SLA, which is termed LMA, is the product of leaf
thickness and density. Thickness, which equals leaf volume
per area (LVA), can be further separated in the volume of
the various anatomical tissues per unit leaf area (Poorter
et al. 2009). The plant C-concentration is a function of the
chemical composition of the various plant organs. Different
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
H. Poorter et al.
P) and the choice of the model depends on which factor most
strongly constrains growth. In the end, however, it is a set
of more or less coordinated traits that makes up the difference between, for example, fast- and slow-growing species
(Lambers & Poorter 1992) or genotypes with different
Rubisco content (Stitt & Schulze 1994). An analysis where
different factorizations can be combined into one analysis is
presented in section 6.
4. THE RELATION BETWEEN
PHOTOSYNTHESIS AND GROWTH: HOW
MECHANISTIC ARE MECHANISTIC MODELS?
Almost by definition, the mechanistic bottom-up models
follow a reductionist approach, where physiological processes drive growth. For C-based models, this implies that the
difference between C-gain in photosynthesis and C-losses in
respiration – plus in principle losses through volatilization,
exudation and biomass turn over – determine the growth rate
of a plant. Physically, this is true by necessity: as plants are
predominantly built on photosynthates, the net balance of C
income and expenses on a whole-plant basis must represent
the increase in mass. However, does this also necessarily
imply that each additional sugar molecule produced during
the photosynthetic process will always lead to the same
amount of structural growth?
(a)
Various research communities work on possibilities to
enhance growth or productivity at a range of integration
levels. Photosynthesis receives special interest because it
forms the basis for all growth, with only a modest fraction of
the incoming light energy really converted into biomass
(Long et al. 2006). However, it is not always realized to what
extent the integration level at which plants are studied and
the experimental design followed affect the results. For individually grown young plants in a growth chamber, where
the wild type would grow for 3 weeks with an RGR of
200 mg g-1 day-1, a transformant with a 10% increased rate of
photosynthesis per unit leaf area can be calculated to achieve
a 52% larger biomass, under the assumption that everything
else in Eqn 3 would remain equal. The relatively large stimulation is due to a feed-forward mechanism, where more photosynthates leads to more leaf area and thereby more light
interception and subsequently more fixed C. This is the usual
condition where large-scale screens for better-performing
genotypes are conducted. In a dense canopy, like for example,
a crop in summer, the situation is different. Simulations of a
closed canopy with transformants that either have a 10%
higher photosynthetic capacity or a 10% higher quantum
yield at the leaf level shows that the effect on simulated gross
C-gain of the whole stand is actually smaller than 10%
(Fig. 2a). As far as additional growth leads to more leaf area,
this will not contribute to much more light interception in a
closed canopy situation. Rather, it results in a canopy with a
higher degree of self-shading. Hence growth models show
High LAI
8
6
4
2
0
q
10
v
q
v
q
v
q
v
(b)
Δ Irradiance at LL
Δ Irradiance at HL
Δ CO2 at LL
8
Δ CO2 at HL
6
4
2
0
A. Differences between individually grown
plants and plants in stands
Low LAI
10
Increase in canopy photosynthesis (%)
8
0
2
4
2
6
–2
LAI (m m )
Figure 2. (a) The percentual increase of canopy photosynthesis
as affected by a hypothetical mutation that increases quantum
yield (indicated as ‘q’) by 10% or a mutation that increases the
photosynthetic parameters Jmax and Vcmax (indicated as ‘v’) by 10%.
(b) The effect on canopy photosynthesis of a 10% increase in light
(continuous lines) or CO2 (broken lines) as dependent on the leaf
area index (LAI) of a monostand of Solanum lycopersicum.
Simulations were done for a range of days in winter (black bars
and lines; average light level 3.0 mol m-2 day-1) and summer (red
bars and lines; average 27.5 mol m-2 day-1), with temperature fixed
to 21 °C and are based on model INTKAM (Marcelis et al. 2009).
that the expected biomass or seed yield stimulation from a
10% increased photosynthetic capacity is more in the order
of 5% (e.g. Boote & Tollenaar 1994; Sinclair & Purcell 2005;
Zuidema et al. 2005). As far as an increased photosynthetic
capacity is connected to larger biomass investments per unit
leaf area (low SLA; Stitt & Schulze 1994) and/or larger
requirements of nitrogen, selection for plants with high photosynthetic capacity may even lead to reduced yield (Boote &
Tollenaar 1994; Sinclair & Purcell 2005).
The strong feed-forward mechanism that exists in individually grown plants is not always appreciated. It may imply that
a clear difference in plant size after a period of time could be
traced back to only a small stimulation in one of the growth
components. A difference in biomass of 50% at the end of an
experiment, for example, is still relatively easily picked up.
But if this was caused by one underlying component (e.g.
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
Physiological mechanisms in plant growth models
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
(mmol m–2 16 h–1)
40
20
0
0
200
400
600
Day time photosynthesis
(mmol m–2 8 h–1)
(b)
1.0
P90
(rel. units)
The idea that each additional sugar produced in the photosynthetic process will lead to an equal amount of growth
seems plausible at first sight. The rate of photosynthesis
expressed per unit leaf area is generally stimulated if plants
get more light, more CO2, more nutrients to invest in the
photosynthetic machinery or more water to allow operation
at a higher stomatal conductance. Growth and productivity
are stimulated under such conditions as well (Monteith 1977;
Poorter & Navas 2003; Farooq et al. 2009). However, there
are a number of observations that do not comply with this
paradigm, such as a very neat, but rather overlooked experiment by Ludwig, Charles-Edwards & Withers (1975). They
enclosed an individual leaf of a tomato plant in a cuvette,
supplied it with controlled levels of light and CO2 during the
day and measured net photosynthesis over the full light
period and respiration during the subsequent night. Interestingly, when Ludwig et al. manipulated photosynthesis during
the day by altering the light level, night respiration was
strongly affected (Fig. 3a). However, when the light level was
kept constant, but daily photosynthesis manipulated by altering the CO2 levels, respiration rate was affected far less.
Apparently, in these leaves, it was not the produced amount
of sugars per se that determined the nightly respiration rate.
Because respiration and growth are often strongly linked,
this may be true for the process of growth as well. As discussed in section 5, the growth response of plants to elevated
CO2 is generally smaller than the growth response to light.
Doubling the CO2 concentration only leads to a modest
increase (~40%) in total plant mass (Poorter & Navas 2003)
with concomitantly considerable starch accumulation
(Stiling & Cornelissen 2007) to an extent that may occasionally even lead to disruption of chloroplasts (Cave, Tolley &
Strain 1981). In quite some cases, downward regulation of
photosynthesis is found (Medlyn et al. 1999), triggered by
increased sugar levels (Van Oosten & Besford 1995) and
resulting in reduced transcription of Rubisco. None of these
down-regulating processes is observed when plants receive
more light. Thus, it seems that not C-availability per se, but
C-availability in conjunction with an additional signal is
required to affect respiration (Fig. 3a) and growth. Such a
signal could well be coming from light-signalling cascades.
Strongly increased levels of non-structural carbohydrates
may then indicate a mismatch between supply of photosynthates on the one hand and demand for growth on the
other.
Rather similar cases could apply under conditions of
drought, low temperature or nutrient stress. It is obvious that
drought decreases photosynthesis, at least partly through
Night time respiration
B. The value of a sugar for individually
grown plants
(a)
60
Leaf photosynthesis
photosynthesis) that only needs to differ by ~10%, the challenge to identify this component is much larger (Stitt &
Zeeman 2012). And in the case that more components of
Eqn 3 contribute, the percentual difference in each of the
components is likely to become smaller than the statistical
noise.
9
0.8
P75
P50
0.6
P25
0.4
P10
0
50
100
% of fruits removed
Figure 3. (a) Leaf respiration integrated over the night period as
a function of the rate of photosynthesis integrated over the day
period before. Data are for Solanum lycopersicum, as published by
Ludwig et al. (1975). Reproduced with permission from Springer
Verlag. Blue squares indicate the night respiration when
photosynthesis during the day was modulated by the application of
a range of light intensities (~70–1200 mmol m-2 s-1) at a constant
CO2 concentration (~300 mmol mol-1). Red circles indicate the
dark respiration when photosynthesis during the day was altered
by applying a range of different CO2 concentrations
(~50–1200 mmol mol-1) at a light intensity of ~370 mmol m-2 s-1.
(b) The net rate of photosynthesis of source leaves as dependent
on the fraction of fruits on the plants that was removed.
Meta-analysis for 24 experiments described in literature. For each
experiment, photosynthesis data were scaled to the value in
control plants (zero-level pruning). The brown line indicates the
median response, the gray area the inter-quartile range (25th–75th
percentile) and the dotted blue lines the 10th and 90th percentile
of a distribution for which we grouped the data into three classes:
no fruit removal (n = 27), 25–75% fruit removal (n = 10) and >75%
fruit removal (n = 29). Literature sources are given in Supporting
Information Supplement S1.
reduced stomatal conductance, and that growth is diminished
as well. Yet, in a thorough analysis of drought effects on gene
expression, metabolic and enzymatic levels as well as photosynthesis and growth in Arabidopsis, Hummel et al. (2010)
found that drought-stressed plants actually had a more
favourable C-balance and concluded from this and other
10
H. Poorter et al.
observations that reduced photosynthesis was not the cause
of the reduced growth, but probably more a consequence
(see also Muller et al. 2011).
Low temperature effects on RGR and growth components
can be variable, but on average, RGR declines through moderate decreases in all growth components (Eagles & Ostgard
1971; Nagai & Makino 2009). Photosynthesis generally
decreases to some extent as well, whereas the starch concentration often increases (Gent 1986; Equiza, Miravé &
Tognetti 1997). The overall picture is that in these cases, the
decrease in RGR is not a direct consequence of the decrease
in photosynthesis either (Körner 2003). Nutrient stress has
similar effects, in the sense that all growth components are
inhibited (Rogers et al. 1998; De Groot et al. 2003), with a
strong decrease in RGR as a consequence. Although, photosynthesis is clearly negatively affected, also in these cases,
there is almost invariably a strong increase in non-structural
carbohydrates as well (Poorter & Villar 1997).
The concept of these so-called source–sink interactions
is certainly not new and has been well advocated in the
1980s and 1990s by, for example Gifford & Evans (1981),
Patrick (1988) Körner (1991) and Farrar (1993). The strong
feedback of sugar demand on photosynthesis has been confirmed in many experiments with crop plants where the
ratio between leaves and fruits was manipulated (Fig. 3b) or
sugar translocation was inhibited by cold-girdling (Krapp
& Stitt 1995), with at least part of the feedback working
via sugar-sensing signals (Paul & Foyer 2001). The source–
sink balance may also strongly affect abortion of flowers,
seeds and fruits, which is a highly relevant process to
include in models if we want to simulate the biomass production of these organs (Marcelis et al. 2004; Mathieu et al.
2008).
In conclusion, a linear chain of bottom-up effects, where
external conditions such as light, CO2 and temperature determine the production of sugars, which subsequently control
growth, may capture a range of observations in a correlative
way reasonably well. However, when it comes to the actual
mechanisms, it may not necessarily grasp the quintessence of
growth regulation. Failure to include this interaction in plant
growth models may lead to erroneous conclusions. For
example, several simulation models that analysed the effect
of elevated CO2 on plant C-budgets and growth showed that
future scenarios particularly stimulate growth under conditions where the CUE is currently low (Lloyd & Farquhar
1996; Ali et al. 2013). It is known from comparative experiments that slow-growing plants and plants that experience
low nutrient levels do respire a larger proportion of their
photosynthates than do fast-growing species (Lambers &
Poorter 1992) and plants grown at high-nutrient levels
(Poorter et al. 1995). So on the basis of these simulation
models, slow-growing species and nutrient-poor plants were
expected to profit most from elevated CO2. However, a metaanalysis of experimental data showed that in reality, such
plants are stimulated less in growth (Poorter 1998). Apparently, a bottom-up model of growth based on sugar availability without inclusion of feedback mechanisms falls short
here.
C. Modelling source–sink interactions
In most growth models to date, the production of plant
biomass is only driven by the availability of photosynthates.
In essence, this approach considers a plant not very different
from a sports car: by improving the combustion, enlarging the
engine or decreasing the resistance (= increased photosynthate production), the speed (= growth rate) can always be
increased. The cases discussed in section 4B illustrate that a
better analogy would be the concept of a bread factory: more
production will lead to more consumption up to a certain
threshold. Beyond that threshold, demand quickly saturates
and additional production will pile up as unsold commodity.
Although the observations of source–sink interaction are
clear, the mechanisms that determine demand for sugars
have not been elucidated yet. This hampers incorporation of
the feedback controls into plant growth models. A number of
models partly accommodate source–sink interactions when it
comes to partitioning of photosynthates. In some, C-gain is
simulated to be source-driven, based on standard calculations of leaf photosynthesis, whereas the partitioning of the
carbon among the different plant organs is sink-driven
(Marcelis & Heuvelink 2007; Jullien et al. 2011). Relative sink
strength of the various organs is then determined by their
potential capacity to accumulate assimilates, and sugars are
partitioned accordingly. Another option in this respect is to
include simulation of sugar loading, phloem transport and
unloading (Marcelis & Heuvelink 2007; Lacointe & Minchin
2008). Most of the models that incorporate these kind of
source–sink interactions have a horticultural background. A
more general approach, focussed on the overall source–sink
limitations on growth, was recently taken by Gent & Seginer
(2012). They modelled vegetative growth responses of plants
to temperature and light based on the hypothesis that over a
wide temperature range, growth is governed by the minimum
of the supply of carbohydrate from photosynthesis, and the
demand for carbohydrate to synthesize new tissue. The transition temperature will of course be species-dependent.
Quereix et al. (2001) included a direct feedback of carbohydrates on the rate of photosynthesis, without going into
molecular details.
It is clear that our understanding of the processes of sugar
mobilization and partitioning currently fall short for a fully
mechanistic simulation model. At the same time, it is also
clear that the output of models without source–sink feedbacks have to be considered critically, especially in cases
where growth takes place at high CO2 levels, low temperature
conditions or low water or nutrient supply.
5. DRCs FOR GROWTH
In the evaluation of plant growth models, especially in the
extent to which they can adequately incorporate the effect of
environmental factors, it is essential to compare the output
with some form of real-world data (Palosuo et al. 2011;
Rötter et al. 2012). A specific experiment where plants were
grown at control and a twice-higher concentration of CO2, for
example, could be used for such a purpose. However DRCs
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
Physiological mechanisms in plant growth models
8
8
(a)
TDM (scaled)
11
(c)
4
4
2
2
1
1
0.5
0.5
Herb.
Woody
0.25
0.125
0
10
20
30
40
10
20
30
40
0.25
0.125
–1
–2
DPI (mol m day )
8
8
TDM (scaled)
(b)
(d)
4
4
2
2
1
1
0.5
0.25
0.125
0
200
400
600
800
1000
0
200
400
600
0.5
Herb. C3
Woody C3 0.25
Herb. C4
0.125
800 1000
–1
[CO2] (mL L )
Figure 4. Dose–response curves (DRCs) of the response of total plant dry mass to (a) daily photon irradiance (DPI) and (b) atmospheric
CO2 concentration. Values in (b) pertain to C3 species only. Panels (c) and (d) indicate median response curves for herbaceous and woody
species, which were significantly different in the case of light (P < 0.05; regression tree analysis) but not in the case of CO2. For completeness,
(d) includes the median-response curve for C4 species as well. For each environmental factor, a reference value was chosen (8 mol m-2 day-1
for light; 370 mL L-1 for CO2) and data for each species in each experiment were scaled to the total dry mass (TDM) values observed or
interpolated for that reference level. For more information on followed methodology see Appendix A and Poorter et al. (2010). The DRCs
are based on ~130 publications for light and ~180 for CO2, which are listed in Supporting Information Supplement S3.
can in principle serve as a far more powerful benchmark.
They basically are empirical models, as discussed in section
1A. A method to derive DRCs based on a large number of
independent investigations has been described by Poorter
et al. (2010). This method has been used, among others, to
construct DRCs for SLA (Poorter et al. 2009) and biomass
allocation (Poorter et al. 2012) for a wider range of environmental factors. They do not indicate the absolute values of a
trait per se, but rather the relative response over the full
environmental range considered and could also be employed
as the lowest, descriptive level of mechanistic plant growth
models.
In order to come up with a calibration tool that may show
how well models do in relation to the issues discussed in
section 4B, we compiled biomass data for ~130 papers in the
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
literature describing experiments with ~250 species grown at
different light levels and ~180 papers where the effect of CO2
was studied for ~240 species. Prerequisite for inclusion in this
meta-analysis was that for a given species, plants of all treatments within an experiment were harvested at the same day.
All biomass values per plant species and experiment were
scaled to the biomass value observed or interpolated at a
common reference value for each environmental factor.
More detailed information is provided in Appendix A. The
DRCs, together with the overall distribution around the
mean are shown in Fig. 4. Light affected growth most over
the range considered (Fig. 4a), whereas the effect of elevated
CO2 across species, although smaller, was more consistent,
given the relatively narrow bands around the median
response (Fig. 4b). Part of the larger variation in response to
12
H. Poorter et al.
Table 2. The effect of irradiance and atmospheric CO2 on growth, considered over different species groups, the reference value used to
normalize data within each experiment and coefficients for the response curves of scaled TDM
Environmental Factor
Species group
Reference level
a
b
c
df
r2
Irradiance
All
Herbs
Woody
All C3
Herbs C3
Woody C3
8 mol m-2 day-1
8 mol m-2 day-1
8 mol m-2 day-1
370 mmol mol-1
370 mmol mol-1
370 mmol mol-1
-52.26
-182.7
-499.9
1.340
1.230
1.474
50.22
179.6
498.1
-177.3
-262.8
-121.2
0.01842
0.007980
0.001624
-0.8274
-0.9088
-0.7464
910
250
660
620
320
300
0.64
0.77
0.62
0.61
0.65
0.56
CO2
Relationship are all significantly non-linear and are described by the equation log2(Y) = a + bXc; with X representing the values of the
environmental factor and Y the scaled biomass values. The scaled biomass values were log2-transformed prior to the regression analysis to allow
for the logarithmic nature of ratios. For each relationship the degrees of freedom ( d.f.) and the r2 are indicated.
light was due to differential responses of the investigated
herbs and woody saplings (Fig. 4c), which was not present for
CO2, at least not with regard to C3 species (Fig. 4d). We
subsequently fitted non-linear equations through the scaled
data points. The statistically derived estimates of the parameters of these equations can be found in Table 2, along with
the r2 of the relationship.
The fitted DRCs can help to evaluate quantitatively
whether the marginal increase in growth because of a marginal increase in photosynthesis is always similar or not, as
discussed earlier. The challenge here is how to scale the two
different environmental factors in a common way. Preliminary measurements on the youngest full-grown leaves of
tomato plants grown in a growth chamber at 400 mmol
mol-1 CO2 and 300 mmol m-2 s-1 light (daylength 16 h; DPI
17.3 mol m-2 day-1; day temperature 22 °C; E. Kaiser, personal communication) showed that a short-term increase in
photosynthesis of 50% above that at ambient levels of light
and CO2 could be achieved by an increase of ~115% in light
or a 95% increase in CO2. The corresponding long-term
increase in growth, based on the DRCs for herbaceous
species in Fig. 4c and d show quite deviating values. Using the
light and CO2 levels at which these tomatoes were growing as
a baseline, the long-term biomass growth stimulation associated with a 115% increase in light or a 95% increase in CO2
can be calculated to be ~120 and 45%, respectively. Hence,
based on these DRCs that reflect total dry mass (TDM)
responses averaged over many species, growth seems to be
more sensitive to changes in light than to increases in CO2. Of
course, the direct connection we make here between shortterm responses of photosynthesis at the leaf level and growth
at the whole-plant level is too simplistic as more factors will
modulate the response. For example, the importance of light
for stimulating photosynthesis increases if individual plants
start to shade themselves, or plants grown in stands develop
larger LAI. This is illustrated in Fig. 2b, where model simulations show that the effect of a 10% increase in light stimulates canopy photosynthesis more at high than low LAI. The
effect of a 10% increase in atmospheric CO2 on the other
hand is smaller at high LAI, which is especially clear at high
light. On top of this shading effect come readjustments by
the plants in the form of alterations in leaf morphology
and anatomy (SLA), allocation (LMF, RMF) and chemical
composition. These differences quickly become complex,
which illustrates both the avail of plant growth simulation
models, as well as the need to properly calibrate those
models, for example, with the DRCs given in Fig. 4.
6. THE SUPRA-CELLULAR SIDE OF
SYSTEMS BIOLOGY
Most of the knowledge applied in the growth models discussed above was developed in a time that molecular biology
was in its infancy. That period was followed by a phase where
the focus in plant biology was very much on the role of
individual genes as the ‘blueprint of life’. This ‘genocentric’
view was accompanied by great expectations for crop
improvement, which are to date not met yet (Sinclair &
Purcell 2005). Some gene mutations cause (embryonic)
lethality, quite some yield plants with hampered growth and
many do not result in phenotypic differences with the wild
type. Mutations or transformations that do improve growth,
on the other hand, are very scarce. The reason for this could
be that control of growth is shared by various organs and
many processes, with relatively strong homeostasis of plant
productivity as a result. It is, on the other hand, well known
that species vary widely in their potential growth rate
(Poorter & van der Werf 1998), and most crop species often
show only intermediate values for RGR. Therefore, there
must be scope for a physiological improvement of crop
performance.
The current advances in transcriptomics, proteomics and
metabolomics quickly push forward our knowledge at the
(sub)cellular level. These approaches allow for a much
broader perspective, where functioning and interaction of a
wide range of genes and gene products is considered simultaneously. Although the challenges are daunting, the field of
systems biology undoubtedly will move forward our insights
into plant functioning. Unfortunately, for most system biologists to date, the cellular level seems to be a logical upper
boundary. In its most simplified form, plants are then considered as a collection of cells, where the main direction of
causation is upward, starting at the gene level, with transcription and translation controlling the protein levels, which subsequently determine the metabolome (e.g. Katari et al. 2010).
It cannot be completely excluded that self-organization of
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
Physiological mechanisms in plant growth models
13
PNC
CUE
MINp
Aa
ULR
Cp
Am
Ea
SLA
DMC
LD
RMF
NIR
LMF
RGR
Figure 5. Correlation network for 15 growth-related traits, describing the interrelations in a comparison of fast- and slow-growing
herbaceous species. Lines in blue indicate positive correlations, in red negative correlations. Thin lines, 0.5 < |r| < 0.707 (0.25 < r2 < 0.50);
intermediate lines, (0.707 < |r| < 0.866 (0.50 < r2 < 0.75); bold lines, |r| > 0.866 (r2 < 0.75). Yellow-coloured nodes indicate rates, grey nodes ratios
in the growth equations; blue nodes, anatomical and chemical traits. Data are taken for the growth of 24 forbs and grasses grown under
constant conditions and optimal nutrient supply in a growth chamber (Poorter & Remkes 1990; Poorter et al. 1990; Poorter & Bergkotte
1992).
groups of cells is sufficient to allow for a properly functioning
plant, even with such distinct organs as leaves, stems and
roots (Yang & Midmore 2009). However, it is more likely that
in the majority of organisms, there is strong downward
control from the organ or plant level on the processes taking
place within the cell (cf. Noble 2012), regulated via all kinds
of hormonal or other signalling cascades. The idea has therefore been advocated by various plant biologists to extend
systems biology to the crop level (Hammer et al. 2004; Yin &
Struik 2010; Lucas, Laplaze & Bennett 2011). Attractive as it
is, this may be a formidable task, which is not easily accomplished. Firstly, there is the problem that our insights into the
cellular systems biology have not matured yet. Secondly,
simulation models generally do not go down more than two
or three integration levels deeper than their variable of interest (crop yield in this case), as time-steps of the iterations
decrease with the inclusion of lower integration levels
whereas complication and noise quickly increase. Thirdly,
including too many processes and parameters in a model may
easily lead to over-fitting.
Another issue in extending systems biology to the crop level
is that the ecophysiological mechanisms in most of the current
models are actually quite crude. We contend that at the
moment, there is still too little insight into the supra-cellular
part of plant system biology. At the leaf level, mechanisms
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
such as gas and heat exchange are generally well understood.
If stomatal conductance increases, so does usually the CO2
diffusion into the leaf and thereby CO2 fixation. However, at
the whole-plant level, our understandings are less clear. What
are the costs of increased hydraulic conductance in terms of
vascular transport capacity (Brodribb, Feild & Sack 2010) or
additional root proliferation? What will happen to
N-metabolism if plants produce less Rubisco (Stitt & Schulze
1994)? How are plants in split-root experiments able to
quickly up-regulate nutrient uptake in one compartment
when nutrients in the other compartment are withheld (Jeudy
et al. 2010) and what then limits nutrient uptake in the control
plants? We badly need the type of simulation models that can
help us in obtaining the insights in how whole plants mechanistically manage the compromises they need to make and the
different roles that the various organs fulfil in that respect.
When sufficient mechanistic detail is included in a whole-plant
model, then it would also be relatively easy to expand to the
molecular mechanisms, such as repression of Rubisco synthesis in the case of sugar accumulation.
A requirement of such a strongly mechanistic model is
that it would adequately represent the trade-offs and correlations that exist among the various processes and state variables. It is therefore of interest to know what the correlation
network is for the traits that together constitute the
14
H. Poorter et al.
[Chl]
Vc
[N]
[Rub]
J
Aa
Ams
Chl/N
[C]
SLA
J/Vc
gs
Rm
Am
Abs
pi/pa
LD
PNUE
Chla/b
LMF
RMF
[NO3]
LVA
Figure 6. Correlation network for 23 photosynthesis- and growth-related traits, describing the interrelations in a comparison of a range of
herbaceous and woody species, grown at low (200) and high (1000 mmol m-2 s-1) light, respectively, for 11 h a day. Lines in blue indicate
positive correlations under both conditions, lines in red consistent negative correlations. Grey lines indicate |r| > 0.6 correlations observed
only at low light, orange lines correlations only found at high light. For these two categories, broken lines indicate negative correlations,
continuous lines positive correlations, respectively. Thin red and blue lines 0.6 < |r| < 0.8 at both low and high light; bold lines |r| > 0.8 at both
intensities; intermediate lines 0.6 < |r| < 0.8 in one case and |r| > 0.8 in the other. The colour-code of the nodes is similar to Fig. 5. Data are
taken for the growth of four woody and six herbaceous species, all eudicots grown under constant conditions and optimal nutrient supply in
a growth chamber (Poorter & Evans 1998; Evans & Poorter 2001).
phenome of the plant. A considerable amount of information is required to analyse such a correlation network, as one
needs both a wide variety of species or genotypes, as well as
a large range of measured traits. We calculated such a correlation network, based on an experiment where ~50 physiological, morphological and chemical traits were measured
along the framework discussed in section 3. These traits were
analysed for 24 herbaceous species, all grown under identical
conditions (Poorter, Remkes & Lambers 1990). A simplified
scheme with 14 of the most important variables is given in
Fig. 5, the full correlation network can be found in Supporting Information Supplement S2.
What can we learn from such a network? Firstly, the positive and negative relationships in such a network could be
confirmations for mechanistic trade-offs that are known
already. For example, species with a high SLA are generally
known to invest relatively little of their biomass in cell walls,
but have high concentrations of leaf organic N and, hence,
relatively high rates of photosynthesis per unit leaf mass (cf.
Lambers & Poorter 1992; Wright et al. 2004). At the wholeplant level, plants with a high allocation to leaves (LMF) are
likely to invest only a smaller fraction of their biomass in the
roots. This may have negative consequences for the amount
of water taken up per unit leaf area, with low stomatal conductance and, hence, a low rate of photosynthesis per leaf
area as a consequence. Secondly, observed correlations may
indicate as yet less-explored feedbacks or feed-forwards that
occur at the supra-cellular level. For example, in this comparison species with a low investment in roots show a high
nutrient uptake rate per unit root mass (NIR). Thirdly, some
previously observed trade-offs, for instance between ULR
and SLA (Villar et al. 2005) or ULR and LMF (Ceriani,
Pierce & Cerabolini 2008) are not found in this dataset. This
leads to the question, which of those could just be spurious
correlations. A further analytical step could then be to
analyse the partial correlations as well, which show the individual relation between two variables while the effect of
all other variables in the network are statistically controlled
for.
Incongruent networks could be obtained if different
groups of species are studied. A very relevant question therefore is how representative this network is. Would the network
be similar if another group of fast- and slow-growing species
would be taken or are they possibly only valid within a specific functional or phylogenetic group of species? And how
strongly does the network depend on the environment? An
indication of the latter can be found in Fig. 6 where a correlation network is given for an experiment with 10 herbaceous
and woody species grown at low and high light levels. Some
of the trait correlations, indicated in blue and red, are of
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
Physiological mechanisms in plant growth models
similar sign and strength at both light levels. The positive
correlation between SLA and Am, as already found in Fig. 5,
is also observed here at both low and high light levels and, in
fact, also in worldwide comparisons of field-grown plants
(Wright et al. 2004). The negative correlations between
SLA, Nm, Am and related photosynthetic traits expressed
on a mass basis on the one hand and leaf density and
C-concentration on the other hand are also consistent in both
environments. However, a number of other correlations only
show up at low light, others only at high light (colour-coded
grey and orange, respectively). Clearly, we start to obtain
generalized information of responses of individual traits
(Poorter et al. 2012), but ultimately, we need to know how the
whole network behaves and understand the extent to what it
can be deformed under various external conditions.
No matter how we acquire the required information, it is
clear that mechanistic simulation models are indispensable to
test our knowledge of the system. The challenge is then to
obtain a mechanistic model that can adequately represent
the observed correlation network and its response to the
environment. As much as applied models are often only calibrated against, for example, the TDM or yield of the plants at
the end of the experimental period, for this type of analysis
model output, should be tested against the experimentally
measured performance of all the relevant state and rate variables in the network. Only in this way, which has been named
‘virtual profiling’ (Génard et al. 2010), we are able to detect
where our model knowledge deviates from the behaviour of
whole plants.
If the virtual profiling of the supra-cellular model
adequately covers the observed correlation network, the
logical next step is to extend such a plant model with the full
molecular detail of the cellular part of systems biology as well
as the patterns and processes at the crop level. This is as
formidable a task as establishing the (sub)cellular network,
given that so many processes and interactions are involved.
However, as some models currently already span the levels
from cell to globe, it would be a missed opportunity if we
would not try now to make the connection between gene and
whole plant or crop (Yin & Struik 2010). Relationships that
have been established between metabolite levels and final
plant mass (Sulpice et al. 2009) could be a good basis to
start with.
CONCLUSIONS
In this review, we discussed a range of plant growth models
with varying physiological detail: (1) empirical models
without mechanisms; (2) mechanistic bottom-up models,
which often focus only on the C-supply part of growth; and
(3) more-or-less mechanistic top-down models factorizing
RGR into increasingly smaller subcomponents. All of them
fall short yet if we want to understand the systems biology
of plant growth at the supra-cellular level. We call for a
dedicated mechanistic modelling approach, which considers
the various trade-offs and feedback loops within the plant,
with inclusion of source–sink interactions as first priority.
Although final biomass or yield would be the indicator for
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment
15
how successful a plant integrates the various processes
and organs, the main result of such a model would be an
improved understanding of the intricate network of physiological and morphological traits and how that is responding
when the environment changes.
ACKNOWLEDGMENTS
Elias Kaiser kindly provided photosynthesis data on tomato
for this paper, while Maarit Maënpäa helped in the literature
analysis. Dimitrios Fanourakis, Jochem Evers, Danny Tholen,
Maarit Maënpäa and two anonymous reviewers made useful
comments on a previous version of the manuscript.
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Received 20 December 2012; received in revised form 3 April 2013;
accepted for publication 14 April 2013
APPENDIX 1
For the analysis of dose–response curves of biomass, the
MetaPhenomics database described by Poorter et al. (2010)
was used. In short, data were collected from a large range of
experiments published in the scientific literature over the last
50 years. Firstly, prerequisite for inclusion was that plants
were grown in two or more environmental conditions in
which the level of light or atmospheric CO2 level was experimentally affected. Secondly, prerequisite was that plants
developed at least 80% of their biomass under the conditions
where the different treatments were applied so that they
were well able to acclimate to their environment. Thirdly,
prerequisite was that all plants for a given species in a given
treatment were harvested at the same day. All biomass data
within a given experiment and species were then standardized relative to the biomass observed at the reference level
listed in Table 2. Subsequently, data were categorized in subclasses over the environmental factor considered; and the
10th, 25th, 50th, 75th and 90th percentile of the scaled TDM
distribution are calculated for each interval (Fig. 4). For both
daily irradiance and CO2, data were fitted with a non-linear
equation of the form log2(Y) = a + Xc, where X is the environmental factor of interest and Y is the scaled biomass value
(Table 2). Within the group of herbaceous and woody species
(all C3 in the case of CO2), we tested whether the duration of
the experiment affected the DRC, but no significant effect
could be found.
References for the literature data that were included in the
analysis are given in Supporting Information Supplement S3.
SUPPORTING INFORMATION
Additional Supporting Information may be found in the
online version of this article at the publisher’s web-site:
Supplement S1. Literature sources for the data distribution
of Fig. 3b, relating the rate of photosynthesis per unit leaf
area to the percentage of fruits removed from the plants.
Supplement S2. Correlation network of 50 different traits,
measured for 24 monocots and eudicots.
Supplement S3. File with a list of references from which the
data for the calculation of dose–response curves of Fig. 4
were derived.
© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment