Physiological mechanisms in plant growth models

Physiological mechanisms in plant growth models: do weneed a supra-cellular systems biology approach?

HENDRIK POORTER1, NIELS P. R. ANTEN2 & LEO F. M. MARCELIS3,4

1IBG-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, 6700AP Wageningen, The Netherlands

ABSTRACT

In the first part of this paper, we review the extent to whichvarious types of plant growth models incorporate ecophysi-ological mechanisms. Many growth models have a centralrole for the process of photosynthesis; and often implicitlyassume C-gain to be the rate-limiting step for biomass accu-mulation. We subsequently explore the extent to which thisassumption actually holds and under what condition con-straints on growth due to a limited sink strength are likely tooccur. By using generalized dose–response curves for growthwith respect to light and CO2, models can be tested againsta benchmark for their overall performance. In the final part,a call for a systems approach at the supra-cellular level ismade. This will enable a better understanding of feedbacksand trade-offs acting on plant growth and its componentprocesses. Mechanistic growth models form an indispensa-ble element of such an approach and will, in the end,provide the link with the (sub-)cellular approaches that areyet developing. Improved insight will be gained if modeloutput for the various physiological processes and morpho-logical variables (‘virtual profiling’) is compared with meas-ured correlation networks among these processes andvariables. Two examples of these correlation networks arepresented.

Key-words: dose–response curves; evolutionary stable strat-egy; photosynthesis; plant growth; simulation; source–sinkinteraction.

INTRODUCTION

Plant growth is a process that is highly relevant in a range ofcontexts. From an evolutionary viewpoint, the ability of anindividual to grow and achieve a certain size in a given envi-ronment is one of the prerequisites to reproduce successfullyand achieve an adequate fitness. In an ecological context,growth and the physiological processes required for thathave a profound impact on the various biogeochemical cyclesin basically all ecosystems of the world, and thereby also onsystem earth as a whole. Finally, from a human perspective,plant growth is of fundamental importance as it forms thebasis of all agricultural productivity. It is therefore not sur-prising that the processes underlying plant growth are the

focus of significant research efforts. There is a large researchcommunity investigating the biophysical and biochemicallimitations on photosynthesis and the way(s) by which pos-sible inefficiencies in light and/or dark reactions could bealleviated (Zhu, Long & Ort 2010). Others study the wayrespiration could be reduced or, at least, could be made less‘wasteful’ in order to have more photosynthates available forgrowth (Affourtit et al. 1999).Yet others work on the efficientuptake or use of nutrients (Lynch 2011) and water (Blum2009) or study the molecular mechanisms that determine celldivision (De Veylder, Beeckman & Inzé 2007). The ultimategoal is often to change or affect these processes in a way thatwill positively shape the growth and productivity of plants.An alternative approach with a top-down direction is fol-lowed by geneticists. They take genotypes with contrastinggrowth rates or yield and try to link this variation directly tospecific genomic regions, and ultimately genes by means ofquantitative trait loci (QTL) approaches or genome-wideassociation mapping. As can be expected from quantitativetraits, such approaches generally show that many loci areinvolved, of which few or none exert strong dominance(Poorter et al. 2005; Bouteillé et al. 2012). In a recent genome-wide association study with rice, for example, the totalexplained phenotypic variance for a wide variety of growth-related traits ranged from 5 to 50%, with up to 16 lociinvolved per trait (Zhao et al. 2011).

Understanding plant growth becomes even more challeng-ing because of the strong effect of the environment, whichmay modulate the various components of the growth proc-esses in different, sometimes contrasting, ways. For example,plants grown at high light intensities generally have higherrates of photosynthesis and thereby a higher rate of biomassproduction per unit leaf area than low-light grown plants.However, plants grown at high light at the same time have areduced amount of leaf area per unit plant mass. At lightlevels higher than 25 mol m-2 day-1, this may lead to a situa-tion where, for quite some species, the growth rate is notstimulated anymore although the rate of photosynthesis perunit leaf area is still increasing (Poorter & Van der Werf 1998;see also section 5). Physiological interactions may becomeeven more complex when two or more environmental factorsinteract.

Studying the genetic and cellular regulation of the variousphysiological processes that take place within the plant willundoubtedly improve our understanding of plant function-ing. However, the most relevant issue in the end is how theseCorrespondence: H. Poorter. e-mail: [email protected]

Plant, Cell and Environment (2013) doi: 10.1111/pce.12123

© 2013 John Wiley & Sons Ltd 1

different processes interact with each other and with theenvironment, and what the implications are for plant growthas a whole. It has long been recognized that modelling couldbe very helpful here (De Wit & Brouwer 1968). Plant growthmodels as a simplification of complex systems have tremen-dous value as a way to structure and integrate availableknowledge, test hypotheses and come up with quantitativeestimates of total plant mass, above-ground mass and/oryield.

Plant growth models come in a wide variety, ranging fromsimple formulas that mathematically capture plant size overtime with just two or three parameters (Blackman 1919) upto highly complicated simulation models that evaluate globalchange effects on the performance of vegetation worldwide(Haxeltine & Prentice 1996). They apply an array of concep-tual approaches and incorporate a range of more-or-lessdetailed (eco-)physiological processes, mostly centredaround the carbon economy of the plant, as this provides thebackbone for all growth.The main focus of the present paperwill be on the physiology and modelling of whole-plantgrowth for individual plants grown in the absence of com-petitors. However, we will also discuss some models whereplants do grow in stands, as the guiding principles are over-lapping to a large extent. Firstly, we pay attention to the typeand amount of mechanism incorporated in the variousgroups of plant growth models to date, discussing the strongand weak points of each of them. Secondly, we focus on theconditions where C may not be the limiting factor for growthand the extent to which so called source–sink feedbacks areincorporated in the mechanistic models. The final part of thepaper discusses the need for a supra-cellular systemsapproach to growth. It shows, with two extensive datasets,how possible trade-offs within the plant could be elucidatedand discusses how mechanistic models could be of help hereto understand these trade-offs within the context of whole-plant functioning.

1. MECHANISMS IN BOTTOM-UP MODELS

Mechanistic models of plant growth – also called process-based models – are models where some form of physiologicalmechanism is employed. Generally, processes at one integra-tion level are used to simulate plant performance or anotherrate or state variable at a higher integration level. The extentof mechanistic detail of these so-called bottom-up modelsvaries strongly.

A. Empirical models

The simplest models of plant mass or productivity areempirical models, also denoted as ‘statistical’ models. Empiri-cal models are frequently used in such different fields asagriculture, horticulture and forestry to describe and/or fore-cast the productivity in monocultures of economically inter-esting plant species. In terms of mechanism, they can beconsidered as a ‘null-model’, as they do not contain anyphysiological processes at all. Rather, they can be seen asdose–response curves (DRCs; see Table 1 for an explanation

of all abbreviations used), which relate biomass or yieldobservations in a given geographic location or climatic zoneto one climatic or edaphic variable of interest. They can alsobe extended to include several independent factors. Simpleor multiple regression techniques then provide an equationthat can be used as a predictor for biomass (Aylott et al.2008; Wullschleger et al. 2010). In plant biology, the basicconcepts of DRCs have been placed in a mathematicalframework by Mitscherlich (1909).

Empirical models are extremely simple yet effective intheir ability to predict the productivity of natural and cropstands with one notable exception: they perform badly if theyare to predict yield outside the boundaries where data havebeen collected (Dourado-Neto et al. 1998). One examplewhere extrapolation may lead to erroneous estimates is thecase of temperature. Generally crops like rice and maize arerelatively cold-sensitive and grow and produce better atwarmer temperatures. However, this may not be extrapo-lated to too high night temperatures, as quite some speciesbecome sterile under those conditions, with yield plummet-ing (Cheng et al. 2009). DRCs of biomass will be furtherdiscussed in section 5.

B. Models that apply the radiation use efficiency(RUE) concept

A popular group of models, which include some degree ofmechanistic detail, make use of the ‘RUE’ concept, which isalso referred to as ‘light use efficiency’ (LUE). These modelstake light availability as an external input and calculate lightinterception by the vegetation, for example based on the leafarea index (LAI). Rather than precisely modelling photosyn-thesis and respiration, they then use an empirical conversionfactor to describe the relation between intercepted lightand the biomass increase of the plant or vegetation(Arkebauer et al. 1994). The growth rate is calculated with asimple ordinary differential equation:

dM dt LUE exp I= ⋅ −( )⋅− ⋅1 k LAI (1)

where dm / dt is the growth rate of crop or stand, k is the lightextinction coefficient and I is the photosynthetic active radia-tion (PAR) incident on the crop. Applications can be foundin, for example, Spitters (1990) and Jones et al. (2003). RUEcan be adjusted downward with an empirical formula ifdrought, nitrogen shortage or temperature stress limit plantgrowth (Yuan et al. 2007; Kergoat et al. 2008). The advantageof this approach is that the time step in dynamic models canbe large (days, seasons), which considerably simplifies thesimulations. Drawback is that the physiology of the plantessentially remains a black box and no mechanistic connec-tion to, for example, the water or nutrient economy of theplant can be made.

C. Photosynthesis – respiration models

The next level of complexity is formed by models that explic-itly simulate photosynthesis and respiration. These models

2 H. Poorter et al.

© 2013 John Wiley & Sons Ltd, Plant, Cell and Environment

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 mol m-2 s-1

ormol m-2 day-1

Abs Absorptance Fraction of I absorbed by the leaf mol mol-1

Am Rate of photosynthesis Net CO2 uptake / leaf mass / time nmol g-1 s-1

Ams Rate of photosynthesis at light saturation Net CO2 uptake / leaf mass / time, measured atsaturating light

nmol g-1 s-1

CP Carbon concentration of a plant Carbon / total plant dry mass mmol C g-1

CY Carbon concentration of constituent Y Carbon concentration of constituent class Y mmol C g-1

C#T Cell number Cell number of tissue T per unit leaf area m-2

CST Cell size Volume of the cells in tissue T mlCUE Carbon use efficiency Fraction of daily fixed C which is used for growth mol mol-1

[C] Carbon concentration per leaf mass Carbon / leaf dry mass mmol C g-1

[Chl] Chlorophyll concentration Chlorophyll / leaf dry massDMC Dry matter content Total plant dry mass / total plant fresh mass g g-1

DPI Daily photosynthetic photon irradiance Flux of quanta in the 400–700 nm range / area / time mol m-2 day-1

DRC Dose-response curve Relationship between a plant variable and a range ofa given environmental factor

Ea Rate of transpiration Transpiration / leaf area / time mmol m-2 s-1

gs Stomatal conductance mmol m-2 s-1

HI Harvest index Reproductive dry mass / total plant dry mass g g-1

I Incident light Photosynthetic irradiance (400–700 nm) / ground area/ time

mol m-2 day-1 or mmol m-2 s-1

J Electron transport capacity Photosynthetic electron transport capacity at lightsaturation / leaf area / time

mmol e- m-2 s-1

k Extinction coefficient Extinction coefficient for light in a stand –LAI Leaf area index total amount of leaf area in crop or vegetation /

ground aream2 m-2

LAR Leaf area ratio Leaf area / total plant dry mass m2 kg-1

LD Leaf density Leaf dry mass / leaf volume g ml-1

LMA Leaf mass per area Leaf dry mass / leaf area g m-2

LMF Leaf mass fraction Leaf dry mass / total plant dry mass g g-1

LNC Leaf nitrogen concentration Leaf Nitrogen / leaf area mol N m-2

LVA Leaf volume per area Leaf volume / leaf area (equivalent to leaf thickness) ml m-2 (= mm)MS Seed mass Mass of the seed gMt Total plant mass Total plant mass at time t gMINp Mineral concentration of a plant Mineral mass / total plant dry mass g g-1

NIR Nitrogen intake rate Nitrogen uptake / root dry mass / time mmol N g-1 day-1

[NO3] Nitrate concentration of the leaves Nitrate / leaf dry mass mg g-1

pi / pa Intercellular CO2 partial pressure relative tooutside

Pa Pa-1

PNC Plant nitrogen concentration Nitrogen / total plant dry mass mmol N g-1

PNUE Photosynthetic nitrogen use efficiency Photosynthesis / leaf organic nitrogen / time mol CO2 mol-1 N s-1

QY Concentration of constituent Y mass of constituent Y / total plant dry mass g g-1

Rm Respiration rate Respiration / leaf dry mass / time nmol g-1 s-1

RGR Relative growth rate Increase in plant mass / total plant dry mass / time mg g-1 day-1

RUE Radiation use efficiency dry matter increase / amount of light intercepted g (mol quanta)-1

RMF Root mass fraction Root dry mass / total plant dry mass g g-1

[Rub] Rubisco concentration Rubisco / leaf dry mass g g-1

SLA Specific leaf area Leaf area / leaf dry mass m2 kg-1

SMF Stem mass fraction Stem dry mass / total plant dry mass g g-1

TDM Total dry mass Dry mass of leaves, stems plus roots gULR Unit leaf rate Increase in total plant dry mass / leaf area / time g m-2 day-1

Vc Rubisco activity Number of carboxylations at light saturation / leafarea / time

mmol m-2 s-1

VAT Volume per area Volume of tissue T per unit leaf area (= tissuethickness)

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).

Physiological mechanisms in plant growth models 3


commonly use the Farquhar-Von Caemmerer-Berry equa-tions as a basis for leaf photosynthesis (Lloyd & Farquhar1996; Mäkelä et al. 2000). Employing the dependencies ofphotosynthesis for light, CO2 and temperature, as well as theamount of leaf area present for a given plant or canopy, suchmodels calculate the total carbon fixation of a plant or veg-etation over a given time step (Goudriaan & Van Laar 1994;Le Roux et al. 2001; Jones et al. 2003). Subsequently sugarsrequired for maintenance respiration are subtracted from thetotal amount of produced photosynthates, and the remainingsugars are then distributed with some rule over the variousvegetative and generative compartments of the plant. In afinal step, these sugars are converted to biomass, after whichthe whole calculation repeats again for the next iteration.Themechanism can be more or less refined by taking into accountthe amount of N in the leaves available for the photosyn-thetic machinery (Niinemets & Tenhunen 1997; Müller,Wernecke & Diepenbrock 2005), the extent to which a plantcanopy is approached as one big leaf or as different leaflayers (Goudriaan & Van Laar 1994; De Pury & Farquhar,1997) and any dynamic restriction due to limited water ornutrient availability or because of temperature constraints(Jones et al. 2003; Hammer et al. 2009).

The physiological limitations of leaf photosynthesis arereasonably well understood and relatively easily incorpo-rated. Other aspects, such as the allocation of C over thevarious plant compartments are less well apprehended. Con-sequently, C-allocation is one of the weaker features of plantmodels (Marcelis & Heuvelink 2007). A range of modelstherefore simply simulate allocation using empirical look-uptables in the simulation programmes (Mäkelä et al. 2000).Further challenges arise if mechanistic models need to dealwith perennial systems such as forest plantations. Dynamicsimulations now have to take into account conversion fromsapwood to heartwood, the turnover of the various organsand decomposition of plant material and associated releaseof nutrients (Lo et al. 2011). The ultimate challenge in mod-elling is probably the realm of ecosystem and global biomefunctioning, where ecophysiological processes at the cellularlevel have to be combined with soil and climate propertiesover a time frame of centuries and for a wider range of plantfunctional types that may compete with each other, whileallowing for acclimation of plants to changing environmentalconditions (Medlyn, Duursma & Zeppel 2011; Van Bodegomet al. 2012).

D. Functional–structural plant models (FSPMs)

Most of the older mechanistic crop or vegetation modelsconsider the structure of the vegetation in terms of onedescriptor, for which the LAI is the most frequently usedvariable. Consequently, they do not include detail on plantarchitectural traits, which actually may have importantimpacts on the resource acquisition of plants (Pearcy & Yang1996; Rubio et al. 2001). A development of the last decadeare the FSPMs (Pearcy & Yang 1996; Vos, Marcelis & Evers2007; DeJong et al. 2011) that combine the C-basedapproaches described earlier with a more precise structural

description of how the leaves, stems and roots of individualplants are positioned in space and what consequence this willhave for the capture of light and nutrients. These models arenow widely used, especially in relatively detailed analyses.Applications include studies on the physiological regulationof branching patterns (Evers et al. 2011), the morphologicalconsequences of neighbour plant detection (de Wit et al.2012) and the interplay between plant structure and spatialdistribution of diseases (Baccar et al. 2011).

E. Explanatory power of bottom-up models

The mechanistic simulation models of plant growth encapsu-late a considerable amount of ecophysiological knowledgeand can be used to predict the growth rate or productivity ina variety of climatic scenarios. They also form an indispensa-ble help in decision management (Boote, Jones & Pickering1996). More than empirical models, they are able to predictgrowth outside the strict boundaries where conditions forplant performance have been tested experimentally. The rea-soning behind these models is that if we understand thecomponent processes that underlie growth and study themover a wider range of environmental factors, we will comesufficiently close to an accurate prediction of growth whenwe combine all these processes. These models clearly havesome kind of limitation as well (Marcelis, Heuvelink &Goudriaan 1998; Dewar et al. 2009). For example, as much asempirical models do not include temperature effects on ste-rility, if this is outside the tested range (section 1A), mostmechanistic models do not include this sterility effect either.Moreover, uncritical implementation of short-term physi-ological mechanism in a model that aims to simulate long-term acclimation may in the end lead to model results that donot properly represent plant performance. For example, quitesome models include a Q10 of two or more for the tempera-ture effect on respiration, which is reasonable for short-termtemperature fluctuations, but is unrealistic over longer timeframes (Atkin & Tjoelker 2003).

How well do mechanistic models perform in the predictionof crop or timber yield in a given area, and how does thatcompare with empirical models? Although an exact toler-ance limit is generally not stated, crop modellers often seemto accept differences between observed and predictedgrowth of 10–15% as being reasonably good. A preliminarysurvey across a range of papers that explicitly comparedmeasured 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 thedeviation of the simulation from the observed field data was17%. The ranges were wide, though, with a 10th and 90thpercentile of 3 and 38%, respectively. Even if these valueswould have been much lower, this does not necessarily implythat from a scientific perspective our knowledge about themechanisms is sufficiently represented. Wheat crop modelsmay serve as an example here. They probably rank amongthe best designed and validated models for a system, whichis relatively simple because of the annual character of the

4 H. Poorter et al.


plants. Different wheat models, developed by researchgroups based on different continents, are generally perform-ing very well at the geographic location they were developedfor. However, comparative test runs show that each ofthese models performs less when fed with weather datacharacteristic of wheat-growing regions on other continents(Goudriaan 1996). Apparently, each model still includes arange of ‘tweaks and adaptations’ that may make themperform well for the local soil and climate, but render themless generic as was originally anticipated. Similar blind tests,where different models forecasted the production of wheator barley grown at a range of latitudes in Europe, show prettylarge variation in outcome as well (Palosuo et al. 2011; Rötteret al. 2012). Our conclusion is that these models clearly func-tion well when it comes to accommodating year-to-year vari-ation in local climate with the purpose to forecast yield, butthat the mechanisms are still too limited to make them reallygeneric. Care should therefore be exercised when they areused to investigate global change effects or where otherforms of hypothesis testing are applied.

Another issue is whether mechanistic models outperformempirical models. When it comes to prediction of growth oryield, this is not necessarily the case (Alscher, Krug & Liebig2001).This poses an additional challenge for incorporating anadequate amount of physiological mechanism into mechanis-tic models. There is no doubt, however, that mechanisticmodels will provide us with physiological insights that weotherwise would not be able to obtain.

2. BOTTOM-UP APPROACHES WITHGOAL-SEEKING FEATURES

In a number of cases, bottom-up models are combined withspecial algorithms that enable modelling shortcuts in physi-ological processes that are not well understood or that shedlight on evolutionary questions that go beyond the simula-tion 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 arange of options or parameter values, which are then evalu-ated with a specified target in mind. Goal-seeking algorithmsare especially popular where insights into the mechanism arescanty or simulation becomes too time-consuming and cum-bersome (Dewar et al. 2009). A good example at the indi-vidual plant level is the regulation of sugar allocation to thedifferent organs of the plant (Thornley 1995). Rather thantrying to simulate the actual physiological details of the trans-port process, algorithms are applied that computationallyseek at which partitioning of sugars the plants will grow best.In ecology, teleonomic algorithms are applied to model, forexample, the N-distribution within a canopy (Field 1983;Leuning 1995). The nitrogen profile is then not simulated asthe outcome of (re)translocation processes, but rather dis-tributed a priori over the various leaf layers in a way thatmaximizes canopy photosynthesis. In both examples, the

rates of photosynthesis, respiration, etc. are modelled mecha-nistically in a similar way as in other bottom-up models.

B. Evolutionary algorithms

Another approach is the application of so-called ‘evolution-ary algorithms’. In this case, the maximum value for a tar-geted process of interest in the model is sought by evaluatingin a reiterative way the combination of parameters that givesthe best model performance. Zhu, De Sturler & Long (2007),for example, used such an approach in a model that incorpo-rated a wide range of components of the photosynthesisprocess. Under the usual assumption that the model was rightand correctly parameterized, they could show that theN-investment in enzymes of the Calvin cycle was suboptimaland could be improved by increasing the amount of Rubisco,sedoheptulose-1,7-bisphosphatase (SBP) and fructose-1,6-bisphosphate-aldolase (FBP)-aldolase at the expense ofsome other proteins. With adequate knowledge, evolutionaryalgorithms could in principle also be used to study processesat a higher integration level, such as growth.

C. Game theory

Another branch of models mimics the evolutionary processesa step further by involving the response to other plants intothe system. Like functional-structural models (section 1D)they consider a vegetation stand as an assemblage of indi-vidual plants. The difference with most other models dis-cussed here is that they allow the ‘evolution’ of differentstrategies in which the individual of interest may unilaterallyalter its morpho-physiological properties or growth patternsrelative to that of neighbouring plants. By doing so, such aplant may gain additional resources it would not haveacquired if it had not adopted its growth ‘strategy’ by takinginto account the behaviour of neighbouring plants (Anten2005).A good example is the competition for a unidirectionalresource such as light. When an individual becomes tallerthan its neighbours, it can intercept relatively more of theincoming radiation than its competitors (Weiner 1990).Therefore, it may pay off for an individual plant to initiallyinvest more of its resources into height growth, even if thiswould be at the expense of stem stability or investment in leafbiomass (Givnish 1982; Falster & Westoby 2003). In thismanner, a so-called evolutionarily stable strategy (ESS) canbe calculated, which is a strategy such that no alternativestrategy can provide an individual with a higher fitness withina given population of plants.

Intriguingly, a vegetation stand that has achieved an evo-lutionary stable situation for height will be taller than a standwhere maximum biomass is achieved (Givnish 1982). Thisphenomenon of supra-optimal behaviour with respect togrowth seems more general: game theoretical models havesuggested 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 pro-jected leaves (Hikosaka & Hirose 1997) than would be



optimal with respect to maximum whole stand growth. Thesegame theoretical models are particularly useful in determin-ing how evolution drives the structure and functioning ofnatural vegetation. However, this issue may also be relevantin an agricultural setting. If plant breeders select the best-performing plants from a mixture of competing individuals,they may unwittingly select for traits that favour competitiveability. If the models mentioned earlier are right, the conse-quence could be that this comes at a cost of decreased yield.Breeding against these mechanisms could then favourablyincrease productivity (Zhang, Sun & Jiang 1999), although itcould also imply that such plants are less competitive againstweeds.

3. MECHANISTIC TOP-DOWN MODELS

An alternative way to analyse growth is a top-downapproach. Starting with the total biomass of the plant, onecan dig down and factorize the underlying parameters andprocesses into increasingly more detailed components. Thisapproach is often applied to analyse experimental data in asystematic framework based on C-economy principles. Aimof such an analysis is to examine which of the underlyingprocesses vary between treatments, genotypes or species andwhich ones remain relatively constant.

A. Relative growth rate (RGR)

The most basic expression of growth is the so-called ‘absolutegrowth rate’ (AGR), which is the change in size of the plantper unit of time. If AGR is constant, plant mass will increaselinearly over time.This variable does not well encapsulate thechanges in size of young plants, as they will often increasebiomass in a way that is approximately proportional to thebiomass of the plant already present. The principle of pro-portional growth is engrained in the concept of ‘relativegrowth rate’, as proposed by Blackman (1919). If RGR wouldbe strictly constant, then plant mass will follow an exponen-tial trajectory over time:

M M e2 12 1= ⋅ ⋅ −RGR t t( ) (2)

where M2 and M1 represent the mass of the plants at time t2

and t1, respectively. Strict exponential growth, however, is notcommon either for plants. Not only do they show diel fluc-tuations in growth, with a positive RGR during the day andnegative growth during the night period, plants also oftendecrease RGR during ontogeny, because of increased self-shading or larger structural demands. However, an averageRGR over a certain time period may still serve as anadequate description of growth, as long as the newly formedmass is more or less proportional to the plant mass alreadypresent (Causton & Venus 1981).

At some stage during the growth period, the exponentialphase may linearize (Goudriaan & Monteith 1990) as self-shading increases and plants invest more in stems and othernon-leaf structures. At the fruit-ripening stage, many annualspecies will not only show a decline in RGR, but also in AGR,

resulting in an overall S-shaped curve of total plant mass overtime. This can be well described by sigmoidal functions likethe logistic, Gompertz, Richards or b functions (Yin et al.2003). The S-shaped pattern is strongly intensified in compe-tition, where mutual shading and intensified depletion of soilresources hamper growth.

In the comparison of growth of widely spaced plants ofdifferent genotypes or mutants, Eqn 2 may provide impor-tant clues on how to explain observed differences in size. Inits most basic form, this equation can already capture part ofthe growth cycle from seed to vegetative plant, where themass M1 equates seed mass, time t1 represents the day ofgermination and time t2 represents the time at which thebiomass is evaluated (see middle part of Fig. 1). In an analysisof ethylene-insensitive Arabidopsis plants, for example, aconsistent difference in biomass was found at the end ofthe experiment, with mutants being ~50% smaller than the

MS RGR Germ. rate

ULR LAR

SLA LMFAA CUE CP

PNUE LNC LVA LD

S VATS (QY . CY)

S (CST.C#T)

Yield HI

Seed # Seed size

Mt

*

Figure 1. General scheme with a top-down analysis of total plantmass (Mt) into component variables. The breakdown analysis isshown for the growth of the vegetative plant (down) or for thegenerative plant (up, shaded). Abbreviations are listed in Table 1.Green ellipsoids represent rates, red boxes ratios, blue boxeschemical composition, black boxes finer chemical or anatomicaldetail. Note that the factorization indicated by * actually pertainsto the inverse of SLA, that is leaf mass per area.

6 H. Poorter et al.


wild-type plants. Interestingly, the mutants were found tohave exactly the same RGR as the wild type. A possibledifference in germination time could be excluded as well.Thelower dry mass of the mutant was therefore almost com-pletely due to a pleiotropic effect on seed mass, which turnedout to be 40% lower than for the wild type (Tholen,Voesenek & Poorter 2004). In genotypic comparisons of finalbiomass, this seed size effect should always be considered,particularly in interspecific comparisons where seed massmay vary over up to seven orders of magnitude (Moles et al.2007).

B. Factorizing RGR in underlying components

Following not only the progression in plant mass, but also inleaf area allows RGR to be factorized into two underlyingcomponents, one representing the total amount of leaf areaper unit plant mass (leaf area ratio; LAR), the other theincrease in biomass per unit leaf area [unit leaf rate (ULR);an alternative term is net assimilation rate; see Fig. 1 andEvans 1972]. The power of this simple factorization cannotbe overestimated because ULR is often strongly correlatedwith photosynthesis (Poorter & van der Werf 1998). Hence,without doing more than weighing plants and measuring leafarea, already a fairly good indication can be obtainedwhether observed differences in RGR are due to the struc-tural component (LAR) or to the gas exchange, as character-ized by the ULR. This then is achieved without anymeasurements of photosynthesis or respiration, with all theirproblems of scaling up from leaf to whole plant and from theshort term (with measurements mostly carried out overminutes or, at best, hours) to the full day or growth season.

LAR can be factorized further into two components, thefraction of the total biomass allocated to leaves (leaf massfraction; LMF) and the amount of leaf area that is realizedper unit biomass invested in leaves, which is termed specificleaf area (SLA; Fig. 1). RGR, ULR, LAR, SLA and LMF arethe classical parameters used in growth analysis (Evans1972). However the analysis does not need to stop here. ULRcan subsequently be factorized into three components: (1)the daily rate of photosynthesis per unit leaf area (Aa); (2) thefraction of daily fixed C that is not respired or lost by otherprocesses such as exudation and volatilization, but that isused for the building blocks of new biomass (CUE); and – tolink C at the one hand and biomass at the other hand – (3) theC-concentration (Cp) of the newly build material. This equa-tion then becomes (Poorter 2002):

RGRA CUE

CSLA LMF= ⋅ ⋅ ⋅a

p(3)

Further factorization is possible, as shown in Fig. 1. Theinverse of SLA, which is termed LMA, is the product of leafthickness and density. Thickness, which equals leaf volumeper area (LVA), can be further separated in the volume ofthe various anatomical tissues per unit leaf area (Poorteret al. 2009). The plant C-concentration is a function of thechemical composition of the various plant organs. Different

constituents vary widely in their C-concentration, rangingfrom 0% for minerals up to 70% for highly reduced com-pounds like lignin and lipids. Similarly, the rate of photo-synthesis can be broken down in the photosyntheticnitrogen-use efficiency (PNUE, the photosynthetic rate perunit leaf nitrogen) and the amount of nitrogen per unit leafarea, or in even further fractions (Evans 1996). Note that asimilar type of factorization can also be made for reproduc-tive plants, where total mass can be factorized into yield andharvest index, with the first being separated further into seednumber and size (top part of Fig. 1).

C. Explanatory power of top-down models

In the top-down mechanistic model discussed earlier, meas-ured RGR values are taken and broken down into underly-ing components (see Eqn 3). As such, the focus cannot be onhow well the model forecasts final biomass or growth rates, ascalculated growth rates form the start of the analysis. Themain question that can be answered with this type of analysisis how strongly variation in RGR scales with variation ineach of the underlying parameters. As far as such factoriza-tions are multiplicative by nature, there are simple tech-niques available, such as scaling slopes analysis (Renton &Poorter 2011), that can estimate to what extent variation inRGR and underlying components are linked. Applying sucha top-down analysis provides good insight in where the maindifferences in growth rate between genotypes, species orenvironments come from. Additionally, as many scientistsfollow this model in their data analysis, opportunities forwell-founded generalizations from meta-analyses are muchbetter than when all papers followed their idiosyncratic typeof analysis.

There are, however, at least three reasons why this cannotbe the last step in the analysis of plant growth. Firstly, thescheme shown in Fig. 1 tacitly assumes that all the param-eters are independent from each other. However, that israrely the case, as generally a certain amount of covarianceis present between the various growth traits (Renton &Poorter 2011). The second reason why it is wise to be cau-tious with such an analysis is that it still provides an incom-plete picture of the actual growth process. As will bediscussed in section 4B, there are various cases wheregrowth is not limited by the process of photosynthesis andthe availability of photosynthates. Feedback mechanismswill cause photosynthesis to decrease, but well after thegrowth process itself is inhibited. Analysing these growthpatterns using the scaling-slope technique mentionedearlier, would still indicate that RGR and ULR are bothinhibited, and that the change in ULR scales for at least acertain fraction with the decrease in RGR even though theactual cause of the RGR-decrease is not likely to be relatedto sugar availability at all.

The third caution comes from the fact that this analysisonly shows the C-economy perspective of growth. This couldbe problematic as growth is a multidimensional phenom-enon, in which a range of processes interact. In principle,RGR can be factorized relative to different factors (e.g. C, N,



P) and the choice of the model depends on which factor moststrongly constrains growth. In the end, however, it is a setof more or less coordinated traits that makes up the differ-ence between, for example, fast- and slow-growing species(Lambers & Poorter 1992) or genotypes with differentRubisco content (Stitt & Schulze 1994). An analysis wheredifferent factorizations can be combined into one analysis ispresented in section 6.

4. THE RELATION BETWEENPHOTOSYNTHESIS AND GROWTH: HOWMECHANISTIC ARE MECHANISTIC MODELS?

Almost by definition, the mechanistic bottom-up modelsfollow a reductionist approach, where physiological proc-esses drive growth. For C-based models, this implies that thedifference between C-gain in photosynthesis and C-losses inrespiration – plus in principle losses through volatilization,exudation and biomass turn over – determine the growth rateof a plant. Physically, this is true by necessity: as plants arepredominantly built on photosynthates, the net balance of Cincome and expenses on a whole-plant basis must representthe increase in mass. However, does this also necessarilyimply that each additional sugar molecule produced duringthe photosynthetic process will always lead to the sameamount of structural growth?

A. Differences between individually grownplants and plants in stands

Various research communities work on possibilities toenhance growth or productivity at a range of integrationlevels. Photosynthesis receives special interest because itforms the basis for all growth, with only a modest fraction ofthe incoming light energy really converted into biomass(Long et al. 2006). However, it is not always realized to whatextent the integration level at which plants are studied andthe experimental design followed affect the results. For indi-vidually grown young plants in a growth chamber, wherethe wild type would grow for 3 weeks with an RGR of200 mg g-1 day-1, a transformant with a 10% increased rate ofphotosynthesis per unit leaf area can be calculated to achievea 52% larger biomass, under the assumption that everythingelse in Eqn 3 would remain equal. The relatively large stimu-lation is due to a feed-forward mechanism, where more pho-tosynthates leads to more leaf area and thereby more lightinterception and subsequently more fixed C. This is the usualcondition where large-scale screens for better-performinggenotypes are conducted. In a dense canopy, like for example,a crop in summer, the situation is different. Simulations of aclosed canopy with transformants that either have a 10%higher photosynthetic capacity or a 10% higher quantumyield at the leaf level shows that the effect on simulated grossC-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 aclosed canopy situation. Rather, it results in a canopy with ahigher degree of self-shading. Hence growth models show

that the expected biomass or seed yield stimulation from a10% increased photosynthetic capacity is more in the orderof 5% (e.g. Boote & Tollenaar 1994; Sinclair & Purcell 2005;Zuidema et al. 2005). As far as an increased photosyntheticcapacity is connected to larger biomass investments per unitleaf area (low SLA; Stitt & Schulze 1994) and/or largerrequirements of nitrogen, selection for plants with high pho-tosynthetic capacity may even lead to reduced yield (Boote &Tollenaar 1994; Sinclair & Purcell 2005).

The strong feed-forward mechanism that exists in individu-ally grown plants is not always appreciated. It may imply thata clear difference in plant size after a period of time could betraced back to only a small stimulation in one of the growthcomponents. A difference in biomass of 50% at the end of anexperiment, for example, is still relatively easily picked up.But if this was caused by one underlying component (e.g.

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Figure 2. (a) The percentual increase of canopy photosynthesisas affected by a hypothetical mutation that increases quantumyield (indicated as ‘q’) by 10% or a mutation that increases thephotosynthetic 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 leafarea index (LAI) of a monostand of Solanum lycopersicum.Simulations were done for a range of days in winter (black barsand lines; average light level 3.0 mol m-2 day-1) and summer (redbars and lines; average 27.5 mol m-2 day-1), with temperature fixedto 21 °C and are based on model INTKAM (Marcelis et al. 2009).

8 H. Poorter et al.


photosynthesis) that only needs to differ by ~10%, the chal-lenge to identify this component is much larger (Stitt &Zeeman 2012). And in the case that more components ofEqn 3 contribute, the percentual difference in each of thecomponents is likely to become smaller than the statisticalnoise.

B. The value of a sugar for individuallygrown plants

The idea that each additional sugar produced in the photo-synthetic process will lead to an equal amount of growthseems plausible at first sight. The rate of photosynthesisexpressed per unit leaf area is generally stimulated if plantsget more light, more CO2, more nutrients to invest in thephotosynthetic machinery or more water to allow operationat a higher stomatal conductance. Growth and productivityare stimulated under such conditions as well (Monteith 1977;Poorter & Navas 2003; Farooq et al. 2009). However, thereare a number of observations that do not comply with thisparadigm, such as a very neat, but rather overlooked experi-ment by Ludwig, Charles-Edwards & Withers (1975). Theyenclosed an individual leaf of a tomato plant in a cuvette,supplied it with controlled levels of light and CO2 during theday and measured net photosynthesis over the full lightperiod and respiration during the subsequent night. Interest-ingly, when Ludwig et al. manipulated photosynthesis duringthe day by altering the light level, night respiration wasstrongly affected (Fig. 3a). However, when the light level waskept constant, but daily photosynthesis manipulated by alter-ing the CO2 levels, respiration rate was affected far less.Apparently, in these leaves, it was not the produced amountof 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 dis-cussed in section 5, the growth response of plants to elevatedCO2 is generally smaller than the growth response to light.Doubling the CO2 concentration only leads to a modestincrease (~40%) in total plant mass (Poorter & Navas 2003)with concomitantly considerable starch accumulation(Stiling & Cornelissen 2007) to an extent that may occasion-ally even lead to disruption of chloroplasts (Cave, Tolley &Strain 1981). In quite some cases, downward regulation ofphotosynthesis is found (Medlyn et al. 1999), triggered byincreased sugar levels (Van Oosten & Besford 1995) andresulting in reduced transcription of Rubisco. None of thesedown-regulating processes is observed when plants receivemore light. Thus, it seems that not C-availability per se, butC-availability in conjunction with an additional signal isrequired to affect respiration (Fig. 3a) and growth. Such asignal could well be coming from light-signalling cascades.Strongly increased levels of non-structural carbohydratesmay then indicate a mismatch between supply of photosyn-thates on the one hand and demand for growth on theother.

Rather similar cases could apply under conditions ofdrought, low temperature or nutrient stress. It is obvious thatdrought decreases photosynthesis, at least partly through

reduced stomatal conductance, and that growth is diminishedas well. Yet, in a thorough analysis of drought effects on geneexpression, metabolic and enzymatic levels as well as photo-synthesis and growth in Arabidopsis, Hummel et al. (2010)found that drought-stressed plants actually had a morefavourable C-balance and concluded from this and other

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Figure 3. (a) Leaf respiration integrated over the night period asa function of the rate of photosynthesis integrated over the dayperiod before. Data are for Solanum lycopersicum, as published byLudwig et al. (1975). Reproduced with permission from SpringerVerlag. Blue squares indicate the night respiration whenphotosynthesis during the day was modulated by the application ofa range of light intensities (~70–1200 mmol m-2 s-1) at a constantCO2 concentration (~300 mmol mol-1). Red circles indicate thedark respiration when photosynthesis during the day was alteredby 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 dependenton the fraction of fruits on the plants that was removed.Meta-analysis for 24 experiments described in literature. For eachexperiment, photosynthesis data were scaled to the value incontrol plants (zero-level pruning). The brown line indicates themedian response, the gray area the inter-quartile range (25th–75thpercentile) and the dotted blue lines the 10th and 90th percentileof 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 SupportingInformation Supplement S1.



observations that reduced photosynthesis was not the causeof the reduced growth, but probably more a consequence(see also Muller et al. 2011).

Low temperature effects on RGR and growth componentscan be variable, but on average, RGR declines through mod-erate decreases in all growth components (Eagles & Ostgard1971; Nagai & Makino 2009). Photosynthesis generallydecreases to some extent as well, whereas the starch concen-tration often increases (Gent 1986; Equiza, Miravé &Tognetti 1997). The overall picture is that in these cases, thedecrease in RGR is not a direct consequence of the decreasein photosynthesis either (Körner 2003). Nutrient stress hassimilar effects, in the sense that all growth components areinhibited (Rogers et al. 1998; De Groot et al. 2003), with astrong decrease in RGR as a consequence. Although, photo-synthesis is clearly negatively affected, also in these cases,there is almost invariably a strong increase in non-structuralcarbohydrates as well (Poorter & Villar 1997).

The concept of these so-called source–sink interactionsis certainly not new and has been well advocated in the1980s and 1990s by, for example Gifford & Evans (1981),Patrick (1988) Körner (1991) and Farrar (1993). The strongfeedback of sugar demand on photosynthesis has been con-firmed in many experiments with crop plants where theratio between leaves and fruits was manipulated (Fig. 3b) orsugar translocation was inhibited by cold-girdling (Krapp& Stitt 1995), with at least part of the feedback workingvia 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 toinclude in models if we want to simulate the biomass pro-duction of these organs (Marcelis et al. 2004; Mathieu et al.2008).

In conclusion, a linear chain of bottom-up effects, whereexternal conditions such as light, CO2 and temperature deter-mine the production of sugars, which subsequently controlgrowth, may capture a range of observations in a correlativeway reasonably well. However, when it comes to the actualmechanisms, it may not necessarily grasp the quintessence ofgrowth regulation. Failure to include this interaction in plantgrowth models may lead to erroneous conclusions. Forexample, several simulation models that analysed the effectof elevated CO2 on plant C-budgets and growth showed thatfuture scenarios particularly stimulate growth under condi-tions where the CUE is currently low (Lloyd & Farquhar1996; Ali et al. 2013). It is known from comparative experi-ments that slow-growing plants and plants that experiencelow nutrient levels do respire a larger proportion of theirphotosynthates 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 simulationmodels, slow-growing species and nutrient-poor plants wereexpected to profit most from elevated CO2. However, a meta-analysis of experimental data showed that in reality, suchplants are stimulated less in growth (Poorter 1998). Appar-ently, a bottom-up model of growth based on sugar avail-ability without inclusion of feedback mechanisms falls shorthere.

C. Modelling source–sink interactions

In most growth models to date, the production of plantbiomass is only driven by the availability of photosynthates.In essence, this approach considers a plant not very differentfrom a sports car: by improving the combustion, enlarging theengine or decreasing the resistance (= increased photosynt-hate production), the speed (= growth rate) can always beincreased. The cases discussed in section 4B illustrate that abetter analogy would be the concept of a bread factory: moreproduction will lead to more consumption up to a certainthreshold. Beyond that threshold, demand quickly saturatesand additional production will pile up as unsold commodity.Although the observations of source–sink interaction areclear, the mechanisms that determine demand for sugarshave not been elucidated yet. This hampers incorporation ofthe feedback controls into plant growth models.A number ofmodels partly accommodate source–sink interactions when itcomes to partitioning of photosynthates. In some, C-gain issimulated to be source-driven, based on standard calcula-tions of leaf photosynthesis, whereas the partitioning of thecarbon among the different plant organs is sink-driven(Marcelis & Heuvelink 2007; Jullien et al. 2011). Relative sinkstrength of the various organs is then determined by theirpotential capacity to accumulate assimilates, and sugars arepartitioned accordingly. Another option in this respect is toinclude simulation of sugar loading, phloem transport andunloading (Marcelis & Heuvelink 2007; Lacointe & Minchin2008). Most of the models that incorporate these kind ofsource–sink interactions have a horticultural background. Amore general approach, focussed on the overall source–sinklimitations on growth, was recently taken by Gent & Seginer(2012). They modelled vegetative growth responses of plantsto temperature and light based on the hypothesis that over awide temperature range, growth is governed by the minimumof the supply of carbohydrate from photosynthesis, and thedemand for carbohydrate to synthesize new tissue. The tran-sition temperature will of course be species-dependent.Quereix et al. (2001) included a direct feedback of carbohy-drates on the rate of photosynthesis, without going intomolecular details.

It is clear that our understanding of the processes of sugarmobilization and partitioning currently fall short for a fullymechanistic simulation model. At the same time, it is alsoclear that the output of models without source–sink feed-backs have to be considered critically, especially in caseswhere growth takes place at high CO2 levels, low temperatureconditions or low water or nutrient supply.

5. DRCs FOR GROWTH

In the evaluation of plant growth models, especially in theextent to which they can adequately incorporate the effect ofenvironmental factors, it is essential to compare the outputwith some form of real-world data (Palosuo et al. 2011;Rötter et al. 2012). A specific experiment where plants weregrown at control and a twice-higher concentration of CO2, forexample, could be used for such a purpose. However DRCs

10 H. Poorter et al.


can in principle serve as a far more powerful benchmark.They basically are empirical models, as discussed in section1A. A method to derive DRCs based on a large number ofindependent investigations has been described by Poorteret al. (2010). This method has been used, among others, toconstruct DRCs for SLA (Poorter et al. 2009) and biomassallocation (Poorter et al. 2012) for a wider range of environ-mental factors. They do not indicate the absolute values of atrait per se, but rather the relative response over the fullenvironmental range considered and could also be employedas the lowest, descriptive level of mechanistic plant growthmodels.

In order to come up with a calibration tool that may showhow well models do in relation to the issues discussed insection 4B, we compiled biomass data for ~130 papers in the

literature describing experiments with ~250 species grown atdifferent light levels and ~180 papers where the effect of CO2

was studied for ~240 species. Prerequisite for inclusion in thismeta-analysis was that for a given species, plants of all treat-ments within an experiment were harvested at the same day.All biomass values per plant species and experiment werescaled to the biomass value observed or interpolated at acommon reference value for each environmental factor.More detailed information is provided in Appendix A. TheDRCs, together with the overall distribution around themean are shown in Fig. 4. Light affected growth most overthe range considered (Fig. 4a), whereas the effect of elevatedCO2 across species, although smaller, was more consistent,given the relatively narrow bands around the medianresponse (Fig. 4b). Part of the larger variation in response to

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Figure 4. Dose–response curves (DRCs) of the response of total plant dry mass to (a) daily photon irradiance (DPI) and (b) atmosphericCO2 concentration. Values in (b) pertain to C3 species only. Panels (c) and (d) indicate median response curves for herbaceous and woodyspecies, 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 orinterpolated for that reference level. For more information on followed methodology see Appendix A and Poorter et al. (2010). The DRCsare based on ~130 publications for light and ~180 for CO2, which are listed in Supporting Information Supplement S3.



light was due to differential responses of the investigatedherbs and woody saplings (Fig. 4c), which was not present forCO2, at least not with regard to C3 species (Fig. 4d). Wesubsequently fitted non-linear equations through the scaleddata points. The statistically derived estimates of the param-eters of these equations can be found in Table 2, along withthe r2 of the relationship.

The fitted DRCs can help to evaluate quantitativelywhether the marginal increase in growth because of a mar-ginal increase in photosynthesis is always similar or not, asdiscussed earlier. The challenge here is how to scale the twodifferent environmental factors in a common way. Prelimi-nary measurements on the youngest full-grown leaves oftomato plants grown in a growth chamber at 400 mmolmol-1 CO2 and 300 mmol m-2 s-1 light (daylength 16 h; DPI17.3 mol m-2 day-1; day temperature 22 °C; E. Kaiser, per-sonal communication) showed that a short-term increase inphotosynthesis of 50% above that at ambient levels of lightand CO2 could be achieved by an increase of ~115% in lightor a 95% increase in CO2. The corresponding long-termincrease in growth, based on the DRCs for herbaceousspecies in Fig. 4c and d show quite deviating values. Using thelight and CO2 levels at which these tomatoes were growing asa baseline, the long-term biomass growth stimulation associ-ated 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 bemore sensitive to changes in light than to increases in CO2. Ofcourse, the direct connection we make here between short-term responses of photosynthesis at the leaf level and growthat the whole-plant level is too simplistic as more factors willmodulate the response. For example, the importance of lightfor stimulating photosynthesis increases if individual plantsstart to shade themselves, or plants grown in stands developlarger LAI. This is illustrated in Fig. 2b, where model simu-lations show that the effect of a 10% increase in light stimu-lates canopy photosynthesis more at high than low LAI. Theeffect of a 10% increase in atmospheric CO2 on the otherhand is smaller at high LAI, which is especially clear at highlight. On top of this shading effect come readjustments bythe plants in the form of alterations in leaf morphologyand anatomy (SLA), allocation (LMF, RMF) and chemical

composition. These differences quickly become complex,which illustrates both the avail of plant growth simulationmodels, as well as the need to properly calibrate thosemodels, for example, with the DRCs given in Fig. 4.

6. THE SUPRA-CELLULAR SIDE OFSYSTEMS BIOLOGY

Most of the knowledge applied in the growth models dis-cussed above was developed in a time that molecular biologywas in its infancy. That period was followed by a phase wherethe focus in plant biology was very much on the role ofindividual genes as the ‘blueprint of life’. This ‘genocentric’view was accompanied by great expectations for cropimprovement, which are to date not met yet (Sinclair &Purcell 2005). Some gene mutations cause (embryonic)lethality, quite some yield plants with hampered growth andmany do not result in phenotypic differences with the wildtype. Mutations or transformations that do improve growth,on the other hand, are very scarce. The reason for this couldbe that control of growth is shared by various organs andmany processes, with relatively strong homeostasis of plantproductivity as a result. It is, on the other hand, well knownthat species vary widely in their potential growth rate(Poorter & van der Werf 1998), and most crop species oftenshow only intermediate values for RGR. Therefore, theremust be scope for a physiological improvement of cropperformance.

The current advances in transcriptomics, proteomics andmetabolomics quickly push forward our knowledge at the(sub)cellular level. These approaches allow for a muchbroader perspective, where functioning and interaction of awide range of genes and gene products is considered simul-taneously. Although the challenges are daunting, the field ofsystems biology undoubtedly will move forward our insightsinto plant functioning. Unfortunately, for most system biolo-gists to date, the cellular level seems to be a logical upperboundary. In its most simplified form, plants are then consid-ered as a collection of cells, where the main direction ofcausation is upward, starting at the gene level, with transcrip-tion and translation controlling the protein levels, which sub-sequently determine the metabolome (e.g. Katari et al. 2010).It cannot be completely excluded that self-organization of

Table 2. The effect of irradiance and atmospheric CO2 on growth, considered over different species groups, the reference value used tonormalize 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 8 mol m-2 day-1 -52.26 50.22 0.01842 910 0.64Herbs 8 mol m-2 day-1 -182.7 179.6 0.007980 250 0.77Woody 8 mol m-2 day-1 -499.9 498.1 0.001624 660 0.62

CO2 All C3 370 mmol mol-1 1.340 -177.3 -0.8274 620 0.61Herbs C3 370 mmol mol-1 1.230 -262.8 -0.9088 320 0.65Woody C3 370 mmol mol-1 1.474 -121.2 -0.7464 300 0.56

Relationship are all significantly non-linear and are described by the equation log2(Y) = a + bXc; with X representing the values of theenvironmental factor and Y the scaled biomass values. The scaled biomass values were log2-transformed prior to the regression analysis to allowfor the logarithmic nature of ratios. For each relationship the degrees of freedom ( d.f.) and the r2 are indicated.



groups of cells is sufficient to allow for a properly functioningplant, even with such distinct organs as leaves, stems androots (Yang & Midmore 2009). However, it is more likely thatin the majority of organisms, there is strong downwardcontrol from the organ or plant level on the processes takingplace within the cell (cf. Noble 2012), regulated via all kindsof hormonal or other signalling cascades. The idea has there-fore been advocated by various plant biologists to extendsystems biology to the crop level (Hammer et al. 2004; Yin &Struik 2010; Lucas, Laplaze & Bennett 2011). Attractive as itis, this may be a formidable task, which is not easily accom-plished. Firstly, there is the problem that our insights into thecellular systems biology have not matured yet. Secondly,simulation models generally do not go down more than twoor three integration levels deeper than their variable of inter-est (crop yield in this case), as time-steps of the iterationsdecrease with the inclusion of lower integration levelswhereas complication and noise quickly increase. Thirdly,including too many processes and parameters in a model mayeasily lead to over-fitting.

Another issue in extending systems biology to the crop levelis that the ecophysiological mechanisms in most of the currentmodels are actually quite crude. We contend that at themoment, there is still too little insight into the supra-cellularpart of plant system biology. At the leaf level, mechanisms

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, atthe whole-plant level, our understandings are less clear.Whatare the costs of increased hydraulic conductance in terms ofvascular transport capacity (Brodribb, Feild & Sack 2010) oradditional root proliferation? What will happen toN-metabolism if plants produce less Rubisco (Stitt & Schulze1994)? How are plants in split-root experiments able toquickly up-regulate nutrient uptake in one compartmentwhen nutrients in the other compartment are withheld (Jeudyet al. 2010) and what then limits nutrient uptake in the controlplants? We badly need the type of simulation models that canhelp us in obtaining the insights in how whole plants mecha-nistically manage the compromises they need to make and thedifferent roles that the various organs fulfil in that respect.When sufficient mechanistic detail is included in a whole-plantmodel, then it would also be relatively easy to expand to themolecular mechanisms, such as repression of Rubisco synthe-sis in the case of sugar accumulation.

A requirement of such a strongly mechanistic model isthat it would adequately represent the trade-offs and corre-lations that exist among the various processes and state vari-ables. It is therefore of interest to know what the correlationnetwork is for the traits that together constitute the

RGR

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Figure 5. Correlation network for 15 growth-related traits, describing the interrelations in a comparison of fast- and slow-growingherbaceous 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 ratiosin the growth equations; blue nodes, anatomical and chemical traits. Data are taken for the growth of 24 forbs and grasses grown underconstant conditions and optimal nutrient supply in a growth chamber (Poorter & Remkes 1990; Poorter et al. 1990; Poorter & Bergkotte1992).



phenome of the plant. A considerable amount of informa-tion is required to analyse such a correlation network, as oneneeds both a wide variety of species or genotypes, as well asa large range of measured traits. We calculated such a corre-lation network, based on an experiment where ~50 physi-ological, morphological and chemical traits were measuredalong the framework discussed in section 3. These traits wereanalysed for 24 herbaceous species, all grown under identicalconditions (Poorter, Remkes & Lambers 1990). A simplifiedscheme with 14 of the most important variables is given inFig. 5, the full correlation network can be found in Support-ing Information Supplement S2.

What can we learn from such a network? Firstly, the posi-tive and negative relationships in such a network could beconfirmations for mechanistic trade-offs that are knownalready. For example, species with a high SLA are generallyknown 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 whole-plant level, plants with a high allocation to leaves (LMF) arelikely to invest only a smaller fraction of their biomass in theroots. This may have negative consequences for the amountof water taken up per unit leaf area, with low stomatal con-ductance and, hence, a low rate of photosynthesis per leaf

area as a consequence. Secondly, observed correlations mayindicate as yet less-explored feedbacks or feed-forwards thatoccur at the supra-cellular level. For example, in this com-parison species with a low investment in roots show a highnutrient uptake rate per unit root mass (NIR). Thirdly, somepreviously observed trade-offs, for instance between ULRand SLA (Villar et al. 2005) or ULR and LMF (Ceriani,Pierce & Cerabolini 2008) are not found in this dataset. Thisleads to the question, which of those could just be spuriouscorrelations. A further analytical step could then be toanalyse the partial correlations as well, which show the indi-vidual relation between two variables while the effect ofall other variables in the network are statistically controlledfor.

Incongruent networks could be obtained if differentgroups of species are studied.A very relevant question there-fore is how representative this network is.Would the networkbe similar if another group of fast- and slow-growing specieswould be taken or are they possibly only valid within a spe-cific functional or phylogenetic group of species? And howstrongly does the network depend on the environment? Anindication of the latter can be found in Fig. 6 where a corre-lation network is given for an experiment with 10 herbaceousand woody species grown at low and high light levels. Someof the trait correlations, indicated in blue and red, are of

[C]

[NO3]

[N]

Chla/b

[Chl]

Chl/N

[Rub]

SLA

LMF RMF

LD

Abs

pi/pa

Aa

AmRm

Ams

PNUE

J

Vc

J/Vc

LVA

gs

Figure 6. Correlation network for 23 photosynthesis- and growth-related traits, describing the interrelations in a comparison of a range ofherbaceous 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 indicatepositive correlations under both conditions, lines in red consistent negative correlations. Grey lines indicate |r| > 0.6 correlations observedonly 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 bothintensities; 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 aretaken for the growth of four woody and six herbaceous species, all eudicots grown under constant conditions and optimal nutrient supply ina growth chamber (Poorter & Evans 1998; Evans & Poorter 2001).



similar sign and strength at both light levels. The positivecorrelation between SLA and Am, as already found in Fig. 5,is also observed here at both low and high light levels and, infact, also in worldwide comparisons of field-grown plants(Wright et al. 2004). The negative correlations betweenSLA, Nm, Am and related photosynthetic traits expressedon a mass basis on the one hand and leaf density andC-concentration on the other hand are also consistent in bothenvironments. However, a number of other correlations onlyshow up at low light, others only at high light (colour-codedgrey and orange, respectively). Clearly, we start to obtaingeneralized information of responses of individual traits(Poorter et al. 2012), but ultimately, we need to know how thewhole network behaves and understand the extent to what itcan be deformed under various external conditions.

No matter how we acquire the required information, it isclear that mechanistic simulation models are indispensable totest our knowledge of the system. The challenge is then toobtain a mechanistic model that can adequately representthe observed correlation network and its response to theenvironment. As much as applied models are often only cali-brated against, for example, the TDM or yield of the plants atthe end of the experimental period, for this type of analysismodel output, should be tested against the experimentallymeasured performance of all the relevant state and rate vari-ables in the network. Only in this way, which has been named‘virtual profiling’ (Génard et al. 2010), we are able to detectwhere our model knowledge deviates from the behaviour ofwhole plants.

If the virtual profiling of the supra-cellular modeladequately covers the observed correlation network, thelogical next step is to extend such a plant model with the fullmolecular detail of the cellular part of systems biology as wellas the patterns and processes at the crop level. This is asformidable 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 levelsfrom cell to globe, it would be a missed opportunity if wewould not try now to make the connection between gene andwhole plant or crop (Yin & Struik 2010). Relationships thathave been established between metabolite levels and finalplant mass (Sulpice et al. 2009) could be a good basis tostart with.

CONCLUSIONS

In this review, we discussed a range of plant growth modelswith varying physiological detail: (1) empirical modelswithout 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 factorizingRGR into increasingly smaller subcomponents. All of themfall short yet if we want to understand the systems biologyof plant growth at the supra-cellular level. We call for adedicated mechanistic modelling approach, which considersthe 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

how successful a plant integrates the various processesand organs, the main result of such a model would be animproved understanding of the intricate network of physi-ological and morphological traits and how that is respondingwhen the environment changes.

ACKNOWLEDGMENTS

Elias Kaiser kindly provided photosynthesis data on tomatofor this paper, while Maarit Maënpäa helped in the literatureanalysis. Dimitrios Fanourakis, Jochem Evers, Danny Tholen,Maarit Maënpäa and two anonymous reviewers made usefulcomments 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, theMetaPhenomics database described by Poorter et al. (2010)was used. In short, data were collected from a large range ofexperiments published in the scientific literature over the last50 years. Firstly, prerequisite for inclusion was that plantswere grown in two or more environmental conditions inwhich the level of light or atmospheric CO2 level was experi-mentally affected. Secondly, prerequisite was that plantsdeveloped at least 80% of their biomass under the conditionswhere the different treatments were applied so that theywere well able to acclimate to their environment. Thirdly,prerequisite was that all plants for a given species in a giventreatment were harvested at the same day. All biomass datawithin a given experiment and species were then standard-ized relative to the biomass observed at the reference levellisted in Table 2. Subsequently, data were categorized in sub-classes over the environmental factor considered; and the10th, 25th, 50th, 75th and 90th percentile of the scaled TDMdistribution are calculated for each interval (Fig. 4). For bothdaily irradiance and CO2, data were fitted with a non-linearequation of the form log2(Y) = a + Xc, where X is the envi-ronmental 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 ofthe experiment affected the DRC, but no significant effectcould be found.

References for the literature data that were included in theanalysis are given in Supporting Information Supplement S3.

SUPPORTING INFORMATION

Additional Supporting Information may be found in theonline version of this article at the publisher’s web-site:

Supplement S1. Literature sources for the data distributionof Fig. 3b, relating the rate of photosynthesis per unit leafarea 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 thedata for the calculation of dose–response curves of Fig. 4were derived.



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Physiological mechanisms in plant growth models