Under what circumstances can process-based simulation models

Journal of Experimental Botany, Vol. 61, No. 4, pp. 955–967, 2010doi:10.1093/jxb/erp377 Advance Access publication 27 December, 2009

REVIEW PAPER

Under what circumstances can process-based simulationmodels link genotype to phenotype for complex traits? Case-study of fruit and grain quality traits

Nadia Bertin1,*, Pierre Martre2,3, Michel Genard1, Benedicte Quilot4 and Christophe Salon5

1 INRA, UR1115 Plantes et Systemes de Culture Horticoles, F-84 914 Avignon, France2 INRA, UMR1095 Genetique, Diversite et Ecophysiologie des Cereales, F-63 100 Clermont-Ferrand, France3 Universite Blaise Pascal, UMR1095 Genetique, Diversite et Ecophysiologie des Cereales, F-63 100 Clermont-Ferrand, France4 INRA, UR1052 Genetique et Amelioration des Fruits et Legumes, F-84 143 Avignon, France5 INRA, UMR102 Genetique et Ecophysiologie des Legumineuses, F-21 065 Dijon, France

* To whom correspondence should be addressed: E-mail: [email protected]

Received 4 November 2009; Accepted 3 December 2009

Abstract

Detailed information has arisen from research at gene and cell levels, but it is still incomplete in the context of

a quantitative understanding of whole plant physiology. Because of their integrative nature, process-based simulation

models can help to bridge the gap between genotype and phenotype and assist in deconvoluting genotype-by-

environment (G3E) interactions for complex traits. Indeed, G3E interactions are emergent properties of simulationmodels, i.e. unexpected properties generated by complex interconnections between subsystem components and

biological processes. They co-occur in the system with synergistic or antagonistic effects. In this work, different kinds

of G3E interactions are illustrated. Approaches to link model parameters to genes or quantitative trait loci (QTL) are

briefly reviewed. Then the analysis of G3E interactions through simulation models is illustrated with an integrated

model simulation of peach (Prunus persica (L.) Batsch) fruit mass and sweetness, and with a model of wheat (Triticum

aestivum L.) grain yield and protein concentration. This paper suggests that the management of complex traits such as

fruit and grain quality may become possible, thanks to the increasing knowledge concerning the genetic and

environmental regulation of organ size and composition and to the development of models simulating the complexaspects of metabolism and biophysical behaviours at the plant and organ levels.

Key words: Fruit, gene-based model, genotype-by-environment interaction, genotypic parameter, grain, QTL-based model,quality, simulation model.

Introduction

Like many quantitative crop traits, the quality of harvested

organs is a complex issue, which results from many

overlapping physiological processes, genetically and envi-

ronmentally controlled during grain, seed or fruit develop-

ment. Over the last 50 years, yield for various crops has

continuously increased due to genetic and crop management

progresses (Calderini and Slafer, 1998; Cassman, 1999,

2001), but, at the same time, quality attributes have levelledoff or even decreased for numerous products such as cereals

(Oury et al., 2003), grain legumes (Weber and Salon, 2002;

Graham and Vance, 2003), oilseeds (Triboi and Triboi-

Blondel, 2002), fruits for processing (Grandillo et al., 1999)

or fresh fruits (Causse et al., 2003). Thus, a critical question

for the future is how to manage crop quality while

maintaining yield, by finding the best combinations of

genetic resources and cultural practices adapted to, and

respectful of specific environments.

Despite the identification of numerous quantitative traitloci (QTL) for quality traits, and the identification of genes

involved in their control for different species, the genetic

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improvement of crop quality is still a complicated and

rather slow process. Up to now, few physiological functions

have been clearly ascribed to known gene sequences and, to

date, the huge progress in gene discovery has only weakly

aided genetic selection (Miflin, 2000; Sinclair et al., 2004).

This results at first, from the complexity of most of the

traits of interest and of their sensitivity to the environment.

Secondly, the processes involved are controlled by multipleinteracting genes, which themselves interact with the

environment and crop management (Causse et al., 2007).

For instance, in tomato (Solanum lycopersicum L.) fruit,

more than 100 genes located in 16 regions of the genome,

are associated with fruit composition, mainly sugar and acid

contents (Causse et al., 2004; Bermudez et al., 2008).

Consequently, QTLs for a given trait usually explain only

low proportions of the observed trait variations. Moreover,most of these QTLs depend on the environment and on the

genetic background (Borner et al., 1993; Blanco et al., 2002;

Chaıb et al., 2006; Dudley et al., 2007). This usually results

in strong genotype-by-environment (G3E) or genotype-by-

management interactions, which renders the research in

genetics and their applications for selection complex. As

a consequence, in order to analyse the genetic and

environmental determinants of crop attributes, agronomistsand geneticists often have to perform extensive experiments

over several years at different sites or under different

environmental conditions. Although this approach is still

useful to evaluate QTL stability (Prudent et al., 2009), it is

laborious, expensive, and time-consuming and, thus, it is

often limited to the comparison of a low number of

genotypes and traits conducted under restricted environ-

mental conditions.To overcome these difficulties, several authors have

proposed the use of ecophysiological process-based simula-

tion models for analysing QTL or genotype effects on

different processes and for different species. For example,

this has been done for yield in barley (Hordeum vulgare L.;

Yin et al., 2000), phenological development in soybean

[Glycine max (L.) Merr.; Stewart et al., 2003], leaf elonga-

tion rate in maize (Zea mays L.; Reymond et al., 2003), orfruit quality in peach [Prunus persica (L.) Batsch; Quilot

et al., 2005b]. Different approaches have been proposed to

introduce genetic information into simulation models; they

have been applied successfully to predict the parameter

values of specific gene or allele combinations (Shorter et al.,

1991; White and Hoogenboom, 1996; Yin et al., 1999), to

design new ideotypes adapted to target environments

(Kropff et al., 1995; Tardieu, 2003; Letort et al., 2008), andto analyse G3E interactions (Yin et al., 2005).

All of these studies outlined the possibility of process-

based simulation models for predicting G3E interactions

under a wide range of conditions. They also pointed out the

need for upgraded models, in particular to predict complex

traits, and highlighted the necessity to link model parame-

ters with easily measurable physiological traits and known

QTLs or genes (Yin et al., 2004; Struik et al., 2007).Objectives of this paper were to illustrate how process-

based simulation models can help in bridging the gap

between genotype and phenotype, due to their intrinsic

capacity to mimic complex systems and to integrate multi-

scale levels of controls. How G3E interactions emerge from

process-based simulation models is first outlined, and the

model structure necessary for such analysis is briefly

discussed. Ways to introduce genetic information in these

models are subsequently presented and are illustrated using

fruit size and sweetness, and cereal yield and grain proteinconcentration, as two examples.

Genotype-by-environment interactions areemergent properties of process-basedsimulation models

Process-based simulation models are mathematical surro-

gates, and one of their functions is to describe the

interconnections and feedback regulations between sub-

system components (e.g. organs or tissues) and biological

processes (e.g. photosynthesis or protein synthesis). The

notion of a single limiting factor is thereby replaced by theidea of a sequence and/or network of different limitations

operating through the plant’s life cycle. These interconnec-

tions and feedback regulations among the system compo-

nents generate unexpected global system properties, called

emergent properties, which do not appear when the

subsystems are individually considered (Trewavas, 2006).

G3E interactions are emergent properties of the whole

system in which several processes interact, though they canalso operate at the process level.

At the process level, G3E interactions occur when

expression of the genotypic variation of a process depends

on the environment. Three types of G3E interactions can

be observed (Fig. 1). The first type arises from genotype-

dependent responses to an environmental variable (Fig. 1a).

This is the case of fruit or grain demand for carbon, which

is driven by temperature, but the temperature responsecurve is genotype specific (Lescourret et al., 1998). A more

complex situation, although very frequent in plants, is when

a process does not depend directly on environmental

variables, but on plant variables which themselves depend

on environmental variables. In that case, the response of the

process to the plant variable may be unique whatever the

genotype (Fig. 1b). This is the case of light-saturated

photosynthesis which depends on leaf carbohydrate reservethrough a unique response curve, as shown for peach trees

(Prunus persica L.; Quilot et al., 2002). In such a case,

a G3E interaction arises if the plant variable depends both

on the genotype and on the environment, and the process

intensity varies with the plant variable (Fig. 1b). The third

type of interaction at the process level arises when the

response curve of the process to the plant variable also

depends on the genotype, which allows interactions for thesame reason as in the previous case, but also because the

response of the studied process to the plant variable

depends on the genotype (Fig. 1c). This is the case of leaf

photosynthesis response to leaf nitrogen content in rice

which is genotype dependent, as illustrated in Yin and

956 | Bertin et al.


Struik (2008). These three types of interactions can act

together in the whole system allowing either the emergence

of strong interactions at the whole system level or the loss

of interactions when several processes respond in an

opposite way to genotype or environmental variations.

Interactions can also emerge at the level of the whole

system. This can best be illustrated with a simple theoretical

model having just two processes, each of them varyinglinearly with an environmental variable without any G3E

interactions (i.e. the slope of the relationship between the

process and the environmental variable is independent of the

genotype; Fig. 2a, b), and where an output (or intermediate)

variable is the product of these two processes. If, for at least

one of these two processes, the y-intercept of the relationship

depends on the genotype, then the output (or intermediate)

variable varies non-linearly in response to environmentalvariations, and as a consequence, a G3E interaction emerges

at the whole system level (Fig. 2c).

Which models and which parameters to linkgenotype to phenotype?

Some mechanistic models to integrate physiologicalknowledge

Most growth simulation models currently used were origi-

nally developed for agronomic applications. These models

were constructed using empirical response curves or laws

describing the relationship between plant growth and

environmental conditions and management practices (e.g.N dilution curve; Lemaire and Gastal, 1997). Although

these process-control oriented models are robust, they are

less plastic than real plants, hence restricting their capabilities

to accurately represent the wide range of plant responses to

environmental and genetic variations.

Predicting complex issues such as product quality traits in

relation to G3E interactions, requires the design of mecha-

nistic models: such models have to describe physiologicalprocesses and their response to variations in environmental

conditions, to allow physiological feedback features and the

integration of information from different organizational

levels, for instance from cell to organ (Struik et al., 2005;

Genard et al., 2007). According to Chapman et al. (2003),

models need to produce emergent properties, i.e. they should

be able to handle perturbations to any process and self-

correct, as do real plants. As stated by these authors, thisphilosophy of modelling the principles of responses and

feedbacks infers that models should be able to express

complex behaviours. Such models of fruit and seed or grain

quality have been developed over the last decade. Their

current state has recently been reviewed (van Ittersum and

Donatelli, 2003; Bertin et al., 2006; Martre et al., 2009): for

Pro

cess

Plant variable

(b)

G1 G2E1

G1 G2E2

Pro

cess

Environmental variable

Genotype 1

Genotype 2

(a)

E1 E2

Pro

cess

Plant variable

(c)

G1 G2E1

G1 G2E2

Fig. 1. Schematic representation of three types of genotype (G) by

environment (E) interactions at the process level. (a) Direct G3E

interactions, i.e. the response of the process to environmental

variations depends on the genotype. The process may not depend

directly on the environment but on a plant variable. The response

of the process to the plant variable may be unique whatever the

genotype (b). In that case, a genotype-by-environment interaction

is observed if the process varies with the plant variable which itself

depends on G3E interactions. The third type of interactions occurs

when the response curve of the process to the plant variable also

depends on the genotype (c), which allows interactions for the

same reasons than in (b), but also because the response of the

process to the plant variable depends on the genotype.

From genotype to phenotype through simulation models | 957


wheat and seeds, they focus on size and protein concentra-

tion and composition (e.g. starch, gluten-forming proteins,

albumin proteins), which are the most important criterion

determining the end-use value of the product. For fresh

fruits, models of quality describe the main processes control-

ling fruit size, and sugar and acid composition, which are

largely involved in flavour perception. In these models, the

environment is characterized through the measurement ofenvironmental variables (temperature, light, humidity, min-

eral nutrient availability etc), and the plant is characterized

by developmental variables (date of flowering and number of

flowering nodes etc), growth variables (biomass, amount of

retrieved nitrogen etc) and metabolic variables (respiration,

sugar synthesis etc).

In such mechanistic models, it is now possible to link

model parameters with physiological traits or process andto link them with loci or genes. Below, the constraints on

model parameters are defined. The relatively low number of

parameters (a few tens to a couple of hundreds in most

simulation models) in comparison with the 20 000 to 40 000

genes of a plant can be explained by the co-ordinated action

of groups of genes, and the lower effect of a gene expression

when it is replaced in its metabolic pathway, at the cell,

organ or plant level (Salon and Vance, 2004, Fernie et al.,2005). The set of interconnected processes controlled by

such a group of genes was defined by Tardieu (2003) as

‘meta-mechanism’.

Genotypic and generic parameters of simulation models

Though plant traits are generally dependent on genotype,

environment, and management, the parameters of theequations describing these meta-mechanisms are, ideally,

independent of the environment and management. One can

distinguish two types of parameters in a process-based

simulation model: the genotypic parameters and the generic

parameters. Generic parameters do not significantly vary

among genotypes, or even among species. As such, in the

peach growth model (Quilot et al., 2002), the light-saturated

photosynthesis which determines the maximum dry matteraccumulation is a generic parameter since it does not vary

among peach genotypes and even seems stable in the Prunus

genus. By contrast, genotypic parameters (also called

genetic coefficients) are model parameters, (i) of which

values show a significant range of variation among the

studied genotypes, and (ii) which have significant influences

on model outputs (Boote et al., 2001), and thus are likely to

induce changes in important emergent properties. The set ofgenotypic parameters defining a particular genotype repre-

sents a phenotypic fingerprint of this genotype. To be con-

sidered as a ‘good’ genotypic parameter, a model parameter

must be precisely estimated and, ideally, with low labour

cost to be estimated on a large number of genotypes. It

should be process-based and, ideally, the availability of

mutants for this parameter would allow the validation of its

theoretical variations in the model. Examples of ‘good’genotypic parameters are illustrated later.

Environmental variable

Qua

lity

trai

t yP

roce

ss h

Pro

cess

f

Genotype 1

Genotype 2

(a)

(b)

(c)

E1 E2

Fig. 2. Schematic representation of G3E interactions at the whole

system level. A simple system with two processes, f (a) and h (b),

is considered. These two processes vary linearly with the

environment (E), and depend on the genotype without any G3E

interaction. The variations of f and h are described by the following

equations: f(E,G)¼aE+g1(G) and h(E, G)¼bE+g2(G) where a and bare two generic (constant) parameters, and g1(G) and g2(G) are

two parameters which depend on the genotype. A quality variable

(y) which depends on these two processes according to the

equation: y¼f(E,G)3h(E,G), is considered (c). y responds

non-linearly to variations of the environmental variable and

a G3E interaction emerges at the whole system level.

958 | Bertin et al.


Sensitivity analysis of the model to its parameters can

help in identifying important genotypic parameters, and

their putative effects under different climate and manage-

ment practices. Sensitivity analysis of the peach growth

model followed by the analysis of the variation among

genotypes in the values of the most important parameters,

showed that among the 40 parameters of this model, only

10 are genotypic key parameters (Quilot et al., 2005a).

From genotype to phenotype

Making links between model parameters and genes or QTLs,

implies that the model captures sufficient details and physio-

logical functionalities, necessary to simulate the expression

of single genes or a gene network. Several attempts and

approaches have been proposed to include genetic informa-tion into process-based models and to go from genome to

organ (Reymond et al., 2003), plant (Quilot et al., 2005b) or

crop (White and Hoogenboom, 1996; Chapman et al., 2003).

These approaches are briefly reviewed below.

Gene-based modelling

Because genotypic parameters are independent of the

environment, one can theoretically predict their value

knowing the genotype. On this basis, genetic information

can be integrated into simulation models. The phenotype

can then be simulated in silico under various environmentaland management conditions. This approach was pioneered

by White and Hoogenboom (1996) and Hoogenboom and

White (2003) who replaced genotypic parameters of the

BEANGRO simulation model for common bean (Phaseolus

vulgaris L.) by linear functions describing the effect of eight

genes affecting phenology (ppd, Hr, and Tip), growth habit

(Fin and Fd) and seed size (Ssz-1, Ssz-2, and Ssz-3). The

genotypes of 30 common bean cultivars were determined forthese genes, with two alleles for each gene, one dominant

(coded 1) and the other one recessive (coded 0). The new

model, GeneGro, simulated growth and development as

well as BEANGRO, and could even simulate new G3E

interactions, providing major simplifications since the 30

genotypic parameters of the BEANGRO model were

replaced by only eight binary coefficients, the eight loci. As

pointed out by these authors, the genotypes can usually bedetermined more precisely by these coefficients than by

field-determined genotypic parameters, so gene-based mod-

els should also reduce uncertainties in the calibration of

simulation models and facilitate model calibration for new

genotypes. This approach has recently been included into

the soybean simulation model CROPGRO-soybean to

characterize the effect of six loci on growth and develop-

ment, using a set of isogenic lines (Messina et al., 2006).These studies suggest that only a few genes need to be

characterized in order to simulate genetic variations and

G3E interactions for complex traits such as seed size,

challenging the current view that quantitative traits have

polygenic inheritance. However, the genes included in the

BEANGRO and CROPGRO-soybean models may repre-

sent the action of co-regulated groups of genes and thus

they are similar to estimates of QTL. Indeed the three

hypothetical genes controlling seed size for common bean

introduced in GenGro were mainly inferred from QTL

studies. The next steps would be to simulate the regulation

of gene expression(s) and the effects of genes at the process

level rather than through cultivar coefficients.When a trait is controlled by a low number of major

genes, bottom-up modelling of a gene network can also be

attempted. Such an approach has been successfully used to

model flowering time (Welch et al., 2003, 2004) and cell cycle

and expansion in leaves (Beemster et al., 2006) for Arabidop-

sis [Arabidopsis thaliana (L.) Heynh.], but it has not been

applied to fruit or grain quality traits yet. Although gene

networks have the potential for becoming overly complex,there is probably no need to model full networks, as it should

be possible to extract simple rules which could capture the

effects of major genes involved in the network.

Currently, the strongest limitation to develop a gene-

based model for complex traits, is the lack of knowledge

and characterization of specific genes or loci controlling

these traits, including epistatic interactions and pleiotropic

effects, to define the phenotypic fingerprint of cultivars forgenotypic parameters. Moreover, detailed studies to quan-

tify the environmental effects on gene expression and gene

action are also required.

QTL-based modelling

In the absence of information on specific genes or loci, QTL

analysis can be performed on model parameters considered

as quantitative physiological traits. Then, for each genotype

of a mapping population, the values of genotypic parame-

ters can thus be predicted based on the allelic composition

at the molecular markers flanking the QTLs, taking into

account interactions between alleles and among QTLs

(dominance, additivity, and epistasis). This approach waspioneered by Yin et al. (1999, 2000), who recalculated the

value of 10 genotypic parameters of the SYP-BL simulation

model for barley, related to crop growth. The major

weakness of this approach was the ability of the original

model to simulate observed variations. This work has been

extended to barley (Yin et al., 2005) and rice (Oryza sativa

L.; Nakagawa et al., 2005) phenology. The QTL-based

models were able to simulate the phenology of recombinantinbred lines in new environments. QTL-based models were

also developed to analyse the genetic variability of leaf

elongation rate for maize in response to temperature and

soil water deficit (Reymond et al., 2003, 2004). In these

studies, a simple static model based on response curves of

leaf elongation rate to temperature, vapour pressure deficit,

and soil water potential was used. Thirteen maize lines

grown under six contrasted environments were used asmaterial for validating the model, which accounted for 74%

of the genetic and environmental variations of leaf elonga-

tion rate (Reymond et al., 2004).

More recently, this approach was extended to peach

fruit quality. Based on the sensitivity analysis of the virtual



peach fruit model and the analysis of the variation among

139 genotypes in the values of the most important

parameters (Quilot et al., 2005a), 10 genotypic parameters

which strongly affect fruit growth and sugar accumulation

were selected among the 40 parameters of the model, for

a QTL analysis (Quilot et al., 2005b). These genotypic

parameters were substituted in the simulation model by the

sum of QTL effects. The model was then able to accountfor a large part of the genetic and environmental varia-

tions in fruit size (observed and predicted values of fruit

dry mass showed a correlation coefficient of 0.55). In this

example, the QTL analysis of the genotypic parameters

gave some insight on the processes that control quality

traits, as they co-localized on the genetic map with QTLs

for fruit size and sugar content. This suggests putative

physiological interpretations of the functions of genesunder these QTLs. For instance on the linkage groups 1

and 7 of the peach genetic map, QTLs for fruit fresh mass

were located at the same regions as QTLs for genetic

coefficients involved in sugar metabolism, pulp carbon

growth, and in and out water fluxes in the fruit (Quilot

et al., 2005b).

Analysis of G3E interactions throughprocess-based simulation models: case-study of fruit and grain quality traits

The significance of process-based simulation models of

quality traits can be exemplified through the analysis of

both genotypic and environmental effects, using two in-

tegrated models of quality, one for peach fruit and the other

for wheat grain.

Predicting peach fruit size and sweetness index inresponse to tree management and genetic variationsunder variable environmental conditions

The virtual peach fruit model of Lescourret and Genard

(2005) predicts the fresh mass, dry matter content, andsugar composition of fruit, in response to environmental

fluctuations, by coupling three main sub-models (Fig. 3): (i)

a carbon sub-model which calculates the daily carbon

availability (assimilation and remobilization from reserves)

and allocates carbon among vegetative and reproductive

organs, based on organ demand and priority rules. It thus

determines the daily carbon flux to any average fruit of the

Relativehumidity

C f low

H20 loss

Fruit fresh massProportion of flesh

Flesh dry matter content

4 sugarscontent

C02 emission

flesh dry massstone dry mass

C reserves

Temperature

Temperature

CarbonPhotosynthesis

Stem carbon balanceStone and f lesh dry growth

Radiation

Leaf water potential

State of the system

WaterOsmotic pressureTurgor pressureTissue plasticity

Stem water potential

SugarsCarbon partitioning into

sucrose, sorbitol, glucose and f ructose

Amounts of sugars

RespirationSustain and growth

TranspirationFruit conductance

Matter or information fluxesMain outputsEnvironmental inputs

Submodelvariables

Fig. 3. Schematic representation of the virtual peach fruit model (Lescourret and Genard, 2005). Main quality traits predicted by the

model are flesh and stone dry and fresh masses, flesh dry matter and total sugar contents, and fruit sugar content. The model integrates

three sub-models: a carbon sub-model simulates carbon partitioning based on organ demand and priority rules. Sugar accumulation is

simulated by a metabolic sub-model that predicts the increase of total sugar content in the flesh during fruit growth. Fruit fresh mass

accumulation is simulated by a water sub-model that predicts water fluxes as a function of the osmotic and turgor pressures, bio-

rheological cell wall properties, and hydraulic conductivity.

960 | Bertin et al.


stem; (ii) the SUGAR model (Genard and Souty, 1996;

Genard et al., 2003) which uses this daily influx of carbon as

input to simulate the metabolic transformations among

respired CO2, individual sugar metabolism (sucrose, sorbi-

tol, glucose, and fructose) and other compounds (structural

carbohydrates); (iii) a water sub-model (Fishman and

Genard, 1998) that predicts the water fluxes and tissue

expansion as a function of the osmotic and turgor pressures,bio-rheological cell wall properties, and hydraulic conduc-

tivity. The fruit osmotic pressure is calculated from sugar

content and composition simulated by the SUGAR sub-

model. The rules of communication among the three sub-

models are detailed in Lescourret and Genard (2005). The

model predicts fairly well the fruit fresh and sweetness index

in response to wide ranges of tree management practices

(leaf to fruit ratio) and environmental conditions (year; Fig.4a, b). As experimentally observed by Genard et al. (2003),

under low fruit-to-leaf ratios the model predicts that fruit

sugar content increases with fruit size. The simulated

sweetness was slightly underestimated for the sweetest

fruits, hypothetically because of an over-simplified descrip-

tion of carbon metabolism in the SUGAR model.

The ability of the virtual peach fruit model to simulate

genetic variations of fruit quality has been investigated for

a mapping population of 139 hybrid lines (Fig. 4c, d). Ten

genotypic parameters have been assessed for each line

(Quilot et al., 2005a). They allowed 95% and 52%, re-

spectively, of the observed genetic variations in fruit fresh

mass and sweetness index to be explained.

Considering the ability of such models to simulate theeffects of crop management or genetic variations, they can

be used to analyse virtual variations in the system. Let us

consider ten virtual genotypes differing by a single geno-

typic trait involved in carbon allocation among sink organs,

i.e. their potential fruit dry mass which ranged from 10 g to

100 g. This parameter is positively linked to the individual

fruit demand (equation 1 in Lescourret and Genard, 2005).

The environment was manipulated through plant manage-ment, i.e fruit pruning, which varied from 1 to 10 fruits per

branch. This factor affects the level of competition among

growing sinks as the carbon available for growth has to be

shared among individual fruits. The model was run for the

100 combinations of these two factors, and simulations of

fruit fresh mass and sweetness at harvest were analysed. The

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Sim

ulat

ed F

resh

wei

ght (

g)

Observed Fresh weight (g)

(a)

R2=0.95Slope = 0.90RRMSE = 0.13

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

Sim

ulat

ed F

resh

wei

ght (

g)

Observed Fresh weight (g)

(c)

R2=0.95Slope = 0.99RRMSE = 0.08

0

5

10

15

20

0 5 10 15 20

Sim

ulat

ed S

wee

tnes

s (%

)

Observed Sweetness (%)

(d)

R2=0.52Slope = 0.66RRMSE = 0.18

0

3

6

9

12

0 3 6 9 12

Sim

ulat

ed S

wee

tnes

s (%

)

Observed Sweetness (%)

(b)

R2=0.61Slope = 0.58RRMSE = 0.15

Fig. 4. Predicted values at maturity plotted against corresponding observed values for fresh fruit mass (a, c) and sweetness index (b, d)

collected in different experiments on peach fruit exploring the crop management (a, b) and genetic (c, d) variability. (a, b) Data (cv.

Suncrest) represent individual fruits sampled on experiments carried out over three years and at different leaf-to-fruit ratios. Simulations

were performed with a single set of parameters given in Lescourret and Genard (2005). (c, d) Data represent mean fruit value over five

fruits for 139 hybrid lines of a mapping population obtained from the second backcross of an interspecific Prunus persica L.

(Batsch)3Prunus davidiana cross. Simulations were performed considering 10 genotypic parameters (Quilot et al., 2005a). Statistics

concern the linear regression between observed and simulated data. RRMSE indicates the relative root mean squared error. Solid lines

are y¼x.



model predicted a significant management-by-genotype in-

teraction (Fig. 5) emerging from multiple interactions

among the processes involved in both traits, as more simply

illustrated in Fig, 2 for two processes. These interactions

induced a cascade of effects, including feedback effects

which cannot be intuitively predicted. Finally, fruit fresh

mass and fruit sweetness differently responded to fruit load

according to the potential dry mass. In good agreementwith observed data (Johnson and Handley, 1989), these

simulations clearly show that accurate management of fruit

load is essential for genotypes with high fruit size potential

to avoid any detrimental effects on quality. Moreover,

the behaviour of intermediate variables of the model could

help us to understand the physiological causes of such

interactions.

Both the fruit mass and fruit sweetness (deduced fromindividual sugar contents) can be affected by changes in the

carbon and water balances. In the case of low potential

genotypes, fruit mass was limited by the demand whatever

the number of fruits per shoot. The carbon flow, intermedi-

ate variable between the CARBON and SUGAR sub-

models (Fig. 3) was unchanged, as well as the sugar

accumulation, resulting osmotic pressure, and water influx.

Thus, the fruit sweetness remained independent of fruit load.

This was observed for genotypes with a potential fruit dry

mass up to 30 g. For genotypes with higher fruit potential

dry mass, both traits decreased as fruit load increased, andfruit growth was limited by the carbon supply. Conse-

quently, the carbon flow to individual fruits and thus the

accumulation of sugars decreased, as well as the osmotic

pressure. This contributed to reduce the fruit mass in the

WATER sub-model, which could be expected to attenuate

the decrease in sweetness resulting from low sugar accumu-

lation, by limiting the dilution effect. However, the absence

of proportionality among all these processes and thenumerous feedback effects made it difficult to analyse this

response quantitatively. For instance, the slope break of

the sweetness curve observed at a fruit load around 6–7

fruits per branch is difficult to explain, as many factors

might be involved, such as transpiration, osmotic regula-

tion, carbon partitioning between structural and soluble

compounds etc.

This example emphasizes that capturing and unravellingthe cascade of effects behind complex behaviours is not

obvious, because numerous feedback effects and interac-

tions among the physiological processes occur during fruit

development. This example also illustrates how unexpected

behaviours of complex systems can be predicted and

analysed by process-based simulation models. Such simula-

tion analysis can help in selecting the management (fruit

thinning) best adapted to particular genotypes to meetspecific objectives of yield and quality. Then, the main

question is ‘can we trust the model?’ The virtual fruit model

and its sub-models have been published and evaluated

before (Fishman and Genard, 1998; Genard et al., 1998,

2003; Lescourret et al., 1998; Quilot et al., 2002; Lescourret

and Genard, 2005). Moreover, the predicted responses are

in agreement with previous experimental observations

(Johnson and Handley, 1989; Genard et al., 2003).

Predicting wheat grain yield and protein concentrationin response to crop management and genetic variationsunder variable environmental conditions

The wheat simulation model SiriusQuality1 has been de-

veloped to analyse the responses of wheat crops to both

environmental and genetic variations (Martre et al., 2006),

it is based on the crop simulation model Sirius (Jamieson

et al., 1998; Jamieson and Semenov, 2000). It consists of

several sub-models describing soil water and nitrogen

balances and crop development, canopy expansion, bio-

mass, and N accumulation and partitioning, includingresponses to shortages in the supply of soil water and

nitrogen (Fig. 6). Canopy development is simulated as

a series of leaf layers associated with individual main stem

leaves, and tiller production is simulated through the

potential size of any layer. Each leaf layer within the

50

100

150

200

250

0 1 2 3 4 5 6 7 8 9 10

Fru

it m

ass

(g fr

uit-1

)

(a)

High potential genotypes

Low potential genotypes

3

4

5

6

7

8

9

10

11

0 1 2 3 4 5 6 7 8 9 10

Fru

it sw

eetn

ess

(%)

Number of fruits per shoot

(b)High potential genotypes

Low potential genotypes

Fig. 5. Changes in simulated fruit mass (a) and sweetness (b) in

response to modifications of the number of fruits per shoot. The

different lines represent model simulations for ten virtual genotypes

with an increasing potential fruit dry mass from low (10 g) to high

(100 g). Simulations were performed with the virtual peach fruit

model described by Lescourret and Genard (2005) for represen-

tative climatic conditions for south-east France.

962 | Bertin et al.


canopy intercepts light and uses it to produce biomass at an

efficiency calculated from temperature, CO2 concentration,

soil water status, and the ratio of diffuse to direct radiation.

Carbon and nitrogen allocation within the plant is thencalculated as a function of resource (light, nitrogen, and

water) availability using simple priority rules. After anthe-

sis, the translocation of carbon and nitrogen to grains is

first driven by the division of the endosperm cell, then,

during the linear period of grain filling, it mainly results

from the accumulation of starch and storage proteins

(Martre et al., 2006). As illustrated in Fig. 6, the allocation

of carbon and nitrogen to the different plant organs resultsfrom several interrelated feedback regulations. This model

has been calibrated and evaluated for several modern wheat

cultivars and tested in many environments and climates,

including conditions of climate change (Jamieson et al.,

1998, 2000; Jamieson and Semenov, 2000; Martre et al.,

2006). The ability of SiriusQuality1 to simulate grain yield,

nitrogen yield, and protein concentration variations for

both bread wheat and durum wheat (T. turgidum L. subsp.

durum (Desf.) Husn.) in response to crop management (e.g.

sowing date and N fertilization) and environmental con-

ditions (e.g. temperature and water supply) is illustrated in

Fig. 7.This model was used to analyse the effects on bread

wheat (Triticum aestivum L.) grain yield and protein

concentration of interactions between the environment and

a genotypic trait, i.e. the maximum stem nitrogen concen-

tration, which was decreased or increased by 30% compared

to its default value. The nitrogen storage capacity of the

stem is an important trait determining wheat nitrogen use

efficiency and grain protein concentration (Foulkes et al.,1998). In a wheat crop, at anthesis approximately 50% of

total crop nitrogen is stored in the stem and over 80% of

this nitrogen is translocated to the grain during the grain-

filling period. Environmental variations were taken into

account by performing the analysis for 100 years of weather

at three different sites representing the diversity of the

climate in the European wheat growing areas and at two

nitrogen supplies (Fig. 8).

Fig. 6. Simplified schematic representation of the wheat simulation model SiriusQuality1 (Martre et al., 2006) showing the main variables,

influences, and feedbacks. AGDM, average grain dry mass; ANT, anthesis; DM, dry matter; N, nitrogen; Eact, actual evapotranspiration;

Epot, potential evapotranspiration; ET, evapotranspiration; LAI, leaf area index; LUE, light use efficiency; maxStem[N], maximum stem

nitrogen concentration; minStem[N], minimum stem nitrogen concentration; PAR, photosynthetically active radiation; SLN, leaf nitrogen

mass per unit of leaf surface area; SLW, leaf dry mass per unit of leaf surface area.



At high nitrogen supply (Fig. 8a, c, e), a decrease in the

stem nitrogen concentration lessened the protein concentra-

tion without reducing the grain yield, except for the driest

years at Seville where water deficit severally reduced grain

yield (Fig. 8e). Therefore, under high nitrogen inputs,changing the nitrogen storage capacity of the stem may

significantly shift the negative relationship between grain

yield and protein concentration under most European

weather conditions (Martre et al., 2007). In contrast, at low

nitrogen supply (Fig. 8b, d, f), changes in grain protein

concentration in response to variations of the stem nitrogenstorage capacity depended on the year, independently of the

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Sim

ulat

ed g

rain

yie

ld (k

g m

-2)

Observedgrain yield (kg m-2)

1994, bread wheat, N1994, bread wheat, temperature1998, bread wheat, temperature x water2003, durum wheat, sowing date x N2005, durum wheat, sowing date x N

(a)

R2=0.90Slope = 0.99RRMSE = 0.11

0

5

10

15

20

25

30

0 5 10 15 20 25 30

Sim

ulat

ed g

rain

N (g

m-2

)

Observedgrain N (g m-2)

(b)

R2=0.93Slope = 1.00RRMSE = 0.11

0

3

6

9

12

15

18

0 3 6 9 12 15 18

Sim

ulat

ed g

rain

pro

tein

(%dm

)

Observedgrain protein (% dry mass)

(c)

R2=0.85Slope = 0.77RRMSE = 0.08

Fig. 7. Simulated versus observed grain dry mass yield (a),

nitrogen yield (b), and protein concentration (c) for crops of bread

and durum wheat grown in the field with different sowing dates

(November to January) and rates of nitrogen fertilization (0–180 g

N m�2) or under semi-controlled conditions with different post-

anthesis temperature (14–25 �C) and water supply (13–235 mm).

Observed data are means for n¼3 independent replicates.

Statistics concern the linear regression between observed and

simulated data. RRMSE indicates the relative root mean squared

error. Solid lines are y¼x.

0.2 0.4 0.6 0.8 1.0 1.2

Grain yield (kg m-2)

0.2 0.4 0.6 0.8 1.0 1.2-15

-10

-5

0

5

10

15

20Cha

nges

in g

rain

pro

tein

(%

of d

ry m

ass)

-15

-10

-5

0

5

10

15

20

(b)

(d)

(f)

-15

-10

-5

0

5

10

15

20

(a)

(c)

(e)

High N Low N

Fig. 8. Changes in grain protein concentration versus grain yield in

response to changes in stem nitrogen storage capacity simulated

with the wheat simulation model SiriusQuality1 for the winter wheat

cultivar Thesee grown at Clermont-Ferrand, France (A, B), the

winter wheat cultivar Avalon grown at Rothamsted, UK (C, D), and

the spring wheat cultivar Cartaya grown at Seville, Spain (E, F) for

100 years of synthetic weather, generated using the LARS-WG

stochastic weather generator, under high (A, C, E) and low (B, D,

F) nitrogen supplies. For the high and low nitrogen treatments the

crops received 250 and 80 kg N ha�1 of nitrogen fertilizer,

respectively, at specific developmental stages as described by

Martre et al. (2007). The maximum stem nitrogen concentration

was decreased (open circles) or increased (closed circles) by 30%

from its default value of 10 mg N g�1 DM. This range of variation

encompasses the observed genetic range of variations of stem

nitrogen storage capacity for bread wheat (Triboi and Ollier, 1991).

Details of the soil and cultivar characteristics for Clermont-Ferrand

are given in Martre et al. (2007) and for Rothamsted and Seville in

Semenov et al. (2007). The cultivars used at the different sites are

adapted to the local climate.

964 | Bertin et al.


grain yield, and, on average, it had no strong effect on grain

protein concentration. The response of the grain protein

concentration under low nitrogen supply clearly illustrates

the power of a system analysis based on simulations, since

such G3E interactions may be difficult to capture in the

field under a restricted number of environmental conditions.

These two examples illustrate the potential of process-

based simulation models to analyse (i) the effect of simplephysiological parameters on complex traits using a system

approach, and (ii) the interactions among the system

components. However, some care is required when using

crop simulation models to assess the effects of a particular

trait, since the ability of a model to predict subtle G3E

interactions depends on the simplifications and assumptions

made in the model (Boote et al., 2001). On the other hand,

simulation models allow us to focus on the most importantaspects of the physiology and to reveal complex interactions

that were not intuitive.

Outlook

Recent advances in our knowledge of the genetic, environ-

mental, and management control of harvested organ size

and composition have led to the suggestion that their

phenotypic control will become a real possibility in the near

future. Several process-based simulation models are now

able to predict some quality traits of crop production as

a function of genotype and environment, and thus theycould be used to take a first step towards the analysis of

G3E interactions. However, to go further in this analysis, it

is still necessary to enlarge the ability of the model to

simulate the complexity of plant and organ functioning.

Indeed, most of the current models are restricted to the

description of phenology, growth, and carbon–nitrogen–

water balance at the plant or crop level. There is an urgent

need for models that are able to simulate important aspectsof metabolism and biophysical behaviour at the plant and

organ levels (Struik et al., 2005, 2007; Genard et al., 2007).

Great attention should be paid to the uncertainty of

model inputs, for instance, soil characteristics (including

their spatial heterogeneity) or plant endogenous variables,

when using simulation models to analyse the effect of

genetic variations. Indeed, changes in yield or quality traits

in response to genetic variations are often relatively smalland the uncertainty in model inputs may limit the use of

simulation models in predicting quantitatively the pheno-

type from the genotype.

The gap between detailed information emerging from

sciences at the gene and cell levels and the quantitative

understanding of the whole plant physiology is still large.

Models can provide a platform that can accommodate new

advances in this field science (Di Ventura et al., 2006). But,concomitantly to the development of process-based simula-

tion models, more information is needed on the genetic

control of the processes described in these models. In

particular, quantitative data are still lacking to understand

how gene actions are coordinated during plant develop-

ment, and in response to environmental signals. Adequate

data sets, with time series during fruit or grain filling and

adequate description and characterization of the growing

conditions and the genotypes are required. The production

of isogenic lines or mutants, which may be experimentally

described under well characterized environments, will play

an important role for unravelling the physiological pro-

cesses and G3E interactions involved in the control ofquality traits.

Acknowledgements

This work was funded and carried out under the ‘Environmen-

tal determinism of harvested organ quality’ research network

from INRA, Division of Environment and Agronomy.

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Under what circumstances can process-based simulation models