Journal of Experimental Botany, Vol. 61, No. 4, pp. 955–967, 2010
doi:10.1093/jxb/erp377 Advance Access publication 27 December, 2009
REVIEW PAPER
Under what circumstances can process-based simulation
models link genotype to phenotype for complex traits? Casestudy of fruit and grain quality traits
Nadia Bertin1,*, Pierre Martre2,3, Michel Génard1, Bénédicte Quilot4 and Christophe Salon5
1
2
3
4
5
INRA, UR1115 Plantes et Systèmes de Culture Horticoles, F-84 914 Avignon, France
INRA, UMR1095 Génétique, Diversité et Ecophysiologie des Céréales, F-63 100 Clermont-Ferrand, France
Université Blaise Pascal, UMR1095 Génétique, Diversité et Ecophysiologie des Céréales, F-63 100 Clermont-Ferrand, France
INRA, UR1052 Génétique et Amélioration des Fruits et Légumes, F-84 143 Avignon, France
INRA, UMR102 Génétique et Ecophysiologie des Légumineuses, 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-byenvironment (G3E) interactions for complex traits. Indeed, G3E interactions are emergent properties of simulation
models, 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 complex
aspects 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 environmentally controlled during grain, seed or fruit development. 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 levelled
off 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 TriboiBlondel, 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 trait
loci (QTL) for quality traits, and the identification of genes
involved in their control for different species, the genetic
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956 | Bertin et al.
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 multiple
interacting 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; Bermùdez 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 (Börner et al., 1993; Blanco et al., 2002;
Chaı̈b et al., 2006; Dudley et al., 2007). This usually results
in strong genotype-by-environment (G3E) or genotype-bymanagement 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, agronomists
and 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 environmental conditions.
To overcome these difficulties, several authors have
proposed the use of ecophysiological process-based simulation 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 elongation rate in maize (Zea mays L.; Reymond et al., 2003), or
fruit 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), and
to analyse G3E interactions (Yin et al., 2005).
All of these studies outlined the possibility of processbased 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 parameters 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 processbased simulation models can help in bridging the gap
between genotype and phenotype, due to their intrinsic
capacity to mimic complex systems and to integrate multiscale 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 protein
concentration, as two examples.
Genotype-by-environment interactions are
emergent properties of process-based
simulation models
Process-based simulation models are mathematical surrogates, and one of their functions is to describe the
interconnections and feedback regulations between subsystem 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 the
idea of a sequence and/or network of different limitations
operating through the plant’s life cycle. These interconnections and feedback regulations among the system components 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 can
also 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 genotypedependent 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 response
curve 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 reserve
through 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 the
same 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
From genotype to phenotype through simulation models | 957
Process
(a)
Genotype 1
Genotype 2
E2
E1
Environmental variable
(b)
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 varying
linearly 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 environmental
variations, and as a consequence, a G3E interaction emerges
at the whole system level (Fig. 2c).
Process
Which models and which parameters to link
genotype to phenotype?
Some mechanistic models to integrate physiological
knowledge
G1
G2
G1
G2
E2
E1
Plant variable
Process
(c)
G1
G2
G1
G2
E2
E1
Plant variable
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
Most growth simulation models currently used were originally 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 mechanistic models: such models have to describe physiological
processes 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;
Génard 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 selfcorrect, as do real plants. As stated by these authors, this
philosophy 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
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.
958 | Bertin et al.
(a)
Process f
Genotype 1
Genotype 2
Process h
(b)
wheat and seeds, they focus on size and protein concentration 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 controlling fruit size, and sugar and acid composition, which are
largely involved in flavour perception. In these models, the
environment is characterized through the measurement of
environmental variables (temperature, light, humidity, mineral 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 and
to 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’.
(c)
Quality trait y
Genotypic and generic parameters of simulation models
E1
E2
Environmental variable
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 b
are 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.
Though plant traits are generally dependent on genotype,
environment, and management, the parameters of the
equations 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 matter
accumulation 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 of
genotypic parameters defining a particular genotype represents a phenotypic fingerprint of this genotype. To be considered 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.
From genotype to phenotype through simulation models | 959
Sensitivity analysis of the model to its parameters can
help in identifying important genotypic parameters, and
their putative effects under different climate and management 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 physiological functionalities, necessary to simulate the expression
of single genes or a gene network. Several attempts and
approaches have been proposed to include genetic information 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 environmental
and 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 for
these 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 be
determined more precisely by these coefficients than by
field-determined genotypic parameters, so gene-based models 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 development, 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 represent 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 Arabidopsis [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 genebased 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 for
genotypic parameters. Moreover, detailed studies to quantify 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 parameters 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 was
pioneered 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 recombinant
inbred 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 as
material for validating the model, which accounted for 74%
of the genetic and environmental variations of leaf elongation rate (Reymond et al., 2004).
More recently, this approach was extended to peach
fruit quality. Based on the sensitivity analysis of the virtual
960 | Bertin et al.
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 account
for a large part of the genetic and environmental variations 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 genes
under 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).
Carbon
The virtual peach fruit model of Lescourret and Genard
(2005) predicts the fresh mass, dry matter content, and
sugar 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
Stem water
potential
Relative
humidity
Sugars
C f low
flesh dry mass
stone dry mass
C reserves
Temperature
Predicting peach fruit size and sweetness index in
response to tree management and genetic variations
under variable environmental conditions
Fruit fresh mass
Proportion of flesh
Flesh dry matter content
Radiation
Photosynthesis
Stem carbon balance
Stone and f lesh dry growth
The significance of process-based simulation models of
quality traits can be exemplified through the analysis of
both genotypic and environmental effects, using two integrated models of quality, one for peach fruit and the other
for wheat grain.
Temperature
Leaf water
potential
State of the
system
Analysis of G3E interactions through
process-based simulation models: casestudy of fruit and grain quality traits
Water
Carbon partitioning into
sucrose, sorbitol,
glucose and f ructose
Amounts
of sugars
Osmotic pressure
Turgor pressure
Tissue plasticity
4 sugars
content
Respiration
Transpiration
Sustain and growth
Fruit conductance
C02 emission
H2 0 loss
Submodel
variables
Matter or information fluxes
Main outputs
Environmental inputs
Fig. 3. Schematic representation of the virtual peach fruit model (Lescourret and Génard, 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, biorheological cell wall properties, and hydraulic conductivity.
From genotype to phenotype through simulation models | 961
300
(a)
R2=0.95
Slope = 0.90
RRMSE = 0.13
250
200
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%, respectively, of the observed genetic variations in fruit fresh
mass and sweetness index to be explained.
Considering the ability of such models to simulate the
effects 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 genotypic 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 Génard, 2005).
The environment was manipulated through plant management, 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
Simulated Fresh weight (g)
Simulated Fresh weight (g)
stem; (ii) the SUGAR model (Génard and Souty, 1996;
Génard et al., 2003) which uses this daily influx of carbon as
input to simulate the metabolic transformations among
respired CO2, individual sugar metabolism (sucrose, sorbitol, glucose, and fructose) and other compounds (structural
carbohydrates); (iii) a water sub-model (Fishman and
Génard, 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 conductivity. The fruit osmotic pressure is calculated from sugar
content and composition simulated by the SUGAR submodel. The rules of communication among the three submodels 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 Génard 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 description of carbon metabolism in the SUGAR model.
150
100
50
350
250
200
150
100
R2=0.95
Slope = 0.99
RRMSE = 0.08
50
0
0
0
12
50
100 150 200 250
Observed Fresh weight (g)
0
300
(b)
9
6
R2=0.61
Slope = 0.58
RRMSE = 0.15
0
0
3
6
9
Observed Sweetness (%)
100 150 200 250 300 350
(d)
20
3
50
Observed Fresh weight (g)
12
Simulated Sweetness (%)
Simulated Sweetness (%)
(c)
300
15
10
R2=0.52
Slope = 0.66
RRMSE = 0.18
5
0
0
5
10
15
20
Observed Sweetness (%)
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 Génard (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.
962 | Bertin et al.
model predicted a significant management-by-genotype interaction (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 agreement
with 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 from
individual 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
250
(a)
Fruit mass (g fruit-1)
High potential genotypes
200
150
100
Low potential genotypes
50
0
1
2
3
4
5
6
7
8
9
11
(b)
10
Fruit sweetness (%)
10
High potential genotypes
9
the number of fruits per shoot. The carbon flow, intermediate variable between the CARBON and SUGAR submodels (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, and
fruit growth was limited by the carbon supply. Consequently, 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 accumulation, by limiting the dilution effect. However, the absence
of proportionality among all these processes and the
numerous 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 regulation, carbon partitioning between structural and soluble
compounds etc.
This example emphasizes that capturing and unravelling
the cascade of effects behind complex behaviours is not
obvious, because numerous feedback effects and interactions 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 simulation analysis can help in selecting the management (fruit
thinning) best adapted to particular genotypes to meet
specific 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 Génard, 1998; Génard et al., 1998,
2003; Lescourret et al., 1998; Quilot et al., 2002; Lescourret
and Génard, 2005). Moreover, the predicted responses are
in agreement with previous experimental observations
(Johnson and Handley, 1989; Génard et al., 2003).
8
Predicting wheat grain yield and protein concentration
in response to crop management and genetic variations
under variable environmental conditions
7
6
5
Low potential genotypes
4
3
0
1
2
3
4
5
6
7
8
9
10
Number of fruits per shoot
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 Génard (2005) for representative climatic conditions for south-east France.
The wheat simulation model SiriusQuality1 has been developed 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, biomass, and N accumulation and partitioning, including
responses 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
From genotype to phenotype through simulation models | 963
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.
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 then
calculated as a function of resource (light, nitrogen, and
water) availability using simple priority rules. After anthesis, 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 results
from 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 conditions (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 concentration, 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 grainfilling 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).
964 | Bertin et al.
High N
1994, bread wheat, N
1994, bread wheat, temperature
1998, bread wheat, temperature x water
2003, durum wheat, sowing date x N
2005, durum wheat, sowing date x N
15
1,2
5
1,0
0
0,8
-5
0,6
-10
R2=0.90
Slope = 0.99
RRMSE = 0.11
0,4
0,2
0,0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
Observed grain yield (kg m-2)
Simulated grain N (g m-2)
30
(b)
25
20
15
(b)
(c)
(d)
(e)
(f)
-15
20
15
10
5
0
-5
-10
-15
20
15
10
R2=0.93
Slope = 1.00
RRMSE = 0.11
5
0
0
(a)
10
(a)
Changes in grain protein (% of dry mass)
Simulated grain yield (kg m-2)
1,4
Low N
20
5
10
15
20
25
30
Observed grain N (g m-2)
10
5
0
-5
Simulated grain protein (% dm)
-10
18
-15
(c)
0.2
15
0.4
0.6
0.8
1.0
1.2 0.2
0.4
0.6
0.8
1.0
1.2
Grain yield (kg m-2)
12
9
6
R2=0.85
Slope = 0.77
RRMSE = 0.08
3
0
0
3
6
9
12
15
18
Observed grain protein (% dry mass)
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 m2) or under semi-controlled conditions with different postanthesis 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.
At high nitrogen supply (Fig. 8a, c, e), a decrease in the
stem nitrogen concentration lessened the protein concentration 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
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 Thésée 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 ha1 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 g1 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.
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 nitrogen
storage capacity depended on the year, independently of the
From genotype to phenotype through simulation models | 965
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 processbased simulation models to analyse (i) the effect of simple
physiological 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 important
aspects of the physiology and to reveal complex interactions
that were not intuitive.
Outlook
Recent advances in our knowledge of the genetic, environmental, 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 they
could 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 aspects
of metabolism and biophysical behaviour at the plant and
organ levels (Struik et al., 2005, 2007; Génard 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 small
and the uncertainty in model inputs may limit the use of
simulation models in predicting quantitatively the phenotype 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 simulation 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 processes and G3E interactions involved in the control of
quality traits.
Acknowledgements
This work was funded and carried out under the ‘Environmental determinism of harvested organ quality’ research network
from INRA, Division of Environment and Agronomy.
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