Copyright Ó 2009 by the Genetics Society of America
DOI: 10.1534/genetics.109.105429
Simulating the Yield Impacts of Organ-Level Quantitative Trait Loci
Associated With Drought Response in Maize: A ‘‘Gene-to-Phenotype’’
Modeling Approach
Karine Chenu,*,†,1 Scott C. Chapman,‡ Francxois Tardieu,† Greg McLean,* Claude Welcker†
and Graeme L. Hammer§
*Queensland Primary Industries and Fisheries, Agricultural Production Systems Research Unit (APSRU), Department of Employment,
Economic Development and Innovation, Toowoomba, Queensland 4350, Australia, †Institut National de la Recherche Agronomique,
Unité Mixte de Recherche 759, Laboratoire d’Ecophysiologie des Plantes sous Stress Environnementaux, 34060 Montpellier, France,
‡
CSIRO Plant Industry, Queensland Bioscience Precinct, St. Lucia, Queensland 4067, Australia and
§
University of Queensland, School of Land, Crop and Food Sciences, APSRU,
Brisbane, Queensland 4072, Australia
Manuscript received June 4, 2009
Accepted for publication September 9, 2009
ABSTRACT
Under drought, substantial genotype–environment (G 3 E) interactions impede breeding progress for
yield. Identifying genetic controls associated with yield response is confounded by poor genetic
correlations across testing environments. Part of this problem is related to our inability to account for the
interplay of genetic controls, physiological traits, and environmental conditions throughout the crop
cycle. We propose a modeling approach to bridge this ‘‘gene-to-phenotype’’ gap. For maize under
drought, we simulated the impact of quantitative trait loci (QTL) controlling two key processes (leaf and
silk elongation) that influence crop growth, water use, and grain yield. Substantial G 3 E interaction for
yield was simulated for hypothetical recombinant inbred lines (RILs) across different seasonal patterns of
drought. QTL that accelerated leaf elongation caused an increase in crop leaf area and yield in wellwatered or preflowering water deficit conditions, but a reduction in yield under terminal stresses (as such
‘‘leafy’’ genotypes prematurely exhausted the water supply). The QTL impact on yield was substantially
enhanced by including pleiotropic effects of these QTL on silk elongation and on consequent grain set.
The simulations obtained illustrated the difficulty of interpreting the genetic control of yield for
genotypes influenced only by the additive effects of QTL associated with leaf and silk growth. The results
highlight the potential of integrative simulation modeling for gene-to-phenotype prediction and for
exploiting G 3 E interactions for complex traits such as drought tolerance.
C
ROP yield varies greatly among genotypes, but this
genetic variation is not consistent among environments. This presents a major challenge to plant
breeding. Environmentally stable quantitative trait loci
(QTL) were found for drought adaptation traits at the
organ level. But what impacts do such QTL have on
crop yield? We developed a ‘‘gene-to-phenotype’’
modeling approach that integrates physiological processes and incorporates their genetic controls. We
estimated in silico the genotype–environment interactions that organ-level QTL might generate on yield in
different drought conditions. Such a modeling approach opens new avenues for crop improvement.
Genotype–environment interactions—statistical vs.
predictive modeling approaches: Genotype–environment (G 3 E) interactions impede plant breeding
progress for complex traits such as yield and confound
1
Corresponding author: Queensland Primary Industries and Fisheries,
203 Tor St., Toowoomba, QLD 4350, Australia.
E-mail: [email protected]
Genetics 183: 1507–1523 (December 2009)
the interpretation of genetic controls of adaptive traits.
In drought-prone regions, the size of the yield variance
component for G 3 E interactions is frequently greater
than the variance associated with genotype main effects
(see Cooper and Hammer 1996 for examples in wheat,
sorghum, maize, and rice). Over the last century,
numerous statistical methodologies have been developed to analyze these effects and to predict the
expected yield of genotypes across and/or within
subsets of environments (i.e., to measure ‘‘stable/
broad’’ and/or ‘‘specific’’ adaptation). In recent years,
mixed models have increasingly dealt with heterogeneity effects across and within trials to explain genetic
correlations among environments (e.g., Smith et al.
2001). The use of these models has been extended to
identify quantitative trait loci (QTL) associated with
yield variation and to estimate how these are influenced
by various environment covariables (e.g., Boer et al.
2007). Recent developments of this method enable one
to account for genetic correlations among both traits
and environments (Malosetti et al. 2006, 2008) and to
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K. Chenu et al.
detect QTL for nonlinear functions (Ma et al. 2002;
Malosetti et al. 2006), thus providing a powerful
method for eco-physiologically inspired genetic models.
New methods to characterize local environments as
experienced by the plants (i.e., as influenced by G 3 E
interactions) have also been proposed (e.g., Muchow
et al. 1996; Chelle 2005; Sadok et al. 2007; Chenu et al.
2008b). Such environment characterizations were demonstrated to aid the understanding of genotypic response
to environment (e.g., Granier et al. 2006; Chenu et al.
2007) and the unraveling of the yield variance component for G 3 E interactions (Chapman 2008). In a recent
review, Cooper et al. (2006) discussed opportunities to
apply mixed-model methods to exploit G 3 E interactions. A major challenge for these statistical methods is
how to deal with the complex interactions occurring
within plants among genes and among traits, as G 3 E
interactions for yield result from the integration over time
of a multitude of G 3 E interactions at various organism
levels (Van Eeuwijk et al. 2005; Cooper et al. 2009).
Biophysical simulation models that integrate physiological processes and their associated genetic controls
can contribute to the interpretation of G 3 E interactions at different organism levels, including yield
(Hammer et al. 2002; Tardieu 2003; Yin et al. 2004;
Chapman 2008). Such predictive models are appropriate to describe and explore in silico multiple combinations of genotypes (as defined by their alleles) and
environments. Single physiological traits are usually
governed by a multitude of genes, but analyzing a
combination of only 10 genes with two alleles in 10
environments requires data for almost 600,000 combinations (310 3 10 when including heterozygotes). The
enormous number of combinations that breeders
would ideally analyze to identify best-adapted genotypes
highlights a major interest for predictive approaches.
Novel QTL-based or gene-to-phenotype modeling
approaches have been developed to predict gene-tophenotype associations at the crop level, largely focusing on genetic controls associated with plant phenology
(e.g., Hoogenboom et al. 2004; Messina et al. 2006).
However, the simulation of genes/QTL for complex
traits, such as the responses of plant growth and architecture to environment, remains a challenging issue,
which requires the modeling of physiological processes
that are stable across environments (Yin et al. 2000;
Tardieu 2003; Hammer et al. 2006). We propose to
illustrate the utility of such a modeling approach with an
example for maize under drought.
Controls of key organ-level processes for drought
adaptation in maize: Under drought conditions, the
coordination of growth processes to efficiently utilize
the scarce water supply and the sensitivity of grain
production to stress are two key attributes of yield
performance. In maize, substantial genetic variation
has been observed in drought responses of leaf elongation rate (Reymond et al. 2003), which influence canopy
development and thus transpiration and crop water use.
Significant genetic variability has also been observed for
drought response of ear growth rate around flowering
and for response of grain number per ear at maturity
(Edmeades et al. 1993; Vargas et al. 2006). A short
anthesis-silking interval (ASI) (Ribaut et al. 1997) is
an indicator of these effects and has been used effectively
in selection for improved yield under drought (Bolaños
and Edmeades 1993, 1996; Chapman et al. 1997a,b;
Chapman and Edmeades 1999). Recently, several QTL
affecting both leaf elongation and ASI have been found
to colocalize (Welcker et al. 2007).
Sufficient understanding of leaf elongation has been
developed to propose a physiological and genetic model
of leaf elongation response to drought (see Chenu et al.
2008a for additional details). Temperature, evaporative
demand, and soil water deficit were identified as major
environmental factors determining leaf elongation rate
over periods of hours and days, whereas light and plant
carbon balance had minor effects (Ben Haj Salah
and Tardieu 1996, 1997; Tardieu et al. 1999; Sadok
et al. 2007). The parameters for the response curves
of leaf elongation rate to temperature (or ‘‘potential
leaf elongation rate,’’ parameter ‘‘a’’), evaporative demand (‘‘b’’), and soil water status (‘‘c’’) were found to be
genotype specific and stable across environments (Ben
Haj Salah and Tardieu 1996; Reymond et al. 2003).
QTL for these parameters were detected in two populations of temperate maize lines and several of these
QTL colocalized with those identified in a tropical maize
population (Reymond et al. 2003; Sadok et al. 2007;
Welcker et al. 2007). Using such ‘‘environmentally
stable’’ QTL to model leaf elongation rate avoids complex QTL–environment interactions that are commonly
observed for directly measured traits such as leaf length
(Reymond et al. 2004). Leaf elongation rate was successfully simulated over several days in different environments for novel inbred lines defined only by their alleles
at the QTL (Reymond et al. 2003). Chenu et al. (2008a)
incorporated this organ-level model (with time steps of
minutes to hours) into the APSIM–Maize crop simulation model and hence captured the complex interactions of plants with their environment (e.g., the feedback
of leaf growth on soil water depletion) during the entire
crop cycle. For a maize hybrid, Dea, the model produced
accurate predictions of leaf area, biomass, and grain
yield when tested against independent data from contrasting environments (Chenu et al. 2008a).
The aim of the present study was to use crop modeling
to estimate whole-plant effects of major QTL that regulate environmental responses of leaf elongation rate.
The impact of these QTL on maize yield was simulated
for a set of drought scenarios. As some of these QTL
colocalize with QTL for ASI, which is an indicator of
silk expansion rate (Welcker et al. 2007; Fuad-Hassan
et al. 2008), we also examined the consequences of possible pleiotropic effects for QTL controlling elongation
Gene-to-Phenotype Modeling Reveals QTL Impacts
1509
Figure 1.—Schematic view of the ‘‘geneto-phenotype’’ model showing how the leaf
elongation module interacts with the rest
of the APSIM crop model. Environmental
and genetic information is used as inputs
to simulate leaf growth, crop growth and
development, and grain yield. Leaf elongation rate (LER) is a function of leaf
environmental factors [Tm, meristem temperature; T0, base temperature; VPDm-a,
meristem-to-air vapor pressure deficit; c,
predawn leaf water potential (negative values)] and leaf elongation parameters (a,
potential leaf elongation rate; b, response
of leaf elongation rate to VPDm-a; and c,
response of leaf elongation rate to c). High
leaf elongation rate (LER) in a given environment is favored by high values of parameters a and b and low values of c (i.e., LER
favored by high potential leaf elongation
rate and low sensitivity to either high evaporative demand or soil water deficit).
rate of both the leaf and silk tissue. The yield of 1000
hypothetical recombinant inbred lines (RILs) was simulated under managed drought patterns (Tlaltizapán,
Mexico) to describe the ‘‘yield–fitness adaptation landscape.’’ A second set of simulations was conducted for a
sample of years in a rain-fed production region (Sete
Lagoas, Brazil) to evaluate in silico the effects for the
drought patterns experienced in a field production
system. These simulations mimicked ‘‘QTL experiments’’
and were used in mixed-model analyses to quantify the
yield impact of individual leaf elongation QTL, either
with or without their pleiotropic effect on silking and
consequent grain set.
MATERIALS AND METHODS
Overview: The APSIM crop model was adapted to allow
simulation of the effects of QTL on both leaf and silk
elongation (Figure 1). This model uses (i) genetic inputs with
genotype-specific parameters that characterize different plant
traits and (ii) environmental inputs (daily weather data, soil
characteristics, and crop management such as sowing date or
irrigation) to calculate phenotypic values for crop growth,
development, and ultimately grain yield (outputs of the
model). In this study, only the parameters related to drought
response of leaf elongation rate (parameters a, b, and c) and
ASI (ASIdrought) were modified among genotypes. Two hypothetical RIL populations were generated on the basis of known
major QTL for leaf elongation parameters (Table 1, Figure 2),
using the quantitative genetics simulation model QU-GENE
TABLE 1
QTL for parameters of potential leaf elongation rate (a), response to evaporative demand (b),
and response to soil water deficit (c) and for ASI response to drought
Additive effect
QTL name
Chr.
Position
(cM)
qb1
qa1qb2
qa2
qc1
qa3qb3qc2
qc3
qb4qc4
qa4qb5qc5
qa5qb6qc6
qa6qc7
qb7qc8
1
1
2
2
3
4
5
5
8
9
10
154
271
84
174
67
242
79
186
92
67
0
a
(mm °Cd1)
0.147
0.158
0.152
0.228
0.184
0.207
b
(mm °Cd1 kPa1)
c
(mm °Cd1 MPa1)
ASIdrought
(d)
0.289
0.259
0.277
0.261
0.259
0.302
0.309
0.257
0.5
0.080
0.080
0.063
0.065
0.064
0.051
0.060
0.5
0.5
0.5
The chromosome, the position, and the additive effect of the parent 1 allele are presented for all the QTL. QTL are named after
the leaf parameter(s) they affect (e.g., qa1qb2 affects the parameters a and b). Values of a, b, c, and ASIdrought were 5.054 mm per
degree day (mm °Cd1), 0.948 mm °Cd1 kPa1, 4.842 mm °Cd1 MPa1, and 6 days for parent 1 and 5.986 mm °Cd1, 1.552 mm
°Cd1 kPa1, 8.158 mm °Cd1 MPa1, and 6 days for parent 2, respectively. Data are derived from Welcker et al. (2007), who presented the QTL additive effect for the alleles of parent 2, and from Vargas et al. (2006).
1510
K. Chenu et al.
Figure 2.—QTL–trait network for parameters of leaf elongation rate (LER) response and anthesis-silking interval (ASI) under
drought (a, b, c, and ASIdrought). Two populations of 1000 recombinant inbred lines (RILs) each were simulated with QTL affecting
either the parameters involved in LER alone (first population) or parameters for both LER and ASI (second population). For each
trait, arrow thickness is proportional to the additive effect of the QTL considered (red dashed line, negative; green solid line,
positive effect for the allele of parent 1, Table 1). The size of the oval around each QTL is proportional to the number of traits
influenced (degree of pleiotropy), indicating the complexity of each QTL within the network.
(Podlich and Cooper 1998). The QTL of the first population
generated were assumed to control leaf elongation alone
(Reymond et al. 2003), whereas in a second population they
were assumed to influence both leaf and silk elongation
(Welcker et al. 2007). The yield phenotype of each line was
simulated using an adapted APSIM crop model (Chenu et al.
2008a). A first set of simulations was carried out to determine
gene-to-phenotype consequences on yield in managed
drought environments with contrasting soil water contents
and evaporative demands (resulting from different sowing
dates and irrigation managements at Tlaltizapán, Mexico). A
second set of simulations was conducted to estimate effects on
yield of individual QTL for representative conditions experienced in a rain-fed maize-growing region (Sete Lagoas, Brazil;
Table 2).
Phenotype prediction—a crop model to account for leaf
and silk growth effects on yield: Like most crop models,
APSIM (http://www.apsim.info/apsim/) simulates the processes of growth and development of a genotype (usually a commercial cultivar) in response to external environment variables.
In this biophysical simulation model, the crop/genotype is
defined by a set of parameters associated with algorithms that
describe physiological processes (e.g., leaf development, solar
radiation interception, water uptake, biomass and nitrogen
accumulation, and retranslocation). The APSIM model has been
extensively tested, in a broad range of conditions, during the last
20 years (http://www.apsim.info/apsim/). For each environment, the model accepts as input descriptions of soil, weather
data, and management decisions (e.g., date of irrigation and
amount of water supplied). It operates on a daily time step to
simulate the growth and development of the crop over time and
generates phenotypes for a multitude of traits, including crop
leaf area, biomass, the quantity of water transpired every day, and
the grain yield at harvest.
The standard maize crop model of the APSIM simulation
platform (Wang et al. 2002; Keating et al. 2003) was extended
by inclusion of the modified module for leaf development and
expansion (Figure 1) by Chenu et al. (2008a). This allowed
inputs of leaf response parameters (a, b, and c) calculated from
the QTL allelic combination of any genotype. The modular
design of APSIM facilitated such model development, by
enabling the replacement of existing daily leaf-growth routines with new hourly leaf-growth routines based on the leaf
elongation rate (LER) model.
To incorporate the genetic variability for silk elongation
and ASI in response to changes in growth rate due to stress, an
additional algorithm replaced the existing APSIM routine that
described kernel development. On the basis of the model of
Edmeades and Daynard (1979) and the results of Andrade
et al. (1999), kernel number (KN) was estimated from the
mean plant growth rate (PGR) between 130 degree days
before and 260 degree days after flowering,
KN ¼ KNmax ð1 e kðPGRPGRbase;g Þ Þ;
ð1Þ
where KNmax is the potential kernel number reached under
nonlimiting conditions, which was set at 500, on the basis of
field data for the genotype Dea (P. Bertin, unpublished data);
k is a curvature parameter, which was set at 0.83, on the basis of
data from Andrade et al. (1999); and PGRbase,g is a genotypedependent variable corresponding to the x-intercept of the
curve, which quantifies the minimum PGR required for any
Gene-to-Phenotype Modeling Reveals QTL Impacts
1511
TABLE 2
Characteristics of the in silico field experiments conducted using environmental data from
Tlaltizapán (Mexico) and Sete Lagoas (Brazil)
Exp.
ETMex1VPD
ETMex1VPD1
ETMex2VPD
ETMex2VPD1
ETMex3VPD
ETMex3VPD1
ETMex4VPD
ETMex4VPD1
ETBr1median
ETBr2median
ETBr3median
ETBr4median
Location
Sowing date
Water regime
Irradiance
(MJ m2)
Temperature
(°)
VPDm-a
(kPa)
Tlaltizapán, Mexico
Tlaltizapán, Mexico
Tlaltizapán, Mexico
Tlaltizapán, Mexico
Tlaltizapán, Mexico
Tlaltizapán, Mexico
Tlaltizapán, Mexico
Tlaltizapán, Mexico
Sete Lagoas, Brazil
Sete Lagoas, Brazil
Sete Lagoas, Brazil
Sete Lagoas, Brazil
July 1, 1995
September 1, 1995
July 1, 1995
September 1, 1995
July 1, 1995
September 1, 1995
July 1, 1995
September 1, 1995
January 1, 1983
January 1, 1974
January 1, 1990
January 1, 1993
Well watered
Well watered
Early water deficit
Early water deficit
Late water deficit
Late water deficit
Early and late water deficit
Early and late water deficit
Rain fed
Rain fed
Rain fed
Rain fed
28.3
26.7
28.3
26.7
28.3
26.7
28.3
26.7
23.1
23.1
24.1
23.6
24.2
23.6
24.2
23.6
24.2
23.6
24.2
23.6
17.5
24.3
24.3
22.5
1.77
2.06
1.90
2.23
1.78
2.09
1.89
2.24
1.37
1.52
1.82
1.73
Details are presented for (i) the experiments conducted in Tlaltizapán in 1995 with four water regimes controlled by irrigation (ETMex1–4) and two sowing dates conferring moderate and high evaporative demand (‘‘VPD’’ and ‘‘VPD1’’ conditions)
and (ii) the situations (analog years) that were closest to the median for each of the four environment types in Sete Lagoas
(ETBr1–4median). Irradiance (short wave solar), temperature (air temperature), and VPDm-a (vapor pressure difference between
meristem and atmosphere during the daylight period) are averaged for the period from sowing to flowering.
kernels to be initiated. Drought-tolerant genotypes have a
lower PGRbase,g. In practice, genetic variation in PGRbase,g is
rarely measured, but is indirectly evaluated as a change in the
relative timing of anthesis (pollen production on the tassel)
and silking (appearance of silks from the husk), commonly
referred to as ASI. Overall the ‘‘ASI effect’’ of the QTL was thus
attributed to variations in PGRbase,g, while all the other variables
in the model were held constant.
Simulated RIL populations: Eleven major QTL controlling
leaf elongation rate response to drought (Table 1, Figure 2)
were used to create a population of 1000 F2:8 RILs. The
population was generated with the quantitative genetics
simulation model QU-GENE (Podlich and Cooper 1998)
and the Qu-Line/Qu-Cim breeding module (Wang et al.
2004). The QU-GENE User Interface software, together with
the APSIM-LER data generated in this study, can be downloaded from the software webpage (http://www.uq.edu.au/
lcafs/qugene/). Each QTL was assigned a location on the
chromosomes and the two parents were characterized by their
alleles for the QTL. Each allele was described by its additive
effect relative to parent one (‘‘parent 1’’; see below). One
thousand hypothetical RILs were generated from a single cross
between the parents, followed by selfing (F2) and consequent
single-seed descent. In a second population, which comprised
the same 1000 RILs (as defined by their alleles), an additional
pleiotropic effect on ASI-related traits was included for the
four leaf elongation QTL known to colocalize with QTL for
ASI under drought (Vargas et al. 2006; Welcker et al. 2007;
Figure 2).
The positions and additive effect sizes of the QTL for leaf
elongation response to (i) meristem temperature (also referred to as potential leaf elongation rate or parameter a of the
LER model; Figure 1), (ii) evaporative demand, which was
characterized by the meristem-to-air vapor pressure deficit
(parameter b), and (iii) soil water deficit, which was characterized by the predawn leaf water potential (parameter c), were
derived from experimental data reported on the cross
between the two tropical inbred lines, Ac7643 and Ac7729/
TZSR W (Welcker et al. 2007), also referred to as P1 and P2,
respectively (Ribaut et al. 1996, 1997). The 11 QTL for a, b,
and c explained 55, 77, and 66% of the genetic variance,
respectively. Note that no additional ‘‘undetected QTL’’ were
simulated to account for the residual genetic variance.
To obtain yield estimation comparable to hybrid performance, the allelic combinations for the QTL (that defined an
individual RIL) were simulated within the background growth
and development characteristics known for the hybrid Dea
(for detail, see Chenu et al. 2008a) and with a final leaf number
of 20, which is typical of medium to late season tropical maize
(e.g., Chapman and Edmeades 1999) and is similar to that of
the tropical lines P1 and P2 ( J. M. Ribaut, unpublished data).
The values of a, b, and c for the inbred parent lines of the
simulated populations (parent 1 and parent 2) were scaled
from the mean values of P1 and P2 to the values of this
‘‘reference genotype’’ derived from Dea.
The QTL for silk elongation were each assigned similar
effect sizes on ASI, increasing the ASI under drought
(ASIdrought) with an additive effect of 0.5 day each (Vargas
et al. 2006; Welcker et al. 2007) beyond the background value
of the reference genotype of 6 days. For the first RIL
population, PGRbase,g (Equation 1) was set at 1.2 g per day, a
value similar to that for the hybrid used by Andrade et al.
(1999). In the second RIL population, where the QTL effects
on silk elongation were included, PGRbase,g varied from 0.8 to
1.6 g per day on the basis of experimental data scaled to the
reference genotype (Vargas et al. 2006; J. M. Ribaut, unpublished data). As the kernel number response to plant
growth rate (Equation 1) is related to ear growth (Andrade
et al. 1999; Vega et al. 2001; Echarte et al. 2004) and ear
growth rate determines the time of silking and ASI (Edmeades
et al. 1993; Borrás et al. 2007), it was assumed that the genetic
variation in the KN–PGR relation (Equation 1) was related to
the QTL effects for ASI. Genetic variations in PGRbase,g were
estimated as being proportional to genetic variations observed
in ASI under drought (ASIdrought), with the shortest 4-day
ASIdrought corresponding to the lowest PGRbase,g value of 0.8 g
per day and the longest 8-day ASIdrought corresponding to the
greatest PGRbase,g value of 1.6 g per day. A recent study (Borrás
et al. 2009), published after the realization of this work, clearly
1512
K. Chenu et al.
demonstrated the strong link between PGR, ear growth, and
ASI.
First set of virtual experiments—simulation in managed
drought environments to describe the yield-fitness adaptation
landscape: In the first set of simulations, irrigation was applied
to generate four managed-drought types to investigate how
QTL effects translated to crop yield in contrasting climatic
scenarios (Table 2, Figure 3). In these virtual experiments,
crops were sown on July 1, 1995 (moderate evaporative
demand environment), and September 1, 1995 (high evaporative demand environment), using weather data obtained
from CIMMYT for their testing site in Tlaltizapán, Mexico
(18.6°N, 99.1°W, 946 m). Irrigation was managed in silico to
obtain (i) a well-watered treatment (environment type 1, also
called ‘‘ETMex1’’), (ii) an early water deficit from plant emergence to the beginning of the grain-setting period (ETMex2),
(iii) an increasing water deficit during the grain-setting period
(ETMex3), and (iv) a water deficit during both the vegetative
and the grain-setting periods with an irrigation at the beginning of the grain-setting period (ETMex4). Environmental
characteristics for these managed environments (ETMex1–4)
are presented in Table 2 and Figure 3.
A sensitivity analysis was conducted to evaluate the impact of
each of the LER and ASI parameters on leaf area and yield
(Figure 4). Simulations were first performed using reference
values of the different parameters (a, b, c, and ASIdrought), which
were set to the parental mean (i.e., value of the reference
genotype). The sensitivity test was conducted by varying the
value of one parameter at a time (for the full range of potential
allelic values), while the other parameters remained at the
reference value.
To account for the QTL effects on the different traits (‘‘QTL–
trait network’’), the same simulations were then undertaken for
all lines of the two RIL populations (Figure 2). The allelic
combination that defined each RIL was used to calculate the
values of the parameters for that RIL. Pleiotropic effects of
QTL on leaf elongation parameters (due to colocalization of
QTL affecting the a, b, and c parameters) were considered in
simulations with the first population, while additional pleiotropic effects on silk elongation (a, b, c, and ASIdrought) were
considered in the second population. The results of these
simulations were represented as yield–fitness adaptation landscapes (Kauffman 1993; Podlich and Cooper 1998) showing
variation in yield as dependent on values of the traits a, b, and c
for the entire range of possible allelic combinations.
Second set of virtual experiments—simulation and statistical analysis of QTL experiments: In the second set of simulations, long-term simulations employing historical climate
data and conventional agronomic practices were used to characterize and select a set of representative drought environments for Sete Lagoas, Brazil (19.5°S, 44.2°W, 730 m). QTL
experiments for each of these environment types were then
carried out in silico, to mimic what might be experimentally
done in a typical evaluation of a biparental population.
By first modeling the reference genotype (with parental
mean for the values of a, b, c, and ASIdrought), the simulations
were used to estimate yield and characterize the seasonal stress
patterns experienced over years by rain-fed maize in this region. Plants were sown in silico on January 1 from 1960 to 2005,
using the climatic data from Sete Lagoas, Brazil (SECTEC/
SIMEFO–Secretaria da Agricultura do Estado de Goiás).
They were grown in Oxisols/Latosols soils under (i) a virgin
condition where an acidic subhorizon inhibits root growth
beyond 30 cm depth and increases the occurrence of drought
by limiting total transpirable soil water content (TTSW) to 35
mm and (ii) an ameliorated condition (incorporation of
lime to increase subsoil pH) with rooting depth of 90 cm
and TTSW of 90 mm (Heinemann et al. 2008). For each simu-
lation, the temporal pattern of the daily fraction of transpirable soil water (FTSW) was averaged every 100 degree days
from emergence to harvest and centered around flowering. A
cluster analysis was applied to these FTSW patterns, using the
medoid clustering library (pam) in the R statistical package (R
Development Core Team 2008) to identify the four major
environment types encountered. Similar methodologies have
been used by Chapman et al. (2000) and Heinemann et al.
(2008) to classify drought patterns for different target populations of environments.
The situation (combination of year and soil) that was most
similar to the median of each cluster (‘‘median environment’’)
was used for the QTL experiments to estimate the QTL effects
on yield in the two RIL populations. The environments sampled
thus represented the ‘‘best-case’’ scenario where experimental
trials could be conducted to best represent the types of drought
that occur in this given cropping system (i.e., soil, location, year,
management). Environmental characteristics for the median
situations (ETBr1–4median) are presented in Table 2.
The phenotypic data generated for the four median
situations were analyzed by mixed models to estimate the
effects on yield of individual QTL. Data were analyzed
separately for the two populations. The analysis employed
mixed models that were fitted using the ASREML library
(Gilmour et al. 1997) implemented within R (R Development Core Team 2008) and accounted for QTL effects across
multiple environments. In a first analysis, environments and
known QTL were fitted as fixed main effects, and genotypes as
random effects, to estimate the additive yield effects of the
QTL across all environments. In a second analysis, the QTL
were fitted as fixed QTL by environment effects to estimate the
additive yield effects of the QTL within each environment.
Residual genotypic variance components were simultaneously
fitted to all four environments (Smith et al. 2001) to account
for heterogeneity among environments. Significance of each
QTL was determined by a Wald test of the fixed effect (Boer
et al. 2007). Estimates were calculated of the proportion of
genotypic variance explained by QTL across environments.
RESULTS
Simulated yield was increased by greater leaf elongation rate in well-watered and vegetative deficit environments and by lower ASI in all environments: To
analyze the impact of drought and evaporative demand
(VPD), four contrasting soil-moisture patterns were
simulated for two sowing dates with fine tuning of the
irrigation in a rain-free climate (Figure 3). A sensitivity
analysis was conducted to estimate how the parameters
for leaf elongation rate (a, b, and c) and ASI (ASIdrought)
affected the simulated yield (Figure 4); i.e., the value of
each parameter was varied in equal steps from the lowest
to the highest value of all possible allelic combinations
while other parameters were set to the mean of the
parents.
Leaf elongation parameters significantly affected leaf
area index (LAI) and led to an increase or a decrease in
simulated yield, depending on the environment (Figure
4A; each point corresponds to a different value of a, b,
or c). In well-watered conditions (ETMex1), maximum
LAI was .5 m2 of leaf per square meter of land, with
flowering 66 days after sowing and a maximum simu-
Gene-to-Phenotype Modeling Reveals QTL Impacts
Figure 3.—Change in fraction of transpirable soil water
(FTSW) in managed environments (ETMex1–4) for the reference genotype from sowing until harvest. Simulations were
performed for plants sown in July (moderate VPD) and September (high VPD) in Tlaltizapán (Mexico). Irrigation was
managed in silico to obtain four different patterns of drought:
a well-watered treatment (ETMex1, A), a water deficit during
the vegetative period (before the grain-setting period;
ETMex2, B), a water deficit during the grain-setting period
(ETMex3, C), and a water deficit during both the vegetative
and the grain-setting period, with an irrigation at the beginning of the grain-setting period (ETMex4, D). Data are presented here only for the sowing in September.
1513
lated yield of 10–12 tons ha1 (Figure 4A), which is
comparable to field observations under similar conditions (July plantings of 20-leaf maize genotypes) at this
site in Mexico (Edmeades et al. 1999; J. M. Ribaut,
unpublished data). For both planting dates (i.e., moderate and high VPD), parameters that increased LAI
under well-watered or vegetative water deficit conditions had a positive impact on simulated yield with
a yield increase up to 7% (well watered, ETMex1) and
21% (early stress, ETMex2), compared to the reference
genotype. In the presence of a water deficit around
flowering (ETMex3–4), an increase in LAI had a negligible or even a negative impact on simulated yield.
Plants with the greatest LAI were particularly disadvantaged in ETMex3, as they exhausted most of the water
supply prior to the reproductive period, which significantly affected their grain setting. For all these environments (ETMex1–4), a greater VPD reduced both the
simulated LAI and yield.
In the model (equation in Figure 1), high LER in a
given environment was favored by high values of
parameter a (i.e., high potential leaf elongation rate),
high values of b (i.e., low sensitivity to high evaporative
demand), and low values of c (i.e., low sensitivity to soil
water deficit). However, when integrating these leaf
elongation responses to the crop level, an increase in
value of the leaf elongation parameters (a, b, and c)
affected LER, LAI, and yield either positively or negatively depending on the environment (Figure 4, B–D),
because of the plant–environment interactions (e.g., the
feedback of leaf growth on soil water depletion).
Yield impact of potential leaf elongation (parameter a):
The potential leaf elongation rate (parameter a, Figure
4B) was a major determinant of yield, resulting in substantial effects on simulated yield (from 56% to 121%
across environments). Given its positive impact on leaf
elongation and LAI, increased a was positively correlated
with the simulated yield under well-watered and vegetative water deficit situations (ETMex1–2). In environments
subjected to a stress around flowering (ETMex3–4), plants
with higher values of a, and hence greater LAI, exhausted
their water supply and thus yielded less. Similarly, under a
vegetative water deficit (ETMex2), plants with the greatest
values of a (a $ 6 mm per degree day) consumed their
water supply before the end of the vegetative period so
that they had a lower simulated LAI at flowering and a
reduced simulated yield.
Yield impact of leaf-elongation sensitivity to evaporative
demand and water deficit (parameters b and c): In wellwatered environments (ETMex1), a decrease in sensitivity to evaporative demand (higher values of parameter
b; Figure 4C) or to water deficit (lower values of c; Figure 4D) had little impact on yield (,5% change in
simulated yield). Both b and c had greater impacts on
simulated yield under vegetative water deficits, especially at high evaporative demand (ETMex2VPD1). For
the latter condition, increased b improved simulated
1514
K. Chenu et al.
yield up to 14% (Figure 4C). Decreased c had a greater
impact as it improved simulated yield up to 21% under
these conditions. However, when well-watered plants
were subjected to a stress around flowering (ETMex3),
the increase in LAI arising from higher b or lower c led to
greater water consumption and lower yield.
Yield impact of silk elongation (parameter ASIdrought): When
considering the QTL effect associated with silk elongation, an increased ASI (corresponding to an increased
PGRbase,g) was associated with reduced simulated yield in all
environments, especially when evaporative demand and
water deficit were high (Figure 4E). When both vegetative
and reproductive stresses occurred (ETMex4), yield was
more than doubled by favorable (low) ASI and the crop
failed to yield in the simulations when ASI was .7 days.
QTL colocalization limited the possible trait combinations: In the sensitivity analysis (above), the full range
of values was explored for each parameter, assuming no
linkage between the QTL and no associations among
the values of the different parameters (Figure 4).
However, it had been experimentally shown that these
parameters were associated with QTL that colocalized
and thus formed a QTL–trait network (Figure 2). This
limited the possible combinations of parameter values
so that the RIL population had some gaps (shown as
‘‘white spaces’’ in Figure 5). Pleiotropic effects of the
QTL for a and b were negatively correlated, as were
those for b and c, while those for a and c were always
positively correlated (Table 1 and Figure 2). As a result,
lines with the greatest potential leaf elongation rate
(highest values of a) never had low sensitivity of leaf
elongation rate to evaporative demand (high values of b,
Figure 5A) or low sensitivity to soil water deficit (low c,
Figure 5C). Hence, there was no possible QTL combination for ideotypes that would have high leaf elongation rate under both stress and nonstress conditions. In
contrast, some lines with high values of b also had low
values of c (Figure 5B) so that these lines had low
sensitivity to both evaporative demand and soil water
deficit. In the 1000 lines of the population (F2:8), most
lines had intermediate values for a, b, and c while ,5%
of them had extremely high (or low) a, b, or c.
QTL colocalization affected the best-yielding trait
combination: Crop growth, development, and yield of
each RIL were simulated in the eight managed environments (four drought patterns in two evaporativeFigure 4.—Impact on simulated yield of leaf area index
(LAI) at flowering and the parameters for leaf elongation rate
(LER) and ASI (a, b, c, and ASIdrought) under contrasting soil
water and evaporative demand (VPD) conditions (environments described in Table 2 and Figure 3). Simulations were
performed for a reference genotype (parameters set to the
mean of the two parents) with each single parameter modified
independently (one at a time) across the range of its variability.
(A) Impact of LAI on yield for different a, b, and c; (B–E) Deviation in yield relative to the reference genotype for different
values of the parameters a, b, c, and ASIdrought, respectively.
Gene-to-Phenotype Modeling Reveals QTL Impacts
1515
Figure 5.—Structure of
the 1000-member RIL populationsimulated with QU-GENE
on the basis of the QTL–trait
network (Table 1, Figure 1).
Colors indicate the frequency
of occurrence of RILs with
different combinations of values of the leaf expansion rate
(LER) parameters : parameter
a vs. b (A), b vs. c (B) and c vs. a
(C). The top bar (in green)
corresponds to the frequency
of the values of the parameter
singly in the population: parameter a (A), b (B) and c (C).
demand scenarios; Table 2 and Figure 3), taking into
account the QTL effect either on leaf elongation alone
or on both leaf and silk elongation (Figure 2). In both
cases, an increase in evaporative demand tended to
increase the effect of a, b, and c, so only the results for
the high evaporative demand conditions are presented
(Figure 6). Figure 6, A and B, depicts the average effects
of individual parameters on simulated yield, with values
constrained by QTL colocalizations (Figure 2), while
Figure 6, C and D, presents these effects for the different
combinations of parameters a, b, and c, as yield–fitness
adaptation landscapes.
First population (RILs considering QTL for leaf elongation
alone): Compared to the sensitivity analysis, in which leaf
elongation parameters were varied one at a time (Figure
4, B–D), the inclusion of pleiotropic QTL effects for
the leaf elongation parameters (first population; Figure
2) reduced the average impact of a, b, and c on simulated
yield (Figure 6A). As in the sensitivity analysis, an increase in a had either a positive (ETMex1–2 and ETMex4)
or a negative (ETMex3) average impact on simulated
yield (Figure 6, A and C); b had a minor impact on
simulated yield; and the average impact of c was substantial only in the scenario with a vegetative water
deficit during the vegetative phase (ETMex2). However,
in ETMex1 and -3, although the effects of c were small,
they were opposite to those found in the sensitivity
analysis, as in these environments the effects of QTL for
c were mainly due to the pleiotropic effect of these QTL
on a. Hence, the average impacts of a and c on simulated
yield were either positively (ETMex1 and -3) or negatively
(ETMex2 and -4) linked, depending on the water regime
(Figure 6A, I–III).
Second population (RILs considering QTL for both leaf
and silk elongation): When the pleiotropic QTL effects
on both leaf and silk elongation were considered, yield
variability was greatly increased due to substantial
modifications in the simulated yield impacts of parameters a, b, and c (Figure 6, B and D). For instance, the
influence of a in well-watered and vegetative water
deficits (ETMex1–2) was decreased, while the impact of
a was increased for the flowering stresses (ETMex3–4;
Figure 6A, I vs. 6B, I). In all environments, effects of b
and c were increased by the inclusion of ASI effects and
lines with higher b or lower c yielded more (Figures 4, C
and D, and 6B, II and III), as alleles for short ASIdrought
(low PGRbase,g) also conferred reduced sensitivity of leaf
elongation to evaporative demand (high b) and/or soil
water deficit (low c) (Table 1, Figure 2). Overall, the
jointly dominating effects of a and b and of a and c that
were simulated in the first population (illustrated by a
diagonal red/green pattern in Figure 6C, X–XII–XIV–
XVI, and highlighted by a blue arrow in Figure 6C, XII–
XVI) shifted toward a dominating effect of b or c in the
second population (horizontal and vertical red/green
pattern, respectively, in Figure 6D, X–XII–XIV–XVI).
Although the alleles of QTL that confer short ASIdrought
all had either a positive effect on b or a negative effect on
c, c had a greater impact on yield than b in all the stressed
environments (ETMex2–4), as lines with higher c yielded
better regardless of their b value (horizontal green/red
pattern of the impact of b and c; Figure 6D, VII–XI–XV).
Overall, the changes in yield–fitness adaptation landscapes illustrate how the genotype (set of alleles), the
genetic architecture (pleiotropy of QTL for effects
on LER parameters a, b, and c and for QTL affecting
silk elongation), and the environment all combine to
influence the simulated yield. The best-yielding RIL
(indicated by a star in the graphs in Figure 6, C and D)
thus varied depending on both the genetic architecture
and the environment.
High genotype–environment interactions were generated in the two populations in rain-fed maize-growing
environments: A second set of simulations was performed over 45 years for a rain-fed cropping region in
Brazil, and QTL effects were evaluated for scenarios
representing the typical drought patterns found in that
cropping system. The clustering of environments into
four types (Figure 7) indicated that plants experienced
a mild terminal stress with some vegetative stress (ETBr1,
37% of the situations), a stress commencing at the end
of the vegetative period with some relief during grain
filling (ETBr2, 24% of the situations), a mild terminal
stress during the grain set and filling periods (ETBr3,
26% of the situations), or a severe terminal stress during
the grain set and filling periods (ETBr4, 13% of the
1516
K. Chenu et al.
Gene-to-Phenotype Modeling Reveals QTL Impacts
situations). To mimic ‘‘ideal’’ QTL experiments that aim
to sample a representative range of the environments
characteristic of the targeted region, G 3 E interactions
and QTL impact were evaluated for the four sampled
situations that were closest to the median of each
environment type (Figure 8, Table 3).
Large G 3 E interactions for yield were generated
across the four sampled environments (ETBr1–4median,
Figure 8), while flowering date occurred 67 days after
sowing and average yield varied from 2 to 8 tons ha1
(Table 3). Significant variation in yield occurred among
genotypes in ETBr1–2 and ETBr4median, while yields were
similar among genotypes in ETBr3median. The ranking of
genotypes also varied greatly across environments, and
this occurred for both populations (i.e., with QTL
affecting leaf elongation alone or affecting both leaf
and silk elongation). The crossover interaction for the
first population (QTL for leaf elongation alone) occurred mainly in ETBr1median and ETBr4median, with a
magnitude of the variation around 10% in these environments. For the second population (QTL affecting
both leaf and silk elongation), the genotypic variation
in simulated yield was greater in the four sampled
environments, with the highest variability simulated
for ETBr1–2median.
Most QTL significantly affected the simulated yield
in rain-fed maize-growing environments: Significant
impacts on simulated yield were detected for the QTL
in both populations in the four Brazilian median environments, using a mixed-model analysis (Table 3). In
the first population (with leaf elongation effects alone),
all QTL except qc3 had a significant impact on yield
in at least one environment. Five of the 11 QTL (qb1,
qa2, qa4qb5qc5, qa5qb6qc6, and qa6qc7) had a significant yield impact for all four situations, with a mean
additive effect ranging from 12 to 29 kg ha1. The
highest additive effects on yield (up to 125 kg ha1 for
qa6qc7) were simulated in the ETBr1median environment, where plants were well watered and experienced
only a late mild stress. In the sampled environments
(ETBr1–4median), the additive effect of the leaf elongation QTL on yield was driven mainly by QTL for
potential leaf elongation (parameter a), as they had
greater mean QTL effects and explained the major
part of the variance. However, the best-yielding lines
in this ETBr1median environment performed poorly in
1517
ETBr4median (Figure 8). The allelic effects of all QTL
in ETBr1–2median environments were reversed in the
ETBr3–4median environments (i.e., positive effects in
ETBr1–2median were negative in ETBr3–4median and vice
versa; Table 3).
When the silk elongation effect was included in the
simulations (second population), all the QTL for ASI
(qa4qb5qc5, qa5qb6qc6, qb4qc4, and qc1) had a major
impact on the simulated yield in all situations, varying
from 184 to 252 kg ha1 on average (Table 3). The effect
of the other QTL was then no longer significant in many
cases (P , 0.05). Furthermore, the inclusion of the QTL
effects on silk elongation had a substantial impact on
the proportion of yield variance explained by given
QTL. For instance, two QTL for a (qa2 and qa6qc7) that
each explained .20% of the yield variance in the four
environments (ETBr1–4median) when only the leaf
effects were considered, each explained only 2% of
the yield variance when the silk effects were included.
In contrast, the relative yield variance explained by
two QTL associated with ASIdrought (qc1 and qb4c4) went
from ,4% each when only the leaf effects were
considered to 30% each when the effects on silk elongation of these QTL were included. The results for both
effect size and variance explained by the QTL emphasize that, for this QTL–trait network and these environments, the relative importance of QTL for potential leaf
elongation (parameter a) is inferior to that of QTL for
ASI (or PGRbase,g), when both leaf and silk effects are
considered.
DISCUSSION
A gene-to-phenotype model to simulate crop-level
impacts of organ-level environmentally stable genetic
controls: Despite the increasing knowledge on potentially favorable genes and QTL alleles for traits like
drought tolerance, their utility for breeding is difficult
to demonstrate and hence selection for improved yield
is still largely driven by crop-level observations of trait
performance across diverse environmental conditions
(Cooper et al. 2009). Recently, QTL-based models (also
referred as gene-to-phenotype models) have been proposed to begin to integrate the QTL information
obtained from trait-mapping studies to predict trait
values at the crop level. Several models have successfully
Figure 6.—Genotype–environment interactions on simulated yield for the RIL population when considering the QTL effect
either on leaf elongation alone (A and C) or on both leaf and silk elongation (B and D) under contrasting soil water status and for
high evaporative demand conditions (ETMex1–4VPD1; Figure 3). Average yield deviation (%) relative to the mean yield of the two
parents is presented for the lines in each population, depending on their value for the leaf elongation parameters a, b, and c (A
and B) and depending on the combination of their values for these parameters (C and D). In C and D, a box plot presents the
distribution of simulated yield in the panels I–V–IX–XIII for each situation; in the other panels, colors relate to the average yield
impact of the parameters combination (red, negative effect; green, positive effect); the star ( q) indicates the highest-yielding RIL
in each environmental situation; and the crosses (1, 3) represent parents 1 and 2, respectively. The blue arrows indicate the main
gradient from low to high yield in four example panels. They illustrate the shift from a joint domination of the effects of a and c
in the first population (diagonal red/green pattern in Figure 6C, XII–XVI), toward a dominating effect of c in the second population
(vertical red/green pattern in Figure 6D, XII–XVI).
1518
K. Chenu et al.
Figure 7.—Fraction of transpirable soil water (FTSW) over
the crop cycle for simulated maize crops, in Sete Lagoas, Brazil, from 1960 to 2005. Crops were sown on January 1 for both
shallow and deep soil profiles. Situations were clustered into
four environment types (ET) on the basis of the similarity of
their FTSW over time. Gray dashed lines indicate the analog
situation closest to the median. Data are presented for the reference genotype (parameter values corresponding to mean of
the two parents).
simulated the impact of QTL for flowering time on
plant phenology and yield (e.g., Yin et al. 2005a,b;
Messina et al. 2006). However, models focusing on
complex traits such as growth processes resulted in large
discrepancies between observed and predicted values
(e.g., Yin et al. 2000), thus highlighting the importance
of working with environmentally stable processes and
QTL (e.g., Yin et al. 2003). Integrating effects of QTL
affecting parameters related to key traits of sorghum
adaptation was also proposed by Chapman et al. (2003),
but their study was based on hypothetical QTL and did
not incorporate knowledge about the relative size or
interactions between the QTL. The present study illustrates a gene-to-phenotype modeling approach applied
to simulate crop-level impacts of empirical environmentally stable QTL associated with leaf elongation rate.
The approach was further extended to test the potential
impact on yield of colocalizations observed between
some of these QTL and QTL for ASI.
Although the present model has not been directly
evaluated with field experiments, all the components of
the model concerning the QTL for leaf elongation have
been tested against independent data sets: the QTL
effects on leaf elongation parameters (a, b, and c) were
evaluated by predicting the response of new lines under
drought conditions (Reymond et al. 2003), and the
impact of leaf elongation parameters was tested for one
genotype at the crop level under a range of contrasting
drought scenarios (Chenu et al. 2008a). A direct empirical evaluation could potentially be performed with
near-isogenic lines constructed for specific allelic combinations (e.g., lowest- and highest-allelic combinations
for LAI/yield in specific drought types). However, this
would require an extensive number of trials to be sure
that the model is robust against small variations in
‘‘undetected QTL’’ and for the variation in any traits
that are not currently accounted for in the model. The
simulations concerning QTL affecting ASI were also
based on processes reflecting our current knowledge of
the physiological processes involved. However, further
empirical experiments would be required to improve
this part of the model, despite its robustness in agronomic research (see below). Progress could be enhanced
if robust modeling approaches with parameters associated stably with genomic regions could be identified, as
for the leaf elongation component.
Biophysical models to simulate yield–fitness adaptation landscapes and explore genotype–environment
interactions for yield: By synthesizing our current
knowledge on the physiological processes and their
genetic controls, the model presented here allowed the
generation of yield–fitness adaptation landscapes to
explore G 3 E interactions at the crop level. Ideally,
gene-to-phenotype modeling approaches should account for all the complex interplay among genes,
physiological traits, and the environmental conditions.
Fitness adaptation landscapes have been introduced to
Gene-to-Phenotype Modeling Reveals QTL Impacts
1519
Figure 8.—Simulated yield for
a rain-fed crop in Brazil for hypothetical populations of recombinant inbred lines (RILs) when
considering the effects of QTL
on either leaf elongation alone
(A) or both leaf and silk elongation (B). The yield deviation
(%) of each RIL in the population is presented relative to the
average yield of the parents, for
the situation that was closest to
the median in each environment
type (ETBr1–4median). For clarity
only 20 RILs that were randomly
chosen are presented.
explore selection trajectories, given a certain number of
genes (N) and a number of epistatic networks (K)
among genes (NK models; Kauffman 1993). This
approach has been extended for plant breeding applications by introducing the environmental factor (E) to
develop E(NK) models (Podlich and Cooper 1998;
Cooper et al. 2005). While such genetic models are
suitable to consider interactions among genes and
environment for single traits, they define traits as being
statistically influenced only by genes/QTL. They thus
ignore the biophysical constraints that link physiological traits and greatly influence G 3 E interactions for
integrated traits like yield.
In this study, the genetic information that was input in
the model for each parameter trait (a, b, c, and ASIdrought)
corresponded to relatively simple genetic E(NK) models. Each of these E(NK) models was defined by several
QTL (N ranging from 4 to 8 depending on the
considered trait; Table 1, Figure 2), no epistasis (K ¼
0), and only one environment (E ¼ 1), as the additive
effects for each trait did not change across environments (environmentally stable traits). In contrast, the
yield–fitness adaptation landscape that resulted from
the simulations corresponded to a more complex E(NK)
model. This latter model involved 11 QTL (considering
all traits) for yield (N ¼ 11; Table 1) and a large number
TABLE 3
QTL impact on simulated yield and average simulated yield for the two hypothetical RIL populations based on
QTL affecting either leaf expansion alone or both leaf and silk expansion
QTL
qb1
qa1qb2
qa2
qc1b
qa3qb3qc2
qc3
qb4qc4b
qa4qb5qc5b
qa5qb6qc6b
qa6qc7
qb7qc8
Simulated
yield
ETBr1median
(kg ha1)
ETBr2median
(kg ha1)
ETBr3median
(kg ha1)
ETBr4median
(kg ha1)
51/67a
69/87
111/133
40/277
47/63
25/26
45/296
101/137
80/127
125/142
49/54
8118/8355
18/49
14/46
29/70
16/538
5/31
10/15
20/578
17/516
14/446
28/53
20/26
5985/6786
6/2
2/3
8/1
2/61
1/4
1/1
5/61
4.5/68
4/60
9/4
5/3
5578/5634
13/12
15/12
26/22
9/73
10/10
6/6.5
12/73
22/111
18/102
29/22
12/12
2238/2258
Mean QTL
effect
(kg ha1)
Pr
Variance
explained
(%)
12/25
16/31
26/45
11/237
10/27
7/8
12/252
23/208
18/184
29/43
13/176
***/NS
***/NS
***/*
**/***
*/NS
NS/NS
***/***
***/***
***/***
***/*
***/NS
4.4/0.4
7.3/0.6
19.7/1.6
2.6/27.5
3.3/0.3
1.0/0.0
3.6/31.6
15.7/21.8
9.8/16.6
24.9/1.7
4.1/0.2
The analysis was carried out for the situation closest to the median in each environment type found in the Brazilian simulations
(ETBr1–4median, Figure 7). The additive effect in each environment, the average effect over the four environments, the degree of
significance, and the genotypic variance explained are presented for each QTL. Values in boldface type correspond to QTL effects
that were significant (Wald test, P , 0.05) in the considered environment. Additive effects are presented for parent 1. *P , 0.05;
**P , 0.01; ***P , 0.001; NS, nonsignificant.
a
Result for the population based on QTL for leaf elongation only/on QTL for both leaf and silk elongation.
b
QTL affecting ASIdrought.
1520
K. Chenu et al.
Figure 9.—Illustration of the model contribution to weighting QTL effects for integrated traits in various environments. The
two major QTL involved in potential leaf elongation (a) had similar effects on this trait (Input box; Table 1) but they affected
simulated yield in contrasting ways (Output box; Table 3). The plant response associated with these two QTL also varied considerably, depending on the environment. Data depict the effect of the allele on a (for parent 1) on simulated yield in ETBr1median
and ETBr4median, using the population generated with QTL accounting for the effects on both leaf and silk elongation (second
population; Figure 2).
of environments (E), as yield varied across environmental conditions due to the influence of both fluctuating
weather conditions through the crop cycle and crop/
genotype interactions with the environment (e.g., feedback of leaf growth on water balance). The biophysical
model therefore provided the missing ‘‘trait part’’ of the
E(NK) genetic models and allowed tractable NK models
to be defined for key component traits.
In the near future, a combination of statistic and
simulation models may be able to (i) dissect yield into
key component traits that are environmentally stable,
(ii) identify QTL for these traits in mapping populations, and (iii) predict yield of various genotypes on
the basis of their allelic combination for these QTL
with NK models linked to biophysical models (Van
Eeuwijk et al. 2005; Cooper et al. 2009). Currently,
the construction of simulated data as presented in
this study could be used in the development of new
statistical analysis methods for QTL detection, given
that a multitude of crop traits (400 state variables in
the APSIM biophysical model; e.g., leaf area, biomass
components) can be ‘‘known’’ for every day of the crop
cycle in various environments (Cooper et al. 2006;
Chapman 2008).
Genetic controls of both leaf and silk elongation
significantly affected simulated yield under drought
conditions: While several studies have revealed a large
genetic variability in the drought responses of leaf
elongation rate (Reymond et al. 2003, 2004; Welcker
et al. 2007), the effect of such variability on yield has not
yet been assessed, partly because of the cost, impracticality, and limitation relative to empirical assessments.
The simulations performed here across a set of environments representing different drought patterns revealed
that all of the QTL for leaf elongation had a significant
impact on yield except qc3 (Table 3). Large G 3 E
interactions were generated, especially when comparing well-watered or vegetative stress conditions with
terminal water-deficit conditions (Figures 6 and 8, Table
3). Alleles conferring greater leaf elongation rate generally resulted in better simulated yield under wellwatered and early water deficit conditions. In contrast,
such alleles had a negative impact on simulated yield in
situations with drought around flowering and during
grain filling, where plants with greater leaf area were
disadvantaged. Hence, the variability in leaf area resulting from different allelic combinations led to modification in the timing and intensity of plant water
extraction, making it a critical component of yield
performance under drought.
When pleiotropic QTL effects on silk elongation and
ASI were included (second population, Figure 2), QTL
impacts on simulated yield were substantially modified
and enhanced (Figures 6 and 8; Table 3), as the grain
number was then directly affected by the impact of
ASI and PGRbase,g (the threshold plant growth rate for
establishment of grain number; Equation 1). Introducing this silk elongation effect increased by 20 times the
total genotypic variance for yield that was generated for
the four Brazilian sampled environments, with a maximum impact in mild-terminal and flowering stresses
(ETBr1–2median; data not shown). While several assumptions were made about the QTL effect on silk elongation in this study, the ranges of values for the model
parameters were related to observed data (see materials and methods) and the results were consistent with
field observations. As observed in many field studies
(e.g., Bolaños and Edmeades 1996), the simulations
showed that plants with a short ASI (low PGRbase,g) performed better under a water deficit. Furthermore, the
Gene-to-Phenotype Modeling Reveals QTL Impacts
importance of the direct impact of drought around
flowering, as simulated here, was consistent both with
frequent reports on colocalization of QTL affecting ASI
and yield (Ribaut et al. 1996, 1997; Vargas et al. 2006)
and with the exploitation of this correlation in yield
selection programs (Campos et al. 2004). Despite the
importance of ASI under drought, the physiological
processes involved are not yet fully explained. ASI is
known as a reporter trait for rapid ear growth during the
flowering period (Edmeades et al. 1993; Bolaños and
Edmeades 1996). Recently the biophysical basis of ASI
was demonstrated to be driven by the dynamics of ear
growth and plant growth rate (Borrás et al. 2009), thus
reinforcing the hypothesis made in this study. ASI is also
known to be associated with modification of starch and
sucrose dynamics that affect ovary abortion (for review,
see Boyer and Westgate 2004). While studies at the
biochemical and cellular levels may identify an ultimate
cause of ASI, physiological studies have shown that the
phenotype observed under water deficit (delay in silk
emergence) is clearly associated with changes in silk
developmental processes (Fuad-Hassan et al. 2008). In
future models, the quantitative response of silk elongation to environment could be integrated into the crop
model in a more mechanistic fashion, similar to that for
leaf elongation response (Chenu et al. 2008a).
Toward gene-to-phenotype models to assist plant
breeding: Modeling approaches can assist plant breeders to better understand the G 3 E interactions that are
associated with drought tolerance and that reduce yield
heritability (Ceccarelli 1996; Cooper 1996; Bolaños
and Edmeades 1996; Edmeades et al. 1999). Hammer
et al. (2005) demonstrated, with simulations based on
hypothetical genes, that gene-to-phenotype modeling
could aid in optimization of marker-assisted selection
(MAS), by accounting for the confounding effects
associated with environment and gene context dependencies. In the present study, the simulated impact of
QTL on yield varied from negative to positive depending on the environment (Table 3). The quantitative integration of physiological and genetic processes revealed,
for example, that the two major QTL affecting the
potential leaf elongation (parameter a of the model),
despite their similar impact on this trait, had contrasting
effects on simulated yield (Figure 9). Furthermore, the
yield effects of these two QTL greatly differed with the
drought conditions (Figure 9). Sufficiently robust geneto-phenotype models could thus be used to aid decisions on which traits and QTL should be targeted for
broad or specific adaptation and to explore alternative
selection methods (Chapman et al. 2003; Podlich
et al. 1999, 2004; Hammer et al. 2005). To the extent
that leaf and silk elongation have the same genetic basis
for drought response, indirect selection on leaf elongation response could be done to select for reduced ASI
under drought. This would be advantageous as selection could be undertaken (i) during vegetative stages
1521
(allowing crosses within the same season and therefore
shorter cycles of selection), (ii) in either controlled
environments or field trials, and (iii) for vegetative-stage
stresses that are easier to manage than the stresses
around flowering that are currently required for selection on ASI.
To move from theoretical estimation to practical
result is far from straightforward. A major concern of
plant breeders is that many putative drought tolerance
QTL identified are likely to have limited utility in applied breeding because of their dependency on genetic
background or their sensitivity to the environment
(Chapman et al. 2003; Campos et al. 2004; Hammer
et al. 2004; Podlich et al. 2004; Yadav et al. 2004).
Precautions were taken in this study to work with QTL
that were stable across environments and that were, at
least for some of them, confirmed in several genetic
backgrounds (Reymond et al. 2003; Sadok et al. 2007;
Welcker et al. 2007). However, the present model remains a greatly simplified representation of crop growth
dynamics. Besides accounting for only few QTL, no
epistatic effects were considered and only a small
number of pleiotropic effects were included between
QTL for leaf and silk elongation (Figure 2). Cooper
et al. (2005) estimated in a simulation study the degree
to which context-dependent gene effects (undetected
QTL, epistasis, G 3 E interactions, and pleiotropy)
would reduce the effectiveness of known QTL to improve genetic gain. To better represent real-world
conditions, such confounding gene/QTL effects would
need to be considered together with our biophysical
model in an E(NK) genetic model.
Conclusion: The gene-to-phenotype model presented
here illustrates how a new generation of crop models
can integrate information on organ-level QTL effects,
simulate their impact at the whole-plant level, and assist
in weighting their importance in terms of yield in various environments. Within the APSIM crop model, the
leaf submodel used here was based on physiological
processes stable across environments that were characterized by environmentally stable QTL, thus enabling
avoidance of QTL–environment interactions commonly
observed for more complex traits such as leaf area or
biomass accumulation (Yin et al. 1999; Reymond et al.
2004). The addition of the ASI submodel was proposed
to test in silico how colocalizations between some leaf
elongation QTL and some QTL affecting directly the
reproductive processes could affect yield.
The simulation obtained illustrated how genetic architecture, by constraining QTL and trait combinations and
by influencing their impact at the crop level, plays a key
role in the generation of economic phenotype. Work has
to be done now to combine such simulation models
with more complex genetic models and to evaluate their
predictive capacity against empirical data.
The complexity of the G 3 E interactions generated
by this relatively simple model highlights the impor-
1522
K. Chenu et al.
tance of modeling approaches that synthesize the current biological knowledge to explore the highly complex
gene-to-phenotype system.
We thank P. Bertin for data on the hybrid Dea, J. M. Ribaut for
data on the mapping population (P1 by P2) and climatic data for
Tlaltizapán, and A. Heinemann for climatic data for Sete Lagoas. We
also thank A. Doherty and N. Hansen for technical support. This
project was partly funded by the Generation Challenge Program.
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Communicating editor: E. S. Buckler