simulating the yield impacts of organ-level quantitative ... · overview: the apsim crop model was...

Copyright � 2009 by the Genetics Society of AmericaDOI: 10.1534/genetics.109.105429

Simulating the Yield Impacts of Organ-Level Quantitative Trait LociAssociated 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,Unite 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, 2009Accepted for publication September 9, 2009

ABSTRACT

Under drought, substantial genotype–environment (G 3 E) interactions impede breeding progress foryield. Identifying genetic controls associated with yield response is confounded by poor geneticcorrelations across testing environments. Part of this problem is related to our inability to account for theinterplay of genetic controls, physiological traits, and environmental conditions throughout the cropcycle. We propose a modeling approach to bridge this ‘‘gene-to-phenotype’’ gap. For maize underdrought, we simulated the impact of quantitative trait loci (QTL) controlling two key processes (leaf andsilk elongation) that influence crop growth, water use, and grain yield. Substantial G 3 E interaction foryield was simulated for hypothetical recombinant inbred lines (RILs) across different seasonal patterns ofdrought. QTL that accelerated leaf elongation caused an increase in crop leaf area and yield in well-watered 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 substantiallyenhanced 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 forgenotypes influenced only by the additive effects of QTL associated with leaf and silk growth. The resultshighlight the potential of integrative simulation modeling for gene-to-phenotype prediction and forexploiting G 3 E interactions for complex traits such as drought tolerance.

CROP yield varies greatly among genotypes, but thisgenetic variation is not consistent among environ-

ments. This presents a major challenge to plantbreeding. Environmentally stable quantitative trait loci(QTL) were found for drought adaptation traits at theorgan level. But what impacts do such QTL have oncrop yield? We developed a ‘‘gene-to-phenotype’’modeling approach that integrates physiological pro-cesses and incorporates their genetic controls. Weestimated in silico the genotype–environment interac-tions that organ-level QTL might generate on yield indifferent drought conditions. Such a modeling ap-proach opens new avenues for crop improvement.

Genotype–environment interactions—statistical vs.predictive modeling approaches: Genotype–environ-ment (G 3 E) interactions impede plant breedingprogress for complex traits such as yield and confound

the interpretation of genetic controls of adaptive traits.In drought-prone regions, the size of the yield variancecomponent for G 3 E interactions is frequently greaterthan 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 devel-oped to analyze these effects and to predict theexpected yield of genotypes across and/or withinsubsets of environments (i.e., to measure ‘‘stable/broad’’ and/or ‘‘specific’’ adaptation). In recent years,mixed models have increasingly dealt with heterogene-ity effects across and within trials to explain geneticcorrelations among environments (e.g., Smith et al.2001). The use of these models has been extended toidentify quantitative trait loci (QTL) associated withyield variation and to estimate how these are influencedby various environment covariables (e.g., Boer et al.2007). Recent developments of this method enable oneto account for genetic correlations among both traitsand environments (Malosetti et al. 2006, 2008) and to

1Corresponding author: Queensland Primary Industries and Fisheries,203 Tor St., Toowoomba, QLD 4350, Australia.E-mail: [email protected]

Genetics 183: 1507–1523 (December 2009)

detect QTL for nonlinear functions (Ma et al. 2002;Malosetti et al. 2006), thus providing a powerfulmethod for eco-physiologically inspired genetic models.New methods to characterize local environments asexperienced by the plants (i.e., as influenced by G 3 Einteractions) have also been proposed (e.g., Muchow

et al. 1996; Chelle 2005; Sadok et al. 2007; Chenu et al.2008b). Such environment characterizations were dem-onstrated to aid the understanding of genotypic responseto environment (e.g., Granier et al. 2006; Chenu et al.2007) and the unraveling of the yield variance compo-nent for G 3 E interactions (Chapman 2008). In a recentreview, Cooper et al. (2006) discussed opportunities toapply mixed-model methods to exploit G 3 E interac-tions. A major challenge for these statistical methods ishow to deal with the complex interactions occurringwithin plants among genes and among traits, as G 3 Einteractions for yield result from the integration over timeof a multitude of G 3 E interactions at various organismlevels (Van Eeuwijk et al. 2005; Cooper et al. 2009).

Biophysical simulation models that integrate physio-logical processes and their associated genetic controlscan contribute to the interpretation of G 3 E inter-actions at different organism levels, including yield(Hammer et al. 2002; Tardieu 2003; Yin et al. 2004;Chapman 2008). Such predictive models are appropri-ate to describe and explore in silico multiple combina-tions of genotypes (as defined by their alleles) andenvironments. Single physiological traits are usuallygoverned by a multitude of genes, but analyzing acombination of only 10 genes with two alleles in 10environments requires data for almost 600,000 combi-nations (310 3 10 when including heterozygotes). Theenormous number of combinations that breederswould ideally analyze to identify best-adapted genotypeshighlights a major interest for predictive approaches.Novel QTL-based or gene-to-phenotype modelingapproaches have been developed to predict gene-to-phenotype associations at the crop level, largely focus-ing on genetic controls associated with plant phenology(e.g., Hoogenboom et al. 2004; Messina et al. 2006).However, the simulation of genes/QTL for complextraits, such as the responses of plant growth and archi-tecture to environment, remains a challenging issue,which requires the modeling of physiological processesthat are stable across environments (Yin et al. 2000;Tardieu 2003; Hammer et al. 2006). We propose toillustrate the utility of such a modeling approach with anexample for maize under drought.

Controls of key organ-level processes for droughtadaptation in maize: Under drought conditions, thecoordination of growth processes to efficiently utilizethe scarce water supply and the sensitivity of grainproduction to stress are two key attributes of yieldperformance. In maize, substantial genetic variationhas been observed in drought responses of leaf elonga-tion rate (Reymond et al. 2003), which influence canopy

development and thus transpiration and crop water use.Significant genetic variability has also been observed fordrought response of ear growth rate around floweringand for response of grain number per ear at maturity(Edmeades et al. 1993; Vargas et al. 2006). A shortanthesis-silking interval (ASI) (Ribaut et al. 1997) isan indicator of these effects and has been used effectivelyin selection for improved yield under drought (Bolanos

and Edmeades 1993, 1996; Chapman et al. 1997a,b;Chapman and Edmeades 1999). Recently, several QTLaffecting both leaf elongation and ASI have been foundto colocalize (Welcker et al. 2007).

Sufficient understanding of leaf elongation has beendeveloped to propose a physiological and genetic modelof leaf elongation response to drought (see Chenu et al.2008a for additional details). Temperature, evaporativedemand, and soil water deficit were identified as majorenvironmental factors determining leaf elongation rateover periods of hours and days, whereas light and plantcarbon balance had minor effects (Ben Haj Salah

and Tardieu 1996, 1997; Tardieu et al. 1999; Sadok

et al. 2007). The parameters for the response curvesof leaf elongation rate to temperature (or ‘‘potentialleaf elongation rate,’’ parameter ‘‘a’’), evaporative de-mand (‘‘b’’), and soil water status (‘‘c’’) were found to begenotype specific and stable across environments (Ben

Haj Salah and Tardieu 1996; Reymond et al. 2003).QTL for these parameters were detected in two pop-ulations of temperate maize lines and several of theseQTL colocalized with those identified in a tropical maizepopulation (Reymond et al. 2003; Sadok et al. 2007;Welcker et al. 2007). Using such ‘‘environmentallystable’’ QTL to model leaf elongation rate avoids com-plex QTL–environment interactions that are commonlyobserved for directly measured traits such as leaf length(Reymond et al. 2004). Leaf elongation rate was suc-cessfully simulated over several days in different environ-ments for novel inbred lines defined only by their allelesat the QTL (Reymond et al. 2003). Chenu et al. (2008a)incorporated this organ-level model (with time steps ofminutes to hours) into the APSIM–Maize crop simula-tion model and hence captured the complex interac-tions of plants with their environment (e.g., the feedbackof leaf growth on soil water depletion) during the entirecrop cycle. For a maize hybrid, Dea, the model producedaccurate predictions of leaf area, biomass, and grainyield when tested against independent data from con-trasting environments (Chenu et al. 2008a).

The aim of the present study was to use crop modelingto estimate whole-plant effects of major QTL that reg-ulate environmental responses of leaf elongation rate.The impact of these QTL on maize yield was simulatedfor a set of drought scenarios. As some of these QTLcolocalize with QTL for ASI, which is an indicator ofsilk expansion rate (Welcker et al. 2007; Fuad-Hassan

et al. 2008), we also examined the consequences of pos-sible pleiotropic effects for QTL controlling elongation

1508 K. Chenu et al.

rate of both the leaf and silk tissue. The yield of 1000hypothetical recombinant inbred lines (RILs) was simu-lated under managed drought patterns (Tlaltizapan,Mexico) to describe the ‘‘yield–fitness adaptation land-scape.’’ A second set of simulations was conducted for asample of years in a rain-fed production region (SeteLagoas, Brazil) to evaluate in silico the effects for thedrought patterns experienced in a field productionsystem. These simulations mimicked ‘‘QTL experiments’’and were used in mixed-model analyses to quantify theyield impact of individual leaf elongation QTL, eitherwith or without their pleiotropic effect on silking andconsequent grain set.

MATERIALS AND METHODS

Overview: The APSIM crop model was adapted to allowsimulation of the effects of QTL on both leaf and silkelongation (Figure 1). This model uses (i) genetic inputs withgenotype-specific parameters that characterize different planttraits and (ii) environmental inputs (daily weather data, soilcharacteristics, and crop management such as sowing date orirrigation) to calculate phenotypic values for crop growth,development, and ultimately grain yield (outputs of themodel). In this study, only the parameters related to droughtresponse of leaf elongation rate (parameters a, b, and c) andASI (ASIdrought) were modified among genotypes. Two hypo-thetical RIL populations were generated on the basis of knownmajor QTL for leaf elongation parameters (Table 1, Figure 2),using the quantitative genetics simulation model QU-GENE

Figure 1.—Schematic view of the ‘‘gene-to-phenotype’’ model showing how the leafelongation module interacts with the restof the APSIM crop model. Environmentaland genetic information is used as inputsto simulate leaf growth, crop growth anddevelopment, and grain yield. Leaf elon-gation rate (LER) is a function of leafenvironmental factors [Tm, meristem tem-perature; T0, base temperature; VPDm-a,meristem-to-air vapor pressure deficit; c,predawn leaf water potential (negative val-ues)] and leaf elongation parameters (a,potential leaf elongation rate; b, responseof leaf elongation rate to VPDm-a; and c,response of leaf elongation rate to c). Highleaf elongation rate (LER) in a given envi-ronment is favored by high values of param-eters a and b and low values of c (i.e., LERfavored by high potential leaf elongationrate and low sensitivity to either high evap-orative demand or soil water deficit).

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)a

(mm �Cd�1)b

(mm �Cd�1 kPa�1)c

(mm �Cd�1 MPa�1)ASIdrought

(d)

qb1 1 154 0.080qa1qb2 1 271 0.147 �0.080qa2 2 84 0.158qc1 2 174 �0.289 �0.5qa3qb3qc2 3 67 �0.152 0.063 �0.259qc3 4 242 0.277qb4qc4 5 79 0.065 �0.261 �0.5qa4qb5qc5 5 186 �0.228 0.064 �0.259 �0.5qa5qb6qc6 8 92 �0.184 0.051 �0.302 �0.5qa6qc7 9 67 �0.207 �0.309qb7qc8 10 0 0.060 �0.257

The chromosome, the position, and the additive effect of the parent 1 allele are presented for all the QTL. QTL are named afterthe 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 perdegree day (mm �Cd�1),�0.948 mm �Cd�1 kPa�1, 4.842 mm �Cd�1 MPa�1, and 6 days for parent 1 and 5.986 mm �Cd�1,�1.552 mm�Cd�1 kPa�1, 8.158 mm �Cd�1 MPa�1, and 6 days for parent 2, respectively. Data are derived from Welcker et al. (2007), who pre-sented the QTL additive effect for the alleles of parent 2, and from Vargas et al. (2006).

Gene-to-Phenotype Modeling Reveals QTL Impacts 1509

(Podlich and Cooper 1998). The QTL of the first populationgenerated were assumed to control leaf elongation alone(Reymond et al. 2003), whereas in a second population theywere assumed to influence both leaf and silk elongation(Welcker et al. 2007). The yield phenotype of each line wassimulated using an adapted APSIM crop model (Chenu et al.2008a). A first set of simulations was carried out to determinegene-to-phenotype consequences on yield in manageddrought environments with contrasting soil water contentsand evaporative demands (resulting from different sowingdates and irrigation managements at Tlaltizapan, Mexico). Asecond set of simulations was conducted to estimate effects onyield of individual QTL for representative conditions experi-enced in a rain-fed maize-growing region (Sete Lagoas, Brazil;Table 2).

Phenotype prediction—a crop model to account for leafand silk growth effects on yield: Like most crop models,APSIM (http://www.apsim.info/apsim/) simulates the pro-cesses of growth and development of a genotype (usually a com-mercial cultivar) in response to external environment variables.In this biophysical simulation model, the crop/genotype isdefined by a set of parameters associated with algorithms thatdescribe physiological processes (e.g., leaf development, solarradiation interception, water uptake, biomass and nitrogenaccumulation, and retranslocation). The APSIM model has beenextensively tested, in a broad range of conditions, during the last20 years (http://www.apsim.info/apsim/). For each environ-ment, the model accepts as input descriptions of soil, weatherdata, and management decisions (e.g., date of irrigation andamount of water supplied). It operates on a daily time step tosimulate the growth and development of the crop over time and

generates phenotypes for a multitude of traits, including cropleaf area, biomass, the quantity of water transpired every day, andthe grain yield at harvest.

The standard maize crop model of the APSIM simulationplatform (Wang et al. 2002; Keating et al. 2003) was extendedby inclusion of the modified module for leaf development andexpansion (Figure 1) by Chenu et al. (2008a). This allowedinputs of leaf response parameters (a, b, and c) calculated fromthe QTL allelic combination of any genotype. The modulardesign of APSIM facilitated such model development, byenabling the replacement of existing daily leaf-growth rou-tines with new hourly leaf-growth routines based on the leafelongation rate (LER) model.

To incorporate the genetic variability for silk elongationand ASI in response to changes in growth rate due to stress, anadditional algorithm replaced the existing APSIM routine thatdescribed kernel development. On the basis of the model ofEdmeades and Daynard (1979) and the results of Andrade

et al. (1999), kernel number (KN) was estimated from themean plant growth rate (PGR) between 130 degree daysbefore and 260 degree days after flowering,

KN ¼ KNmaxð1� e�kðPGR�PGRbase;g ÞÞ; ð1Þ

where KNmax is the potential kernel number reached undernonlimiting conditions, which was set at 500, on the basis offield data for the genotype Dea (P. Bertin, unpublished data);k is a curvature parameter, which was set at 0.83, on the basis ofdata from Andrade et al. (1999); and PGRbase,g is a genotype-dependent variable corresponding to the x-intercept of thecurve, which quantifies the minimum PGR required for any

Figure 2.—QTL–trait network for parameters of leaf elongation rate (LER) response and anthesis-silking interval (ASI) underdrought (a, b, c, and ASIdrought). Two populations of 1000 recombinant inbred lines (RILs) each were simulated with QTL affectingeither the parameters involved in LER alone (first population) or parameters for both LER and ASI (second population). For eachtrait, 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 traitsinfluenced (degree of pleiotropy), indicating the complexity of each QTL within the network.


http://www.apsim.info/apsim/




kernels to be initiated. Drought-tolerant genotypes have alower PGRbase,g. In practice, genetic variation in PGRbase,g israrely measured, but is indirectly evaluated as a change in therelative timing of anthesis (pollen production on the tassel)and silking (appearance of silks from the husk), commonlyreferred to as ASI. Overall the ‘‘ASI effect’’ of the QTL was thusattributed to variations in PGRbase,g, while all the other variablesin the model were held constant.

Simulated RIL populations: Eleven major QTL controllingleaf elongation rate response to drought (Table 1, Figure 2)were used to create a population of 1000 F2:8 RILs. Thepopulation was generated with the quantitative geneticssimulation 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 withthe APSIM-LER data generated in this study, can be down-loaded from the software webpage (http://www.uq.edu.au/lcafs/qugene/). Each QTL was assigned a location on thechromosomes and the two parents were characterized by theiralleles for the QTL. Each allele was described by its additiveeffect relative to parent one (‘‘parent 1’’; see below). Onethousand hypothetical RILs were generated from a single crossbetween the parents, followed by selfing (F2) and consequentsingle-seed descent. In a second population, which comprisedthe same 1000 RILs (as defined by their alleles), an additionalpleiotropic effect on ASI-related traits was included for thefour leaf elongation QTL known to colocalize with QTL forASI under drought (Vargas et al. 2006; Welcker et al. 2007;Figure 2).

The positions and additive effect sizes of the QTL for leafelongation response to (i) meristem temperature (also re-ferred to as potential leaf elongation rate or parameter a of theLER model; Figure 1), (ii) evaporative demand, which wascharacterized by the meristem-to-air vapor pressure deficit(parameter b), and (iii) soil water deficit, which was charac-terized by the predawn leaf water potential (parameter c), werederived from experimental data reported on the crossbetween 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’’ weresimulated to account for the residual genetic variance.

To obtain yield estimation comparable to hybrid perfor-mance, the allelic combinations for the QTL (that defined anindividual RIL) were simulated within the background growthand development characteristics known for the hybrid Dea(for detail, see Chenu et al. 2008a) and with a final leaf numberof 20, which is typical of medium to late season tropical maize(e.g., Chapman and Edmeades 1999) and is similar to that ofthe tropical lines P1 and P2 ( J. M. Ribaut, unpublished data).The values of a, b, and c for the inbred parent lines of thesimulated populations (parent 1 and parent 2) were scaledfrom 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 similareffect 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 valueof the reference genotype of 6 days. For the first RILpopulation, PGRbase,g (Equation 1) was set at 1.2 g per day, avalue similar to that for the hybrid used by Andrade et al.(1999). In the second RIL population, where the QTL effectson silk elongation were included, PGRbase,g varied from 0.8 to1.6 g per day on the basis of experimental data scaled to thereference genotype (Vargas et al. 2006; J. M. Ribaut, un-published data). As the kernel number response to plantgrowth rate (Equation 1) is related to ear growth (Andrade

et al. 1999; Vega et al. 2001; Echarte et al. 2004) and eargrowth rate determines the time of silking and ASI (Edmeades

et al. 1993; Borras et al. 2007), it was assumed that the geneticvariation in the KN–PGR relation (Equation 1) was related tothe QTL effects for ASI. Genetic variations in PGRbase,g wereestimated as being proportional to genetic variations observedin ASI under drought (ASIdrought), with the shortest 4-dayASIdrought corresponding to the lowest PGRbase,g value of 0.8 gper day and the longest 8-day ASIdrought corresponding to thegreatest PGRbase,g value of 1.6 g per day. A recent study (Borras

et al. 2009), published after the realization of this work, clearly

TABLE 2

Characteristics of the in silico field experiments conducted using environmental data fromTlaltizapan (Mexico) and Sete Lagoas (Brazil)

Exp. Location Sowing date Water regimeIrradiance(MJ m�2)

Temperature(�)

VPDm-a

(kPa)

ETMex1VPD� Tlaltizapan, Mexico July 1, 1995 Well watered 28.3 24.2 1.77ETMex1VPD1 Tlaltizapan, Mexico September 1, 1995 Well watered 26.7 23.6 2.06ETMex2VPD� Tlaltizapan, Mexico July 1, 1995 Early water deficit 28.3 24.2 1.90ETMex2VPD1 Tlaltizapan, Mexico September 1, 1995 Early water deficit 26.7 23.6 2.23ETMex3VPD� Tlaltizapan, Mexico July 1, 1995 Late water deficit 28.3 24.2 1.78ETMex3VPD1 Tlaltizapan, Mexico September 1, 1995 Late water deficit 26.7 23.6 2.09ETMex4VPD� Tlaltizapan, Mexico July 1, 1995 Early and late water deficit 28.3 24.2 1.89ETMex4VPD1 Tlaltizapan, Mexico September 1, 1995 Early and late water deficit 26.7 23.6 2.24ETBr1median Sete Lagoas, Brazil January 1, 1983 Rain fed 23.1 17.5 1.37ETBr2median Sete Lagoas, Brazil January 1, 1974 Rain fed 23.1 24.3 1.52ETBr3median Sete Lagoas, Brazil January 1, 1990 Rain fed 24.1 24.3 1.82ETBr4median Sete Lagoas, Brazil January 1, 1993 Rain fed 23.6 22.5 1.73

Details are presented for (i) the experiments conducted in Tlaltizapan in 1995 with four water regimes controlled by irriga-tion (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 betweenmeristem and atmosphere during the daylight period) are averaged for the period from sowing to flowering.


http://www.uq.edu.au/lcafs/qugene/



demonstrated the strong link between PGR, ear growth, andASI.

First set of virtual experiments—simulation in manageddrought environments to describe the yield-fitness adaptationlandscape: In the first set of simulations, irrigation was appliedto generate four managed-drought types to investigate howQTL effects translated to crop yield in contrasting climaticscenarios (Table 2, Figure 3). In these virtual experiments,crops were sown on July 1, 1995 (moderate evaporativedemand environment), and September 1, 1995 (high evapo-rative demand environment), using weather data obtainedfrom CIMMYT for their testing site in Tlaltizapan, Mexico(18.6�N, 99.1�W, 946 m). Irrigation was managed in silico toobtain (i) a well-watered treatment (environment type 1, alsocalled ‘‘ETMex1’’), (ii) an early water deficit from plant emer-gence 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 vegetativeand the grain-setting periods with an irrigation at the be-ginning of the grain-setting period (ETMex4). Environmentalcharacteristics for these managed environments (ETMex1–4)are presented in Table 2 and Figure 3.

A sensitivity analysis was conducted to evaluate the impact ofeach of the LER and ASI parameters on leaf area and yield(Figure 4). Simulations were first performed using referencevalues of the different parameters (a, b, c, and ASIdrought), whichwere set to the parental mean (i.e., value of the referencegenotype). The sensitivity test was conducted by varying thevalue of one parameter at a time (for the full range of potentialallelic values), while the other parameters remained at thereference value.

To account for the QTL effects on the different traits (‘‘QTL–trait network’’), the same simulations were then undertaken forall lines of the two RIL populations (Figure 2). The alleliccombination that defined each RIL was used to calculate thevalues of the parameters for that RIL. Pleiotropic effects ofQTL on leaf elongation parameters (due to colocalization ofQTL affecting the a, b, and c parameters) were considered insimulations with the first population, while additional pleio-tropic effects on silk elongation (a, b, c, and ASIdrought) wereconsidered in the second population. The results of thesesimulations were represented as yield–fitness adaptation land-scapes (Kauffman 1993; Podlich and Cooper 1998) showingvariation in yield as dependent on values of the traits a, b, and cfor the entire range of possible allelic combinations.

Second set of virtual experiments—simulation and statis-tical analysis of QTL experiments: In the second set of simu-lations, long-term simulations employing historical climatedata and conventional agronomic practices were used to char-acterize and select a set of representative drought environ-ments for Sete Lagoas, Brazil (19.5�S, 44.2�W, 730 m). QTLexperiments for each of these environment types were thencarried out in silico, to mimic what might be experimentallydone in a typical evaluation of a biparental population.

By first modeling the reference genotype (with parentalmean for the values of a, b, c, and ASIdrought), the simulationswere used to estimate yield and characterize the seasonal stresspatterns experienced over years by rain-fed maize in this re-gion. 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 Goias).They were grown in Oxisols/Latosols soils under (i) a virgincondition where an acidic subhorizon inhibits root growthbeyond 30 cm depth and increases the occurrence of droughtby limiting total transpirable soil water content (TTSW) to 35mm and (ii) an ameliorated condition (incorporation oflime to increase subsoil pH) with rooting depth of 90 cmand TTSW of 90 mm (Heinemann et al. 2008). For each simu-

lation, the temporal pattern of the daily fraction of transpir-able soil water (FTSW) was averaged every 100 degree daysfrom emergence to harvest and centered around flowering. Acluster analysis was applied to these FTSW patterns, using themedoid clustering library (pam) in the R statistical package (RDevelopment Core Team 2008) to identify the four majorenvironment types encountered. Similar methodologies havebeen used by Chapman et al. (2000) and Heinemann et al.(2008) to classify drought patterns for different target pop-ulations of environments.

The situation (combination of year and soil) that was mostsimilar to the median of each cluster (‘‘median environment’’)was used for the QTL experiments to estimate the QTL effectson yield in the two RIL populations. The environments sampledthus represented the ‘‘best-case’’ scenario where experimentaltrials could be conducted to best represent the types of droughtthat occur in this given cropping system (i.e., soil, location, year,management). Environmental characteristics for the mediansituations (ETBr1–4median) are presented in Table 2.

The phenotypic data generated for the four mediansituations were analyzed by mixed models to estimate theeffects on yield of individual QTL. Data were analyzedseparately for the two populations. The analysis employedmixed models that were fitted using the ASREML library(Gilmour et al. 1997) implemented within R (R Develop-

ment Core Team 2008) and accounted for QTL effects acrossmultiple environments. In a first analysis, environments andknown QTL were fitted as fixed main effects, and genotypes asrandom effects, to estimate the additive yield effects of theQTL across all environments. In a second analysis, the QTLwere fitted as fixed QTL by environment effects to estimate theadditive yield effects of the QTL within each environment.Residual genotypic variance components were simultaneouslyfitted to all four environments (Smith et al. 2001) to accountfor heterogeneity among environments. Significance of eachQTL was determined by a Wald test of the fixed effect (Boer

et al. 2007). Estimates were calculated of the proportion ofgenotypic variance explained by QTL across environments.

RESULTS

Simulated yield was increased by greater leaf elon-gation rate in well-watered and vegetative deficit envi-ronments and by lower ASI in all environments: Toanalyze the impact of drought and evaporative demand(VPD), four contrasting soil-moisture patterns weresimulated for two sowing dates with fine tuning of theirrigation in a rain-free climate (Figure 3). A sensitivityanalysis was conducted to estimate how the parametersfor leaf elongation rate (a, b, and c) and ASI (ASIdrought)affected the simulated yield (Figure 4); i.e., the value ofeach parameter was varied in equal steps from the lowestto the highest value of all possible allelic combinationswhile other parameters were set to the mean of theparents.

Leaf elongation parameters significantly affected leafarea index (LAI) and led to an increase or a decrease insimulated yield, depending on the environment (Figure4A; each point corresponds to a different value of a, b,or c). In well-watered conditions (ETMex1), maximumLAI was .5 m2 of leaf per square meter of land, withflowering 66 days after sowing and a maximum simu-


lated yield of 10–12 tons ha�1 (Figure 4A), which iscomparable to field observations under similar condi-tions (July plantings of 20-leaf maize genotypes) at thissite in Mexico (Edmeades et al. 1999; J. M. Ribaut,unpublished data). For both planting dates (i.e., mod-erate and high VPD), parameters that increased LAIunder well-watered or vegetative water deficit condi-tions had a positive impact on simulated yield witha yield increase up to 7% (well watered, ETMex1) and21% (early stress, ETMex2), compared to the referencegenotype. In the presence of a water deficit aroundflowering (ETMex3–4), an increase in LAI had a negli-gible or even a negative impact on simulated yield.Plants with the greatest LAI were particularly disadvan-taged in ETMex3, as they exhausted most of the watersupply prior to the reproductive period, which signifi-cantly affected their grain setting. For all these environ-ments (ETMex1–4), a greater VPD reduced both thesimulated LAI and yield.

In the model (equation in Figure 1), high LER in agiven environment was favored by high values ofparameter a (i.e., high potential leaf elongation rate),high values of b (i.e., low sensitivity to high evaporativedemand), and low values of c (i.e., low sensitivity to soilwater deficit). However, when integrating these leafelongation responses to the crop level, an increase invalue of the leaf elongation parameters (a, b, and c)affected LER, LAI, and yield either positively or nega-tively depending on the environment (Figure 4, B–D),because of the plant–environment interactions (e.g., thefeedback of leaf growth on soil water depletion).

Yield impact of potential leaf elongation (parameter a):The potential leaf elongation rate (parameter a, Figure4B) was a major determinant of yield, resulting in sub-stantial effects on simulated yield (from �56% to 121%across environments). Given its positive impact on leafelongation and LAI, increased a was positively correlatedwith the simulated yield under well-watered and vegeta-tive water deficit situations (ETMex1–2). In environmentssubjected to a stress around flowering (ETMex3–4), plantswith higher values of a, and hence greater LAI, exhaustedtheir water supply and thus yielded less. Similarly, under avegetative water deficit (ETMex2), plants with the greatestvalues of a (a $ 6 mm per degree day) consumed theirwater supply before the end of the vegetative period sothat they had a lower simulated LAI at flowering and areduced simulated yield.

Yield impact of leaf-elongation sensitivity to evaporativedemand and water deficit (parameters b and c): In well-watered environments (ETMex1), a decrease in sensitiv-ity to evaporative demand (higher values of parameterb; Figure 4C) or to water deficit (lower values of c; Fig-ure 4D) had little impact on yield (,5% change insimulated yield). Both b and c had greater impacts onsimulated yield under vegetative water deficits, espe-cially at high evaporative demand (ETMex2VPD1). Forthe latter condition, increased b improved simulated

Figure 3.—Change in fraction of transpirable soil water(FTSW) in managed environments (ETMex1–4) for the refer-ence genotype from sowing until harvest. Simulations wereperformed for plants sown in July (moderate VPD) and Sep-tember (high VPD) in Tlaltizapan (Mexico). Irrigation wasmanaged in silico to obtain four different patterns of drought:a well-watered treatment (ETMex1, A), a water deficit duringthe 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 vegetativeand the grain-setting period, with an irrigation at the begin-ning of the grain-setting period (ETMex4, D). Data are pre-sented here only for the sowing in September.


yield up to 14% (Figure 4C). Decreased c had a greaterimpact as it improved simulated yield up to 21% underthese conditions. However, when well-watered plantswere subjected to a stress around flowering (ETMex3),the increase in LAI arising from higher b or lower c led togreater water consumption and lower yield.

Yield impact of silk elongation (parameter ASIdrought): Whenconsidering the QTL effect associated with silk elonga-tion, an increased ASI (corresponding to an increasedPGRbase,g) was associated with reduced simulated yield in allenvironments, especially when evaporative demand andwater deficit were high (Figure 4E). When both vegetativeand reproductive stresses occurred (ETMex4), yield wasmore than doubled by favorable (low) ASI and the cropfailed to yield in the simulations when ASI was .7 days.

QTL colocalization limited the possible trait combi-nations: In the sensitivity analysis (above), the full rangeof values was explored for each parameter, assuming nolinkage between the QTL and no associations amongthe values of the different parameters (Figure 4).However, it had been experimentally shown that theseparameters were associated with QTL that colocalizedand thus formed a QTL–trait network (Figure 2). Thislimited the possible combinations of parameter valuesso that the RIL population had some gaps (shown as‘‘white spaces’’ in Figure 5). Pleiotropic effects of theQTL for a and b were negatively correlated, as werethose for b and c, while those for a and c were alwayspositively 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 leafelongation 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 combi-nation for ideotypes that would have high leaf elonga-tion rate under both stress and nonstress conditions. Incontrast, some lines with high values of b also had lowvalues of c (Figure 5B) so that these lines had lowsensitivity to both evaporative demand and soil waterdeficit. In the 1000 lines of the population (F2:8), mostlines 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 traitcombination: Crop growth, development, and yield ofeach RIL were simulated in the eight managed environ-ments (four drought patterns in two evaporative-

Figure 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 soilwater and evaporative demand (VPD) conditions (environ-ments described in Table 2 and Figure 3). Simulations wereperformed for a reference genotype (parameters set to themean of the two parents) with each single parameter modifiedindependently (one at a time) across the range of its variability.(A) Impact of LAI on yield for different a, b, and c; (B–E) De-viation in yield relative to the reference genotype for differentvalues of the parameters a, b, c, and ASIdrought, respectively.


demand scenarios; Table 2 and Figure 3), taking intoaccount the QTL effect either on leaf elongation aloneor on both leaf and silk elongation (Figure 2). In bothcases, an increase in evaporative demand tended toincrease the effect of a, b, and c, so only the results forthe high evaporative demand conditions are presented(Figure 6). Figure 6, A and B, depicts the average effectsof individual parameters on simulated yield, with valuesconstrained by QTL colocalizations (Figure 2), whileFigure 6, C and D, presents these effects for the differentcombinations of parameters a, b, and c, as yield–fitnessadaptation landscapes.

First population (RILs considering QTL for leaf elongationalone): Compared to the sensitivity analysis, in which leafelongation parameters were varied one at a time (Figure4, B–D), the inclusion of pleiotropic QTL effects forthe leaf elongation parameters (first population; Figure2) reduced the average impact of a, b, and c on simulatedyield (Figure 6A). As in the sensitivity analysis, an in-crease in a had either a positive (ETMex1–2 and ETMex4)or a negative (ETMex3) average impact on simulatedyield (Figure 6, A and C); b had a minor impact onsimulated yield; and the average impact of c was sub-stantial only in the scenario with a vegetative waterdeficit 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 sensitivityanalysis, as in these environments the effects of QTL forc were mainly due to the pleiotropic effect of these QTLon a. Hence, the average impacts of a and c on simulatedyield 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 leafand silk elongation): When the pleiotropic QTL effectson both leaf and silk elongation were considered, yieldvariability was greatly increased due to substantialmodifications in the simulated yield impacts of param-eters a, b, and c (Figure 6, B and D). For instance, theinfluence of a in well-watered and vegetative waterdeficits (ETMex1–2) was decreased, while the impact ofa 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 andlines with higher b or lower c yielded more (Figures 4, Cand D, and 6B, II and III), as alleles for short ASIdrought

(low PGRbase,g) also conferred reduced sensitivity of leafelongation to evaporative demand (high b) and/or soilwater deficit (low c) (Table 1, Figure 2). Overall, thejointly dominating effects of a and b and of a and c thatwere simulated in the first population (illustrated by adiagonal 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 thesecond population (horizontal and vertical red/greenpattern, 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 onc, c had a greater impact on yield than b in all the stressedenvironments (ETMex2–4), as lines with higher c yieldedbetter regardless of their b value (horizontal green/redpattern of the impact of b and c; Figure 6D, VII–XI–XV).

Overall, the changes in yield–fitness adaptation land-scapes illustrate how the genotype (set of alleles), thegenetic architecture (pleiotropy of QTL for effectson LER parameters a, b, and c and for QTL affectingsilk elongation), and the environment all combine toinfluence 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 architectureand the environment.

High genotype–environment interactions were gen-erated in the two populations in rain-fed maize-growingenvironments: A second set of simulations was per-formed over 45 years for a rain-fed cropping region inBrazil, and QTL effects were evaluated for scenariosrepresenting the typical drought patterns found in thatcropping system. The clustering of environments intofour types (Figure 7) indicated that plants experienceda mild terminal stress with some vegetative stress (ETBr1,37% of the situations), a stress commencing at the endof the vegetative period with some relief during grainfilling (ETBr2, 24% of the situations), a mild terminalstress during the grain set and filling periods (ETBr3,26% of the situations), or a severe terminal stress duringthe grain set and filling periods (ETBr4, 13% of the

Figure 5.—Structure ofthe1000-memberRILpopula-tionsimulatedwithQU-GENEon the basis of the QTL–traitnetwork (Table 1, Figure 1).Colors indicate the frequencyof occurrence of RILs withdifferent combinations of val-ues of the leaf expansion rate(LER)parameters :parametera vs. b (A), b vs. c (B) and c vs. a(C). The top bar (in green)corresponds to the frequencyof the values of the parametersingly in the population: pa-rameter a (A), b (B) and c (C).


situations). To mimic ‘‘ideal’’ QTL experiments that aimto sample a representative range of the environmentscharacteristic of the targeted region, G 3 E interactionsand QTL impact were evaluated for the four sampledsituations that were closest to the median of eachenvironment type (Figure 8, Table 3).

Large G 3 E interactions for yield were generatedacross the four sampled environments (ETBr1–4median,Figure 8), while flowering date occurred �67 days aftersowing and average yield varied from 2 to 8 tons ha�1

(Table 3). Significant variation in yield occurred amonggenotypes in ETBr1–2 and ETBr4median, while yields weresimilar among genotypes in ETBr3median. The ranking ofgenotypes also varied greatly across environments, andthis occurred for both populations (i.e., with QTLaffecting leaf elongation alone or affecting both leafand silk elongation). The crossover interaction for thefirst population (QTL for leaf elongation alone) oc-curred mainly in ETBr1median and ETBr4median, with amagnitude of the variation around 10% in these envi-ronments. For the second population (QTL affectingboth leaf and silk elongation), the genotypic variationin simulated yield was greater in the four sampledenvironments, with the highest variability simulatedfor ETBr1–2median.

Most QTL significantly affected the simulated yieldin rain-fed maize-growing environments: Significantimpacts on simulated yield were detected for the QTLin both populations in the four Brazilian median envi-ronments, using a mixed-model analysis (Table 3). Inthe first population (with leaf elongation effects alone),all QTL except qc3 had a significant impact on yieldin at least one environment. Five of the 11 QTL (qb1,qa2, qa4qb5qc5, qa5qb6qc6, and qa6qc7) had a signif-icant yield impact for all four situations, with a meanadditive effect ranging from �12 to 29 kg ha�1. Thehighest additive effects on yield (up to 125 kg ha�1 forqa6qc7) were simulated in the ETBr1median environ-ment, where plants were well watered and experiencedonly a late mild stress. In the sampled environments(ETBr1–4median), the additive effect of the leaf elonga-tion QTL on yield was driven mainly by QTL forpotential leaf elongation (parameter a), as they hadgreater mean QTL effects and explained the majorpart of the variance. However, the best-yielding linesin this ETBr1median environment performed poorly in

ETBr4median (Figure 8). The allelic effects of all QTLin ETBr1–2median environments were reversed in theETBr3–4median environments (i.e., positive effects inETBr1–2median were negative in ETBr3–4median and viceversa; Table 3).

When the silk elongation effect was included in thesimulations (second population), all the QTL for ASI(qa4qb5qc5, qa5qb6qc6, qb4qc4, and qc1) had a majorimpact on the simulated yield in all situations, varyingfrom 184 to 252 kg ha�1 on average (Table 3). The effectof the other QTL was then no longer significant in manycases (P , 0.05). Furthermore, the inclusion of the QTLeffects on silk elongation had a substantial impact onthe proportion of yield variance explained by givenQTL. For instance, two QTL for a (qa2 and qa6qc7) thateach explained .20% of the yield variance in the fourenvironments (ETBr1–4median) when only the leafeffects were considered, each explained only 2% ofthe yield variance when the silk effects were included.In contrast, the relative yield variance explained bytwo QTL associated with ASIdrought (qc1 and qb4c4) wentfrom ,4% each when only the leaf effects wereconsidered to �30% each when the effects on silk elon-gation of these QTL were included. The results for botheffect size and variance explained by the QTL empha-size that, for this QTL–trait network and these environ-ments, the relative importance of QTL for potential leafelongation (parameter a) is inferior to that of QTL forASI (or PGRbase,g), when both leaf and silk effects areconsidered.

DISCUSSION

A gene-to-phenotype model to simulate crop-levelimpacts of organ-level environmentally stable geneticcontrols: Despite the increasing knowledge on poten-tially favorable genes and QTL alleles for traits likedrought tolerance, their utility for breeding is difficultto demonstrate and hence selection for improved yieldis still largely driven by crop-level observations of traitperformance across diverse environmental conditions(Cooper et al. 2009). Recently, QTL-based models (alsoreferred as gene-to-phenotype models) have been pro-posed to begin to integrate the QTL informationobtained from trait-mapping studies to predict traitvalues at the crop level. Several models have successfully

Figure 6.—Genotype–environment interactions on simulated yield for the RIL population when considering the QTL effecteither on leaf elongation alone (A and C) or on both leaf and silk elongation (B and D) under contrasting soil water status and forhigh evaporative demand conditions (ETMex1–4VPD1; Figure 3). Average yield deviation (%) relative to the mean yield of the twoparents is presented for the lines in each population, depending on their value for the leaf elongation parameters a, b, and c (Aand B) and depending on the combination of their values for these parameters (C and D). In C and D, a box plot presents thedistribution of simulated yield in the panels I–V–IX–XIII for each situation; in the other panels, colors relate to the average yieldimpact of the parameters combination (red, negative effect; green, positive effect); the star ( q) indicates the highest-yielding RILin each environmental situation; and the crosses (1, 3) represent parents 1 and 2, respectively. The blue arrows indicate the maingradient from low to high yield in four example panels. They illustrate the shift from a joint domination of the effects of a and cin 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).


simulated the impact of QTL for flowering time onplant phenology and yield (e.g., Yin et al. 2005a,b;Messina et al. 2006). However, models focusing oncomplex traits such as growth processes resulted in largediscrepancies between observed and predicted values(e.g., Yin et al. 2000), thus highlighting the importanceof working with environmentally stable processes andQTL (e.g., Yin et al. 2003). Integrating effects of QTLaffecting parameters related to key traits of sorghumadaptation was also proposed by Chapman et al. (2003),but their study was based on hypothetical QTL and didnot incorporate knowledge about the relative size orinteractions between the QTL. The present study illus-trates a gene-to-phenotype modeling approach appliedto simulate crop-level impacts of empirical environmen-tally stable QTL associated with leaf elongation rate.The approach was further extended to test the potentialimpact on yield of colocalizations observed betweensome of these QTL and QTL for ASI.

Although the present model has not been directlyevaluated with field experiments, all the components ofthe model concerning the QTL for leaf elongation havebeen tested against independent data sets: the QTLeffects on leaf elongation parameters (a, b, and c) wereevaluated by predicting the response of new lines underdrought conditions (Reymond et al. 2003), and theimpact of leaf elongation parameters was tested for onegenotype at the crop level under a range of contrastingdrought scenarios (Chenu et al. 2008a). A direct em-pirical evaluation could potentially be performed withnear-isogenic lines constructed for specific allelic com-binations (e.g., lowest- and highest-allelic combinationsfor LAI/yield in specific drought types). However, thiswould require an extensive number of trials to be surethat the model is robust against small variations in‘‘undetected QTL’’ and for the variation in any traitsthat are not currently accounted for in the model. Thesimulations concerning QTL affecting ASI were alsobased on processes reflecting our current knowledge ofthe physiological processes involved. However, furtherempirical experiments would be required to improvethis part of the model, despite its robustness in agron-omic research (see below). Progress could be enhancedif robust modeling approaches with parameters associ-ated stably with genomic regions could be identified, asfor the leaf elongation component.

Biophysical models to simulate yield–fitness adapta-tion landscapes and explore genotype–environmentinteractions for yield: By synthesizing our currentknowledge on the physiological processes and theirgenetic controls, the model presented here allowed thegeneration of yield–fitness adaptation landscapes toexplore G 3 E interactions at the crop level. Ideally,gene-to-phenotype modeling approaches should ac-count for all the complex interplay among genes,physiological traits, and the environmental conditions.Fitness adaptation landscapes have been introduced to

Figure 7.—Fraction of transpirable soil water (FTSW) overthe crop cycle for simulated maize crops, in Sete Lagoas, Bra-zil, from 1960 to 2005. Crops were sown on January 1 for bothshallow and deep soil profiles. Situations were clustered intofour environment types (ET) on the basis of the similarity oftheir FTSW over time. Gray dashed lines indicate the analogsituation closest to the median. Data are presented for the ref-erence genotype (parameter values corresponding to mean ofthe two parents).


explore selection trajectories, given a certain number ofgenes (N) and a number of epistatic networks (K)among genes (NK models; Kauffman 1993). Thisapproach has been extended for plant breeding appli-cations by introducing the environmental factor (E) todevelop E(NK) models (Podlich and Cooper 1998;Cooper et al. 2005). While such genetic models aresuitable to consider interactions among genes andenvironment for single traits, they define traits as beingstatistically influenced only by genes/QTL. They thusignore the biophysical constraints that link physiologi-cal traits and greatly influence G 3 E interactions forintegrated traits like yield.

In this study, the genetic information that was input inthe model for each parameter trait (a, b, c, and ASIdrought)corresponded to relatively simple genetic E(NK) mod-els. Each of these E(NK) models was defined by severalQTL (N ranging from 4 to 8 depending on theconsidered trait; Table 1, Figure 2), no epistasis (K ¼0), and only one environment (E ¼ 1), as the additiveeffects for each trait did not change across environ-ments (environmentally stable traits). In contrast, theyield–fitness adaptation landscape that resulted fromthe simulations corresponded to a more complex E(NK)model. This latter model involved 11 QTL (consideringall traits) for yield (N¼ 11; Table 1) and a large number

Figure 8.—Simulated yield fora rain-fed crop in Brazil for hypo-thetical populations of recombi-nant inbred lines (RILs) whenconsidering the effects of QTLon either leaf elongation alone(A) or both leaf and silk elonga-tion (B). The yield deviation(%) of each RIL in the popula-tion is presented relative to theaverage yield of the parents, forthe situation that was closest tothe median in each environmenttype (ETBr1–4median). For clarityonly 20 RILs that were randomlychosen are presented.

TABLE 3

QTL impact on simulated yield and average simulated yield for the two hypothetical RIL populations based onQTL affecting either leaf expansion alone or both leaf and silk expansion

QTLETBr1median

(kg ha�1)ETBr2median



(kg ha�1)

Mean QTLeffect

(kg ha�1) Pr

Varianceexplained

(%)

qb1 51/67a 18/49 �6/�2 �13/�12 12/25 ***/NS 4.4/0.4qa1qb2 69/87 14/46 �2/3 �15/�12 16/31 ***/NS 7.3/0.6qa2 111/133 29/70 �8/�1 �26/�22 26/45 ***/* 19.7/1.6qc1b 40/277 16/538 �2/61 �9/73 11/237 **/*** 2.6/27.5qa3qb3qc2 �47/�63 �5/�31 1/�4 10/�10 �10/�27 */NS 3.3/0.3qc3 �25/�26 �10/�15 1/1 6/6.5 �7/�8 NS/NS 1.0/0.0qb4qc4b 45/296 20/578 �5/61 �12/73 12/252 ***/*** 3.6/31.6qa4qb5qc5b �101/137 �17/516 4.5/68 22/111 �23/208 ***/*** 15.7/21.8qa5qb6qc6b �80/127 �14/446 4/60 18/102 �18/184 ***/*** 9.8/16.6qa6qc7 �125/�142 �28/�53 9/4 29/22 �29/�43 ***/* 24.9/1.7qb7qc8 49/54 20/26 �5/�3 �12/�12 13/176 ***/NS 4.1/0.2Simulated

yield8118/8355 5985/6786 5578/5634 2238/2258

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 ofsignificance, and the genotypic variance explained are presented for each QTL. Values in boldface type correspond to QTL effectsthat 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.


of environments (E), as yield varied across environmen-tal conditions due to the influence of both fluctuatingweather conditions through the crop cycle and crop/genotype interactions with the environment (e.g., feed-back of leaf growth on water balance). The biophysicalmodel therefore provided the missing ‘‘trait part’’ of theE(NK) genetic models and allowed tractable NK modelsto be defined for key component traits.

In the near future, a combination of statistic andsimulation models may be able to (i) dissect yield intokey component traits that are environmentally stable,(ii) identify QTL for these traits in mapping popula-tions, and (iii) predict yield of various genotypes onthe basis of their allelic combination for these QTLwith NK models linked to biophysical models (Van

Eeuwijk et al. 2005; Cooper et al. 2009). Currently,the construction of simulated data as presented inthis study could be used in the development of newstatistical analysis methods for QTL detection, giventhat a multitude of crop traits (�400 state variables inthe APSIM biophysical model; e.g., leaf area, biomasscomponents) can be ‘‘known’’ for every day of the cropcycle in various environments (Cooper et al. 2006;Chapman 2008).

Genetic controls of both leaf and silk elongationsignificantly affected simulated yield under droughtconditions: While several studies have revealed a largegenetic variability in the drought responses of leafelongation rate (Reymond et al. 2003, 2004; Welcker

et al. 2007), the effect of such variability on yield has notyet been assessed, partly because of the cost, impracti-cality, and limitation relative to empirical assessments.The simulations performed here across a set of environ-ments representing different drought patterns revealedthat all of the QTL for leaf elongation had a significant

impact on yield except qc3 (Table 3). Large G 3 Einteractions were generated, especially when compar-ing well-watered or vegetative stress conditions withterminal water-deficit conditions (Figures 6 and 8, Table3). Alleles conferring greater leaf elongation rate gen-erally resulted in better simulated yield under well-watered and early water deficit conditions. In contrast,such alleles had a negative impact on simulated yield insituations with drought around flowering and duringgrain filling, where plants with greater leaf area weredisadvantaged. Hence, the variability in leaf area re-sulting from different allelic combinations led to modi-fication in the timing and intensity of plant waterextraction, making it a critical component of yieldperformance under drought.

When pleiotropic QTL effects on silk elongation andASI were included (second population, Figure 2), QTLimpacts on simulated yield were substantially modifiedand enhanced (Figures 6 and 8; Table 3), as the grainnumber was then directly affected by the impact ofASI and PGRbase,g (the threshold plant growth rate forestablishment of grain number; Equation 1). Introduc-ing this silk elongation effect increased by 20 times thetotal genotypic variance for yield that was generated forthe four Brazilian sampled environments, with a max-imum impact in mild-terminal and flowering stresses(ETBr1–2median; data not shown). While several assump-tions were made about the QTL effect on silk elonga-tion in this study, the ranges of values for the modelparameters were related to observed data (see materi-

als and methods) and the results were consistent withfield observations. As observed in many field studies(e.g., Bolanos and Edmeades 1996), the simulationsshowed that plants with a short ASI (low PGRbase,g) per-formed better under a water deficit. Furthermore, the

Figure 9.—Illustration of the model contribution to weighting QTL effects for integrated traits in various environments. Thetwo major QTL involved in potential leaf elongation (a) had similar effects on this trait (Input box; Table 1) but they affectedsimulated yield in contrasting ways (Output box; Table 3). The plant response associated with these two QTL also varied consid-erably, 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 (secondpopulation; Figure 2).


importance of the direct impact of drought aroundflowering, as simulated here, was consistent both withfrequent reports on colocalization of QTL affecting ASIand yield (Ribaut et al. 1996, 1997; Vargas et al. 2006)and with the exploitation of this correlation in yieldselection programs (Campos et al. 2004). Despite theimportance of ASI under drought, the physiologicalprocesses involved are not yet fully explained. ASI isknown as a reporter trait for rapid ear growth during theflowering period (Edmeades et al. 1993; Bolanos andEdmeades 1996). Recently the biophysical basis of ASIwas demonstrated to be driven by the dynamics of eargrowth and plant growth rate (Borras et al. 2009), thusreinforcing the hypothesis made in this study. ASI is alsoknown to be associated with modification of starch andsucrose dynamics that affect ovary abortion (for review,see Boyer and Westgate 2004). While studies at thebiochemical and cellular levels may identify an ultimatecause of ASI, physiological studies have shown that thephenotype observed under water deficit (delay in silkemergence) is clearly associated with changes in silkdevelopmental processes (Fuad-Hassan et al. 2008). Infuture models, the quantitative response of silk elonga-tion to environment could be integrated into the cropmodel in a more mechanistic fashion, similar to that forleaf elongation response (Chenu et al. 2008a).

Toward gene-to-phenotype models to assist plantbreeding: Modeling approaches can assist plant breed-ers to better understand the G 3 E interactions that areassociated with drought tolerance and that reduce yieldheritability (Ceccarelli 1996; Cooper 1996; Bolanos

and Edmeades 1996; Edmeades et al. 1999). Hammer

et al. (2005) demonstrated, with simulations based onhypothetical genes, that gene-to-phenotype modelingcould aid in optimization of marker-assisted selection(MAS), by accounting for the confounding effectsassociated with environment and gene context depen-dencies. In the present study, the simulated impact ofQTL on yield varied from negative to positive depend-ing on the environment (Table 3). The quantitative inte-gration of physiological and genetic processes revealed,for example, that the two major QTL affecting thepotential leaf elongation (parameter a of the model),despite their similar impact on this trait, had contrastingeffects on simulated yield (Figure 9). Furthermore, theyield effects of these two QTL greatly differed with thedrought conditions (Figure 9). Sufficiently robust gene-to-phenotype models could thus be used to aid deci-sions on which traits and QTL should be targeted forbroad or specific adaptation and to explore alternativeselection methods (Chapman et al. 2003; Podlich

et al. 1999, 2004; Hammer et al. 2005). To the extentthat leaf and silk elongation have the same genetic basisfor drought response, indirect selection on leaf elonga-tion response could be done to select for reduced ASIunder drought. This would be advantageous as selec-tion could be undertaken (i) during vegetative stages

(allowing crosses within the same season and thereforeshorter cycles of selection), (ii) in either controlledenvironments or field trials, and (iii) for vegetative-stagestresses that are easier to manage than the stressesaround flowering that are currently required for selec-tion on ASI.

To move from theoretical estimation to practicalresult is far from straightforward. A major concern ofplant breeders is that many putative drought toleranceQTL identified are likely to have limited utility in ap-plied breeding because of their dependency on geneticbackground 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 QTLthat were stable across environments and that were, atleast for some of them, confirmed in several geneticbackgrounds (Reymond et al. 2003; Sadok et al. 2007;Welcker et al. 2007). However, the present model re-mains a greatly simplified representation of crop growthdynamics. Besides accounting for only few QTL, noepistatic effects were considered and only a smallnumber of pleiotropic effects were included betweenQTL for leaf and silk elongation (Figure 2). Cooper

et al. (2005) estimated in a simulation study the degreeto which context-dependent gene effects (undetectedQTL, epistasis, G 3 E interactions, and pleiotropy)would reduce the effectiveness of known QTL to im-prove genetic gain. To better represent real-worldconditions, such confounding gene/QTL effects wouldneed to be considered together with our biophysicalmodel in an E(NK) genetic model.

Conclusion: The gene-to-phenotype model presentedhere illustrates how a new generation of crop modelscan integrate information on organ-level QTL effects,simulate their impact at the whole-plant level, and assistin weighting their importance in terms of yield in vari-ous environments. Within the APSIM crop model, theleaf submodel used here was based on physiologicalprocesses stable across environments that were charac-terized by environmentally stable QTL, thus enablingavoidance of QTL–environment interactions commonlyobserved for more complex traits such as leaf area orbiomass accumulation (Yin et al. 1999; Reymond et al.2004). The addition of the ASI submodel was proposedto test in silico how colocalizations between some leafelongation QTL and some QTL affecting directly thereproductive processes could affect yield.

The simulation obtained illustrated how genetic archi-tecture, by constraining QTL and trait combinations andby influencing their impact at the crop level, plays a keyrole in the generation of economic phenotype. Work hasto be done now to combine such simulation modelswith more complex genetic models and to evaluate theirpredictive capacity against empirical data.

The complexity of the G 3 E interactions generatedby this relatively simple model highlights the impor-


tance of modeling approaches that synthesize the cur-rent biological knowledge to explore the highly complexgene-to-phenotype system.

We thank P. Bertin for data on the hybrid Dea, J. M. Ribaut fordata on the mapping population (P1 by P2) and climatic data forTlaltizapan, and A. Heinemann for climatic data for Sete Lagoas. Wealso thank A. Doherty and N. Hansen for technical support. Thisproject was partly funded by the Generation Challenge Program.

LITERATURE CITED

Andrade, F. H., C. Vega, S. Uhart, A. Cirilo, M. Cantarero et al.,1999 Kernelnumberdeterminationinmaize.CropSci.39:453–459.

Ben-Haj-Salah, H., and F. Tardieu, 1996 Quantitative analysis ofthe combined effects of temperature, evaporative demand andlight on leaf elongation rate in well-watered field and labora-tory-grown maize plants. J. Exp. Bot. 47: 1689–1698.

Ben-Haj-Salah, H., and F. Tardieu, 1997 Control of leaf expansionrate of droughted maize plants under fluctuating evaporative de-mand. A superposition of hydraulic and chemical messages?Plant Physiol. 114: 893–900.

Boer, M. P., D. Wright, L. Feng, D. W. Podlich, L. Luo et al.,2007 A mixed-model quantitative trait loci (QTL) analysis formultiple-environment trial data using environmental covariablesfor QTL-by-environment interactions, with an example in maize.Genetics 177: 1801–1813.

Bolanos, J., and G. O. Edmeades, 1993 Eight cycles of selection fordrought tolerance in lowland tropical maize. II. Responses in re-productive behavior. Field Crops Res. 31: 253–268.

Bolanos, J., and G. O. Edmeades, 1996 The importance of the an-thesis silking interval in breeding for drought tolerance in trop-ical maize. Field Crops Res. 48: 65–80.

Borras, L., M. E. Westgate, J. P. Astini and L. Echarte,2007 Coupling time to silking with plant growth rate in maize.Field Crops Res. 102: 73–85.

Borras, L., J. P. Astini, M. E. Westgate and A. D. Severini,2009 Modeling anthesis to silking in maize using a plant bio-mass framework. Crop Sci. 49: 937–948.

Boyer, J. S., and M. E. Westgate, 2004 Grain yields with limitedwater. J. Exp. Bot. 55: 2385–2394.

Campos, H., M. Cooper, J. E. Habben, G. O. Edmeades and J. R.Schussler, 2004 Improving drought tolerance in maize: a viewfrom industry. Field Crops Res. 90: 19–34.

Ceccarelli, S., 1996 Positive interpretation of genotype by environ-ment interactions in relation to sustainability and biodiversity, pp.467–486 in Plant Adaptation and Crop Improvement, edited by M.Cooper and G. L. Hammer. CAB International, Wallingford, UK.

Chapman, S., M. Cooper, D. Podlich and G. Hammer,2003 Evaluating plant breeding strategies by simulating geneaction and dryland environment effects. Agron. J. 95: 99–113.

Chapman, S. C., 2008 Use of crop models to understand genotypeby environment interactions for drought in real-world and simu-lated plant breeding trials. Euphytica 161: 195–208.

Chapman, S. C., and G. O. Edmeades, 1999 Selection improvesdrought tolerance in tropical maize populations: II. Direct andcorrelated responses among secondary traits. Crop Sci. 39:1315–1324.

Chapman, S. C., J. Crossa and G. O. Edmeades, 1997a Genotype byenvironment effects and selection for drought tolerance in tropi-cal maize. I. Two mode pattern analysis of yield. Euphytica 95: 1–9.

Chapman, S. C., J. Crossa, K. E. Basford and P. M. Kroonenberg,1997b Genotype by environment effects and selection fordrought tolerance in tropical maize. II. Three-mode pattern anal-ysis. Euphytica 95: 11–20.

Chapman, S. C., M. Cooper, G. L. Hammer and D. G. Butler,2000 Genotype by environment interactions affecting grain sor-ghum. II. Frequencies of different seasonal patterns of droughtstress are related to location effects on hybrid yields. Aust. J.Agric. Res. 51: 209–221.

Chelle, M., 2005 Phylloclimate or the climate perceived by individ-ual plant organs: What is it? How to model it? What for? New Phy-tol. 166: 781–790.

Chenu, K., N. Franck and J. Lecoeur, 2007 Simulations of virtualplants reveal a role for SERRATE in the response of leaf develop-ment to light in Arabidopsis thaliana. New Phytol. 175: 472–481.

Chenu, K., S. C. Chapman, G. L. Hammer, G. Mclean, H. Ben Haj

Salah et al., 2008a Short-term responses of leaf growth rate towater deficit scale up to whole-plant and crop levels: an inte-grated modeling approach in maize. Plant Cell Environ. 31:378–391.

Chenu, K., H. Rey, J. Dauzat, G. Lydie and J. Lecoeur,2008b Estimation of light interception in research environ-ments: a joint approach using directional light sensors and 3Dvirtual plants applied to sunflower (Helianthus annuus) and Ara-bidopsis thaliana in natural and artificial conditions. Funct. PlantBiol. 35: 850–866.

Cooper, M., 1996 A strategy for yield improvement of wheat whichaccommodates large genotype by environment interactions, pp.487–511 in Plant Adaptation and Crop Improvement, edited by M.Cooper and G. L. Hammer. CAB International, Wallingford, UK.

Cooper, M., and G. L. Hammer, 1996 Plant Adaptation and CropImprovement. CAB International, International Rice Research In-stitute and the International Crops Research Institute for theSemi-Arid Tropics, Wallingford, UK.

Cooper, M., D. W. Podlich and O. S. Smith, 2005 Gene-to-phenotype models and complex trait genetics. Aust. J. Agric.Res. 56: 895–918.

Cooper, M., D. W. Podlich, C. M. Loffler, F. Van Eeuwijk and S. C.Chapman, 2006 Genotype-by-environment interactions underwater-limited conditions, pp. 51–96 in Drought Adaptation in Cere-als, edited by J.-M. Ribaut. Food Products Press, New York.

Cooper, M., F. A. Van Eeuwijk, G. L. Hammer, D. W. Podlich

and C. Messina, 2009 Modeling QTL for complex traits: detec-tion and context for plant breeding. Curr. Opin. Plant Biol. 12:231–240.

Echarte, L., F. H. Andrade, C. R. C. Vega and M. Tollenaar,2004 Kernel number determination in Argentinean maize hy-brids released between 1965 and 1993. Crop Sci. 44: 1654–1661.

Edmeades, G. O., and T. B. Daynard, 1979 The development ofplant-to-plant variability in maize at different planting densities.Can. J. Plant Sci. 59: 561–575.

Edmeades, G. O., J. Bolanos, M. Hernandez and S. Bello,1993 Causes for silk delay in lowland tropical maize. CropSci. 33: 1029–1035.

Edmeades, G. O., J. Bolanos, S. C. Chapman, H. R. Lafitte andM. Banziger, 1999 Selection improves drought tolerance in trop-ical maize populations: I. Gains in biomass, grain yield, and harvestindex. Crop Sci. 39: 1306–1315.

Fuad-Hassan, A., F. Tardieu and O. Turc, 2008 Drought-inducedchanges in anthesis-silking interval are related to silk expansion:a spatio-temporal growth analysis in maize plants subjected to soilwater deficit. Plant Cell Environ. 31: 1349–1360.

Gilmour, A. R., B. R. Cullis and A. P. Verbyla, 1997 Accountingfor natural and extraneous variation in the analysis of field ex-periments. J. Agric. Biol. Environ. Stat. 2: 269–293.

Granier, C., L. Aguirrezabal, K. Chenu, S. J. Cookson, M. Dauzat

et al., 2006 PHENOPSIS, an automated platform for repro-ducible phenotyping of plant responses to soil water deficitin Arabidopsis thaliana permitted the identification of an acces-sion with low sensitivity to soil water deficit. New Phytol. 169:623–635.

Hammer, G., S. Chapman, E. van Oosterom and D. Podlich,2005 Trait physiology and crop modeling as a framework to linkphenotypic complexity to underlying genetic systems. Aust. J.Agric. Res. 56: 947–960.

Hammer, G., M. Cooper, F. Tardieu, S. Welch, B. Walsh et al.,2006 Models for navigating biological complexity in breedingimproved crop plants. Trends Plant Sci. 11: 587–593.

Hammer, G. L., M. J Kropff, T. R. Sinclair and J. R. Porter,2002 Future contributions of crop modeling—from heuristicsand supporting decision-making to understanding geneticregulation and aiding crop improvement. Eur. J. Agron. 18:15–31.

Hammer, G. L., T. R. Sinclair, S. C. Chapman and E. van Oosterom,2004 On systems thinking, systems biology, and the in silicoplant. Plant Physiol. 134: 909–911.


Heinemann, A., M. Dingkuhn, D. Luquet, J. Combres and S. Chapman,2008 Characterization of drought stress environments for uplandrice and maize in central Brazil. Euphytica 162: 395–410.

Hoogenboom, G., J. W. White and C. D. Messina, 2004 Fromgenome to crop: integration through simulation modeling. FieldCrops Res. 90: 145–163.

Kauffman, S. A., 1993 The Origins of Order: Self-Organization and Selec-tion in Evolution. Oxford University Press, London/New York/Oxford.

Keating, B. A., P. S. Carberry, G. L. Hammer, M. E. Probert,M. J. H. Robertson et al., 2003 An overview of APSIM, a modeldesigned for farming systems simulation. Eur. J. Agron. 18:267–288.

Ma, C. X., G. Casella and R. L. Wu, 2002 Functional mapping ofquantitative trait loci underlying the character process: a theoret-ical framework. Genetics 161: 1751–1762.

Malosetti, M., R. G. F. Visser, C. Celis-Gamboa and F. A. Van

Eeuwijk, 2006 QTL methodology for response curves onthe basis of non-linear mixed models, with an illustration tosenescence in potato. Theor. Appl. Genet. 113: 288–300.

Malosetti, M., J. M. Ribaut, M. Vargas, J. Crossa and F. A.Eeuwijk, 2008 A multi-trait multi-environment QTL mixedmodel with an application to drought and nitrogen stress tri-als in maize (Zea mays L.). Euphytica 161: 241–257.

Messina, C. D., J. W. Jones, K. J. Boote and C. E. Vallejos, 2006 Agene-based model to simulate soybean development and yieldresponses to environment. Crop Sci. 46: 456–466.

Muchow, R. C., M. Cooper and G. L. Hammer, 1996 Charac-terizing environmental challenges using models, pp. 349–364in Plant Adaptation and Crop Improvement, edited by M. Cooper

and G. L. Hammer. CAB International, Wallingford, UK.Podlich, D. W., and M. Cooper, 1998 QU-GENE: a simulation plat-

form for quantitative analysis of genetic models. Bioinformatics14: 632–653.

Podlich, D. W., M. Cooper and K. E. Basford, 1999 Computer sim-ulation of a selection strategy to accommodate genotype-by-envi-ronment interaction in a wheat recurrent selection program.Plant Breed. 118: 17–28.

Podlich, D. W., C. R. Winkler and M. Cooper, 2004 Mapping asyou go: an effective approach for marker-assisted selection ofcomplex traits. Crop Sci. 44: 1560–1571.

R Development Core Team, 2008 R: a language and environmentfor statistical computing. R Foundation for Statistical Comput-ing, Vienna. http://www.R-project.org.

Reymond, M., B. Muller, A. Leonardi, A. Charcosset andF. Tardieu, 2003 Combining quantitative trait loci analysisand an ecophysiological model to analyze the genetic variabil-ity of the responses of maize leaf growth to temperature andwater deficit. Plant Physiol. 131: 664–675.

Reymond, M., B. Muller and F. Tardieu, 2004 Dealing with thegenotype x environment interaction via a modeling approach:a comparison of QTLs of maize leaf length or width with QTLsof model parameters. J. Exp. Bot. 55: 2461–2472.

Ribaut, J. M., D. A. Hoisington, J. A. Deutsch, C. Jiang and D.Gonzalez-De-Leon, 1996 Identification of quantitative traitloci under drought conditions in tropical maize. 1. Flowering pa-rameters and the anthesis-silking interval. Theor. Appl. Genet.92: 905–914.

Ribaut, J. M., C. Jiang, D. Gonzalez-De-Leon, G. O. Edmeades andD. A. Hoisington, 1997 Identification of quantitative trait lociunder drought conditions in tropical maize. 2. Yield componentsand marker-assisted selection strategies. Theor. Appl. Genet. 94:887–896.

Sadok, W., P. Naudin, B. Boussuge, B. Muller, C. Welcker et al.,2007 Leaf growth rate per unit thermal time follows QTL-dependent daily patterns in hundreds of maize lines under

naturally fluctuating conditions. Plant Cell Environ. 30:135–146.

Smith, A., B. Cullis and R. Thompson, 2001 Analyzing variety byenvironment data using multiplicative mixed models and adjust-ments for spatial field trend. Biometrics 57: 1138–1147.

Tardieu, F., 2003 Virtual plants: modeling as a tool for the genomicsof tolerance to water deficit. Trends Plant Sci. 8: 1360–1385.

Tardieu, F., C. Granier and B. Muller, 1999 Modelling leaf ex-pansion in a fluctuating environment: Are changes in specificleaf area a consequence of changes in expansion rate? New Phy-tol. 143: 33–44.

Van Eeuwijk, F. A., M. Malosetti, X. Y. Yin, P. C. Struik and P.Stam, 2005 Statistical models for genotype by environmentdata: from conventional ANOVA models to eco-physiologicalQTL models. Aust. J. Agric. Res. 56: 883–894.

Vargas, M., F. A. Van Eeuwijk, J. Crossa and J. M. Ribaut,2006 Mapping QTLs and QTL x environment interaction forCIMMYT maize drought stress program using factorial regressionand partial least squares methods. Theor. Appl. Genet. 112:1009–1023.

Vega, C. R. C., F. H. Andrade, V. O. Sadras, S. A. Uhart and O. R.Valentinuz, 2001 Seed number as a function of growth: a com-parative study in soybean, sunflower and maize. Crop Sci. 41:748–754.

Wang, E., M. Robertson, G. L. Hammer, P. Carberry, D.Holzworth et al., 2002 Development of a generic crop modeltemplate in the cropping system model APSIM. Eur. J. Agron. 18:121–140.

Wang, J., M. Van Ginkel, R. Trethowan, G. Ye, I. Delacy et al.,2004 Simulating the effects of dominance and epistasis on se-lection response in the CIMMYT wheat breeding program usingQuCim. Crop Sci. 44: 2006–2018.

Welcker, C., B. Boussuge, C. Bencivenni, J. M. Ribaut and F.Tardieu, 2007 Are source and sink strengths genetically linkedin maize plants subjected to water deficit? A QTL study of the re-sponses of leaf growth and of anthesis-silking interval to waterdeficit. J. Exp. Bot. 58: 339–349.

Yadav, R. S., C. T. Hash, F. R. Bidinger, K. M. Devos and C. J.Howarth, 2004 Genomic regions associated with grain yieldand aspects of post-flowering drought tolerance in pearl milletacross stress environments and tester background. Euphytica136: 265–277.

Yin, X., P. Stam, C. J. Dourleijn and M. J. Kropff, 1999 AFLP map-ping of quantitative trait loci for yield-determining physiologicalcharacters in spring barley. Theor. Appl. Genet. 99: 244–253.

Yin, X., P. Struik and M. Kropff, 2004 Role of crop physiology inpredicting gene-to-phenotype relationships. Trends Plant Sci. 9:426–432.

Yin, X. Y., S. D. Chasalow, C. J. Dourleijn, P. Stam and M. J. Kropff,2000 Coupling estimated effects of QTLs for physiological traitsto a crop growth model: predicting yield variation among re-combinant inbred lines in barley. Heredity 85: 539–549.

Yin, X. Y., P. Stam, M. J. Kropff and A. Schapendonk, 2003 Cropmodeling, QTL mapping, and their complementary role in plantbreeding. Agron. J. 95: 90–98.

Yin, X. Y., P. C. Struik, J. J. Tang, C. H. Qi and T. J. Liu,2005a Model analysis of flowering phenology in recombinantinbred lines of barley. J. Exp. Bot. 56: 959–965.

Yin, X. Y., P. C. Struik, F. A. Van Eeuwijk, P. Stam and J. J. Tang,2005b QTL analysis and QTL-based prediction of floweringphenology in recombinant inbred lines of barley. J. Exp. Bot.56: 967–976.

Communicating editor: E. S. Buckler


http://www.R-project.org

http://www.R-project.org

simulating the yield impacts of organ-level quantitative ... · overview: the apsim crop model was...

Documents