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235
©2009, Elsevier Inc.
2009
Carlos Messina , Graeme Hammer , Zhanshan Dong , Dean Podlich and Mark Cooper
CHAPTER 10
Modelling Crop Improvement in a
G E M Framework via Gene – Trait –
Phenotype Relationships
1. INTRODUCTION
Crop performance is determined by the combined effects of the genotype of the crop and the environmen-
tal conditions of the production system. Improving crop performance to satisfy an increasing demand for
plant products is a constant challenge to plant scientists. Plant breeders approach this challenge by search-
ing the genetic space for superior genotypes that have improved performance across the environments of
the production system ( Figure 1 ), while agronomists pursue the same goal by optimising management
for the cohort of elite genotypes developed by plant breeding. Historically, plant breeding and agronomy
have co-evolved, and both have contributed to improved crop performance. This iterative process has been
extremely successful in creating superior crops as demonstrated by the steady increase in maize yields in the
USA ( Duvick et al., 2004 ; Duvick and Cassman, 1999 ; Castleberry et al., 1984 ), and the consistent but dis-
continuous progress in wheat yield in Australia (Chapter 2). Crop physiology and modelling, although use-
ful to interpret and describe the physiological process underpinning such yield improvements (i.e. Gifford
et al., 1984 ; Duncan et al., 1978 ; Duvick et al., 2004 ; Slafer, 1994 ; Otegui and Slafer, 2000 ), have provided
little guidance for how to apply these concepts to improve the effi ciency of the breeding process ( Campos
et al., 2004 ; Evans, 1976 ; Sinclair et al., 2004 ; Lee, 1995 ).
The current paradigm of creating improved crops by breeding new genotypes and then optimising their
management at a later stage of the crop improvement process constrains breeders and agronomists to
exploring a reduced set of the vast space defi ned by the full set of possible genotype (G) and management
(M) combinations. In addition, variable environmental (E) conditions interacting with G and M (G E M)
complicates the defi nition of the possible paths towards realised genetic gain in production environments
and limits our ability to make inferences on the effects of alternative management practices. The size and
complexity of the G E M system, and the diffi culty of dealing with many interactions simultaneously, has
traditionally being tackled by crop scientists through a discipline-centred approach that deals with com-
ponents of the G E M interactions separately, most frequently as G E by plant breeders and M E by
agronomists ( Cooper and Hammer, 1996 ; Boote et al., 1996 ; Loomis and Connor, 1992 ). An open ques-
tion is whether enhanced rates of crop improvement can be realised by a more integrated approach. The
quantifi cation of these interactions relies on the use of statistical methods (i.e. Cooper and Hammer, 1996 ),
yet interpretation of these G E M interactions could be improved by means of crop modelling and simu-
lation applied to understand their causes and their relevance to the target production system ( Cooper and
Hammer, 1996 ; Löffl er et al., 2005 ).
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
236
The vast size and complexity of the G E M space that confronts breeders and agronomists present many
challenges to the defi nition of practical approaches for developing improved crops and management prac-
tices as integrated and coordinated products since most of this space remains unobserved. The exhaustive
empirical exploration of this space is not feasible. This led to the proposition that development of superior
cultivars is limited by the ability to simultaneously identify favourable combinations of genomic regions
and sustainable management systems that optimise resource capture in cropping systems operating in a tar-
get population of environment (TPE), given the resources available to plant breeders and agronomists to
search among possible G M combinations ( Cooper and Hammer, 1996 ; Hammer and Jordan, 2007 ). In
a context of rapid technological innovation in agronomy (Chapters 2 and 3), environmental change ( Karl
and Trenberth, 2003 ; Chapter 20) and increasing costs per unit yield gain ( Duvick and Cassman, 1999 ), it is
opportune to contemplate the following questions:
■ Can we explore the G E M space more effectively?
■ Can we leverage advances in knowledge of G E M interactions, and associated physiological con-
cepts, to tackle this complexity in an integrated approach to develop improved crops?
It can be anticipated that positive answers to these two questions would lead to crop improvement methods
that enable breeders and agronomists to project trajectories in the G E M space into the future and gain
insights into the consequences of manipulating genomes to create improved crops for targeted management
and environments. Central to these methods are the quantifi cation of gene-to-phenotype (GP) relationships
for key traits in the reference population of a breeding program and the capacity of the framework to iden-
tify genetic hypotheses that could be tested and utilised in the breeding program.
Signifi cant efforts have been made to tackle the GP problem by seeking approaches that link information
at the level of gene or genomic region to the expressed phenotype in a manner that is useful for selection
0
50
100
150
200
250
300
0
4
8
12
16
20
Grain yield (bu/ac)
Grain yield (Mg/ha)
1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
Year of release
Full irrigation
Drought stress flowering
Drought stress-Grain fill
Target population of environments
FIGURE 1
Maize yield improvement for a set of Pioneer hybrids released between 1920 and 2007 grown in the target population of
environments ( y 1.43 x 78.95; r 2 0.96), full irrigation ( y 1.51 x 129.4; r 2 0.88) and drought stress imposed at
fl owering ( y 1.39 x 28.6; r 2 0.90), or grain fi lling ( y 0.99 x 86; r 2 0.90). Linear regressions estimate using 1930 as
base year. Conversion factor between bu/a and Mg/ha is 0.06271.
237
( Cooper et al., 2002, 2005 ; Hammer et al., 2006 ; Tardieu, 2003 ). An emergent synthesis of the promising
approaches to the GP problem involves advancing mathematical models of crop growth and development
to link genetic variation in adaptive traits to physiological determinants, developing advanced statistical
methods that help relate genomic regions to parameters in the model control equations ( van Eeuwijk et al.,
2005 ) and modelling of the G E M systems as an extension of Kauffman’s NK model ( Box 1 ). The inte-
gration of these tools and their application in breeding has proven to be non-trivial. There is still debate
about the level of details needed for crop growth models to be able to integrate processes across levels of
organisation while predicting emergent functional consequences for the organism that arise from the inter-
play among gene networks, cell metabolism, plant organs, individuals in the crop and the environment
(Hammer et al., 2006 ).
The aim of this chapter is to introduce fundamental concepts of modelling natural systems using a G E M
framework and discuss prospects for an integrated approach for improving crop performance that tackles
the G E M interactions holistically. First, we outline general principles of modelling biophysical systems,
including a description of fundamental components of crop models. Second, we describe G E M sys-
tems and introduce GP models, the E(NK) framework and concepts of adaptation landscapes as applied to
plant breeding. Finally, we demonstrate and discuss the application of the framework by studying genetic
improvement of maize in the US Corn Belt.
2. MODELLING BIOPHYSICAL SYSTEMS
Crop models are implementations of theoretical frameworks in the form of a series of quantitative expres-
sions. As such, crop models formalise and integrate concepts from disciplines such as physiology, microme-
teorology, soil science and biophysics into an interrelated system of mathematical equations that describes
the dynamic growth and development of a crop ( de Wit, 1982 ; Thornley and Johnson, 2000 ). Crop models
represent a simplifi ed view of all or part of the natural system. The motivation for seeking a simplifi ed quan-
titative representation of the target system is to help scientists approach complex problems by focusing on
the important components and achieve their research objectives. The structure and complexity of a crop
model (e.g. time step for integration) thus depends on the research or technology objective. In this con-
text, crop modelling should be viewed as an iterative process in which model predictions become testable
hypotheses, and the results of testing these hypotheses generate feedback to the model-building process
The E ( NK ) model, and an informal extension to accommo-
date M, provides a framework to consider adaptation and
fi tness landscape. In this model N represent the number
of genes involved in determining the performance of the
genotype, K the average level of epistasis (interactions
between a gene and any of the other N 1 genes for a
given E ) and E the number of environment types in the
TPE ( Cooper and Podlich, 2002 ). The parenthesis notation
indicates that the number of genes and the level of epis-
tasis can change with E, and by extension with M. The
simplest form of the model assumes one environment
and management to generate a fi xed structure or poten-
tial surface, on which peaks are positions sought through
breeding. The two-allele diploid NK N:0 family of mod-
els, which corresponds to the additive fi nite locus genetic
model used in quantitative genetics, has a landscape
characterised by a single peak and a smooth surface, that
is, the trait performance of genetically similar individu-
als are highly correlated. Landscapes become more rug-
ged as K (level of epistasis) increases. In the limit where
K N 1 ( N:N 1 family of models), the landscape is
fully random ( Kauffman, 1993 ). For a given family of NK
models, changes in environment types and their frequen-
cies induce deformations to the adaptation landscapes;
the magnitude of the deformation depends on the under-
lying trait physiology ( Cooper and Podlich, 2002 ).
BOX 1 The E(NK) Model
2. Modelling Biophysical Systems
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
238
to improve the representation of the biological and physical processes and the model structure whenever
necessary. Simulation, which involves exercising the model in order to study system dynamics and prop-
erties, is a critical activity in this iterative model-building approach, as it provides a method to study the
natural system through the properties captured in the quantitative model. With an acceptable model, such
research can help understand emergent behaviour of the system and conceive new concepts that translate
into new knowledge, sometimes expressed in the form of new equations and algorithms. The result of the
systems modelling and simulation process is the assimilation of knowledge into an integrated theoretical
framework from which quantitative predictions and testable hypotheses are proposed for experimental
investigation ( Hammer and Jordan, 2007 ; Thornley and Johnson, 2000 ).
The crop models in use today integrate physiological knowledge developed through more than 30 years
of empirical research ( Sinclair and Seligman, 1996 ). Since the fi rst developments by de Wit in the 1960s
(van Ittersum et al., 2003 ), many crop models have been built with different scope and objectives in mind.
A recent symposium on Farming Systems Design listed more than 70 models ( http://www.iemss.org/
farmsys07/index.php ). The review of all these models and their component processes is beyond the scope of
this chapter. A description of the most common modelling platforms used in agricultural sciences and their
‘pedigree’ can be found elsewhere ( Jones et al., 2003 ; Keating et al., 2003 ; van Ittersum et al., 2003 ; Stöckle
et al., 2003 ). Reference publications provide detailed treatments and models for simulating energy balance and
transpiration ( Jones, 1992 ; Nobel, 2005 ), photosynthesis ( Nobel, 2005 ; Boote and Loomis, 1991 ), different
aspects of soil water and nutrient balance ( Hanks and Ritchie, 1991 ; Ritchie, 1998 ; Loomis and Connor, 1992 )
and soil carbon dynamics ( Parton et al., 1988, 1994 ). Chapter 20 (Section 4) outlines modelling approaches
with emphasis on grain yield and climate change. With a narrower, more specifi c focus, other chapters dis-
cuss modelling approaches for capture and effi ciency in the use of radiation (Chapter 7) and aspects of grain
quality (Chapter 16). Here we outline common modelling approaches and fundamental components of crop
models with emphasis on genetic, environmental, management and G EM drivers of grain yield.
Crop models of interest in crop physiology, and in particular those suitable to modelling G E M inter-
actions, are continuous, dynamic (include a time dimension) and foremost explanatory ( Thornley and
Johnson, 2000 ; Hammer et al., 2006 ). This type of model can be viewed as a bridge across levels of biologi-
cal organisation enabling the researcher to understand the behaviour of a system based on the knowledge
gained by experimentation on its key component systems ( de Wit, 1982 ). Experience has indicated that
stable and credible models usually do not include components that simulate physiological determinants
occurring at more than two levels of organisation away form the target level ( Hammer et al., 2004 ; Sinclair
and Seligman, 1996 ). Explanatory models thus focus on modelling processes that are formalised as rate
variables ( Figure 2 ; de Wit, 1982 ; Loomis et al., 1979 ). The separation of states of the system from underpin-
ning determinant processes enables the identifi cation of useful links among the environment, physiological
processes and genetic determinants, and to formalise these links as metaprocesses that provide the backbone
for GP modelling ( Figure 2b ; Tardieu, 2003 ; Hammer et al., 2006 ).
2.1. Anatomy of a crop model
Figure 3 highlights interactions between crop processes, and between crop processes and the environment, as
captured in a generic simulation model. Algorithms associated with key aspects of plant growth and devel-
opment are critical features of crop models. Plant development sets out the master control of the timing of
events in the plant life cycle (i.e. transition between vegetative and reproductive growth; duration of repro-
ductive growth). Plant growth is driven by organ development (e.g. canopy, roots), and the ability of the crop
to capture resources (light, water and nitrogen) and convert them into vegetative and reproductive biomass.
2.1.1. Development
The prediction of the duration of the crop life cycle, and the timing of milestones that affect resource capture
and partitioning, is the central component of any crop model; Chapter 12 summarises the environmental
2. Modelling Biophysical Systems 239
State
variable
Constant
State
variable
Rate Rate
Rate Rate
(a)
(b)
FIGURE 2
(a) Representation of a system model using a state-variable approach and drawn according to the convention of Forrester (1961) .
(b) Integration of the NK model to predict systems state based on any genetic architecture via its effects on process rates.
Grain Development Potential leaf
area dev Biomass Partitioning Nitrogen Water
RootsVegetativeReproductive
Temperature Radiation WaterNitrogen
Photoperiod
FIGURE 3
Schematic of major components of a crop model, their interactions among components and with the environment.
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
240
and genetic controls of crop development. There are many models of crop development through the various
phases of the crop life cycle ( Hammer et al., 1989 ; McMaster and Wilhelm, 1997 ; Ritchie and NeSmith,
1991 ; Grimm et al., 1994 ; Erskine et al, 1990 ; Sinclair, 1996 ). Because the genetic architecture of plant devel-
opment is only incipient ( Simpson et al., 1999 ; Koornneef et al., 1998 ; Corbesier et al., 2007 ; Tamaki et al.,
2007 ), models of crop development remain empirical descriptions of the relationship between development
rates and temperature and photoperiod. The metaphor of physiological day is an appealing and intuitive
approach to model crop development. The concept proposes that under optimal temperature and photo-
period, the development rate is at its maximum and that the rate decreases as these conditions deviate from
the optimum ( Hammer et al., 1989 ). Then a development milestone (e.g. transition of a meristem from
vegetative to reproductive) is reached after n physiological days, which is the inverse of the maximum devel-
opment rate. The algorithm that implements this concept is represented by the following set of equations
(Grimm et al., 1994 ; Soltani et al., 2006 ):
Rt FN FT() ( ) ( )=× (1)
where R ( t) is the development rate (derivative of development with respect to time) on day t;F ( N) is the
night length (or photoperiod) function; and F ( T) is the temperature function. F ( N) and F ( T) are computed
each day and assume values between zero and one. A value of one represents the greatest development rate
and occurs when one ‘physiological day ’ is achieved in one calendar day. The generalised representation of
these multiple linear response functions is illustrated for F ( T ) as:
FT T T
FT TT
TT TTT
FT
b
b
opt b
bopt
()
()
()
=<
=−
−<<
0
11
if
if
==<<
=−
−<<
12
2
22
if
if
1
TTT
FT TT
TT TTT
F
opt opt
opt
uopt
opt u
()
(TTTT
u
)=>0 if (2)
where Tb is the base temperature below which no development occurs; T opt1 and T opt2 are the lower and
upper bounds of the optimal temperature range for development; and Tu is the upper temperature limit for
development. Similar equations could be used to model effects of abiotic stresses on development ( Boote
et al., 1998 ).
2.1.2. Capture of resources and crop growth
Crop growth depends on the ability of the crop to capture resources and convert them to biomass.
Assuming no nutrients or pest limitations, radiation and water are the key drivers of growth, and crop bio-
mass increments can be calculated by identifying whether the crop is primarily limited by radiation or water
(Monteith, 1988 ; Chapman et al., 1993 ). Elsewhere, the book presents detailed accounts of capture and effi -
ciency in the use of water (Chapter 6), radiation (Chapter 7) and nitrogen (Chapter 8). Here we deal briefl y
with radiation and water, from a modelling perspective.
2.1.2.1. Radiation-limited growth
In light-limited situations, above-ground crop growth rate depends on the radiation intercepted and radia-
tion use effi ciency (RUE). RUE has been studied widely and considered relatively stable for many given spe-
cies ( Sinclair and Muchow, 1999 ). However, recent studies have identifi ed increases in RUE in modern elite
maize hybrids ( Lindquist et al., 2005 ). Although the cause of this increase remains unknown, other studies
2. Modelling Biophysical Systems 241
in wheat ( Miralles and Slafer, 1997 ) have linked differences in RUE with root –shoot partitioning for lines
varying in height. RUE can be derived from the photosynthetic response to light of leaf elements in the
canopy and is dependent on the leaf nitrogen status of those leaf elements, via effects on maximum pho-
tosynthetic rate ( Sinclair and Horie, 1989 ), and the amount and nature of the incident radiation ( Hammer
and Wright, 1994 ). Hence, RUE is a canopy-level measure of photosynthetic performance that sets limits on
productivity under potential growth conditions.
The extent of radiation intercepted depends on the canopy leaf area and architecture. Light interception is
commonly modelled via the Beer –Lambert Law of light extinction in a canopy ( Monsi and Saeki, 2005 ),
which quantifi es the exponential decay of light with increasing leaf area. The extinction coeffi cient ( k) is
dependent on leaf angle (LA) in the canopy. Lower k is associated with more erect leaves ( Monsi and Saeki,
2005 ), which can increase crop growth rate and RUE in canopies with high leaf area index by distributing
light more effectively over the layers of leaf area within the canopy ( Duncan et al., 1967 ). Hence, the devel-
opment of the canopy leaf area is critical to the dynamics of radiation-limited crop growth through the
crop cycle.
2.1.2.2. Water-limited growth
The demand for water in transpiration can be determined from the ratio of crop growth and transpiration
effi ciency (TE), with the latter adjusted for the effect of daytime vapour pressure defi cit ( Tanner and Sinclair,
1983; Sinclair et al., 1984 ). While this biophysical approach is robust for estimating transpiration demand,
recent studies ( Kemanian et al., 2005 ) have indicated it needs some adjustments under low-vapour-pressure-
defi cit conditions (Section 6.4 in Chapter 7).
Water-limited situations occur when the potential supply of water from root uptake cannot meet transpira-
tion demand. In that situation, crop growth can be calculated as the product of the transpiration supply and
TE ( Monteith, 1988 ; Chapman et al., 1993 ). The supply of water from the soil can be modelled via predict-
ing the depth of the root system and the amount of water that can be extracted from each occupied layer.
The extraction potential follows an exponential decay equation ( Passioura, 1983 ) that depends on the mois-
ture content of the layer and a coeffi cient ( kl) that quantifi es the relevant soil –root system attributes that
infl uence water extraction patterns. This approach, fi rst outlined by Monteith (1986) , has been applied suc-
cessfully in a number of species ( Meinke et al., 1993 ; Robertson et al., 1993 ; Thomas et al., 1995 ; Dardanelli
et al., 1997, 2004 ).
In water-limited situations, given any specifi c soil condition, crop water uptake depends on the nature of the
plant root system and its spatial arrangement. The extraction front velocity of sorghum and maize roots is
about 3 cm day
1 up to fl owering ( Robertson et al., 1993 ; Dardanelli et al., 1997 ). In both crops, a rooting
depth of around 2 m has been observed by early grain fi lling. The lateral spread of root systems is usually
not incorporated in crop models, but it can also infl uence their occupancy of the soil and uptake capacity.
Studies on root architecture in wheat ( Manschadi et al., 2006 ) have noted a relationship among encompass-
ing seminal root angle (RA), root system architecture and consequent water extraction from the soil. The
variety with the narrower RA occupied a smaller soil volume but was able to extract more water, especially
at depth. In maize, Campos et al. (2004) observed differences in water extraction between old and modern
maize hybrids. During a period of water limitation, the old hybrid extracted more water from shallow soil
depth, whereas the new hybrid appeared to be more effective at depth. A simulation study that included
a two-dimensional root development model showed that such differences in rooting behaviour provide a
plausible explanation for genetic improvement of drought tolerance as a component of the historical maize
yield trends in the US Corn Belt ( Hammer et al., 2008 ; Figure 1 ).
2.1.3. Canopy development
The potential for both light capture and water use are dependent on the canopy leaf area and the nature of its
display. In cereal crops, potential leaf appearance and expansion are controlled by temperature and modelled
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
242
as functions of thermal time that defi ne the temperature-driven rates of leaf initiation, appearance and
expansion rate ( Tardieu et al., 1999 ; Hammer et al., 1993 ; Carberry et al., 1993 ; Birch et al., 1998b ; Chenu
et al., 2008 ; Ritchie and NeSmith, 1991 ). Potential rates of area growth are then reduced by water status,
nitrogen or carbohydrate availability if any of these factors become limiting.
Approaches to predicting canopy leaf area growth have been developed at whole-plant and individual leaf
levels. At the whole-plant level, functions describing the progression of potential leaf area with thermal time
have been used to estimate potential leaf area growth ( Amir and Sinclair, 1991 ; Hammer and Muchow, 1994 ;
Sadras and Hall, 1988 ). At the individual leaf level, functions quantifying the potential size of individual
leaves have been used in conjunction with estimates of leaf appearance rate ( Birch et al., 1998a ; Dwyer and
Stewart, 1986 ; Jones and Kiniry, 1986 ). A number of studies (e.g. Birch et al., 1998b ; Clerget et al., 2008 )
have shown that leaf initiation and appearance rates are stable when expressed in thermal time units.
Perhaps the least understood yet complex determinant of canopy development is the process of canopy
senescence. Senescence is an emergent behaviour of the canopy that results from the dynamic interplay
among resource capture, reproductive growth, the very own structure of the canopy and internal and external
signals. Approaches to predicting canopy senescence have been developed for whole plants and canopies. In
the absence of water and nitrogen stress, senescence is often modelled as a function of thermal time ( Jones
and Kiniry, 1986 ; Muchow and Carberry, 1989 ; Sadras and Hall, 1988 ), potential plant leaf area ( Birch
et al., 1998a ) and the rate of green leaf area increase ( Villalobos et al., 1996 ). Models that simulate water
and nitrogen balances simulate leaf area senescence as a proportion of green leaf area and the severity of the
abiotic stress ( Jones and Kiniry, 1986 ) or as the result of the balance between nitrogen supply and demand.
The latter suite of models enables nitrogen remobilisation and sink strength to drive leaf senescence
(Sinclair, 1986 ; Villalobos et al., 1996 ; Boote et al., 1998 ; Borrell et al., 2001).
2.1.4. Reproductive growth
There are a number of approaches to simulating the growth of reproductive organs. The simplest models do
not distinguish among yield components, fertile plants and tillers, fruit and seed number and weight; all
components are lumped together in a coeffi cient (harvest index) that describes the fraction of total growth
that corresponds to reproductive structures ( Figure 4a ; Sinclair, 1986 ; Muchow et al., 1990 ; Hammer et al.,
1995). This approach is robust for the simulation of variation in yield across a range of environments but
lacks suffi cient detail to describe genotypic effects such as differences in maturity in sorghum ( Hammer and
Broad, 2003 ), as well as other genotypic effects underpinning yield improvement and tolerance to stresses.
0 400 800
0.0
0.4
0.8
Thermal time postflowering
Harvest index
02468 12
0
400
800
Plant growth rate (g pl1day1)
Kernels per plant
0
400
800
Kernels per plant
ME
CA
SP
246810
Plant growth rate (g pl1day1)(a) (b) (c)
FIGURE 4
Models to simulate reproductive growth: (a) harvest index approach, and approach based on kernel number as a function of plant
growth rate around fl owering using (b) bilinear or (c) negative exponential or hyperbolic function. ME: maximum ear size representing
kernel number at high plant growth rates; SP: initial slope and curvature integrate processes of silk exertion, synchronism in
pollination, within-ear carbon allocation and kernel abortion; CA: carbon allocation to the ear and barrenness threshold.
3. Modelling Genotype–Environment–Management Systems 243
More detailed models simulate barrenness, grain set and growth as separate processes. Grain growth is often
simulated using a linear approximation of the commonly observed sigmoid growth pattern. The maxi-
mum grain growth rate is assumed characteristic of the genotype and independent of the kernel number
(e.g. Duncan et al., 1978; Jones et al., 2003 ). Recent fi ndings in maize questioned this assumption and sug-
gested the need to model potential kernel growth rate as a function of plant growth per kernel around fl ow-
ering time ( Gambín et al., 2006 ). Once the potential is established, realised grain growth rate is determined
by daily plant growth and the extent of carbon and nitrogen remobilisation (e.g. Jones et al., 2003 ; Keating
et al., 2003 ; Boote et al., 1998 ).
Grain set is often modelled as a function of cumulative intercepted radiation ( Ritchie and Alagarswamy,
2003 ; Andrade et al., 1993 ), crop growth rate (e.g. Andrade et al., 1999 ; Jones et al., 2003 ; Jiang and Egli,
1995; Vega et al, 2001 ; Tollenaar et al., 1992 ) or ear (panicle) growth rate ( van Oosterom and Hammer,
2008 ) during a critical developmental period around fl owering. The onset and duration of the critical win-
dow for grain set determination varies among crops (e.g. Otegui and Bonhomme, 1998 ; Fischer, 1985; Jiang
and Egli, 1995 ). Critical windows for grain set are discussed in Chapters 12 (Section 5) and 15 (Section
3.2.2) from a breeding perspective and in Chapter 3 (Figure 4) from the viewpoint of integrating crops in
cropping systems.
Figure 4b and 4c illustrate approaches to modelling kernel set in maize. Figure 4b is the function imple-
mented in CERES-Maize ( Jones and Kiniry, 1986 ) and could be considered the simplest approximation of
the non-linear model in Figure 4c ( Andrade et al., 1999 ; Tollenaar et al., 1992 ). Regardless of the mathemati-
cal formulation of the non-linear model, this form implicitly incorporates concepts of sink limitation due to
maximum ear size (ME) and prolifi cacy (asymptote, ME; Figure 4c ), silk exertion dynamics, synchronism in
pollination, within-ear carbon allocation (CA) and kernel abortion (initial slope and curvature, SP; Figure 4c )
and CA to the ear and barrenness (threshold, CA; Figure 4c ). Ritchie and Alagarswamy (2003) extended the
non-linear model shown in Figure 4c to simulate barrenness by modelling the fraction of ear-bearing plants
as a function of cumulative intercepted radiation. An immediate advance on the framework, as proposed by
Vega et al. (2001) , is to explicitly simulate carbon partitioning to the ear and how this mass is converted into
viable kernels. More mechanistic approaches to simulate fruit set, often applied to simulate pod number in
legume crops, consider these fruits as populations of competing and interacting sinks for carbon and nitro-
gen. In this framework, fruit number at any time during the reproductive stage of the crop results from the
balance between the addition of fruits as determined by crop development and the removal of fruits resulting
from abortion due to insuffi cient resources ( Wardlaw, 1990 ; Boote et al., 1998 ).
3. MODELLING GENOTYPE –ENVIRONMENT–MANAGEMENT
SYSTEMS
A fundamental step in modelling is to defi ne the purpose of the model or framework to be developed, the
type of problems that the model should help investigate and solve and a concept map that relates the tar-
get natural system and the corresponding abstractions that become components of the framework ( Peart
and Curry, 1998 ; Thornley and Johnson, 2000 ). These principles were followed to design applications of
crop growth models, and associated physiological concepts, to enhance plant breeding ( Cooper et al., 2002 ;
Chapman et al., 2003 ). More often, these applications have focused on valuing traits and attempts to design
universal ideotypes (e.g. Boote and Tollenaar, 1994 ; Boote et al., 2001 ; Aggarwal et al., 1997 ; Yin et al., 2003 ;
Sinclair and Muchow, 2001 ), and to understand genotype by environment interactions ( Chapman et al.,
2000, 2002a, b ; Löffl er et al., 2005 ). The development of these latter methods was dominated by typological
thinking (e.g. Donald , 1968 ; Long et al., 2006 ; Century et al., 2008 ; Lee and Tollenaar, 2007 ) rather than
population genetics concepts (e.g. frequency of favourable alleles, traits and phenotypes changing in a breed-
ing population) as proposed in evolutionary ( Nowak, 2006 ) and breeding studies ( Cooper and Podlich,
2002 ). Approaches that sought to fi nd universal ideotypes have imposed limitations on the successful
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
244
integration of physiological knowledge into breeding programs by largely ignoring breeding objectives,
germplasm context dependencies and genetic sources of unexplained phenotypic variation, and by often
placing undue reliance on the ability of models to connect genetics and physiology to credibly predict sub-
tle interactions and feedbacks associated with genetic variation for traits within the reference germplasm of a
breeding program ( Hammer et al., 2002 ).
3.1. Breeding objectives and purpose of framework
To defi ne a relevant context for modelling the G E M system, it is convenient to distinguish between
breeding objectives where:
(i) a genetic answer to the problem is known; for example, a target genotype has been identifi ed, and
the objective is to close the genetic gap between the current germplasm and the defi ned target to
test the hypothesis, for example, to increase resistance to a biotic factor by introgressing alleles from
exotic germplasm;
(ii) plausible genetic answers to the problem are currently unknown; for example, to increase grain yield
or drought tolerance beyond those of the elite commercial products.
It is clear that the opportunity for modelling and physiology to contribute to plant breeding is closely tied to
the second class of breeding objective, and that these should be components of a suite of methods to help
breeders address questions about trade-offs between traits, the structure of adaptation landscapes, plausible
selection trajectories towards interesting trait phenotypes and genotypes, the likelihood of fi nding improved
genotypes in the adjacent possible genetic space and outcomes of competing selection and breeding strate-
gies ( Hammer et al., 2006 ).
3.2. Concept map
Figure 5 shows a simplifi ed yet extended concept map to build a G E M system ( Cooper and Hammer,
1996). Cooper et al. (2002) formalised the concept that was later demonstrated in a theoretical study for
sorghum by Chapman et al. (2003) . The testing of the hypotheses proposed in the theoretical study is cur-
rently underway ( Hammer et al., 2005 ). In this dynamic and iterative framework, empirical data are contin-
ually analysed and used to encode knowledge for model building and enhancement ( Podlich et al., 2004 ).
Model-based predictions and concepts become genetic, physiological and agronomic hypotheses to test
through experimentation in the real world of the target G E M system. A central concept to the quantita-
tive framework is that of adaptation landscapes to represent the complexity of the G E M system to be
explored, equivalent to the concept of fi tness landscapes discussed in evolutionary studies ( Wright, 1932 ;
Kauffman, 1993 ; Fontana et al., 1989 ). Applying this framework, plant breeding can be viewed as a set of
search strategies applied to that landscape or search space and constrained by the germplasm available to
the breeder, the prescribed agronomic management and the environments sampled in the fi eld trials. In
this framework, a breeding population can be thought of as a cluster of individuals located at neighbouring
positions that fl ow through regions of the adaptation landscape in response to selection ( Kauffman, 1993 ;
Cooper et al., 2002 ).
3.3. Defi nition and consideration of the search space and
adaptation landscapes
The search space could be defi ned by the outcome of all possible combinations of genomic regions, environ-
ments and management practices. A narrow-sense defi nition of this space, perhaps a practical one, assumes
limits imposed by the germplasm available to the breeder, the target agronomic management and the com-
position of the TPE. A broad-sense defi nition can extend the search space to include novel cropping systems
(Section 5 in Chapter 3), alternative environment scenarios (Chapter 20; Ainsworth et al., 2008 ; Karl and
3. Modelling Genotype–Environment–Management Systems 245
Trenberth, 2003 ) and novel sources of germplasm and engineered genetic elements (e.g. Century et al., 2008 ).
The G E M search space has an associated adaptation landscape. The E(NK) model ( Box 1 ), and an infor-
mal extension to accommodate M, provides a framework to consider this landscape.
A number of approaches were proposed to parameterise the E(NK) model and assign a fi tness value
to a given genotype:
1. constructing Boolean networks and assigning fi tness contributions to each gene from a statistical
distribution ( Kauffman et al., 2004 ; Kauffman, 1993);
2. defi ning inheritance models using empirical evidence from quantitative genetics parameters ( Wang
et al., 2003 ; Cooper et al., 2005 );
3. specifying gene networks to represent attributes of known genetic networks and biochemical path-
ways (e.g. Ravasz et al., 2002 ; Bhalla and Iyengar, 1999 ; Peccoud et al., 2004 );
4. directly parameterising, using results from mapping studies ( Cooper et al., 2005 );
5. considering the E ( NK ) model as the consequence of N genes that control variation for physiologi-
cal traits, the number of E identifi ed for the TPE and the physiological relations encoded in a crop
model that determine the patterns of crop growth and development ( Cooper et al., 2002 ; Chapman
et al., 2003 ; Hammer et al., 2005 ).
Observation
encoding
Natural
system
Formal
system
Decoding
prediction
Real world Mathematical
world
E
Temperature
Radiation
Water…
N
Gene networks
M
Population
Water…
PM(E(N:K ))
Search space
Environmental characterisation
Trait modeling
Phenotype prediction
Germplasm
Gene mapping
Germplasm characterisation
Breeding
program
Quantitative
Genetics modeling
Expression
Proteins
Metabolites
Traits
K
FIGURE 5
Concept map, main system components and model-building framework for modelling genotype – environment – management
systems in the context of plant breeding. G: genotype; M: management; N: number of genes involved; E: environment; K: average
level of epistatic interactions; P: phenotype.
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
246
Approach 5 can be considered as partitioning the predictable component of the GP relationship continuum
into gene-to-trait (physiological process) and trait-to-phenotype relationships; crop models predict crop per-
formance phenotypes associated with trait performance (e.g. yield), based on the interplay among traits,
environment cues and resources and management ( Figure 5 ).
3.4. Crop modelling as a component in gene-to-phenotype mapping
The links between genes and phenotypes can be approached using top-down or bottom-up methods. Top-
down methods use physiological dissection and integration via crop modelling to work from whole-plant
phenotypes to the molecular genomic level ( Hammer et al., 2004 ). This is also the classical forward genet-
ics approach used to study the genetic architecture of traits; observe phenotypic variation and attempt to
determine an appropriate genetic model to explain the phenotypic variation. When applying crop models
to enhance genetic discovery, the central paradigm of this method is the focus on understanding and mod-
elling processes at or around the level of organisation at which phenotypic predictions are being targeted
and use a level of abstraction necessary to model processes and functional controls following the philoso-
phy pioneered by de Wit and Penning de Vries (1983) of ‘modelling plant hormone action without mod-
elling the hormones ’. The bottom-up approach integrates knowledge at the molecular level, across levels
of organisation, to explain trait phenotypic variation ( Minorsky, 2003 ; Yuan et al., 2008 ). This method is
aligned with the reverse genetics approach to gene discovery (Section 2 in Chapter 14). It has been argued
that the application of such bottom-up approaches to understand the genetic architecture of complex traits
would face several challenges common to the study of other complex systems and in particular the chal-
lenge of integration of genetic information to capture emergent behaviour at the whole-plant level, with
limited scientifi c understanding ( Hammer et al., 2004 ). Simulation and propagation of errors across spatial
and temporal scales that could vary by orders of magnitude would complicate making accurate predictions
(Thornley and Johnson, 2000 ).
3.4.1. From the top-down
Top-down approaches have been tried with variable success. Yin et al. (2003) described the use of a crop
model for barley based on the SUCROS crop model ( Goudriaan and Van Laar, 1994 ) with quantitative
trait loci (QTL) mapping to predict yields from QTL allele information. The model used as inputs the spe-
cifi c leaf area, the leaf N concentration, the fraction of biomass partitioned to leaves and to spikes and
the separation of the life cycle into vegetative and reproductive stages. Using 94 recombinant inbred lines,
these parameters were mapped, allele values for each QTL and trait calculated and yield predictions made
using the ecophysiological model. Predictions for yield were clustered in two meaningful groups, based
on two- and six-row types of virtually constant yield within each group. A similar study that used a crop
model to link information for known loci and model parameters led to the Genegro model ( White and
Hoogenboom, 1996 ). This model incorporated effects of seven genes affecting phenology, growth habit and
seed size of common bean ( Phaseolus vulgaris L.). The parameters in the Genegro model were derived from
the states of alleles at each of the seven loci, using a set of linear functions. These linear functions were esti-
mated by regressing allele values (alleles were coded as either 1 or 0) against model parameters calibrated
(‘reverse engineered ’) using a set of fi eld trials. Genegro accurately predicted dry bean phenological develop-
ment but poorly explained yield variations between sites ( Hoogenboom et al., 1997 ). These two examples
demonstrate the limitations of using reverse engineering approaches to GP modelling and the importance
of understanding the genetic architecture that controls the trait of interest. The ability of Genegro to predict
bean phenology is due to a fundamental understanding of the genetic controls and genotypic variability
on the response of beans to temperature and photoperiod ( Coyne, 1970 ; Kornegay et al., 1993 ; White and
Laing, 1989 ).
GP models developed for individual physiological components showed promising results for both plant
development ( Messina et al., 2006 ; Yin et al., 2005 ) and leaf growth ( Reymond et al., 2003 ). Yin et al.
(2005) combined ecophysiological modelling for phenology (of the form presented in Eq. 1) and QTL
3. Modelling Genotype–Environment–Management Systems 247
composite mapping to predict barley response to temperature and photoperiod. Parameters for the eco-
physiological model were fi rst estimated for genotypes, and QTL mapping was conducted on the popula-
tion variation for these parameters. Using the allele values for each QTL and consequent model parameters,
predictions were made for a set of recombinant inbred line genotypes in eight environments. The QTL-
based model accounted for 72% of the observed variation among the recombinant inbred lines. Messina
et al. (2006) used a photothermal model (Eq. 1) to determine allele values at six QTL loci for soybean
model parameters. The model accounted for 75% of the time-to-maturity variance when tested in multi-
environment trials (MET). Reymond et al. (2003) mapped QTL for the parameters of an ecophysiological
model of leaf elongation rate (LER) for maize ( Ben Haj Salah and Tardieu, 1997 ),
LER T T a b VPD c=− + +()( )
0ψ(3)
where T is meristem temperature, VPD vapour pressure defi cit and c soil water potential; b and c are con-
stants coding for the response of LER to VPD and soil water potential after correction for T effects; a and T
0
are the slope and x-intercept of the LER response to meristem temperature. Under optimal soil water and
VPD conditions, LER becomes a function of temperature alone and the model becomes equivalent to Eq. 1.
Upon parameterisation of 11 recombinant inbred lines at marker loci, the model accounted for 74% of the
variability of LER. Further evaluation demonstrated the model useful for describing genetic variation in LER
for a large number of recombinant inbred lines ( Sadok et al., 2007 ).
3.4.2. Genes, traits, phenotypes and adaptation
The LER model is a useful example to illustrate the concept of partitioning the GP continuum into gene-
to-trait and trait-to-phenotype relationships and to connect the biophysical and the NK models. The state
model in Eq. 3 can be reformulated to formally incorporate QTL effects as
dL
dt Tw w w w
ij i ij i ij i ij i
= −∑ ∑ +∑ +∑()( )QTL QTL QTL VPD QTL ψ(4)
where wij are allele values of each QTL
i for the parameter j. Further generalisation suggests specifying Eq. 4
in terms of the NK model as
dL
dt TNKNK NK NK
jj j j
=− + +()( )VPD ψ(5)
where the NK model is allowed to vary among parameters j. That is, the genetic networks associated with
each of the model parameters could have common components; pleiotropic effects are formally incorpo-
rated via shared nodes among networks; epistasis is implemented as described earlier ( Box 1 ). This formu-
lation based on the NK model can be extended to the E ( NK) model where network topology is allowed to
vary in response to environment cues. Error terms could be included in the model to account for compo-
nents of the unexplained variation in the GP relation continuum ( Cooper et al., 2005 ).
The model in Eq. 5 fully describes the gene-to-trait relation. However, Eq. 5 applies only to single leaf and
scaling of some sort from the organ to the whole plant is necessary to map the G E M space into the phe-
notype space (e.g. plant leaf area). Chenu et al. (2008) developed a model that coordinates the growth of
all leaves of a plant and uses the single-leaf LER model to drive growth. The framework was implemented as
a component of APSIM ( Keating et al., 2003 ), which provided the dynamic feedback effects on leaf growth
via transpiration and soil water uptake. Because the LER model is integrated within a crop growth-m odelling
framework, the likely impact of genetic variation for QTL affecting LER on adaptation (e.g. grain yield)
could be assessed as demonstrated in previous studies for sorghum ( Chapman et al., 2003 ) and soybeans
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
248
(Messina et al., 2006 ). In summary, crop models have the potential to map the G E M space into pheno-
type and adaptation landscapes. To enable these connections, however, thorough basic physiological and
genetic studies are necessary to support the model architecture and provide validated evidence for the physi-
ological determinants of genetic variation in adaptive traits.
3.5. Breeding programs as search strategies in genetic space
Plant breeders create new genotypes with improved crop performance and adaptation to a TPE by observing,
understanding, predicting and creating new trajectories in genotype and phenotype space. Three fundamen-
tal processes under the breeders ’ control support the creation of these trajectories: (i) development of geno-
typic novelty through strategic sampling of germplasm, recombination and segregation; (ii) design of testing
systems that adequately sample the TPE for evaluation of cultivars and expose genetic variation for traits of
interest; and (iii) selection as a means to change gene frequencies in the germplasm to improve adaptation
relative to the current set of cultivars. Breeders ’ decisions on these three components defi ne the breeding
strategy, and therefore the regions of the adaptation landscape that the breeding program would explore in
search of peaks of adaptation and crop performance.
Breeding simulation provides a means to predict trajectories in GP space. QU-GENE ( Podlich and Cooper,
1998) is a computer simulation platform to specify genetic models in the context of the E ( NK) frame-
work and G E M systems in order to evaluate alternative breeding strategies. The stochastic components
in QU-GENE implement the simulation of genetic recombination and segregation, within the search for
genotypes with higher fi tness in the adaptation landscape; note the analogy between this component in
QU-GENE and global optimisation algorithms ( Mitchell, 1996 ). Specifi c modules in QU-GENE simulate the
processes involved in the creation, evaluation and selection of genotypes within the breeding program and
implement the simulation of breeding strategies such as mass selection, pedigree and single-seed descent,
double haploid, S1 recurrent selection and half-sib reciprocal recurrent selection.
4. CASE STUDY: MAIZE BREEDING IN THE USA
Despite the complexity of the mechanisms underpinning yield determination, conventional breeding has
effectively increased maize yield in well-watered and water-limited environments of the US Corn Belt ( Figure 1 ;
Duvick and Cassman, 1999 ; Duvick et al., 2004 ; Campos et al., 2006 ). Trajectories from over 50 years of
maize breeding in the US Corn Belt show that many traits have changed markedly, even when there was no
direct selection for these traits. These include decreases in tassel size, protein concentration in kernels, rate
of leaf senescence during grain fi lling, root and stalk lodging, rows of kernels per ear, and anthesis-silking
interval, and increases in LA (more erect leaves), ears per plant, kernel weight and harvest index ( Duvick and
Cassman, 1999 ; Duvick et al., 2004 ; Lee and Tollenaar, 2007 ). The future direction of these trajectories is a
subject of debate ( Lee and Tollenaar, 2007 ; Century et al., 2008 ; Tuberosa et al., 2007 ; Pennisi, 2008 ) and
opens the opportunity to apply the framework described in the previous section to address questions of rel-
evance to breeding. This section illustrates the use of a coupled crop system – breeding model to study past
trajectories in GP space and outline plausible future trajectories in maize breeding.
4.1. Genotype –environment–management system
This study used the GP framework described in Section 3 to build a G E M system representative of past
and present maize production in the US Corn Belt. The breeding objective is to improve yield in the TPE
beyond that of current germplasm. The purpose of the framework is to study past trajectories in maize
breeding and to provide insights on future trait trajectories, given representative environment types and
plausible changes in management. Components of this framework were constructed by modelling adaptive
traits of interest to breeders based on their physiological determinants ( Section 2 ); linking genetic variation
to those determinants in the context of the NK model ( Box 1 ); simulating maize phenotypes for relevant
249
genotypes, managements and environments; classifying production environments ( Section 4.1.3 ); and sim-
ulating trait trajectories in genetic space for breeding programs conditioned to defi ned environments and
management ( Figure 5 ).
4.1.1. Trait modelling
A Pioneer proprietary module of APSIM-Maize was developed to incorporate adaptive traits of interest for
trait variation relevant to Pioneer elite hybrids. The module includes algorithms that implement concepts
that link RA with spatial and dynamics aspects of root exploration and occupancy of soil layers; thus RA
controls time of access and intensity of resource capture ( Hammer et al., 2008 ). LA and RUE are connected
by implementing a series of equations to model canopy photosynthesis ( Duncan et al., 1967 ; Hammer
and Wright, 1994 ; Loomis and Connor, 1992 ). The module includes algorithms to model aspects of maize
reproductive biology relevant to yield, including the connections between kernel set and CA to the ear and
within the ear ( Vega et al., 2001 ; Cárcova and Otegui, 2007 ), silking dynamics and synchronism in pollina-
tion (SP) ( Cárcova et al., 2003 ; Borrás et al., 2007 ) and ME ( Tollenaar et al., 1992 ). The model accounted
for the connection between growth and development ( Borrás et al., 2007 ), the co-regulation of kernel set
and kernel size ( Gambín et al., 2006 ) and their response to timing of drought stress during reproductive
stages. Figure 6 compares simulated and observed yields for Pioneer hybrid P90-1 grown in a rain-free envi-
ronment under six irrigation regimes. These regimes covered full irrigation control (FI) and fi ve treatments
where water was withdrawn for 500 °Cd for overlapping periods separated by 100 –200 °C d (S1 –S5) at the
commencement of the treatment.
4.1.2. Linking genotypes and traits
To demonstrate an application of the framework, genetic variation for fi ve adaptive traits was defi ned using
an additive genetic model based on three genes (equal effects) and two alleles per locus ( NK 3:0). It was
assumed that there were unique sets of genes for each trait and that genes were unlinked. Thus, for the
purpose of demonstration here, the genetic model does not include epistasis and pleiotropic effects at the
level of the genetic architecture of the fi ve traits. For a single trait, this genetic model results in 27 unique
genotypes but only 7 unique expression states, given the additive effects model. For each locus, one allele
was considered to increase expression relative to the alternative allele. For example, at a given gene A, it is
defi ned that allele A increases trait expression ( ) relative to the allele a ( ). Then the expression state for
the genotype is defi ned by the sum across genes of the effects of the alleles. For example, given the addi-
tive model, the genotypes AAbbcc,aaBBcc,aabbCC and AaBbcc all have the same expression state of two
(e.g. two positive alleles each). For this simulation experiment, which was based on fi ve adaptive traits, the
genetic model defi nes 14 10
6 genotypes but only 1.6 10
4 expression states. This fi rst approximation of
the genetic architecture of the component traits is substantiated by multiple QTL mapping studies. It is the
simplest representation suggested by the data that would enable the simulation and representation of the
full adaptation landscape. Other genetic models could be considered and implemented in the framework,
and would have generated different relations among genotypes, expression states and phenotypes.
This simulation experiment included genetic models for fi ve adaptive traits: RA, LA, CA to reproductive
growth, synchronous pollination (SP) and potential ear size (ME). Model parameters for the latter three
traits could be interpreted as determinants of CA, SP and ME in the current models of kernel set outlined in
Figure 4c . Herein, we refer to these traits and interpret the results in the context of the kernel set response to
plant growth rates.
4.1.3. Environmental classifi cation
Maize phenotypes were simulated for a range of plant densities (8 and 12 pl m
2), soil types (high and low
soil water holding capacity; Löffl er et al., 2005 ), 4 soil water contents at sowing and 50 years of weather in
central Iowa, using APSIM-Maize ( Keating et al., 2003 ) and Pioneer proprietary modules. Soil water content
4. Case Study: Maize Breeding in the USA
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
250
at sowing was estimated by simulating long-term soybean –maize rotations and clustering results to form
groups of water content distribution in the soil profi le at sowing. Each combination of plant density, soil
type and soil water content at sowing defi nes a unique environment and could thus be considered as one of
many possible outcomes in a multi-environment trial.
Each of the 800 (2 2 4 50) simulated production environments was classifi ed based on water sup-
ply and demand patterns ( Hammer et al., 2005 ; Chapman et al., 2000 ) for a reference genotype. APSIM-
Maize was parameterised and run for the Pioneer hybrid 3394 as the reference genotype; see Hammer et al.
(2008) for model parameterisation. Daily outputs of the ratio of water supply to demand were averaged
every 100 °C d from emergence. Cluster analysis, using the k-means algorithm, revealed four major environ-
ment types depicted in Figure 7 . The frequency of occurrence was 18% for severe terminal stress (ET1), 20%
for early grain fi ll stress (ET4), 25% for moderate terminal stress (ET2) and 37% for no stress (ET3).
1000
(a)
(b)
(c)
2000
3000
6000
0
250
500
FI S1 S2 S3 S4 S5
Kernel weight (mg) Kernel number (m2) Yield (g m2)
Irrigation management
OBS
SIM
FIGURE 6
Assessing model capacity to predict (a) yield and yield components, (b) kernel number and (c) kernel weight under six regimes of
water supply. FI: full irrigation; S1 – S5, water was withdrawn for 500 ° C d over overlapping periods of 100 – 200 ° C d. Experiment
details are provided in Campos et al. (2006) .
4. Case Study: Maize Breeding in the USA 251
4.1.4. Adaptation landscape
The adaptation landscape was generated with yield as the measure of fi tness. APSIM-Maize was run for each
of the 16 10
4 expression states corresponding to unique combinations of adaptive traits, and each of the
1.6 10
3 environments and management combinations. Model parameters not determined by a genetic
model, thus by any expression state, were set to the values determined for the hybrid 3394. This is a realistic
representation of the execution of the framework in a real breeding program where genetic improvement
is sought relative to a reference germplasm. For the purpose of this example, all conclusions about genetic
improvement are drawn in reference to the hybrid 3394.
4.1.5. Breeding simulation
For each environment type and management, reciprocal recurrent selection with pedigree selection within
two heterotic groups was simulated using QU-GENE ( Podlich and Cooper, 1998 ; Podlich et al., 2004 ).
The QU-GENE software managed the creation, evaluation and selection of genotypes within the breeding
program. Reference breeding populations were created by specifying allele frequencies to 0.5 in two heter-
otic groups; any other starting point could have been considered. The evaluation system was set to a single
breeding program and 10 testing sites. Each testing site sampled the TPE ( Figure 7 ) in proportion to the
frequency of occurrence of each environment type. Trait trajectories in G space conditioned to E and M
emerge from breeding simulations that are similar to the trajectories reported for the sequence of hybrids
in Figure 1 . Selection experiments were conducted under a unique environment and management (e.g. ET1
and 8 pl m
2 ), and for a sample of environments and plant populations.
4.2. Structure of simulated adaptation landscapes
Adaptation landscapes could be characterised by different metrics and graphical representations ( Kauffman,
1993; Cooper and Podlich, 2002 ; Wright, 1932 ; Nowak, 2006 ; Fontana, 2002 ). In this example, the adapta-
tion landscape was represented as a set of conditional cross sections for grain yield in the G and P dimen-
sions (herein referred to as a GP plot). The grain yield distributions are conditional on the expression states
for a defi ned trait. For example, for LA, there are seven expression states and therefore seven yield distribu-
tions. The yield distribution is generated by the yield variation created by all other traits conditional on the
defi ned expression level for the selected trait of interest. The GP dimension views can be constructed for
Relative transpiration
Thermal time from sowing
0
0.2
0.4
0.6
0.8
1
1.2
100 400 700 1000 1300 1600
ET2
ET3
ET4
ET1
FIGURE 7
Drought stress patterns for environment types (ET) that defi ne the Target Population of Environments. Relative transpiration
simulated for a reference hybrid.
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
252
specifi c environments or a combination of environments. Genotype relative frequencies at regular intervals
for yield are shown as a heat map to visualise the distributions ( Figure 8 ). This graphical representation of
landscapes allows the identifi cation of features such as position of global maxima, trends in central ten-
dency and local optima for yield with respect to G and expression states, presence of saddles and plateau
regions. The global maximum is identifi ed as the maximum in the y-axis across all frequency distributions.
In the example presented for drought stress environments, this maximum corresponds to genotype AABBCC
for RA and ddeeff for LA ( Figure 8 ). Local optima correspond to the maximum yield conditioned to G. Both
global and local optima provide information about opportunities and paths to yield improvement in the
adjacent genetic space, given the reference populations of the breeding program.
Trends could be identifi ed in local optima and central tendencies. In environment ET3, trends in yield with
respect to the expression state of LA are evident in both central tendency and local optima ( Figure 8 ). In
contrast, in ET1, the landscape is rather fl at for genotype bins 1 –4 (genotype ddeeff corresponds to bin 1),
but there is a marked non-linear trend in the local optima. This trend reveals a point of instability due to
the presence of a saddle and has implications for breeding. Yield increase is feasible by either increasing or
decreasing LA. The resulting changes in allele frequencies, and LA phenotypes, in a breeding population
selected for yield increase, will depend on the initial frequencies of alleles. At this point in G space, the
behaviour of the breeding system and the potential for genetic improvement become dependent on initial
conditions. The global maximum in ET1 can only be reached by increasing the frequency of alleles. The
alternative trajectory leads to a higher peak in the adaptation landscape but compromises the potential for
continuous genetic gains due to variations in LA.
Deep…………Shallow Erect…………Floppy
Root angle Leaf angle
Low………………High Low…………….High
Yield
AABBCC….…..aabbcc ddeeff….…..DDEEFF
Genotype
Trait
Effect
Drought stress Well watered
FIGURE 8
Breeding trajectories (thick lines) in a gene-to-phenotype adaptation landscape. Black dots represent individuals in the breeding
population; dot size is proportional to the number of individuals. The thin line represents central tendency across genotypic bins.
Landscapes correspond to environment type severe terminal stress (ET1) and no stress (ET3). Breeding simulation conducted for
drought stress environments. Genotype frequency is colour coded in Plate 1.
4. Case Study: Maize Breeding in the USA 253
Changes in environment types can induce deformations to the adaptation landscapes. The magnitude of any
such deformation depends on the underlying trait physiology. Figure 8 illustrates this effect for RA and LA.
Yield increased with increasing frequencies of alleles conditioning the expression states for RA. Greater
water capture associated with deeper root systems had a positive effect on simulated yields under ET1. In
contrast, there were no marked effects on yield in ET3, which is manifested as a smooth and fl at landscape
(Figure 8 ). The comparison of landscapes for LA in ET1 and ET3 reveals a trade-off between light capture
and RUE and water use. Yield increased with the increasing frequency of alleles (erect-leaf-type pheno-
types) under no-stress environments where light capture and its distribution within the canopy limits car-
bon assimilation and yield. The opposite pattern is evident in drought stress conditions where improved
RUE generates higher water use, which intensifi es the severity of stress during reproductive stages. Water
conservation strategies that improve the partitioning of water use between vegetative and reproductive stages
are discussed in Chapter 6 (Section 3).
The landscape structure generated for this small G E M system has complex features as viewed through the
GP plots. The complexity of the landscape is assessed by the analysis of all GP cross sections. The presence of
weak trends in a given cross section indicates that a given trait is not a strong determinant of yield response
in the context of all other traits ( Figure 8 ). But the absence of any trends across all cross sections indicates
a rugged landscape, where peaks in grain yield performance are dependent on the expression states for
multiple traits. The example presented in Figure 8 illustrates this contrast. While the adaptation landscape
view for ET3 is determined to a large extent by the frequency of alleles for erect-leaf-type phenotypes,
landscapes for ET1 are rather fl at, with trends for both RA and LA and the presence of saddles. Adaptation
landscapes under drought stress are more complex than in the absence of stress, and the GP plots indicate
multiple paths are plausible for crops to cope with stress. The characterisation and understanding of adap-
tation landscapes and how these respond to E help to study, interpret and anticipate response to selection.
The approach allows assessment of the relevance of traits in the context of all other traits under consider-
ation in a specifi c environment, and aids in strategically selecting germplasm for breeding objectives that
target specifi c sections of GP space.
4.3. Exploring trajectories in GP space: what traits can
improve adaptation?
Breeding simulation is a step beyond the study of the structure of adaptation landscapes and has been
used to assess breeding strategies ( Podlich et al., 1999 ; Chapman et al., 2003 ; Wang et al., 2003 ; Cooper
et al., 2005 ) and the integration of molecular technologies into breeding methods ( Podlich et al., 2004 ;
Cooper et al., 2005 ; Hammer et al., 2005 ). In the example presented here, breeding simulation was used to
study plausible trait phenotype trajectories in GP space under contrasting management and drought stress
environments ( Figures 8 and 9 ). Each trajectory represents the average of an ensemble of 20 QU-GENE runs
(i.e. 20 replications of the breeding program starting from the same reference breeding population). The
common pattern across environment types and management in the allele frequency dynamics is the unique-
ness in the relevance of traits and their interdependence. The relevance of a given trait could be judged by
the onset and the rate of change in allele frequencies conditioning the expression states of the trait, and the
effects of traits on yield at other loci. When the MET was simulated at commercial plant densities, LA was
the fi rst trait to change allele frequencies towards the alleles, reaching fi xation upon 20 cycles of selection.
The direction of change, however, was opposite in the two environment types. LA decreased (shift towards
erect leaf type) with increasing cycles of selection in ET3 (no stress) and increased (shift towards fl oppy leaf
type) at about the same rate in ET1 (severe terminal stress). Similar patterns were simulated for high-density
stands, but the rate of change was not as pronounced as under commercial density, and a delay in the onset
of change was evident in ET3.
The frequency of the alleles for RA increased in successive cycles of breeding when selecting for yield in
drought environment type ET1. Conservative water use and enhanced water capture in deep soil layers dom-
inated the trajectories, particularly during the fi rst cycles ( Figure 9 ). The value of this yield improvement
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
254
strategy was demonstrated in maize populations selected for increased osmotic adjustment ( Chimenti et al.,
2006 ). Although this physiological mechanism underpinning the enhanced ability to access water stored in
deep soil layers may not be valuable in some germplasm ( Bolaños and Edmeades, 1991 ), the effectiveness
of the strategy to improve the maintenance of leaf area, growth and yield in the simulation experiments
provides the basis for a testable hypothesis. The reduction in RA, resulting in a deep root system, implies a
redistribution of root mass among soil layers. The feasibility of this alternative path towards accessing addi-
tional water in deep soil layers is supported by evidence of genetic variation in root architecture ( Tuberosa
et al., 2002 ; Tuberosa and Salvi, 2006 ), variations in patterns of soil water uptake between modern and
old hybrids ( Campos et al., 2004 ) and root architecture response to selection ( Edmeades et al., 2000 ). It
is apparent from the breeding simulations that this strategy is not universal ( Figure 9 ) and its contribution
to yield improvement is constrained to defi ned domains in the G EM space. Water use increased with
increasing plant population, thus limiting some of the benefi ts of enhanced water capture as indicated by a
lower rate of change in alleles for RA. Chapter 13 discusses in detail root attributes for improved capture
of resources.
In high-stress environments, ET1 and 12 pl m
2, the breeding simulations showed that selection for yield
favoured mechanisms to cope with stress. The frequency of alleles for CA and SP rapidly increased in
successive cycles of selection. The interpretation of these changes is that selection for yield results in lower
thresholds to biomass allocation to the ear, to kernel set, and vigorous and synchronous silking ( Figures 4c
and 9 ). In contrast, when METs were simulated for low-stress environments and commercial plant populations,
Cycles of selection
Frequency of alleles
0 5 10 15 20 0 5 10 15 20
0.0
0.5
1.0
0.0
0.5
1.0
(a) (b)
(c) (d)
FIGURE 9
Mean changes in gene frequencies for alleles associated with root angle (RA), leaf angle (LA), potential ear size (ME), threshold
carbon allocation to the ear and barrenness (CA) and synchronous pollination (SP) with cycle of selection. Selection simulated for
specifi c management: 8 pl m 2 (a, b) and 12 pl m 2 (c, d); and two contrasting environment types: severe terminal drought stress
(ET1) (a, c) and no stress (ET3) (b, d). Traits are colour coded in Plate 2.
4. Case Study: Maize Breeding in the USA 255
selection favoured the main mechanism to realise the environmental potential by increasing alleles ’ con-
tribution to augment light interception and RUE (as discussed above) and to increase ME. There was a con-
current increase in alleles for both traits ME and LA. Empirical evidence supporting this trait trajectory was
documented for mid-maturity maize selected in Argentina ( Luque et al., 2006 ). The frequency of alleles for
CA to the ear changed slowly from cycle 0 to 15. A break point becomes apparent following the realisation of
improvements in resource capture and use effi ciency, and alleles for LA are close to fi xation in cycle 15 of the
simulation; thus allocation to the ear becomes a limitation to yield improvement.
4.4. Breeding opportunities for broad and specifi c adaptation
Plant breeders often face the dilemma of designing breeding strategies with the right balance of efforts
directed towards breeding for broad versus specifi c adaptation. Necessary conditions for breeding for spe-
cifi c adaptation are the occurrence of repeatable environment types, and the existence of genetic variation in
traits that generate positive, sizable and repeatable G E M interactions. Breeding simulations in Figure 9
could be studied as the outcome of a breeding strategy to evaluate opportunities for specifi c adaptation. Trait
phenotype trajectories in Figure 9 suggest opportunities for improvements in both broad and specifi c adap-
tation to drought stress within the context of the simulated reference population of the breeding program.
The increase in frequencies of alleles contributing to higher CA and SP, regardless of the environment
type and crop management, suggests a breeding strategy that favours selection for alleles for these traits as
a means to improve broad adaptation. Although change in root architecture contributed to yield improve-
ment only in ET1 ( Figure 9 ), the absence of crossover G E M interactions ( Figures 8 and 9 ) suggests that
selection for alleles for RA could be one component of a breeding strategy seeking improvement for broad
adaptation. Successful improvement for this trait can create genotypes with enhanced yield stability (i.e. less
susceptibility to drought stress) and thus extend their domain of adaptation in the G E M space. It is also
feasible to conceive selection for alleles for RA as a component of a breeding strategy designed to improve
specifi c adaptation to drought stress. Because changes in allele frequencies for LA generated crossover G E
interactions ( Figure 8 ), this physiological trade-off forces plant breeders to accommodate selection for spe-
cifi c adaptation in the breeding program. To this end, it is necessary to formally defi ne the TPE based on
the classifi cation of environments by type ( Figure 7 ). The application of weights to the data from the multi-
environment trials to match the environment-type expectations of the TPE, weighted selection strategy, was
shown to increase response to selection ( Podlich et al., 1999 ).
This study simulated genetic gains for yield when breeding for specifi c conditions ( Figure 9 ) relative to those
attained if selection samples the TPE. Simulated genetic gains differed little for selection performed in only
ET3 environments, compared with the entire TPE. In contrast, genetic gains for selection in ET1, regardless
of the management, were double those attained when selection was conducted in the entire TPE (data not
shown). Management contributions to the rate of genetic gains were evident but of lower magnitude than
those due to environment variation. These results lead to the proposition that incorporating knowledge on
G E M into breeding can increase genetic gain and hasten crop improvement.
4.5. Opportunities to enhance molecular breeding
Since the discovery of molecular markers and their application to the construction of molecular maps and
to the mapping and dissection of quantitative traits ( Lander and Botstein, 1989 ; Lander and Schork, 1994 ;
Paterson et al., 1991 ), molecular marker technologies have been successfully integrated into many aspects of
plant breeding. Opportunities for molecular breeding and use of marker-assisted selection were the motiva-
tions for in silico studies and reviews (Chapter 14; Cooper et al., 2005, 2006 ; Lee, 1995 ). But the realisation
of the potential use of DNA markers to improve methods for predicting expected phenotypes of progeny
from parental information as suggested by Paterson et al. (1991) , and its utilisation in breeding programs,
came about after signifi cant developments in analyses and prediction methods, often based on a mixed-
model framework (i.e. Malosetti et al., 2007 ; van Eeuwijk et al., 2005 ; Boer et al., 2007 ), and improvements
in and the deployment of information management technologies ( Cooper et al., 2006 ; Graham, 2008 ).
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
256
Many of the activities within molecular breeding rely on statistical models that summarise associations
between genotypic and phenotypic variations. These statistical models often provide a static view of traits and
their association with genomic regions (QTL). The treatment and analysis on a trait-by-trait basis limits these
methods to effectively capture the dynamic relationships between traits, leaving to the breeder the subjective
interpretation of the interplay and emerging trade-offs among traits. As evidence accumulates towards the
need for considering epistasis and pleiotropy for the deployment of enhanced methods for molecular breed-
ing, it is opportune to contemplate the utility of the G EM modelling approach outlined in this chapter
as a framework for considering the biological and physiological interplay of QTL, traits and environments
in a way that adds value to the well-established and effective statistical framework for molecular breeding. In
the G EM framework, epistasis and pleiotropic effects are emergent properties of the physiological frame-
work ( Hammer et al., 2006 ). The trait trajectories depicted in Figure 9 illustrate the conditional dependencies
among traits to contribute to yield improvement. While the genetic models defi ned for all traits in this study
were additive at the individual trait level, the grain yield value of the different alleles for a given trait is condi-
tional to the state of other loci as demonstrated by the non-linear structure of the trait trajectories in genotype
space. These simulations suggest that physiological dissection and modelling can help assign biological func-
tion to QTLs, and explain and resolve G EM interactions, thus providing a foundation to improve molecu-
lar breeding strategies in maize. This argument could be extended to the application of the framework to
known genes for the assessment of their function at the whole-plant level, that is, to assess the extent to which
the effects of gene expression at the molecular level propagate across levels of organisation. The framework
could be used for designing in silico breeding strategies that make use of transgenics as a step prior to the ini-
tiation of experimentation that would require signifi cant management and investment. Hammer et al. (2005)
demonstrated in a theoretical study of sorghum that marker-assisted selection could be improved (enhanced
rate of yield increase over cycles of selection) by considering knowledge from trait physiology and modelling.
4.6. How consistent are simulated trajectories with changes in
traits due to genetic improvement for yield?
To interpret the results of the breeding simulation in the context of observed trait trajectories, we must defi ne
the environment types, changes in management and selection objectives that prevail during the selection pro-
cess. Major breeding objectives are to increase yield and yield stability across years and geographies. Selection
decisions in the past were mostly driven by data collected in the TPE; that is, a large fraction of the data driv-
ing selection decisions were obtained in environments that exposed maize crops to low drought stress ( Löffl er
et al., 2005 ). However, as the TPE is by defi nition a mixture of environments, in certain years, drought stress
could have contributed to the pool of data and germplasm improvement. Crop management also changed
through time, with plant population, irrigation and N use increasing since 1960 ( Cassman and Liska, 2007 ).
In the context outlined above for dominant environment types, management practices and breeding objec-
tives, the expectation set by outcomes of breeding simulation ( Figures 8 and 9 ) is to observe a rapid decrease
in LA (towards hybrids with an erect leaf type) associated with improved RUE in high-density stands, to
some degree deeper root systems selected in drought-prone environments and dry years and increased ker-
nel set due to higher resource allocation to the ear. Observed trait trajectories for selection in the north-
central USA compare well with the expectations from the breeding simulation ( Duvick et al., 2004 ; Figure
10 ). After the onset of the era of intensive agriculture in the early 1960s, LA scores increased linearly, reach-
ing a plateau denoted for hybrids released since the late 1980s. Breeding simulation indicated this trajectory
in the absence of nitrogen limitations and in ET3 ( Figures 7 and 9 ), which together with ET2 (low stress
around fl owering) accounts for 65% of environment types in the TPE. Both simulated and observed leaf
scores ( Figures 9 and 10 ) indicated that breeding for yield had moved the breeding populations towards a
region in the G space that optimises light capture and use effi ciency under E M typical of intensive agricul-
ture, with apparent little room for further contributions to yield improvement.
Changes in root architecture in response to selection have not been documented. However, there is evi-
dence for a reduction in biomass allocation to roots in the topsoil ( Bruce et al., 2002 ). This observation is
4. Case Study: Maize Breeding in the USA 257
consistent with a predicted trajectory towards deeper root systems and lower root density in upper soil layers
(Figure 9 ). Lower RAs predict a more uniform water use pattern in depth and time as well as a more uni-
form biomass distribution in the profi le. Campos et al. (2004) showed that older hybrids use more (less)
water from the top (bottom) soil layers than modern hybrids. As suggested by breeding simulation, these
observed patterns of increased water capture and conservative water use may have resulted as a consequence
of selecting hybrids with yield stability across locations and years. Based on simulated trait trajectories for
ET1 environments, it is suggested that there is unrealised potential to progress further yield stability in main
production areas in the maize belt and yield under drought stress.
Reproductive traits ME, CA and SP increased in successive cycles of breeding ( Figure 9 ), leading to the
creation of hybrids with increased CA to the ear and increased kernel set for a given E and M ( Figure 4c ).
1920 1940 1960 1980 2000
0
1
2
3
4
5
6
7
8
9
10
75
80
85
90
95
100
105
110
Leaf angle score Ears per plant (%)
Year of release
(a)
(b)
FIGURE 10
Observed trajectories in non-barren plants (a) leaf angle score (b) in a series of Pioneer hybrids released between 1930 and 2007.
Leaf angle scores range from 0 to 10 assigned to fl oppy-type and erect-type hybrids.
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
258
Empirical evidence and theoretical predictions agree well in that selection for yield increased the kernel
number per plant, per ear and per unit area ( Chapman and Edmeades, 1999 ; Echarte et al., 2004 ; Campos
et al., 2006 ; Luque et al., 2006 ; Tollenaar et al., 1992 ; Duvick et al., 2004 ; Edmeades et al., 2000 ), and fer-
tile ears per plant largely contributed to this increase ( Duvick et al., 2004 ; Chapman and Edmeades, 1999 ;
Tollenaar et al., 1992 ). Increased partitioning and reduced barrenness in the context of the modelling
framework are related to the reduction in CA ( Figures 4c and 9 ). Simulated trait trajectories are consistent
with measurements by Echarte et al. (2004) but not by Luque et al. (2006) and Tollenaar et al. (1992) .
In the latter two studies, model parameters linked to ME and CA to the ear were correlated. Because of
such correlation, it is diffi cult to contrast model predictions with empirical evidence. The framework used
in this study captures some aspects of the underpinning mechanisms causal of barrenness but further
advancement on the model, perhaps through incorporating theoretical aspects of interplant competition
(Pagano et al., 2007 ; Pagano and Maddonni, 2007 ), will be necessary to better connect genetic variation
and physiological determinants of barrenness. Luque et al. (2006) observed increases in ME only under
high-yield environments, in agreement with predicted trait trajectories in this study ( Figure 9 , environ-
ment type ET3).
5. CONCLUDING REMARKS
This chapter reviewed and summarised theoretical developments towards a framework that integrates quan-
titative genetics, breeding simulation and modelling of physiological traits and dynamic GP relations. Such
a framework is intended to enable breeders and agronomists to project trajectories in the G E M space
into the future and gain insights on the consequences of manipulating genomes to the creation of improved
crops for target management and environments.
A central concept emphasised throughout this study and applied to the different aspects of modelling and
simulation is the iterative nature of the process, and thus the need to integrate modelling and simulations
as one component of the breeding program. The execution of this framework is feasible only through such
integration that forces individuals to align breeding objectives, physiological questions and genetic hypoth-
eses, which ultimately have to be tested in the breeding program.
This study demonstrated in silico the validity of a method to effectively explore the G EM state space, to
integrate and apply physiological concepts to plant breeding and the value of leveraging this knowledge to
develop improved crops. Nevertheless, executing this framework poses a number of grand challenges, and
a signifi cant scientifi c and technological ground has yet to be covered. There is a clear need to advance the
scientifi c debate about the detail and complexity needed for crop growth models to be able to integrate
processes across levels of organisation while predicting emergent functional consequences for the organ-
ism. Related to this issue is the need for a considerable effort and investment in creating knowledge and
developing robust links between genetic variation for adaptive traits relevant to breeders and the underly-
ing physiological determinants. Despite the agreement between observed and simulated trait trajectories
for the past 50 years of breeding in the US Corn Belt, there is a clear need for a theoretical and empirical
demonstration that these technologies can be used to improve future rates of genetic gain in elite breeding
populations.
We are optimistic that breeding simulation will help understand observed breeding trajectories for traits
contributing to yield improvement; identify emergent, in some cases counterintuitive, behaviour of the
breeding system; and quantify trait and environmental context dependencies. This understanding, along
with quantitative knowledge of QTL function, via trait dissection and integration using physiological mod-
elling and a G EM framework, will enable predictions to be evaluated in the target breeding program.
This emerging breeding technology can help manage and adapt germplasm to effectively navigate through
the G EM space, producing improved hybrids that meet the needs of changing farming systems and
environments.
References 259
REFERENCES
Aggarwal , P.K. , Kropff , M.J. , Cassman , K.G. , ten Berge , H.F.M. , 1997 . Simulating genotypic strategies for increasing rice
yield potential in irrigated, tropical environments . Field Crops Res. 51 ,5 – 17 .
Ainsworth , E.A. , Rogers , A. , Leakey , A.D.B. , 2008 . Targets for crop biotechnology in a future high-CO
2 and high-O
3 world .
Plant Physiol. 147 , 13 – 19 .
Amir , J. , Sinclair , T.R. , 1991 . A model of the temperature and solar radiation effects on spring wheat growth and yield .
Field Crops Res. 28 , 47 – 58 .
Andrade , F.H. , Uhart , S.A. , Frugone , M. , 1993 . Intercepted radiation at fl owering and kernel number in maize: Shade ver-
sus plant density effects . Crop Sci. 33 , 482 – 485 .
Andrade , F.H. , Vega , C. , Uehart , S. , Cirilio , A. , Cantarero , M. , Valentinuz , O. , 1999 . Kernel number determination in
maize . Crop Sci. 39 , 453 – 459 .
Bhalla , U.S. , Iyengar , R. , 1999
. Emergent properties of networks of biological signaling pathways . Science 283 ,381 – 387 .
Ben Haj Salah , H. , Tardieu , F. , 1997 . Control of leaf expansion rate of droughted maize plants under fl uctuating evapora-
tive demand: A superposition of hydraulic and chemical messages? Plant Physiol. 114 , 893 – 900 .
Birch , C.J. , Hammer , G.L. , Rickert , K.G. , 1998a . Improved methods for predicting individual leaf area and leaf senescence
in maize ( Zea mays L.) . Aust. J. Agric. Res. 49 , 249 – 262 .
Birch , C.J. , Rickert , K.G. , Hammer , G.L. , 1998b . Modelling leaf production and crop development in maize ( Zea mays L.)
after tassel initiation under diverse conditions of temperature and photoperiod . Field Crops Res. 58 ,81 – 95 .
Boer , M.P. , Wright , D. , Feng , L. , Podlich ,
D.W. , Luo , L. , Cooper , M. , van Eeuwijk , F.A. , 2007 . A mixed-model quantitative
trait loci (QTL) analysis for multiple-environment trial data using environmental covariables for QTL-by-environment
interactions, with an example in maize . Genetics 177 , 1801 – 1813 .
Bola ños , J. , Edmeades , G.O. , 1991 . Value of selection for osmotic potential in tropical maize . Agron. J. 83 , 948 – 956 .
Boote , K.J., Jones , J.W. , Hoogenboom, G.H. , 1998 . Simulation of crop growth: CROPGRO model . In: R.M. Peart and R.B. Curry
(Eds.), Agricultural Systems Modelling and Simulation . Marcel Dekker , New York , pp. 651 – 693 .
Boote , K.J. , Jones , J.W. , Pickering , N.B. , 1996 . Potential uses and limitations of crop models . Agron. J. 88 , 704 – 716 .
Boote ,
K.J. , Kroft , M.J. , Brindraban , P.S. , 2001 . Physiology and modelling of traits in crop plants: Implications for genetic
improvement . Agric. Syst. 70 , 395 – 420 .
Boote, K.J., Loomis, R.S., 1991. Modelling Crop Photosynthesis – From Biochemistry to Canopy. CSSA Special Publication
Number 19. American Society of Agronomy, Crop Science Society of America, Madison, WI.
Boote , K.J. , Tollenaar , M. , 1994 . Modelling genetic yield potential . In: K.J. Boote , J.M. Bennett , T.R. Sinclair and
G.M. Paulsen (Eds.), Physiology and Determination of Crop Yield . ASA-CSSA-SSSA , Madison, WI , pp. 533 – 561 .
Borr ás, L. , Westgate , M.E. , Astini , J.P. , Echarte , L. , 2007 . Coupling time to silking with plant growth rate in maize . Field
Crops Res. 102 , 73 – 85 .
Borrell , A.K. , Hammer , G.L. , and van Oosterom ,
E. , 2001 . Stay-green: A consequence of the balance between supply and
demand for nitrogen during grain fi lling ? Ann. Appl. Biol. 138 ,91 – 95 .
Bruce , W.B. , Edmeades , G.O. , Barker , T.C. , 2002 . Molecular and physiological approaches to maize improvement for
drought tolerance . J. Exp. Bot. 53 ,13 – 25 .
Campos , H. , Cooper , M. , Edmeades , G.O. , L öffl er , C. , Schussler , J.R. , Iba ñez, M. , 2006 . Changes in drought tolerance in
maize associated with fi fty years of breeding for yield in the US Corn Belt . Maydica 51 , 369 – 381 .
Campos , H., Cooper , M. , Habben , J.E. , Edmeades , G.O. , Schussler , J.R. , 2004 . Improving drought tolerance in maize: A
view from industry
. Field Crops Res. 90 , 19 – 34 .
Carberry , P.S. , Muchow , R.C. , Hammer , G.L. , 1993 . Modelling genotypic and environmental control of leaf area dynamics
in grain sorghum. II. Individual leaf level
. Field Crops Res. 33 ,311 – 328 .
C árcova , J. , Andrieu , B. , Otegui , M.E. , 2003 . Silk elongation in maize: Relationship with fl ower development and pollina-
tion . Crop Sci. 43 , 914 – 920 .
C árcova , J. , Otegui , M.E. , 2007 . Ovary growth and maize kernel set . Crop Sci. 47 , 1104 – 111 0 .
Cassman , K.G. , Liska , A.J. , 2007 . Food and fuel for all: Realistic or foolish? . Biofuels Bioprod. Bioref. 1 , 18 – 23 .
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
260
Castleberry , R.M. , Crum , C.W. , Krull , C.F. , 1984 . Genetic yield improvement of US maize cultivars under varying fertility
and climatic environments . Crop Sci. 24 , 33 – 36 .
Century , K. , Reuber , T.L. , Ratcliffe , O.J. , 2008 . Regulating the regulators: The future prospects for transcription-factor-based
agricultural biotechnology products . Plant Physiol. 147 ,20 – 29 .
Chapman , S. , Cooper , M. , Podlich , D. , Hammer , G. , 2003 . Evaluating plant breeding strategies by simulating gene action
in dryland environment effects . Agron. J. 95 , 99 – 113 .
Chapman , S. , Edmeades , G.O. , 1999 . Selection improves drought tolerance in tropical maize populations. II. Direct and
correlated responses among secondary traits . Crop Sci. 39 , 1315 – 1324 .
Chapman , S.C. ,
Cooper , M. , Hammer , G.L. , 2002 a . Using crop simulation to interpret broad adaptation and genotype by
environment effects for sorghum in water-limited environments . Aust. J. Agric. Res. 53 ,1 – 11 .
Chapman , S.C. , Cooper , M. , Hammer , G.L. , 2002 b . Using crop simulation to generate genotype by environment interac-
tion effects for sorghum in water-limited environments . Aust. J. Agric. Res. 53 , 379 – 389 .
Chapman , S.C. , Cooper , M. , Hammer , G.L. , Butler , D. , 2000 . Genotype by environment interactions affecting grain sor-
ghum. II. Frequencies of different seasonal patterns of drought stress are related to location effects on hybrid yields .
Aust. J. Agric. Res. 50 , 209 – 222 .
Chapman , S.C. , Hammer , G.L. , Meinke , H. , 1993 . A sunfl ower simulation model: I. Model development . Agron. J. 85 ,
725 – 735 .
Chenu , K. , Chapman , S.C. , Hammer , G.L. , Mclean , G. , Ben Haj Salah , H., Tardieu , F. , 2008 . Short-term responses of leaf
growth rate to water defi cit scale up to whole-plant and crop levels: An integrated modelling approach in maize . Plant
Cell Environ. 31 , 378 – 391 .
Chimenti , C.A. , Marcantonio , M. , Hall , A.J. , 2006 . Divergent selection for osmotic adjustment results in improved drought
tolerance in maize ( Zea mays L.) in both early growth and fl owering phases . Field Crops Res. 95 , 305 – 315 .
Clerget , B. , Dingkuhn , M.
, Goze , E. , Rattunde , H.F.W. , Ney , B. , 2008 . Variability of phyllochron, plastochron and rate of
increase in height in photoperiod-sensitive sorghum varieties . Ann. Bot. 101 , 579 – 594 .
Cooper, M., Chapman, S.C., Podlich, D.W., Hammer, G.L., 2002. The GP problem: Quantifying gene-to-phenotype rela-
tionships. In Silico Biol. 2, 151–164 (Available on-line at
http://www.bioinfo.de/isb/2002/02/0013/ ; verifi ed 14 Aug.
2008).
Cooper , M. , Hammer , G.L. , 1996 . Plant Adaptation and Crop Improvement . CAB International , Wallingford, UK .
Cooper , M. , Podlich , D. , 2002 . The E ( NK) model: Extending the NK model to incorporate gene-by-environment interac-
tions and epistasis for diploid genomes . Complexity 7 ,31 – 47 .
Cooper , M. , Podlich , D.W. , Smith , O.S. , 2005 . Gene-to-phenotype models and complex trait genetics . Aust. J. Agric. Res.
56 , 895 – 918 .
Cooper , M. , Smith , O.S. , Merrill , R.E. , Arthur , L. , Podlich , D.W. , Loeffl er , C.M. , 2006 .
Integrating breeding tools to gener-
ate information for effi cient breeding: Past, present, and future . In: K.R. Lamkey and M. Lee (Eds.), Plant Breeding:
The Arnel R. Hallauer International Symposium . Blackwell Publishing , Oxford, UK , pp. 141 – 154 .
Corbesier , L. , Vincent , C. , Jang , S. , Fornara , F. , Fan , Q. , Searle , I. , Giakountis , A. , Farrona , S. , Gissot , L. , Turnbull , C. ,
Coupland , G. , 2007 . FT protein movement contributes to long-distance signalling in fl oral induction of Arabidopsis .
Science 316 , 1030 – 1033 .
Coyne , D.P. , 1970 . Genetic control of a photoperiodic-temperature response for fl owering in beans ( Phaseolus vulgaris L.) .
Crop Sci. 10 , 246 – 248 .
Dardanelli , J.L. , Bachmeier , O.A. , Sereno , R. , Gil , R. , 1997 . Rooting depth and soil water extraction patterns of different
crops in a silty loam Haplustoll . Field Crops Res. 54 , 29 – 38 .
Dardanelli , J.L. , Ritchie , J.T. , Calmon , M. , Andriani , J.M. , Collino , D.J. , 2004
. An empirical model of water uptake . Field
Crops Res. 87 , 59 – 71 .
de Wit , C.T. , 1982 . Simulation of living systems . In: F.W.T. Penning de Vries and H.H. van Laar (Eds.), Simulation of Plant
Growth and Crop Production . Pudoc , Wageningen, The Netherlands , pp. 3 – 19 .
de Wit , C.T. , Penning de Vries , F. W. T . , 1983 . Crop growth models without hormones .
Neth. J. Agric. Sci. 31 , 313 – 323 .
Donald , C.M. , 1968 . The breeding of crop ideotypes . Euphytica 17 , 385 – 403 .
References 261
Duncan , W.G. , Loomis , R.S. , Williams , W.A. , Hanau , R. , 1967 . A model for simulating photosynthesis in plant communi-
ties . Hilgardia 38 ,181 – 205 .
Duncan , W.G. , McCloud , D.E. , McGraw , R.L. , Boote , K.J. , 1978 . Physiological aspects of peanut yield improvement . Crop
Sci. 18 , 1015 – 1020 .
Duvick , D.N. , Cassman , K.G. , 1999 . Post –Green Revolution trends in yield potential of temperate maize in the north-
central United States . Crop Sci. 39 , 1622 – 1630 .
Duvick , D.N. , Smith , J.S.C. , Cooper , M.
, 2004 . Long-term selection in a commercial hybrid maize breeding program . Plant
Breed. Rev. 24 ,109 – 151
.
Dwyer , L.M. , Stewart , D.W. , 1986 . Leaf area development in fi eld-grown maize . Agron. J. 78 , 334 – 343 .
Echarte , L. , Andrade , F.H. , Vega , C.R.C. , Tollenaar , M. , 2004 . Kernel number determination in Argentinean maize hybrids
released between 1965 and 1993 . Crop Sci. 44 , 1654 – 1661 .
Edmeades , G.O. , Baeziger , M., Ribaut, J. , 2000 . Chapter 6. Maize improvement for drought-limited environments . In: M.E.
Otegui and G.A. Slafer (Eds.), Physiological Basis for Maize Improvement . Food Products Press
, New York , pp. 75– 112 .
Erskine , W. , Ellis , R.H. , Summerfi eld , R.J. , Roberts , E.H. , Hussain , A. , 1990 . Characterization of responses to temperature
and photoperiod for time to fl
owering in a world lentil collection . Theor. Appl. Genet. 80 , 193 – 199 .
Evans , L.T. , 1976 . Crop Physiology: Some Case Histories . Cambridge University Press , Cambridge, UK .
Fischer , R.A. , 1985 . Number of Kernels in wheat crops and the infl uence of solar radiation and temperature . J. Agri. Sci.
UK. 105 , 447 – 461 .
Fontana , W. , 2002 . Modelling ‘evo-devo ’ with RNA . Bioessays 24 , 1164 – 1177 .
Fontana , W. , Schnabl , W. , Schuster , P. , 1989 . Physical aspects of evolutionary optimization and adaptation . Phys. Rev. A
40 ,3301 – 3321 .
Forrester , J.W. , 1961 . Industrial Dynamics . Wiley , New York .
Gamb ín, B.L. , Borr ás,
L. , Otegui , M.E. , 2006 . Source –sink relations and kernel weight differences in maize temperate
hybrids . Field Crops Res. 95 , 316 – 326 .
Gifford , R.M. , Thorne , J.H. , Hitz , W.D. , Giaquinta , R.T. , 1984 . Crop productivity and photoassimilate partitioning . Science
225 ,801 – 808 .
Goudriaan , J. , van Laar , H.H. , 1994 . Modelling potential crop growth processes . Kluwer Academic Publishers , Dordrecht,
The Netherlands .
Graham, G.I., 2008. The development and use of genetic information in a breeding program. Maize Genetics Conference
Abstracts 50, T3.
Grimm , S.S. , Jones , J.W. , Boote , K.J. , Herzog , D.C. , 1994 . Modeling the occurrence of reproductive stages after fl owering
for four soybean cultivars . Agron. J. 86 ,31 – 38 .
Hammer , G. , Cooper
, M. , Tardieu , F. , Welch , S. , Walsh , B. , van Eeuwijk , F. , Chapman , S. , Podlich , D. , 2006 . Models for
navigating biological complexity in breeding improved crop plants . Trends Plant Sci.
11 , 1360 – 1385 .
Hammer , G.L. , Broad , I.J. , 2003 . Genotype and environment effects on dynamics of harvest index during grain fi lling in
sorghum . Agron. J. 95 , 199 – 206 .
Hammer , G.L. , Carberry , P.S. , Muchow , R.C. , 1993 . Modelling genotypic and environmental control of leaf area dynamics
in grain sorghum. I. Whole plant level . Field Crops Res. 33 , 293 – 31 0 .
Hammer , G.L. , Chapman , S. , van Oosterom , E. , Podlich , D.W. , 2005 .
Trait physiology and crop modelling as a framework
to link phenotypic complexity to underlying genetic systems . Aust. J. Agric. Res. 56 , 947 – 960 .
Hammer, G.L., Dong, Z., McLean, G., Doherty, A., Messina, C., Schusler, J., Zinselmeier, C., Paszkiewicz, S., Cooper, M.,
2009. Can changes in canopy and/or root system architecture explain historical maize yield trends in the US corn
belt? Crop Sci., 49, 299–312.
Hammer , G.L. , Jordan, D.R. , 2007 . An integrated systems approach to crop improvement . In: J.H.J. Spierts , P.C. Struik
and H.H. van Laar (Eds.), Scale and Complexity in Plant Systems Research: Gene-Plant-Crop Relations . Springer ,
Dordrecht, The Netherlands , pp. 45 – 61 .
Hammer , G.L., Kropff, M.J., Sinclair , T.R. , Porter , J.R. , 2002 . Future contributions of crop modelling from heuristics and sup-
porting decision making to understanding genetic regulation and aiding crop improvement . Eur. J. Agron. 18 , 15– 31 .
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
262
Hammer , G.L. , Muchow , R.C. , 1994 . Assessing climatic risk to sorghum production in water-limited subtropical environ-
ments. I. Development and testing of a simulation model . Field Crops Res. 36 ,221 – 234 .
Hammer , G.L. , Sinclair , T.R. , Boote , K.J. , Wright , G.C. , Meinke , H. , Bell , M.J. , 1995 . A peanut simulation model: I. Model
development and testing . Agron. J. 87 , 1085 – 1093 .
Hammer , G.L. , Sinclair , T.R. , Chapman , S.C. , van Oosterom , E. , 2004 . On systems thinking, systems biology, and the
in silico plant . Plant Physiol. 134 , 909 – 911 .
Hammer , G.L. , Wright , G.C. , 1994 . A theoretical analysis of nitrogen and radiation use effi ciency in peanut . Aust. J. Agric.
Res. 45 , 575 –
579 .
Hammer , G.L. , Vanderlip , R.L. , Gibson , G. , Wade , L.J. , Henzell , R.G. , Younger , D.R. , Warren , J. , Dale , A.B. , 1989 . Genotype
by environment interaction in grain sorghum II. Effects of temperature and photoperiod on ontogeny . Crop Sci. 29 ,
376 – 384 .
Hanks, J., Ritchie, J.T., 1991. Modelling Plant and Soil Systems, Agronomy Series 31. ASA-CSSA-SSSA, Madison, WI.
Hoogenboom , G. , White , J.W. , Acosta-Gallegos , J. , Gaudiel , R.G. , Myers , J.R. , Silbernagel , M.J. , 1997 . Evaluation of a crop
simulation model that incorporates gene action . Agron. J. 89 , 613 – 620 .
Jiang , H. , Egli , D.B. , 1995 . Soybean seed number and crop growth rate during fl owering
. Agron. J. 87 , 264 – 267 .
Jones , C.A. , Kiniry , J.R. , 1986 . CERES-Maize, a simulation model of maize growth and development . Texas A &M University
Press , College Station, TX .
Jones , H.G. , 1992 . Plants and microclimate: A quantitative approach to environmental plant physiology , 2nd ed .
Cambridge University Press , New York .
Jones , J.W. , Hoogenboom, G., Porter , C.H., Boote , K.J., Batchelor , W.D. , Hunt, L.A., Wilkens , P.W . , Singh, U., Gijsman, A.J.,
Ritchie , J.T. , 2003 . The DSSAT cropping system model . Eur. J. Agron. 18 , 235– 265 .
Karl , T.R. , Trenberth , K.E. , 2003 . Modern global climate change . Science 302 , 1719 – 1723 .
Kauffman , S. , 1993 .
The origins of order: Self-organization and selection in evolution . Oxford University Press , New York .
Kauffman , S., Peterson , C. , Samuelsson , B. , Troein , C. , 2004 . Genetic networks with canalyzing Boolean rules are always
stable . Proc. Natl. Acad. Sci. U.S.A. 101 ,17102 – 17107 .
Keating , B.A. , Carberry , P.S. , Hammer , G.L. , Probert , M.E. , Robertson , M.J. , Holzworth , D. , Huth , N.I. , Hargreaves , J.N.G. ,
Meinke , H., Hochman, Z., McLean, G., Verburg , K., Snow , V. , Dimes , J.P. , Silburn, M., Wang , E., Brown , S., Bristow , K.L.,
Asseng, S., Chapman, S., McCown , R.L., Freebairn, D.M., Smith, C.J. , 2003 . An overview of APSIM, a model designed
for farming systems simulation
. Eur. J. Agron. 18 , 267– 288 .
Kemanian , A.R. , Stockle , C.O. , Huggins , D.R. , 2005 . Transpiration-use effi ciency of barley . Agric. For. Meteorol. 130 ,1 – 11 .
Koornneef , M. , Alonso-Blanco , C. , Peeters , A.J.M. , Soppe , W. , 1998 . Genetic control of fl owering time in Arabidopsis .
Annu. Rev. Plant Physiol. Plant Mol. Biol. 49 , 345 – 370 .
Kornegay , J. , White , J.W. , Dominguez , J.R. , Tejada , G. , Caijiao , C. , 1993 . Inheritance of a photoperiod response in Andean
and Mesoamerican common bean . Crop Sci. 33 , 977 – 984 .
Lander , E.S. , Botstein ,
D. , 1989 . Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps .
Genetics 121 , 185 – 199 .
Lander , E.S. , Schork , N.J. , 1994 . Genetic dissection of complex traits . Science 265 , 2037 – 2048 .
Lee , E.A. , Tollenaar , M. , 2007 . Physiological basis of successful breeding strategies for maize yield . Crop Sci. 47 ,
S-202 – S-215 .
Lee , M. , 1995 . DNA markers and plant breeding programs . Adv. Agron. 55 , 265 – 344 .
Lindquist , J.L. , Arkebauer , T.J. , Walters , D.T. , Cassman , K.G. , Dobermann , A. , 2005 . Maize radiation use effi ciency under
optimal growth conditions . Agron. J. 97 , 72 – 78
.
L öffl er , C.M. , Wei , J. , Fast , T. , Gogerty , J. , Langton , S. , Bergman , M. , Merrill , R.E. , Cooper , M. , 2005 . Classifi cation of maize
environments using crop simulation and geographic information systems . Crop Sci. 45 , 1708 – 1716 .
Long , S.P. , Zhu , X.G. , Naidu , S.L. , Ort , D.R. , 2006 . Can improvement in photosynthesis increase crop yields? Plant Cell
Environ. 29 , 315 – 330 .
Loomis , R.S. , Connor , D.J. , 1992 . Crop Ecology. Productivity and Management in Agricultural Systems . Cambridge
University Press , Cambridge, UK .
References 263
Loomis , R.S. , Rabbinge , R. , Ng , E. , 1979 . Explanatory models in crop physiology . Annu. Rev. Plant Physiol. 30 , 339 – 367 .
Luque , S.F. , Cirilo , A.G. , Otegui , M.E. , 2006 . Genetic gains in grain yield and related physiological attributes in Argentine
maize hybrids . Field Crops Res. 95 , 383 – 397 .
Malosetti , M. , van der Linden , C.G. , Vosman , B. , van Eeuwijk , F.A. , 2007 . Mixed-model approach to association map-
ping using pedigree information with an illustration of resistance to Phytophthora infestans in potato . Genetics 175 ,
879 – 889 .
Manschadi , A.M. , Christopher , J. , deVoil , P. , Hammer , G.L. , 2006 . The role of root architectural traits in adaptation of
wheat to water-limited environments . Funct. Plant Biol. 33
, 823 – 837 .
McMaster , G.S. , Wilhelm , W.W. , 1997 . Growing degree-days: One equation, two interpretations . Agric. For. Meteorol. 87 ,
291 – 300 .
Meinke , H. , Hammer , G.L. , Want , P. , 1993 . Potential soil water extraction by sunfl ower on a range of soils . Field Crops
Res. 32 , 59 – 81 .
Messina , C.D. , Jones , J.W. , Boote , K.J. , Vallejos , C.E. , 2006 . A gene-based model to simulate soybean development and
yield responses to environment . Crop Sci. 46 , 456 – 466 .
Minorsky , P.V. , 2003 . Achieving the in silico plant: Systems biology and the future of plant biological research . Plant
Physiol. 132 , 404 – 409 .
Miralles , D.J. , Slafer
, G.A. , 1997 . Radiation interception and radiation use effi ciency of near-isogenic wheat lines with dif-
ferent height . Euphytica 97 ,201 – 208 .
Mitchell , M. , 1996 . An Introduction to Genetic Algorithms . MIT Press , Cambridge, MA .
Monsi , M. , Saeki , T. , 2005 . On the factor light in plant communities and its importance for matter production . Ann. Bot.
95 , 549 – 567 .
Monteith , J.L. , 1986 . How do crops manipulate water supply and demand? Philos. Trans. R. Soc. Lond. A 316 , 245 – 259 .
Monteith , J.L. , 1988 . Does transpiration limit the growth of vegetation or vice-versa? J. Hydrol. 100 , 57 – 68 .
Muchow , R.C. , Carberry , P.S. , 1989 . Environmental control of phenology and leaf growth in tropically adapted maize .
Field Crops Res. 20 ,221 – 236 .
Muchow ,
R.C. , Sinclair , T.R. , Bennett , J.M. , 1990 . Temperature and solar radiation effects on potential maize yield across
locations . Agron J. 82 , 338 – 343 .
Nobel , P. , 2005 . Physicochemical and Environmental Plant Physiology , 3rd ed. Elsevier Academic Press , Burlington, MA .
Nowak , M.A. , 2006 . Evolutionary Dynamics: Exploring the Equations of Life . Harvard University Press , Cambridge MA .
Otegui , M.E. , Bonhomme , R. , 1998 . Grain yield components in maize: I. Ear growth and kernel set . Field Crops Res. 56 ,
247 – 256 .
Otegui , M.E. , Slafer , G.A. , 2000 . Physiological Basis for Maize Improvement . The Hawthorne Press , New York .
Pagano , E. , Cela , S. , Maddonni , G.A. , Otegui , M.E. , 2007
. Intra-specifi c competition in maize: Ear development, fl owering
dynamics and kernel set of early-established plant hierarchies . Field Crops Res. 102 , 198 – 209 .
Pagano , E. , Maddonni , G.A. , 2007 . Intra-specifi c competition in maize: early established hierarchies differ in plant growth
and biomass partitioning to the ear around silking . Field Crops Res. 101 , 306 – 320 .
Parton , W.J. , Ojima , D.S. , Cole , C.V. , Schimel , D.S. , 1994 . A general model for soil organic matter dynamics: Sensitivity
to litter chemistry, texture and management . In: R.B. Bryant and R.W. Arnold (Eds.), Quantitative Modelling of Soil
Forming Processes, SSSA Special Publication 39 . Soil Science Society of America , Madison, WI , pp. 147 – 167 .
Parton , W.J. , Stewart , J.W.B. , Cole , C.V. , 1988 . Dynamics of C, N, P and S in grassland soils: A model . Biogeochemistry 5 ,
109 – 131 .
Passioura ,
J.B. , 1983 . Roots and drought resistance . Agric. Water Manag. 7 , 265 – 280 .
Paterson , A.H. , Tanksley , S.D. , Sorrells , M.E. , 1991 . DNA markers in plant improvement . Adv. Agron.
46 , 39 – 85 .
Peart , R.M. , Curry , R.B. , 1998 . Agricultural Systems Modelling and Simulation . Marcel Dekker , New York .
Peccoud , J. , Vander Velden , K. , Podlich , D. , Winkler , C. , Arthur , L. , Cooper , M. , 2004 . The selective values of alleles in a
molecular network model are context dependent . Genetics 166 , 1715 – 1725 .
Pennisi , E. , 2008 . The blue revolution, drop by drop, gene by gene . Science 320
,171 – 173 .
CHAPTER 10: Modelling Crop Improvement: GⴛEⴛM
264
Podlich , D.W. , Cooper , M. , 1998 . QU-GENE: A simulation platform for quantitative analysis of genetic models .
Bioinformatics 14 , 632 – 653 .
Podlich , D.W. , Cooper , M. , Basford , K.E. , 1999 . Computer simulation of a selection strategy to accommodate genotype-
environment interactions in a wheat recurrent selection programme . Plant Breed. 118 , 17 – 28 .
Podlich , D.W. , Winkler , C.R. , Cooper , M. , 2004 . Mapping as you go: Effective approach for marker-assisted selection of
complex traits . Crop Sci. 44 , 1560 – 1571 .
Ravasz , E. , Somera , A.L. , Mongru , D.A. , Oltavi , Z.N. , Barab ási, A.L. , 2002
. Hierarchical organization of modularity in met-
abolic networks . Science 297 , 1551 – 1555 .
Reymond , M., Muller , B. , Leonardi , A. , Charcosset , A. , Tardieu , F. , 2003 . Combining quantitative trait loci analysis and an
ecophysiological model to analyze the genetic variability of the responses of maize leaf growth to temperature and
water defi cit . Plant Physiol. 131 , 664 – 675 .
Ritchie , J.T. , 1998 . Soil water balance and plant water stress . In: G.Y. Tsuji , G. Hoogenboom and P.K. Thornton (Eds.),
Understanding Options for Agricultural Production . Kluwer Academic Publishers , Dordrecht, The Netherlands ,
pp. 41 – 54 .
Ritchie , J.T. , Alagarswamy , G. , 2003 . Model concepts to express genetic differences in maize yield components . Agron. J.
95 ,4 – 9 .
Ritchie, J.T., NeSmith, D.S., 1991. Temperature and crop development. In: J. Hanks, J.T. Ritchie (Eds.), Modelling Plant
and Soil Systems, Agronomy Series 31. ASA-CSSA-SSSA, Madison, WI, pp. 5 –29.
Robertson , M.J. , Fukai , S. , Ludlow , M.M. , Hammer
, G.L. , 1993 . Water extraction by grain sorghum in a sub-humid envi-
ronment. I. Analysis of the water extraction pattern . Field Crops Res. 33 ,81 – 97 .
Sadok , W. , Naudin , P. , Boussuge , B. , Muller , B. , Welcker , C., Tardieu , F. , 2007 . Leaf growth rate per unit thermal time
follows QTL-dependent daily patterns in hundreds of maize lines under naturally fl uctuating conditions . Plant Cell
Environ. 30 , 135 – 146 .
Sadras , V.O . , Hall , A.J. , 1988 . Quantifi cation of temperature, photoperiod and population effects on plant leaf area in
sunfl ower crops
. Field Crops Res. 18 , 185 – 196 .
Simpson , G.G. , Gendall , A.R. , Dean , C. , 1999 . When to switch to fl owering . Annu. Rev. Plant Physiol. Plant Mol. Biol. 15 ,
519 – 550 .
Sinclair , T. , Purcell , L. , Sneller , C.H. , 2004 . Crop transformation and the challenge to increase yield potential . Trends Plant
Sci. 9 ,70 – 75 .
Sinclair , T.R. , 1986 . Water and nitrogen limitations in soybean grain production. I. Model development . Field Crops Res.
15 , 125 – 141 .
Sinclair , T.R. , 1996 . Limits to crop yield? In: K.J. Boote , J.M. Bennett , T.R. Sinclair and G.M. Paulsen (Eds.), Physiology and
Determination of Crop Yield . ASA-CSSA-SSSA , Madison, WI , pp. 509 – 531 .
Sinclair , T.R. , Horie , T. , 1989 . Leaf nitrogen, photosynthesis, and crop radiation use effi ciency: A review . Crop Sci. 29 ,
90 – 98 .
Sinclair , T.R. , Muchow
, R.C. , 1999 . Radiation use effi ciency . Adv. Agron. 65 , 215 – 265 .
Sinclair , T.R. , Muchow , R.C. , 2001 . System analysis of plant traits to increase grain yield on limited water supplies . Agron.
J. 93 , 263 – 270 .
Sinclair , T.R. , Seligman , N.G. , 1996 . Crop modeling: From infancy to maturity . Agron. J. 88 , 698 – 704 .
Sinclair , T.R. , Tanner , C.B. , Bennett , J.M. , 1984 . Water-use effi ciency in crop production . Bioscience 34 , 36 – 40 .
Slafer , G.A. , 1994 . Genetic improvement of fi eld crops . Marcel Dekker , New York .
Soltani , A. , Hammer , G.L. , Torabi
, B. , Robertson , M.J. , Zeinali , E. , 2006 . Modelling chickpea growth and development:
Phenological development . Field Crops Res. 99 ,1 – 13 .
Stöckle , C.O. , Donatelli , M. , Nelson , R. , 2003 . CropSyst, a cropping systems simulation model . Eur. J. Agron. 18 ,
289 – 307 .
Tamaki , S. , Matsuo , S. , Wong , H.L. , Yokoi , S. , Shimamoto , K. , 2007 . Hd3a protein is a mobile fl owering signal in rice .
Science 316 , 1033 – 1036 .
References 265
Tanner , C.B. , Sinclair , T.R. , 1983 . Effi cient water use in crop production: Research or re-search? In: H.M. Taylor , W.R.
Jordan and T.R. Sinclair (Eds.), Limitations to Effi cient Water Use in Crop Production . ASA-CSSA-SSSA , Madison, WI ,
pp. 1 – 27 .
Tardieu , F. , 2003 . Virtual plants: Modelling as a tool for the genomics of tolerance to water defi cit . Trends Plant Sci. 8 ,
9 – 14 .
Tardieu , F. , Granier , C. , Muller , B. , 1999 . Modelling leaf expansion in a fl uctuating environment: Are changes in specifi c
leaf area a consequence of changes in expansion rate? New Phytol. 143 , 33 – 43 .
Thomas , Fukai , S., Hammer , G.L. , 1995 . Growth and yield response of barley and chickpea to water stress under three
environments in southeast Queensland. II. Root growth and soil water extraction pattern . Aust. J. Agric. Res. 46 ,
35 –
48 .
Thornley , J.H.M. , Johnson , I.R. , 2000 . Plant and Crop Modelling . The Blackburn Press , New Jersey .
Tollenaar , M. , Dwyer , L.M. , Stewart , D.W. , 1992 . Ear and kernel formation in maize hybrids representing three decades of
grain yield improvement in Ontario . Crop Sci. 32 , 432 – 438 .
Tuberosa , R. , Salvi , S. , 2006 . Genomics-based approaches to improve drought tolerance of crops . Trends Plant Sci. 11 ,
405 – 412 .
Tuberosa , R., Salvi , S. , Giuliani , S. , Sanguinetti , M.C. , Bellotti , M. , Conti , S. , Landi , P. , 2007 . Genome-wide approaches to
investigate and improve maize response to drought . Crop Sci. 47 , S-120
– S-141 .
Tuberosa , R. , Salvi , S. , Sanguinetti , M.C. , Landi , P. , Maccaferri , M. , Conti , S. , 2002 . Mapping QTLs regulating morpho-
physiological traits and yield: Case studies, shortcomings and perspectives in drought-stressed maize . Ann. Bot. 89 ,
941 – 963 .
van Eeuwijk , F.A. , Malosetti , M. , Yin , X. , Struik , P.C. , Stam , P. , 2005 . Statistical models for genotype by environment data:
From conventional ANOVA models to eco-physiological QTL models . Aust. J. Agric. Res. 56 , 883 –
894 .
van Ittersum , M.K. , Leffelaar , P.A. , van Keulen , H. , Kropff , M.J. , Bastiaans , L. , Goudriaan , J. , 2003 .
On approaches and
applications of the Wageningen crop models . Eur. J. Agron. 18 ,201 – 234 .
van Oosterom , E.J. , Hammer , G.L. , 2008 . Determination of grain number in sorghum . Field Crops Res. 108 , 259 – 268 .
Vega , C.R.C. , Andrade , F.H. , Sadras , V.O. , Uhart , S.A. , Valentinuz , O.R. , 2001 . Seed number as a function of growth.
A comparative study in soybean, sunfl ower, and maize . Crop Sci. 41 , 748 – 754 .
Villalobos , F.J. , Hall , A.J. , Ritchie , J.T. , Orgaz , F. , 1996 . Oilcrop-sun: A development, growth and yield model of the sun-
fl ower crop . Agron. J. 88 ,403 – 415 .
Wang , J. , van Ginkel , M. , Podlich
, D. ,Ye. , G. , Trethowan , R. , Pfeiffer , W. , DeLacy , I.H. , Cooper , M. , Rajaram , S. , 2003 .
Comparison of two breeding strategies by computer simulation . Crop Sci. 43 , 1764 – 1773 .
Wardlaw , I.F. , 1990 . Tansley Review No. 27: The control of carbon partitioning in plants . New Phytol. 116 ,341 – 381 .
White , J.W. , Hoogenboom , G. , 1996 . Simulating effects of genes for physiological traits in a process-oriented crop model .
Agron. J. 88 , 416 – 422 .
White , J.W. , Laing , D.R. , 1989 . Photoperiod response of fl owering in diverse genotypes of common bean ( Phaseolus vul-
garis ) . Field Crops Res. 22 , 113 – 128 .
Wright, S., 1932. The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: Proceedings of the 6th
International Congress of Genetics. Ithaca, New York, pp. 356
–366.
Yin , X. , Stam , P. , Kropff , M.J. , Schapendonk , A.H.C.M. , 2003 . Crop modelling, QTL mapping, and their complementary
role in plant breeding . Agron. J. 95 ,90 – 98 .
Yin , X. , Struik , P.C. , van Eeuwijk , F.A. , Stam, P. , Tang , J. , 2005 . QTL analysis and QTL-based prediction of fl owering phe-
nology in recombinant inbred lines of barley . J. Exp. Bot. 56 , 967 – 976 .
Yuan , J.S. , Galbraith , D.W. , Dai , S.Y. , Griffi n , P. , Sterwart , N. Jr. , 2008 . Plant systems biology comes of age . Trends Plant
Sci. 13 , 165 – 171 .
