Crop Modeling, QTL Mapping, and their Complementary Role in
Plant Breeding
(Draft paper to be presented in the Symposium on Crop Modeling and Genetics, and to be subsequently
reviewed for publication in Agronomy Journal)
Abbreviations: AFLP, amplification fragment length polymorphism; DS, development stage;
G×E, genotype-by-environment interaction; h2, heritability; MAB, marker-assisted breeding; QTL,
quantitative trait locus; QTL×E, QTL-by-environment interaction; RFLP, restriction fragment length
polymorphism; RIL, recombinant inbred line; SLA, specific leaf area.
ABSTRACT
Crop modelers and geneticists have been independently thinking of their role in plant breeding
from their own perspective. However, to improve breeding efficiency, interdisciplinary collaborations
become increasingly important. The objective of this paper is to explore a collaborative role of
modelers and geneticists in ideotype breeding for high productivity. The advance in the genetic
approach of using molecular marker to map quantitative trait loci (QTLs) is described. The uses and
limitations of QTL mapping and crop modeling to assist breeding are outlined. Progress of a recent
research of using QTL information in crop modeling is summarized. Since QTL analysis can remove
part of random errors of measured model-input parameters, QTL information can successfully be
coupled to crop model to replace measured parameters. QTL-based modeling overcomes the limitations
in ideotyping of using models that ignore the genetics of their input traits. On the other hand, crop
modeling can potentially be a powerful tool to resolve genotype-by-environment interactions and
dissect yield into characters that might be under simpler genetic control. Based on the complementary
aspects of crop modeling and QTL mapping, we proposed an integral approach to supporting ideotype
breeding. To enable this approach to be effective, there is a need to develop models capable of
predicting yield differences among genotypes of a population under various environmental conditions.
Breeding for high-yielding cultivars for specific environments is a major
challenge to achieve world food security in the new century. Through extensive
selection, largely on an empirical basis of field observations, breeders have been
successful in creating high-yield cultivars of main food crops. In many instances,
progresses have been attained from changes in relatively few genes, e.g. those
involved in plant height and photoperiodism. However, further improvement has been
1
increasingly difficult (Bindraban 1997). Difficulties of manipulating yield are related
to its genetic complexity: polygenic nature, interactions between genes (epistasis), and
environment-dependent expression of genes (Ribaut and Hoisington 1998).
Plant physiology has developed as a powerful discipline, but only in a limited
number of instances has it led to crop improvement. The role of physiology has rather
been to provide possible explanation for the improvements that have been achieved by
breeders. Miflin (2000) has indicated that this situation is likely to change in the
future if the links between physiology and genetics of the processes described are
established. Through a joint inter-disciplinary venture, it is possible to develop new
knowledge and tools for more efficient crop improvement (Shorter et al. 1991).
An important advance in crop physiology during the last three decades is the
development of dynamic process-based crop growth models for predicting yields
under different environments (Loomis et al. 1979; Whisler et al. 1986; Boote et al.
1996). These models represent causality between processes and consider interactions
among processes and responses of these processes to environmental variables, and can
give predictions that are not restricted to the same environments where the model
parameters are estimated. The potential of applying these models to plant breeding is
high (Jackson et al. 1996), e.g. the explanation of yield differences of genotype on the
basis of individual physiological characteristics and the use of this knowledge for
evaluating plant ideotypes (e.g. Kropff et al. 1995). To be effective to assist breeding,
however, crop modeling requires understanding of the genetics of the factors that
determine variation of crop yield (Shorter et al. 1991; Stam 1998).
An exciting development during the last decade in quantitative genetics was the
ability to identify genome regions responsible for variation of a specific trait, due to
the advent of molecular markers (Paterson et al. 1988). The acronym QTLs, which
2
stands for Quantitative Trait Loci, has come to refer to polygenes for quantitative
trait. Numerous studies have been reported on identification of QTLs for various traits
in humans, animals and plants. Individual input parameters of a crop growth model, as
a special type of quantitative traits, are amenable to QTL analysis (Yin et al. 1999b).
In this paper, we discuss uses and limitations of crop modeling and QTL analysis
in assisting plant breeding. The complementary aspects of crop modeling and QTL
analysis are explored to develop an integrated approach for ideotype breeding.
Crop modeling as a tool to assist plant breeding
Almost all crop models are defined in the way that they require two types of
inputs: environmental inputs (i.e. weather variables and management actions) and
physiological inputs. The latter are used in individual processes as parameters for
characterizing genotypic differences. These parameters are also referred to as ‘genetic
coefficients’ (Hunt et al. 1993; White and Hoogenboom 1996) or model-input traits
(Yin et al. 2000b). Given the expectation that model-input parameters are under
genetic control, crop modeling has been considered to be a useful tool to assist
breeding (Loomis et al. 1979; Whisler et al. 1986; Boote et al. 1996). There have been
studies to explore the use of models in various aspects of breeding:
— To identify major yield-determining traits (Bindraban 1997; Yin et al. 2000a).
— To define optimum selection environment (Aggarwal et al. 1997a).
— To optimize single trait value (Boote and Tollenaar 1994; Yin et al. 1997).
— To design ideotypes consisting of multiple traits (Penning de Vries 1991;
Dingkuhn et al. 1993; Kropff et al. 1995; Haverkort and Kooman 1997).
— To assist multi-location testing (Dua et al. 1990) and explain genotype ×
environment interactions (G×E).
3
Irrespective of which application, all these studies were using results of
simulations. The endpoint of these studies appears to be suggestions for possible
methods that breeders may use. Direct experimental confirmations and objective
comparisons of modeled suggestions with approaches already used in breeding
programs are rare. Stam (1998), from a geneticist’s and breeder’s point of view,
expressed his concerns about this modeling approach. First, a practical problem of
breeding is that the majority of the traits that are to be assessed with this modeling
approach are hard to measure with the required accuracy. Second, the genetics of the
model-input traits is largely behind screen. For example, in designing an ideotype by
modeling, it is assumed, either tacitly or explicitly, that these traits can be combined
at will in a singe genotype. Such an assumption completely ignores the possible
existence of constraints and correlations among the traits. Constraints might be
imposed simply by the fact the little genetic variation exists in the genetic material
available to selection. Models may not identify those traits that could be changed for
which gains via breeding may be easiest (Jackson et al. 1996). Correlations between
the modeled traits, due either to a tight linkage between QTLs or to pleiotropy of a
single QTL underlying the traits, may seriously hamper the realization of an ideotype.
The need to consider the genetics of model-input traits was also recognized by
modelers themselves (Aggarwal et al. 1997b; White and Hoogenboom 1996).
Given the predefined narrow focus and use of existing cultivars often with limited
genotypic range in most physiological or modeling studies, Jackson et al. (1996)
pointed out the need to work with relevant populations and the close integration of
these studies with an active breeding program. After all, plant breeding is genetic
improvement; knowledge of the genetic basis of phenotypic variation, whether
described in terms of conventional agronomic traits or physiological model-input
4
traits, is crucial to successful breeding (Stam 1998). To assist to develop more
efficient breeding strategies, crop modeling requires understanding of the genetic
basis of the factors that determine variation in crop growth (Shorter et al. 1991).
White and Hoogenboom (1996) presented a model for bean (Phaseolus vulgaris
L.), in which they applied linear regression to estimate values for more than 20
model-input traits from allelic information of seven known genes. This approach
assumed that all the traits were controlled by pleiotropic effects of the seven genes,
ignoring possible additional trait-specific genes. The advance during the last decade in
quantitative genetics for mapping trait-specific QTLs can help in this respect.
QTL mapping and its applications
In genetics, relative distance of genes on the genome is mapped on the basis of the
frequency of recombination between genes estimated from scoring genotypes of
progeny of a cross (Kearsy and Pooni 1996). Mapping quantitative traits is difficult
because the genotype is never unambiguously determined from the phenotype.
Classical quantitative genetics pursues a different approach, using general terms such
as means, variances, heritabilities (h2), built on assumptions, e.g. that effects of
individual genes on a trait are small and accumulative. These assumptions shed little
light on the individual genes themselves (Prioul et al. 1997).
To map quantitative traits, supplementary information from recognizable singlegene marker loci is required. The first attempts to link a quantitative trait to a major
gene locus in plants date back to Sax (1923), who studied seed weight and color in an
F2 of a cross in bean. Seed color involved the segregation of a single gene, P/p. Seed
weight differed among the three color genotypes (Fig. 1). Either the P/p locus had a
pleiotropic effect on weight or there was a QTL (or QTLs) closely linked to P/p.
5
Major gene mutants, however, are few and may not exist in a population under
study. Because QTLs may occur throughout the genome, a large number of markers
are required to locate them. Early studies of quantitative traits suffered from the lack
of major-gene markers that could make a complete map. This was overcome with the
realization that maps could be constructed by using pieces of chromosomal DNA as
markers (Botstein et al. 1980). The first such molecular markers were fragments
produced by restriction enzyme digestion, designated RFLPs. RFLPs are naturally
occurring, abundant in most species, and simply inherited Mendelian characters.
Unlike morphological markers, RFLPs are not true genes because a gene codes for
something whereas RFLP does not since it is possibly the resultant of single base
change in a non-coding region1. There are a growing number of alternative markers
(e.g. AFLPs), based on small differences in base sequence; information about them
now becomes widely available (e.g. Staub and Serquen 1996; Jones et al. 1997).
Up until the mid-1980s, most of the mapped genes were mutant genes with clearcut phenotypic effects; thus mapping gradually progressed by looking at progeny
from crosses between the carrier of the new gene with genotypes carrying previously
mapped gene(s) (e.g. Woodward 1957). With the advent of DNA markers, we are in
the position of analyzing a large number of recognizable loci segregating
simultaneously in the same cross. To handle the large number of loci, a variety of
software has been developed which establishes the overall map that gives the best fit
to the combined data. Fig. 2 gives such a map of AFLP markers on chromosome 3 for
a barley (Hordeum vulgare L.) population, made by the use of the JoinMap software
(Stam 1993). Needless to say, information about the genome position of mutant loci is
important for building a molecular marker map, because previously mapped mutant
1
About 10% of the genome is actually coding, much of the rest being spacer DNA, though the amount
of spacer DNA varys substantially between species.
6
loci (e.g. the denso locus in Fig. 2) can be used as ‘anchor’ markers that assign new
markers to different linkage groups. A growing number of plant genome databases
now become accessible through the Web sites (e.g. http://probe.nalusda.gov/).
Once a complete marker linkage map is constructed, it can be used to localize
QTLs for a quantitative trait, as first demonstrated by Paterson et al. (1988). The basis
of all QTL detection is the statistical analysis of association between markers and
phenotypic trait values (see Fig. 3). Statistical technique for using a complete marker
map to detect QTLs has reached a fairly high level of sophistication (e.g. Lander and
Botstein, 1989; Jansen 1995), and has not yet come to a stand still (Kearsey and
Farquhar 1998). The number of literature reports on QTL analysis is growing rapidly.
Almost all QTL studies, regardless of the crop or trait to which they are applied, have
come to support a main result of the first study (Paterson et al. 1988) that even for
highly complex traits, a small number of QTLs explained a large part of the genetic
variability. This challenges the classical quantitative genetics, which assumes the
effects of many genes with small and similar actions.
Two complementary uses of the QTL approach have emerged: the fundamental
and the applied (Prioul et al. 1997). The first one, which is of interest for
physiologists, targets QTLs by determining their contribution to physiological
components of macroscopic traits. Not only does the QTL approach provide
unequivocal answers to a range of physiological questions, it also generate new
insight into a causality between components that would have been difficult to obtain
by conventional physiological approaches (e.g. Simko et al. 1997). The importance of
the QTL approach is shown by the special issue of New Phytologist (1997), 137(1),
which was entirely devoted to proselytizing physiologists to take a genetic approach.
7
The second use of the QTL studies, which is of interest for breeders, is markerassisted breeding (MAB). This is to use markers for tagging QTLs of interest so as to
pyramid favorable QTL alleles and break their linkage with undesirable alleles (Lee
1995; Ordon et al. 1998; Ribaut and Hoisington 1998). An apparent use of MAB is
the marker-steered introgression with valuable single genes from exotic donors to
enhance elite breeding material (Stam 1998), which allows faster recovery of the
recipient-parent genome than the conventional recurrent backcrossing (Ribaut and
Hoisington 1998). As alien species or land-races are rich in resistance genes and
resistances are simply inherited relative to yield traits, the application of markers for
tagging of resistance genes in major crops has progressed rapidly (Ordon et al. 1998).
A major challenge for MAB is to deal with traits controlled by multiple interactive
and environment-dependent QTLs, such as yield and yield-relating traits that often
have low h2. While simulation studies (e.g. Van Berloo and Stam 1998) have showed
that MAB can be superior to the conventional phenotype-based approach for traits of
low h2, no experiment has clearly demonstrated the superiority (Ribaut and
Hoisington 1998). Manipulating these traits is difficult because of their intrinsic
complexities: polygenic control, epistasis and G×E. Existing QTL-detection methods
seem not to have a sufficient precision to deal with these complexities. With traits like
yield of low h2, many QTLs may be segregating, and the QTL locations may have
wide confidence intervals. The most likely location of a useful QTL may appear to be
between a pair of markers, but it could actually be as far as 20 cM away (Kearsey and
Farquhar 1998)2. While recent multiple-QTL methods (e.g. Jansen 1995) can reduce
QTL-location confidence intervals (Fig. 4A) and resolve two or more linked QTLs,
2
One cM (centiMorgan) corresponds to 1% recombination per meiosis, and is equivalent to 299 kilobase pairs (kbp) in arabidopsis, and 6214 kbp in wheat; a typical structural gene, coding for a
polypeptide chain, is between 1 and 2 kbp long (Kearsey and Pooni, 1996). In this sense, a QTL
8
the efficacy of these methods closely depends on whether markers are evenly
distributed in the map. In principle, epistasis of QTLs can be included within the
frame of these multiple-QTL methods. However, the rapid increase in the number of
parameters, difficulties to decide which interactions to include, and the computational
burden force us to assume the absence of epistasis. New methods have been
developed to evaluate QTL-by-environment interactions (QTL×E) using multipleenvironment data (e.g. Jiang and Zeng 1995); but the information obtained cannot be
applied to predict phenotypes in independent environments (Stratton 1998).
Combining crop modeling and QTL mapping
The first study to link crop modeling and QTL mapping was conducted recently
for barley (Yin et al. 1999a,b; Yin et al. 2000b), using the SYP-BL crop model (Yin et
al. 2000a). Main model-input traits include pre-flowering duration, post-flowering
duration, specific leaf area (SLA), leaf nitrogen concentration, fraction of biomass
partitioned to leaves, and that partitioned to spikes. The QTL approach was applied to
these traits, using a population consisting of 94 recombinant inbred lines (RILs) from
a cross of two-row spring barley cultivars, Apex and Prisma (Yin et al. 1999b). AFLP
marker linkage map was established for this population (see Fig. 2 for the case of
chromosome 3). By analyzing the association between trait phenotypes and marker
genotypes of the 94 RILs, QTLs were found for each of the above model-input traits.
Most traits were associated, though to different extents, with the denso dwarfing gene
with the dwarfing allele from Prisma. This gene was mapped as a morphological
marker on the long arm of chromosome 3 (Fig. 2). The importance of this gene on a
number of traits, based on QTL analysis, is highlighted in Fig. 3. The result with the
detected by any approach is not a true gene, but only the indicated genome region that most likely
contains gene(s) responsible for the variation of the trait under study.
9
RIL population that the major QTL for so many different traits mapped at the same
position as the denso gene is in support of the pleiotropy of this gene (Yin et al.
1999b). This provides direct evidence for the genetic background and the
interdependence of various model-input parameters, which has received little
consideration from modelers (Aggarwal et al. 1997b; Stam 1998). However, as noted
later, the information obtained cannot be applied to other crosses.
Physiological aspects of traits were considered in QTL analysis, using SLA as the
example (Yin et al. 1999a). The SLA was measured six times: one conducted at the
same development stage (DS) for all RILs (at flowering), four at specific days prior to
flowering, and the last one at 14 days after flowering. When SLA of each
measurement time was directly analyzed, one to three QTLs were detected. The denso
gene was found to affect SLA strongly at all measurement times, e.g. 27 days after
emergence (Fig. 4A), except at flowering. If SLA of the different RILs was corrected
for differences in physiological age at the time of measurement, using the phenology
sub-model in SYP-BL, QTLs were detected for SLA at only three stages. Moreover,
the effect of the denso gene was no longer significant during the pre-flowering stages,
e.g. at the DS 0.35 (Fig. 4B). The effect of the denso gene detected in the first
instance was therefore the consequence of its direct effect on the pre-flowering
duration that can be seen in Fig. 3. This demonstrates the role of crop models in
considering physiology of traits, which has so far been received little attention from
geneticists. Advances in using DNA markers to map QTLs have led to suggestions of
using genetic approaches in plant physiology (e.g. Prioul et al. 1997). Our research
suggests that the reverse be true and that potential uses of physiology and modeling
should be explored, especially given that any great move in reliability of QTLdetection methods can hardly be achieved in future (Kearsey and Farquhar 1998).
10
Next, the identified QTLs were coupled to the SYP-BL model by replacing the
original measured input trait values with those predicted from the QTL effects (Yin et
al. 2000b). This generated a QTL-based model for barley, QTL-BL. Yields predicted
by both models correlated with the observed values, despite substantial unexplained
variation (Fig. 5). The QTL-BL model predicted yield differences slightly better than
the SYP-BL model. Similar results were obtained when the models were applied to a
season independent from the one at which the original input traits used for QTL
analysis were measured (results not shown). The slightly better performance of QTLBL could be due to less random noise in the QTL-based values. Random error in
measured model-input traits, relative to other plant traits, can be large because
measurements involve several steps and are based on a small plant sample in a plot.
Part of the error was removed statistically in QTL analysis, giving an advantage of the
QTL-BL model that uses smoothened input values, especially of those traits that were
not important for yield determination (Yin et al. 2000a). However, this advantage is
obtained at the cost of ignoring some genetic effects because the QTLs detected for a
trait often do not fully explain its genetic variation. Nonetheless, the correlation
between the two sets of yield prediction was high (r > 0.88), indicating that QTL
information can successfully replace measured parameters (Yin et al. 2000b).
Expectations and future perspective
Obviously, there remains substantial yield variation that was not explained by the
existing model (Fig. 5). For a model to be an effective tool in breeding, it must
accurately simulate the difference in performance among relatively similar lines in a
population (McLaren 1995). Current models have to be improved in this context, in
considerations of both input traits and feedback structure. The random errors in input
11
traits of current models are largely caused by field samplings. The need for
destructive samplings to determine input parameters is a major limitation in using
them in breeding, because of not only the required amount of work but also very
limited available material (Aggarwal et al. 1997b). A difficulty in using existing
models to explain genotypic yield differences is that their input parameters may vary
with environment (Yin et al. 2000a). This has to be overcome to enable the models to
extrapolate G×E, the expected advantage of process-based models over any databased genetic models (Shorter et al. 1991; Hunt et al. 1993).
If models are capable of predicting G×E, they can assist QTL analysis to resolve
QTL×E, a major problem that hampers the use of MAB in yield breeding (Lee 1995;
Ribaut and Hoisington 1998). The QTL×E is commonly obtained when growing a
mapping population under a range of environments. An example for this is flowering
time in Arabidopsis, examined under various day-length and vernalization regimes
(Jansen 1995). It turned out that day-length and/or vernalization influence the effect
of some QTLs, indicating QTL×E in a statistical sense. However, this information on
interaction cannot be applied to new environments (Stratton 1998). From a
physiologists’ point of view, the impact of environments has to be minimized to
identify the true genetic effect. Phenology models separate different aspects of
flowering responses to photothermal environments (Atkinson and Porter 1996).
Parameters in a physiologically robust phenology model are genetically determined
and are not altered by environment, but predict flowering date of genotypes in a wide
range of environments (Roberts et al. 1996). It is therefore expected that the QTLs
and their effects, detected for model parameters, will not be environment-dependent.
Being a potentially powerful tool to resolve G×E, crop modeling could be
integrated into the framework of MAB for an improved breeding approach (Fig. 6).
12
Within this integral approach, crop model is evaluated to be capable of predicting
performance of genotypes under diverse environments. Mapping is performed to
dissect variation of input traits of the model into individual QTLs, which, in turn, will
be coupled to the model. Once the physiological and genetic bases of yield responses
to environments are adequately quantified, ideotypes can be proposed for a specific
environment (Atkinson and Porter 1996), in terms of the constitution of the QTLs for
yield-determining model-input traits. This overcomes the limitations in designing
ideotypes of using models that ignore any genetic constraints and correlations among
the traits. Information obtained can be applied to any environment because of the high
ability of extrapolation of crop modeling. With this integral approach, a classical
difficulty in genetics, epistasis for which existing QTL approaches do not seem to
have the required power (Stam 1998), may be addressed, which is indicated in Fig. 6.
This is because epistasis is often found for phenotypes that are achieved through
interactive and interrelated metabolic and ontogenetic pathways (Lee 1995). Epistasis
might be reduced or even disappear if input traits of a model that accounts for
interrelations among relevant processes are analyzed. Such possibility agrees with the
awareness of geneticists that epistasis can often be removed by a physiologically
based scaling of trait values (Kearsey and Pooni 1996).
This integral approach, however, cannot solve all limiting factors in using MAB,
especially non-transferability of information obtained from one cross to another. The
non-transferability can be largely due to the possibility that a QTL detected in one
cross does simply not segregate in a second cross because the parents of the second
cross carry identical alleles at that QTL. A gene ‘important’ for physiologist or
modeler may be useless for geneticist or breeder because if the gene is physiologically
crucial, its variation over generations of breeding will have been strongly counter-
13
selected (Prioul et al. 1997); so no QTL will be detected at this gene locus. Another
point that should be underlined is that geneticists usually score a few traits on many
genotypes (often > 100) of a segregating population and modelers do the opposite.
This means that implementation of our integral approach needs large experiments,
assessing many traits in many genotypes. Therefore, the physiological model should
be developed such that its input parameters can be quickly determined or through the
way by which tissue can be harvested and frozen for later analysis.
Using regression analysis, Virk et al. (1996) has shown that variation of many
agronomic traits in rice (Oryza sativa L.) germplasm is associated with allelic
variation of markers, indicating that marker-trait association present not only in
segregating populations but also across a crop germplasm collection. If this turns out
to be general, QTL-based modeling may be applicable to a germplasm collection, for
which important markers identified by, for example, multiple regression, are used as
the surrogate of QTLs. Since the chance that a specific marker maps to different
genome positions in different populations within a species is low (e.g. Waugh et al.
1997), we could use markers identified from a germplasm collection to infer the
position of QTLs controlling the trait. This is especially true when the integrated map
of using across-population markers is increasingly becoming available for different
species (e.g. Haanstra et al. 1999). The applicability of marker information across
germplasm collection would allow the genetically-based crop modeling to be
performed without recourse to the use of a mapping population.
CONCLUSIONS
Crop modeling and quantitative genetics are independently evolved disciplines.
Crop models are now increasingly being used to assist plant breeding, in particular, to
14
define crop ideotypes for different environments. The development in quantitative
genetics of using molecular markers to identify QTLs provides a new perspective for
determining the value of crop model input parameters. On the other hand, crop
models can potentially assist QTL mapping in various ways, especially in
extrapolating information to a new environment and in dissecting yield into simple
physiological components that are more likely related directly to gene expression. The
exploration of the complementary aspects of modeling and mapping would allow the
biological meaning of model-input parameters to be more explicit. An integral
approach was thereof proposed to support ideotype breeding. Development of crop
models, which need little destructive sampling to estimate their input parameters and
can be sufficiently accurate to model G×E of a genetic population, is the future
challenge to enable this approach to be positively used in a breeding program.
15
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Figure legends
Fig. 1. Seed-color genotypes and seed weight in an F2 of a cross between two lines
of bean (data of Sax 1923).
Fig. 2. AFLP markers ordered for chromosome 3 of the genetic map, established
by the use of JoinMap (Stam 1993), for Apex × Prisma RIL population of barley
(redrawn from Yin et al. 1999b). The map is oriented with the short arm of the
chromosome at the top. Markers are labeled E45M55-408, E44M58-196, etc. Marker
positions are counted in genetic map units (cM) from the terminal marker on the
short-arm. The position of the dwarfing gene, denso, is highlighted.
Fig. 3. The QTL mapping of six traits in barley (data of the 1997 field experiment
reported by Yin et al. 1999b). By moving the position of the putative QTLs along the
genetic map (horizontal axis), a profile of QTL likelihood (expressed in LOD) was
produced for each chromosome and results are given here for chromosome 3. The
interval mapping method described by Lander and Botstein (1989) was used. The
peak of the LOD profile indicates the most likely position of a QTL affecting the trait
under study. Results indicate a major QTL at 126.4 cM on chromosome 3 (note that,
this is also the position of the denso gene as shown in Fig. 2).
Fig. 4. Plot of QTL likelihood (LOD) over chromosome 3 for SLA measured at 27
days after emergence (DAE), and for SLA corrected at the same DS of 0.35, roughly
equivalent to the time of 27 DAE (redrawn from Yin et al. 1999a). The horizontal line
at a height of 2.5 indicates the threshold for the presence of a QTL. The thin curve is
from the use of the interval mapping method (Lander and Botstein 1989) and thick
one is from the use of the multiple-QTL mapping method (Jansen 1995).
Fig. 5. Comparisons between observed grain yields (with moisture content of
14%) in the 1997 experiment and those predicted by the two models, QTL-BL and
SYP-BL (redrawn from Yin et al. 2000b). The distinction of two clusters in yields
predicted by QTL-BL matches the segregation of the denso gene, which affected most
model-input traits.
Fig. 6. Proposed framework of combining physiological modeling and genetic
mapping for an integral approach to assist ideotype breeding.
19