Agronomy Journal 95:20-31 (2003)
© 2003 American Society of Agronomy
SYMPOSIUM PAPERS
Crop Modeling and the Identification of Stable Coefficients that May Reflect Significant Groups of Genes
L. A. Hunta,
M. P. Reynoldsb,
K. D. Sayreb,
S. Rajaramb,
J. W. White*,b and
W. Yana
a Dep. of Plant Agriculture, Univ. of Guelph, Guelph, ON, Canada N1G 2W1
b International Maize and Wheat Improvement Centre (CIMMYT), Apt. Postal 6-641, 06600 Mexico, D.F., Mexico
* Corresponding author (j.white{at}cgiar.org)
Received for publication May 1, 2001.
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ABSTRACT
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Knowledge about the functioning of a crop system can be embedded in simulation models of crop growth and development. Such quantitative models have until now made extensive use of physiological knowledge, but modeling could benefit greatly by incorporating genetic information. Equally, because models can help resolve environmentally varying characteristics into stable characteristics that reflect groups of genes, genomics research could benefit from modeling efforts. The use of the model Cropsim to analyze wheat (Triticum aestivum L.) growth and development is demonstrated. Data on reproductive development were well fitted when the life cycle was divided into phases, although photoperiodic sensitivity varied between phases. Describing leaf appearance satisfactorily required introducing an effect of photoperiod. Understanding the need for a breakdown into phases of development, for varying photoperiodic sensitivities, and for photoperiodic control of leaf appearance, could be enhanced by genomic studies. Simulating growth of wheat over successive seasons required changing supposedly stable genotypic characteristics. Furthermore, growth of near inbred lines incorporating the Lr19 chromosome translocation varied with genotypic background. These results also indicate that, given the variation in modeling outputs from year to year, care should be taken in the application of models to long-term problems, and that efforts should be devoted to model improvement. Further development of crop models will benefit from associating genomic analysis with field experiments and model analyses. Much could be gained from increased interaction among model developers, field experimenters, and genomics researchers.
Abbreviations: GCTE, global change and terrestrial ecosystems • PAR, photosynthetically active radiation • QTLs, quantitative trait loci
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INTRODUCTION
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CROP SIMULATION MODELS integrate current understanding of the determinants of crop growth and development in a mathematical framework that allows dynamic simulation of the processes that ultimately lead to yield (e.g., van Keulen and Seligman, 1987; Ritchie, 1991a; Hammer and Muchow, 1991). Many of the models incorporate knowledge derived from physiological studies but, to the present, few if any incorporate knowledge derived from genomic studies. Some, however, make use of coefficients that represent the characteristics of individual cultivars. Such coefficients are intended to summarize different aspects of the genetic make-up of the individual, and so represent in numerical terms either the presence or absence of a group of genes that operate together as an interconnecting network, or the presence or absence of specific genes (White and Hoogenboom, 1996). All coefficients, regardless of whether they represent many or individual genes, have been derived by inference from phenotypic characteristics measured in different environments. Such derivation can be made by using data for the cultivar under consideration directly, or for the cultivar's progenitors, with this latter approach only being effective when the parents have an identical gene make-up for the coefficient under consideration.
Techniques for determining the group coefficients have generally involved iteration (see Hunt et al., 1993). Often, however, the coefficients derived using data from one set of environments are often different from those derived using data from a contrasting set of environments (e.g., different years or sites). Such variation in coefficients has highlighted one of the major challenges of quantitative crop simulation modeling—namely, that any model should be structured such that the coefficients are constants for the genotype under consideration. It is in this arena that genomic knowledge relating to the genes and genetic interactions involved in any particular physiological expression could be of immediate value to quantitative crop modelers. In time, direct measurement of the genetic make-up of any cultivar in question, perhaps through functional analysis of gene expression using DNA-chips (Schena et al., 1995; Lemieux et al., 1998; Ramsey, 1998), may give an immediate measure of one or more of the required coefficients. To reach this stage, however, it will be important that genomics researchers have a clear indication as to which coefficients are stable and so could be usefully correlated with the results emanating from the use of new multiple gene approaches such as DNA-chips. Such correlation work would continue an activity that has formed the backdrop of much of our present understanding of gene function (Coen, 1999).
The most fundamental aspect to an effective simulation of crop performance is development, the passage of the crop through its life-cycle as a function of time. Postembryonic development consists largely of the reiterative production of organ primordia at the shoot apical meristem. In most species, the apical meristem initially gives rise to vegetative organs such as leaves, and in some cases axillary axes, but at some point either the apical or one or more of the axillary axes make a transition to reproductive development and the production of flowers. Within this developmental framework, the vegetative organs grow to different sizes dependent on an array of interactions between genotypes and environment, while subsequent to floral transition, floral organs, and seeds grow to achieve their environmentally dependent final sizes. Obviously, a multitude of genetic factors are involved in development and growth, such that even the identification of all genes involved in these processes is a mammoth task, let alone their representation in comprehensive models. The sequencing of the genomes of several plant species is progressing apace, however, while work to assess gene function, in large part using the model plant Arabidopsis thaliana, has led to the conceptualization of comprehensive gene-based models of the flowering process. In such work, much use has and is being made of mutants and genetic variants, and of comparisons across species, with comparative genomics emerging as a major branch of genomics in general (see Laurie, 1997).
In the development of comprehensive gene-based models of the flowering process (see Levy and Dean, 1998b), however, little use appears to have been made of morphological and physiological knowledge of the whole biological system, nor of modeling approaches that have endeavored to capture such understanding in a quantitative framework. Indeed, Hay and Ellis (1998) noted that in much work exploring the molecular basis of flowering in Arabidopsis, the effect of different mutations has been characterized in terms of the effect on time to opening of the first flower, or the appearance of the first stigma, and has not involved more quantitative measures of development such as the number of leaves initiated by the apex. In this paper, we endeavor to show how quantitative modeling approaches can be used to help summarize and quantify the conceptualized models of the flowering process that have emerged, and that will increasingly emerge from genomic work, and to identify areas that have not been accounted for in existing conceptualizations. We will then apply this approach to growth aspects to highlight some areas where genomic techniques to characterize a genotype at any particular developmental stage could usefully be undertaken. Predominantly, we will draw on information obtained from wheat (Triticum aestivum L.), although we will also make use of insights gained with the model plant, Arabidopsis thaliana. We will start with some general background information on plant development.
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GENERAL MORPHOLOGY OF DEVELOPMENT
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The embryo of the mature cereal caryopsis contains the primordia of the first three or four leaves of the future main stem (Kirby and Appleyard, 1984). Initiation of primordia at the apex resumes at germination, and often two or more leaves will have been initiated by the time that the first true leaf emerges through the coleoptile. After a while, the apex stops initiating leaf primordia and begins to initiate floral primordia, a change that determines the final number of leaves produced by the main-stem. In the field, this number normally varies from 6 to 16 in wheat, but with as few as 5 in some exceptional cultivars that are virtually insensitive to photoperiod and have little or no vernalization requirement (e.g., a selection from cv. Sunset, Slafer and Rawson, 1995a; and the Yunan landrace Dianxiyangmai, Miao et al., 1992). The change to the initiation of floral primordia appears to be loosely associated with a change in the rate of primordia initiation (Kirby and Appleyard, 1984; Hay and Kirby, 1991; Fig. 1), but the point of inflection does not always coincide with the initiation of the first reproductive primordium (Delécolle et al., 1989) nor with the morphological stage termed double ridge, which is widely used as a sign of the switch from vegetative to reproductive development at the stem apex. Indeed, the double ridges can appear when as few as 50% or as many as 80% of the final spikelet number are presented (Delécolle et al., 1989). Such a difference indicates variation (genetic and environmental) in the control of development subsequent to double ridges.
The interval between the appearance (emergence) of successive leaves of a stem (the phyllochron) is around twice the interval between the appearance of leaf primordia at the apex (the plastochron), depending upon cultivar, location, and sowing date (Frank and Bauer, 1995). It generally remains constant for a while subsequent to early establishment but may change around the time of floral initiation (e.g., Hay and Delécolle, 1989) or during the appearance of the last few leaves (e.g., Hotsonyame and Hunt, 1997; Slafer and Rawson, 1997). Such alterations in phyllochron may reflect the coordination of phyllochron and plastochron, since leaf initiation is thought to be controlled predominantly by temperature, whereas the rate of spikelet initiation is also influenced by photoperiod. The extension of stem internodes, and the resulting appearance of the spike, is also thought to be closely coordinated with leaf appearance (Hay and Kirby, 1991). Recently, however, Sylvester-Bradley et al. (1998) reported that the stem extension stage is not a good indicator of leaf emergence stage.
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GENERAL PHYSIOLOGY AND GENOMICS OF DEVELOPMENT
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The change in the fate of primordia initiated at the apical meristem is controlled by environmental and endogenous factors (Bernier, 1988; McDaniel et al., 1992). However, because some species must reach a certain age or size before they can flower, the vegetative meristem is thought to first pass through a juvenile phase in which it is incompetent to respond to internal or external signals that would trigger flowering in an adult meristem (Levy and Dean, 1998a). The acquisition of reproductive competence is sometimes marked by changes in the morphology or physiology of vegetative structures in a process known as vegetative phase change (Poethig, 1990; Lawson and Poethig, 1995).
In some species, the timing of flowering is primarily influenced by environmental factors that serve to communicate the time of year and/or growth conditions favorable for sexual reproduction and seed maturation. These factors include photoperiod (i.e., daylength), light quality (spectral composition), light quantity (photon flux density), vernalization (exposure to a long period of cold), and nutrient and water availability. Other species are less sensitive to environmental variables and appear to flower in response to internal cues such as plant size or number of vegetative nodes.
Over the years, physiological and more recently, genomic studies have led to three models for the control of flowering time (reviewed in Bernier, 1988; Thomas and Vince-Prue, 1997). Of these, the most widely accepted at the moment appears to be the multifactorial control model, in which a number of promoters and inhibitors, including phytohormones and assimilates, are assumed to control the developmental transition. According to this model, flowering can only occur when the limiting factors are present at the apex in the appropriate concentrations and at the right times. This model attempts to account for the diversity of flowering responses by proposing that different factors could be limiting for flowering in different genetic backgrounds and/or under particular environmental conditions.
Genetic analysis of flowering time in cereals and Arabidopsis supports the hypothesis that the transition to flowering is under multifactorial control (reviewed in Snape et al., 1996; Koornneef et al., 1998). Indeed, multiple genes that control flowering time have been identified in all of these species. At least 80 loci that affect flowering time in Arabidopsis (Levy and Dean, 1998b), and >20 loci in cereals (Miura and Worland, 1994) have been characterized, far more than the widely known major genes for insensitivity to vernalization (VrnA1, VrnB1, and VrnD1 on the long arms of 5A, 5B, and 5D, respectively; and Vrn5, short arm 7B) and for insensitivity to photoperiod (PpdD1, PpdB1, and PpdA1 on the short arms of 2D, 2B, and 2A), respectively, in wheat (Worland et al., 1987; Laurie et al., 1994; Worland, 1996; Laurie, 1997; Law and Worland, 1997). Moreover, some of these genes act to promote flowering and others to repress it; some interact with environmental variables, and others appear to act autonomously. Further, based on work with Arabidopsis (see Levy and Dean, 1998b), some are involved with switching the fate of the meristem from vegetative to floral (floral meristem identity genes), others with directing the formation of the various flower parts (organ identity genes). Genes that control flowering time can thus be expected to interact with floral meristem identity genes.
For Arabidopsis, Martinez-Zapater et al. (1994) organized the various flowering time responses into a model known as the MCDK model. The model relied upon the existence of one or more floral repressors whose effect could be reversed in several ways, resulting in the initiation of flowering. Reversal stimuli include exposure to long days, which was assumed to lead to the action of a suite of genes, and low-temperature vernalization, which stimulates the expression of a gene whose effect could possibly be transmitted via control of the level of growth substances. In this scheme, short-day repression of flowering occurred through the action of an array of genes on the signaling function of growth substances. In addition to these environmentally modulated effects, the model allowed for flowering without induction by a constitutive pathway, including both promotion and repression, and involving many genes that presumably encompass those termed earliness per se in some cereal work (Laurie, 1997; Slafer and Rawson, 1995b).
Levy and Dean (1998b) presented a somewhat similar model with four pathways (shown in simplified form in Fig. 2). Two of these pathways appear to monitor the endogenous developmental state of the plant. One of these, a floral repression pathway(s), may be a built-in mechanism that prevents flowering until the plant has reached a certain age or size, whereas a second, autonomous promotion pathway is believed to increasingly antagonize this repression as the plant develops. The other pathways mediate signals from the environment: short and long day promotion pathways that are responsible for floral induction in response to inductive photoperiods, and a vernalization promotion pathway that allows for accelerated development after the plant has experienced a period of cold temperature.
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Fig. 2. Simplified schematic of genetic pathways that control flowering in Arabidopsis. The horizontal line represents the vegetative (V) to floral (F) transition, with the promotive and repressive pathways exerting their influence on the rate of progress along this pathway. Promotive and repressive interactions are represented with arrow or T-bars, respectively. Simplified and modified from Levy and Dean (1998a).
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In all of these models, the photoperiodic promotion pathway presumably involves one or more photoreceptors, which initiate signals that interact with a circadian clock. Somehow, daylength is measured, and when the length of the dark period increases, genes that promote flowering are activated. This activation leads, in turn, to the upregulation of floral meristem identity genes and, thereafter, flowering. In many cases, however, the response is quantitative so that the upregulation is more complex than would be the case for a qualitative response in which a critical photoperiod could be identified. Light quality may also be involved because red light generally inhibits and far red light promotes flowering (e.g., in Arabidopsis; Martinez-Zapater et al., 1994).
The vernalization promotion pathway involves exposure to a period of cold temperature (typically 2 to 8 wk at approximately 4°C, but see Yan and Hunt, 1999b). The process is slow and quantitative but requires active metabolism (reviewed in Chouard, 1960; Vince-Prue, 1975). The site of perception of vernalization is the shoot apex (e.g., Curtis and Chang, 1930; Metzger, 1988), but all actively dividing cells, not only those at the shoot apex, may be capable of responding to vernalization (Wellensiek, 1964). Unlike photoperiod induction, vernalization prepares the plant to flower but does not itself evoke flowering. There is often a temporal separation between the time at which vernalization is complete and reproductive initiation, which commonly occurs after a period of growth at warmer temperatures. Vernalization is required in each generation for winter annuals and biennials and each growth year for perennials, which suggests that meiosis or some other aspect of reproductive growth resets the requirement for vernalization (Levy and Dean, 1998b).
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QUANTITATIVE MODELING OF DEVELOPMENT
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Given the mass of information available on both the sequence of events during reproductive development, and the physiologic-genetic structure underlying these events, it is clear that any quantitative model should take account both of the different phases passed through during ontogeny, and the conceptual models developed on the basis of classical physiological and molecular genetic work. Many crop models divide the life cycle up into a number of phases (e.g., Ceres wheat; Ritchie, 1991b), but often it is difficult to relate some of these phases to discrete events during the life cycle and to developmental scales used by agronomists (e.g., the Zadoks scale; Tottman and Broad, 1987). The sequence of phases used in the Cropsim model (Hunt and Pararajasingham, 1995) can be related, however, to the scales used by agronomists (Table 1).
Within such a phasic development framework, the essence of the developmental model presented by Levy and Dean (1998b) can be captured in a manner similar to that used in a number of current crop models (e.g., Ritchie, 1991b), with coefficients for the following aspects representing suites of genes involved in the overall process: Phase durations
Temperature response pattern for developmental rate
Vernalization requirement
Temperature response pattern for vernalization
Photoperiod sensitivity for each phase
Photoperiod threshold for each phase
In such a framework, the coefficients, which represent groups of genes rather than individual components, may have promoter or repressor activity. The phase durations, which reflect the impact of temperature, however, cannot be considered separately from the relationship between development rate and temperature. For this aspect, in previous quantitative modeling work, development rate was often assumed to be directly proportional to temperature in the range from a base temperature to some maximum. Such a linear relationship between temperature and development permitted the use of the concept of thermal time, the accumulation of daily temperature above a specified base temperature. In many cases, however, the use of a nonlinear relationship that allows for reduced activity at temperatures near the base and for a smooth transition to the optimum is preferable, both for development per se and vernalization (Yan and Hunt, 1999a, 1999b). For photoperiod sensitivity, a nonlinear response has sometimes been used (Ritchie, 1991b), but work with varieties with no vernalization requirement has shown a linear response to photoperiod (Fig. 3). A linear response to photoperiod would thus appear to capture the essence both of conceptual physiological and genetic models and the responses recorded in experimental work.
As with photoperiod, the effect of accumulated vernalization needs to be quantitatively linked to development rate. Genomic information would suggest that the relationship between accumulated vernalization and rate of development should perhaps be linear, as often assumed in modeling work (see Ritchie, 1991b). Experimental studies (e.g., Davidson et al., 1985; Jedel et al., 1986), however, show that there is often an initial lag period (Fig. 4) that must be accounted for in both conceptual and quantitative modeling efforts. A further coefficient that deals with the nature of such a lag-linear response must thus be introduced in quantitative modeling efforts. Additional coefficients may be necessary to deal with development under drought (see Saini and Westgate, 2000), but these aspects are not considered here.
Additional to all of the aspects considered above, the question of phase independence should also be taken into account (Jamieson et al., 1998). This may be particularly relevant when considering the phase of leaf production after full commitment to reproductive development. Here, phase duration could be dependent on the number of leaf primordia accumulated at the apex before reproductive commitment.
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MODELING ANALYSIS OF DEVELOPMENT IN WHEAT
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Although a conceptual model may encompass much of what is known about a process such as crop development, the reality of the model must be evaluated by determining whether it can effectively summarize recorded performance. In this section, therefore, a simulation model (Cropsim, Version 2000; Hunt and Pararajasingham, 1995), which incorporates the essence of the developmental model derived from molecular work, but with the modifications discussed in the previous section, will be used to determine whether the set of coefficients defined for the model can account for crop development in a number of experiments in which the same cultivar was studied. As discussed before, these coefficients represent the concerted action of a group of genes acting together and thus reflect not only the main effects of the major genes involved, but also the minor and modifying effects of other genes in the genome (i.e., the genetic background in which the major genes operate). In essence, the coefficients summarize the genome rather than individual genes. The trial chosen has been documented in the literature (Hay, 1986; Hay and Delécolle, 1989), as well as an earlier version of the Gencalc analytic software (Hunt et al., 1993). Briefly, the trial was a field study of planting date (from 9 September to 29 April) effects at Auchincrive (55.5°N) in southwestern Scotland during the 1982–1983 season. The number of mainstem leaves was recorded at regular intervals (normally 1–2 wk), and the developmental stage was determined until anthesis, following the procedure of Kirby and Appleyard (1984). The model was run many times with different combinations of values for the various coefficients that are used to characterize each genotype, and the set with the smallest error was selected. All coefficients that may affect development were studied in the analysis, but only those that had a noticeable effect are reported.
For phenological data, information from all planting dates was well fitted (Fig. 5) by the basic model in which early development is divided into a number of phases (germination to double ridges, double ridges to terminal spikelet, terminal spikelet to last leaf fully expanded, and last leaf fully expanded to spike emergence), with different photoperiod sensitivities in each phase. It could be argued that such a result should not be surprising, given that the best result was selected from amongst the outputs of multiple runs with different input coefficients. However, although the procedure allows for the selection of a best fit, it does not ensure that the error of this best fit is acceptable. The error can thus be taken as an indication that the algorithms of the model either constitute, or do not constitute, an effective summarization of the system. More significantly, however, it could be argued that the differing photoperiod sensitivities between phases merely reflected carryover effects from one phase to another (see Jamieson et al., 1998). Before the photoperiod sensitivity changes can be accepted as real and not artifacts of analysis, therefore, further examination dealing with this aspect will be necessary.
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Fig. 5. Measured and simulated time of occurrence of various developmental stages for ‘Hustler’ winter wheat in the planting data study of Hay (1986). Simulations were made using the Cropsim model, 2000 version.
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Development should also be reflected in leaf numbers, but here the data (Hay and Delécolle, 1989) for the earlier planting dates could not be well-fitted by the basic model. The data were well fitted, however, once a function in which leaf appearance was related to photoperiods below a threshold of 14 h was introduced (Fig. 6). Slafer and Rawson (1997) reported no effect of photoperiod on phyllochron in wheat, but it is likely that cultivars differ in this response. Indeed, Sinclair et al. (2001) reported that extending the photoperiod in winter in Florida resulted in greater leaf growth in a number of tropical grasses, and commented that some recent cultivars had less sensitivity to photoperiod than older cultivars.
The coefficients necessary to achieve a reasonable fit to all data are shown in Table 2. These data highlight the different apparent photoperiod sensitivities in succeeding developmental phases. Although further analysis accounting for carryover effects will be necessary to confirm the reality of these changes, the findings do conform with results of genomic work in indicating that different sets of genes are involved with switching the fate of the meristem from vegetative to floral, and in directing the formation of flower parts. Further, the analysis highlights the fact that one or more factors additional to temperature are implicated in the control of leaf appearance and perhaps also apical activity during the winter period when daylengths are short. Earlier experimental and modeling analyses have also shown that the rate of leaf appearance is under the control of factors other than temperature (see McMaster, 1997), but physiological work to date has not unraveled the underlying factors. Further understanding could benefit from genomic analysis in which the degree of expression of different arrays of genes is studied concurrently in plants growing in environments that generate different leaf appearance–temperature relationships.
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Table 2. Coefficients summarizing the development of ‘Maris Hustler’ winter wheat in the planting date study of Hay (1986). Summarizations were made using the Cropsim model, 2000 version.
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MODELING ANALYSIS OF GROWTH IN WHEAT
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In contrast to reproductive development, genomic knowledge does not appear to have been wrapped together in a cohesive model of growth and yield. Work with quantitative trait loci (QTLs) related to yield, however, has shown that QTL expression often depends on the genetic background in which the QTL is found (Stuber et al., 1999), suggesting that a comprehensive model would be highly desirable. Because of this lack of genomic information, the development of quantitative crop simulation models has relied on knowledge derived from physiological studies. Here, one crop simulation model (Cropsim; Hunt and Pararajasingham, 1995), Version 2000, is used to illustrate how modeling can highlight areas where genomic work might concentrate. Three simulation analyses will be reported. Each deals with the growth of irrigated wheat crops that were well supplied with N so that water and N stresses should not have been factors in determining yield.
The first set of trials deal with wheat in Arizona (see Kimball et al., 1999 for a recent analysis of some data from these trials and for other references). For these trials, growth aspects such as aboveground dry weights, leaf areas, and grain numbers could not be well fitted using the same coefficients for crops grown in each of four different seasons. To achieve reasonable fits, changes had to be made to the coefficients for overall radiation use efficiency, for leaf area expansion, and for grain set (Table 3). When such changes were made, reasonable fits to the data were (Fig. 7 and 8).
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Table 3. Coefficients necessary to achieve reasonable fits to field data for irrigated ‘Yecora’ spring wheat supplied with at least 250 kg/ha of N in four separate growing seasons in Arizona.
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Fig. 7. Measured and simulated leaf area indices for irrigated ‘Yecora’ spring wheat supplied with at least 250 kg/ha of N in Arizona. Data from Pinter, Kimball et al. (GCTE datasets). Simulations were made using the Cropsim model, version 2000.
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Fig. 8. Measured and simulated above ground dry matter for irrigated ‘Yecora’ spring wheat supplied with at least 250 kg/ha of nitrogen in Arizona. Data from Pinter, Kimball et al. (GCTE datasets). Simulations were made using the Cropsim model, version 2000.
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Similar changes to the same coefficients as above were necessary to achieve reasonable fits between simulated and measured data for the same cultivar in field trials run over a 6-yr period at the CIMMYT location in Obregon, Mexico (Sayre et al., 1997). In these trials, the radiation use efficiency coefficient varied between 1.9 and 2.5 g/MJ PAR and the grain number coefficient between 18 and 25 grains/g (Table 4).
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Table 4. Coefficients necessary to achieve reasonable fits to field data for irrigated ‘Yecora’ spring wheat supplied with >250 kg/ha of N in six separate growing seasons in Northern Mexico.
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The third set of data, also obtained from a trial at the CIMMYT location in Obregon, Mexico in the 1998–1999 season (M.P. Reynolds, unpublished data), in which a number of standard cultivars were analyzed along with near isogenic lines (NILs) that contained the Lr19 gene for leaf rust resistance from an interchromosomal translocation involving Agropyron elongation (Singh et al., 1998). In a number of studies, these NILs have shown improved productivity compared with the cultivars from which they were derived. In the study used here, the Lr19 lines differed in a number of characteristics from their progenitors, with the differences being dependent on the original cultivar. In particular, the apparent radiation use efficiency (apparent because radiation interception was calculated from simulated leaf area data) was generally less for the Lr19 lines than for the standards before anthesis, and greater afterward, but with some notable exceptions (Table 5). Similarly, the grain number coefficient was generally greater for the Lr19 lines, but with one exception, and with the positive effect of the gene or chromosome segment appearing to differ between lines.
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Table 5. Coefficients necessary to achieve reasonable fits to field data for irrigated spring wheat supplied with at least 250 kg/ha of N in a trial at Obregon, Mexico during the 1998–1999 growing season.
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These data show that at least three of the coefficients that are extremely important for yield can vary considerably among years and cultivars. This variation could reflect the impact of many factors, included among which could be plant population, disease, pest (e.g., aphids), soil conditions (e.g., micro-nutrients, salt, structure as affected by previous management), and irrigation timing and precision. Further, the data also show that the effect of a particular gene conditioning response to one or more of such environmental challenges cannot be considered without reference to the genetic background in which it is placed. Such a conclusion is not surprising because similar effects have been known for many years by plant breeders and pathologists. For example, the Sr2 gene for stem rust resistance in wheat is known to cause a discoloration of parts of the chaff, a condition known as pseudo black chaff, but with the amount of discoloration being highly dependent on the cultivar, and with some (e.g., Pavon, from the CIMMYT program) having only a small area discolored (R.P. Singh, personal communication, 2000). There is also an environmental influence on the expression of the condition. Further, the 1RS 1BL translocation, which is generally thought to increase yield in wheat (Braun et al., 1998; Villareal et al., 1998), appears to have no effect, or even a negative effect in certain genetic backgrounds (R.P. Singh, personal communication, 2000). Even where a gene is known to affect a particular trait, therefore, its presence/absence should only be used as a coefficient in quantitative models when coupled with one or more additional coefficients that account for other genes and genetic networks that affect the trait in question. Efforts must thus be made to associate phenotypic traits with groups of genes whose effect is stable over genotypes and environments.
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PERSPECTIVES
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Rapid progress is being made in elucidating certain aspects of the molecular control of floral transition, particularly in the model species Arabidopsis (Levy and Dean, 1998b). As the genes controlling flowering time in Arabidopsis become better defined, the question as to how they correspond to genes that regulate flowering time in species of economic importance will come to the fore, and efforts on comparative mapping will likely be enhanced. Indeed, genes identified in Arabidopsis that control aspects of pathways regulating flowering may be used to identify similar genes in cereals including wheat. The analyses reported here, however, show that there are significant gaps in the knowledge of certain aspects of the development of wheat (e.g., differences in response to environmental signals in different phases; environmental controls of leaf appearance). Molecular work around these aspects, and in particular around changes in sensitivity to environmental factors through the life cycle of the crop, and in the nature of the response to environmental factors and internal changes, should thus be undertaken vigorously. Molecular techniques now make it possible to follow gene expression in different tissues and at different times (e.g., Sheldon et al., 1999), which completely provides new avenues for exploring changes in response to environmental signals over time. The application of such techniques should be given as high a priority as comparative mapping of aspects that may form only part of the overall picture in economic species such as wheat.
In using the results of such efforts in modeling, the grouping of genes into packages that can be characterized in terms of discrete coefficients would appear to hold more immediate promise than endeavoring to model directly from an array of individual genes to field performance. Such a task that would not only involve the bridging of many levels of biological organization, but also require computers of greater capability than are available currently (White and Hoogenboom, 2003). Grouping may also make it easier to develop approaches that could be used to determine coefficients directly using DNA-chips and other approaches used to characterize genomes. As such work progresses, there will be need for ever closer interaction between quantitative modelers and genomic scientists. Such interaction will be necessary to ensure not only that the knowledge built-up from genome based analysis encompasses all aspects of significance to performance in the field environment, but also that genome based knowledge and conceptual models can be linked in a quantitative manner to field performance.
Less progress than with flowering appears to have been made in elucidating the molecular control of growth processes and yielding ability. Further, analyses such as reported here show that physiological understanding, much less genomic, of yielding ability in any specific environment still has large knowledge gaps. The fact that reasonable simulations of yield in different years could only be made when the overall radiation use, leaf expansion, and grain number coefficients were changed indicates that factors that are not currently taken into account in some modeling efforts are operative in field situations. The fact that unaccounted factors are operative in field situations can also be deduced from data dealing with the sequence of grain yields over years for crops grown under irrigation in areas where the radiation and temperature environment varies little over years, and where obvious yield reducing aspects (e.g., disease, lodging) are not present. Such a sequence (K.D. Sayre, unpublished data, 1999) is shown in Fig. 9 for wheat in the Yaqui Valley in Mexico. These data show that yield varied far more among years than could be accounted for by minor changes in overall radiation receipt and temperature. Similarly, the presence of currently unaccounted for factors can be inferred from data obtained from careful studies involving the same cultivar at different sites and over years. On the basis of one such study with wheat in the UK, Sylvester-Bradley et al. (1998) wrote in their concluding remarks that "The uncertain understanding of growth exemplified by this discussion indicates the degree of difficulty that there is in anticipating grain yield. It cannot be considered realistic at the present state of understanding, to predict yield with any certainty, before the grain has mostly filled."
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Fig. 9. Average bread wheat and durum wheat yields in on-farm trials conducted in the Yaqui Valley of Sonora, Mexico. Data from K.D. Sayre (unpublished data, 1999).
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The nature of these unaccounted for factors is a matter of speculation. Tollenaar and Wu (1999) have emphasized that response to unknown stresses is important in determining productivity. The need for different coefficients in future modeling efforts may thus have its basis in one or more responses to unknown stresses and challenges, atmospheric, edaphic, and biotic, that the crops have to face as they progress through their life cycle. Further, the fact that the apparent radiation use efficiency is much lower than values that should be achievable relatively easily (Reynolds et al., 2000) suggests that response to stresses may be restricting productivity even in the best years, and that there is considerable potential for yield improvement if such stresses could be overcome either managementally or genetically. There are managemental opportunities for yield improvement (e.g., Hobbs et al., 1998). There are also genetic opportunities stemming, for example, from increased knowledge of the impact of nematodes and other root pathogens, and from the discovery and mobilization of sources of resistance to such problems (Nicol et al., 2000). Further opportunities are likely to be discovered if the genetic controls associated with reduced radiation use efficiency, leaf expansion, and grain set can be identified and subsequently engineered. Progress in this arena would benefit from joint research involving field experimenters, crop modelers, and genomic researchers, with the crop modelers providing an analysis of the field data that could be used as a touchstone against which information from genomics research could be associated. Some initial steps in this direction have already been taken (e.g., Yin et al., 1999, 2000), but much more effort to associate data from field research with that from molecular work needs to be made.
The analysis of some of the effects of the Lr19 gene/chromosome segment complements results from genomic investigations of flowering and work relating QTLs to yield. It emphasizes that interactions within the genome make it essential that whole-genome knowledge and approaches be used whenever studying the role of specific genes (see Bouchez and Hofte, 1998). With whole genome approaches, the focus shifts from the individual genetic components to their place in plant systems, to the study of a large number of genes in parallel, and to the study and conceptualization of networks of control. Genomic approaches thus correspond to the approaches adopted by most plant breeders and many pathologists, who have long argued that individual genes must always be considered in the context of their genetic background, and to those modelers who have been concerned with the characterization of individual genotypes in terms of summary coefficients. Knowledge of the presence or absence of specific alleles may help in the characterization of specific genotypes, as argued by White and Hoogenboom (2003), but until the complete network of control is elucidated, summarization of the network effects will also be essential. Crop modeling can play an essential role in analyzing field data to give quantitative expression to these background effects and to provide a yardstick against which genomic information on the whole group of background genes can be judged. The capability of crop modeling to give a quantitative summary of the effect of groups of genes whose expression is environmentally invariant, and to identify groups of genes important to performance, should thus ensure that quantitative crop modeling will become a tool used directly in genomics research in the years to come. Equally, the conceptualizations that stem from genomics should help guide the improvement of quantitative models, as now appears possible with reproductive development, until ultimately whole networks of genes and their interactions can be determined at the genomic level and used directly in comprehensive models.
Such work will inevitably be time and resource consuming. Because it still appears to be difficult, at least with wheat, to define model coefficients that are stable over different environments, some of the time and resources necessary to address outstanding problems could well be obtained by directing efforts away from the many black box applications (e.g., long-term climate change effects, and long-term economic analyses) of models, to model improvement and enhancement, and to closer interaction with agronomists and genomics researchers. This suggestion should not be construed as a general criticism of such model application work, but rather as a plea for more balance in research, and for application only within the known performance limits of a given crop model. It is to be hoped that the challenges and opportunities stemming from recent advances in genomics will help in this regard.
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ACKNOWLEDGMENTS
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The authors thank Dr. R.K.M. Hay of the Scottish Agriculture Services Agency and Dr. B.A. Kimball and Dr. P.J. Pinter of the U.S. Water Conservation Laboratory for their willingness to supply some of the weather and crop data used in these analyses. The authors also thank the above along with many others too numerous to mention individually for spending time to discuss issues covered in this paper.
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