Adapting APSIM to model the physiology and genetics of complex adaptive traits in field crops.

Progress in molecular plant breeding is limited by the ability to predict plant phenotype based on its genotype, especially for complex adaptive traits. Suitably constructed crop growth and development models have the potential to bridge this predictability gap. A generic cereal crop growth and development model is outlined here. It is designed to exhibit reliable predictive skill at the crop level while also introducing sufficient physiological rigour for complex phenotypic responses to become emergent properties of the model dynamics. The approach quantifies capture and use of radiation, water, and nitrogen within a framework that predicts the realized growth of major organs based on their potential and whether the supply of carbohydrate and nitrogen can satisfy that potential. The model builds on existing approaches within the APSIM software platform. Experiments on diverse genotypes of sorghum that underpin the development and testing of the adapted crop model are detailed. Genotypes differing in height were found to differ in biomass partitioning among organs and a tall hybrid had significantly increased radiation use efficiency: a novel finding in sorghum. Introducing these genetic effects associated with plant height into the model generated emergent simulated phenotypic differences in green leaf area retention during grain filling via effects associated with nitrogen dynamics. The relevance to plant breeding of this capability in complex trait dissection and simulation is discussed.

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title: Gene-to-phenotype models and complex trait genetics
abstract: The premise that is explored in this paper is that in some cases, in order to make progress in the design of molecular breeding strategies for complex traits, we will need a theoretical framework for quantitative genetics that is grounded in the concept of gene-networks. We seek to develop a gene-to-phenotype (G→P) modelling framework for quantitative genetics that explicitly deals with the context-dependent gene effects that are attributed to genes functioning within networks, i.e. epistasis, gene × environment interactions, and pleiotropy. The E(NK) model is discussed as a starting point for building such a theoretical framework for complex trait genetics. Applying this framework to a combination of theoretical and empirical G→P models, we find that although many of the context-dependent effects of genetic variation on phenotypic variation can reduce the rate of genetic progress from breeding, it is possible to design molecular breeding strategies for complex traits that on average will outperform phenotypic selection. However, to realise these potential advantages, empirical G→P models of the traits will need to take into consideration the context-dependent effects that are a consequence of epistasis, gene × environment interactions, and pleiotropy. Some promising G→P modelling directions are discussed.

title: Scale and Complexity in Plant Systems Research : Gene-Plant-Crop Relations
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title: Virtual plants: modelling as a tool for the genomics of tolerance to water deficit.
abstract: Modelling can simulate the responses of virtual plants carrying diverse combinations of alleles under different scenarios of abiotic stress. The main difficulty is mathematically expressing the genetic variability of responses to environmental conditions. Modelling via gene regulatory networks is not feasible for such complex systems, but plants can be modelled using response curves to environmental conditions that are 'meta mechanisms' at plant level. Each genotype is represented by a set of response parameters that are valid under a wide range of conditions. Transgenesis of one function experimentally affected one response parameter only. Transgenic plants or plants carrying any combination of quantitative trait loci might therefore be simulated and tested under different climatic scenarios, before genetic manipulations are performed.

title: Role of crop physiology in predicting gene-to-phenotype relationships.
abstract: Robust crop physiological modelling could become an essential tool in explaining crop behaviour using insights from functional genomics. Current crop models can predict crop performance over a range of environmental conditions. Recently, quantitative trait loci (QTL) information has been incorporated into crop models, which has shown the potential for narrowing genotype–phenotype gaps and for applying QTL-based models to the analysis of genotype-by-environment interactions. For further progress, the model structure must be upgraded to allow more physiological feedback features to be incorporated. Model input parameters should be designed to be grounded potentially in gene-level understanding. Integration of crop modelling into genetic and genomic research should enhance the future position of crop physiology in ‘plant breeding by design'.

title: Models for navigating biological complexity in breeding improved crop plants.
abstract: Progress in breeding higher-yielding crop plants would be greatly accelerated if the phenotypic consequences of making changes to the genetic makeup of an organism could be reliably predicted. Developing a predictive capacity that scales from genotype to phenotype is impeded by biological complexities associated with genetic controls, environmental effects and interactions among plant growth and development processes. Plant modelling can help navigate a path through this complexity. Here we profile modelling approaches for complex traits at gene network, organ and whole plant levels. Each provides a means to link phenotypic consequence to changes in genomic regions via stable associations with model coefficients. A unifying feature of the models is the relatively coarse level of granularity they use to capture system dynamics. Much of the fine detail is not directly required. Robust coarse-grained models might be the tool needed to integrate phenotypic and molecular approaches to plant breeding.

title: Modelling Crop Improvement in a G×E×M Framework via Gene–Trait–Phenotype Relationships
abstract: This chapter introduces fundamental concepts of modeling natural systems using a G×E×M framework and discusses the prospects for an integrated approach for improving crop performance that tackles the G×E×M interactions holistically. It outlines general principles of modeling biophysical systems, including a description of fundamental components of crop models. It describes G×E×M systems and introduces gene-to-phenotype (GP) models and concepts of adaptation landscapes as applied to plant breeding. The chapter discusses the application of the framework by studying genetic improvement of maize in the US Corn Belt. It reviews and summarizes theoretical developments toward a framework that integrates quantitative genetics, breeding simulation, and modeling 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.

title: Trait physiology and crop modelling as a framework to link phenotypic complexity to underlying genetic systems
abstract: New tools derived from advances in molecular biology have not been widely adopted in plant breeding for complex traits because of the inability to connect information at gene level to the phenotype in a manner that is useful for selection. In this study, we explored whether physiological dissection and integrative modelling of complex traits could link phenotype complexity to underlying genetic systems in a way that enhanced the power of molecular breeding strategies. A crop and breeding system simulation study on sorghum, which involved variation in 4 key adaptive traits-phenology, osmotic adjustment, transpiration efficiency, stay-green-and a broad range of production environments in north-eastern Australia, was used. The full matrix of simulated phenotypes, which consisted of 547 location-season combinations and 4235 genotypic expression states, was analysed for genetic and environmental effects. The analysis was conducted in stages assuming gradually increased understanding of gene-to-phenotype relationships, which would arise from physiological dissection and modelling. It was found that environmental characterisation and physiological knowledge helped to explain and unravel gene and environment context dependencies in the data. Based on the analyses of gene effects, a range of marker-assisted selection breeding strategies was simulated. It was shown that the inclusion of knowledge resulting from trait physiology and modelling generated an enhanced rate of yield advance over cycles of selection. This occurred because the knowledge associated with component trait physiology and extrapolation to the target population of environments by modelling removed confounding effects associated with environment and gene context dependencies for the markers used. Developing and implementing this gene-to-phenotype capability in crop improvement requires enhanced attention to phenotyping, ecophysiological modelling, and validation studies to test the stability of candidate genetic regions.

title: Short-term responses of leaf growth rate to water deficit scale up to whole-plant and crop levels: an integrated modelling approach in maize.
abstract: Physiological and genetic studies of leaf growth often focus on short-term responses, leaving a gap to whole-plant models that predict biomass accumulation, transpiration and yield at crop scale. To bridge this gap, we developed a model that combines an existing model of leaf 6 expansion in response to short-term environmental variations with a model coordinating the development of all leaves of a plant. The latter was based on: (1) rates of leaf initiation, appearance and end of elongation measured in field experiments; and (2) the hypothesis of an independence of the growth between leaves. The resulting whole-plant leaf model was integrated into the generic crop model APSIM which provided dynamic feedback of environmental conditions to the leaf model and allowed simulation of crop growth at canopy level. The model was tested in 12 field situations with contrasting temperature, evaporative demand and soil water status. In observed and simulated data, high evaporative demand reduced leaf area at the whole-plant level, and short water deficits affected only leaves developing during the stress, either visible or still hidden in the whorl. The model adequately simulated whole-plant profiles of leaf area with a single set of parameters that applied to the same hybrid in all experiments. It was also suitable to predict biomass accumulation and yield of a similar hybrid grown in different conditions. This model extends to field conditions existing knowledge of the environmental controls of leaf elongation, and can be used to simulate how their genetic controls flow through to yield.

title: Applying modelling experiences from the past to shape crop systems biology: the need to converge crop physiology and functional genomics.
abstract: Functional genomics has been driven greatly by emerging experimental technologies. Its development as a scientific discipline will be enhanced by systems biology, which generates novel, quantitative hypotheses via modelling. However, in order to better assist crop improvement, the impact of developing functional genomics needs to be assessed at the crop level, given a projected diminishing effect of genetic alteration on phenotypes from the molecule to crop levels. This review illustrates a recently proposed research field, crop systems biology, which is located at the crossroads of crop physiology and functional genomics, and intends to promote communications between the two. Past experiences with modelling whole-crop physiology indicate that the layered structure of biological systems should be taken into account. Moreover, modelling not only plays a role in data synthesis and quantitative prediction, but certainly also in heuristics and system design. These roles of modelling can be applied to crop systems biology to enhance its contribution to our understanding of complex crop phenotypes and subsequently to crop improvement. The success of crop systems biology needs commitments from scientists along the entire knowledge chain of plant biology, from molecule or gene to crop and agro-ecosystem.

title: The GP problem: Quantifying gene-to-phenotype relationships
abstract: In this paper we refer to the gene-to-phenotype modeling challenge as the GP problem. Integrating information across levels of organization within a genotype-environment system is a major challenge in computational biology. However, resolving the GP problem is a fundamental requirement if we are to understand and predict phenotypes given knowledge of the genome and model dynamic properties of biological systems. Organisms are consequences of this integration, and it is a major property of biological systems that underlies the responses we observe. We discuss the E(NK) model as a framework for investigation of the GP problem and the prediction of system properties at different levels of organization. We apply this quantitative framework to an investigation of the processes involved in genetic improvement of plants for agriculture. In our analysis, N genes determine the genetic variation for a set of traits that are responsible for plant adaptation to E environment-types within a target population of environments. The N genes can interact in epistatic NK gene-networks through the way that they influence plant growth and development processes within a dynamic crop growth model. We use a sorghum crop growth model, available within the APSIM agricultural production systems simulation model, to integrate the gene-environment interactions that occur during growth and development and to predict genotype-to-phenotype relationships for a given E(NK) model. Directional selection is then applied to the population of genotypes, based on their predicted phenotypes, to simulate the dynamic aspects of genetic improvement by a plant-breeding program. The outcomes of the simulated breeding are evaluated across cycles of selection in terms of the changes in allele frequencies for the N genes and the genotypic and phenotypic values of the populations of genotypes.

title: Integrated physiological and agronomic modelling of N capture and use within the plant.
abstract: Today farmers have several constraints to take into account in managing their crops: (i) competitiveness: productivity must be maintained or increased whereas inputs must be decreased, (ii) the environmental consequences of cultural practices: pesticide and fertilizer use must be decreased, and (iii) product quality must be improved and nitrogen nutrition is an important factor in harvest quality. These new constraints sometimes conflict: maximum yield is often obtained with large amounts of N, increasing the risks of N leaching. The determination of rates and dates for nitrogen application must become more precise in this context. Tools are required for the forecasting of crop requirements, the diagnosis of N deficiencies during the crop cycle and breeding of new adapted varieties. Models and diagnosis indicators have been developed to meet these needs, but those relating to nitrogen are often based on empirical relationships. Moreover, the available models and indicators often fail to account for cultivar-specific responses. The improvement of agronomic tools and the breeding of new varieties adapted to new cropping systems should be based on a thorough understanding of the key metabolic processes involved, and the relative contributions of these processes to yield determination in conditions of fluctuating N supply. For both purposes, more information is required about plant and crop N economy. In this paper, the way in which N absorption and use within the plant and crop, plant responses to deficiencies and excesses of nitrogen are taken into account in major agronomic models is described first. The level of sophistication of the modules comprising these models depends on operational objectives. Secondly, the ways in which the most recent molecular plant physiology findings can, and indeed should, be integrated into models at the crop and crop cycle levels are described. The potential value of this approach for improving current agronomic models and diagnostic tools, and for breeding more efficient varieties is also discussed.

title: Modelling protein content and composition in relation to crop nitrogen dynamics for wheat
abstract: Protein concentration and composition are key components of the end-use value for wheat (Triticum aestivum L.) grain. Although the qualitative composition of the grain is genetically determined, the quantitative composition is significantly modified by growing conditions, and there are important management × genotype × environment interactions. We recently reported a model of grain N accumulation and partitioning for wheat grain. The main assumptions made in this model are: (1) the accumulation of structural/metabolic proteins (albumins-globulins and amphiphils) is sink-driven and is a function of temperature; (2) the accumulation of storage proteins (gliadins and glutenins) is supply limited; (3) on the one hand the allocation of structural/metabolic proteins between albumin-globulin and amphiphilic protein fractions and on the other hand the allocation of storage protein between gliadin and glutenin fractions during grain growth is constant.  The main modifications to Sirius99 concerned the post-anthesis N uptake and remobilisation. After anthesis, the potential rate of crop N uptake was assumed to decrease linearly with accumulated thermal time, and the actual rate of N uptake was limited by the capacity of the stem to store accumulated N. During grain filling the daily rate of N transfer to grain was calculated daily according to the current crop N-status. The coupled model (SiriusQuality1) simulated dynamics of total grain N and of the different grain protein fractions reasonably well. At maturity, measured total grain N ranged from 0.56 to 1.32 mg N grain−1, and the observed and simulated total grain N were well correlated (r2 = 0.82, slope = 1.08) with a mean error of prediction of 0.11 mg N grain−1. The simulated kinetics of crop N accumulation and stem N were closer to the observations with SiriusQuality1 than with Sirius99, in particular during the reproductive stage. At maturity, simulated and observed quantities of albumins-globulins were poorly correlated (r2 = 0.02). Over the 18 experimental cases studied here, the quantity of storage proteins varied more than three-fold, and the observed and simulated quantities of gliadins and glutenins were well correlated (r2 = 0.79 and 0.72, respectively). The simulations of total N and storage proteins accumulation provided by SiriusQuality1 confirmed that accumulation of grain N is overall source- rather than sink-regulated, at least under non-luxury N conditions. SiriusQuality1 provides a simple mechanistic framework that explains environmental effects on grain protein concentration and composition. The next step is to incorporate genetically related model parameters that will portray genotypic differences in protein concentration and composition.

title: A process-based model to simulate nitrogen distribution in wheat (Triticum aestivum) during grain-filling.
abstract: Nitrogen (N) distribution among plant organs plays a major role in crop production and, in general, plant fitness to the environment. In the present study, a process-based model simulating N distribution within a wheat (Triticum aestivum L.) culm during grain filling was developed using a functional-structural approach. A model of turnover of the photosynthetic apparatus was used to describe the fluxes between a common pool of mobile N and each leaf lamina. Grain N accumulation within a time-step was modelled as the minimum between the quantity calculated by a potential function and the N available in the common pool. Nitrogen dynamics in the other organs (i.e. stem, chaff, root N uptake and remobilisation) were accounted for by forced variables. Using a unique set of six parameters, the model was able to simulate the observed N kinetics of each lamina and of the grains under a wide range of crop N supplies and for three cultivars. The time-course of the vertical gradient of lamina N during grain filling was realistically simulated as an emerging property of the local processes defined at the lamina scale. The model described in the present study offers new insight into the interactions between N metabolism, plant architecture and productivity.

title: Infusing the use of seasonal climate forecasting into crop management practice in North East Australia using discussion support software
abstract: Seasonal climate forecasting offers potential for improving management of crop production risks in the cropping systems of NE Australia. But how is this capability best connected to management practice? Over the past decade, we have pursued participative systems approaches involving simulation-aided discussion with advisers and decision-makers. This has led to the development of discussion support software as a key vehicle for facilitating infusion of forecasting capability into practice. In this paper, we set out the basis of our approach, its implementation and preliminary evaluation. We outline the development of the discussion support software Whopper Cropper, which was designed for, and in close consultation with, public and private advisers. Whopper Cropper consists of a database of simulation output and a graphical user interface to generate analyses of risks associated with crop management options. The charts produced provide conversation pieces for advisers to use with their farmer clients in relation to the significant decisions they face. An example application, detail of the software development process and an initial survey of user needs are presented. We suggest that discussion support software is about moving beyond traditional notions of supply-driven decision support systems. Discussion support software is largely demand-driven and can compliment participatory action research programs by providing cost-effective general delivery of simulation-aided discussions about relevant management actions. The critical role of farm management advisers and dialogue among key players is highlighted. We argue that the

title: Simulating the Yield Impacts of Organ-Level Quantitative Trait Loci Associated With Drought Response in Maize: A “Gene-to-Phenotype” Modeling Approach
abstract: Under drought, substantial genotype–environment (G × E) interactions impede breeding progress for yield. Identifying genetic controls associated with yield response is confounded by poor genetic correlations across testing environments. Part of this problem is related to our inability to account for the interplay of genetic controls, physiological traits, and environmental conditions throughout the crop cycle. We propose a modeling approach to bridge this “gene-to-phenotype” gap. For maize under drought, we simulated the impact of quantitative trait loci (QTL) controlling two key processes (leaf and silk elongation) that influence crop growth, water use, and grain yield. Substantial G × E interaction for yield was simulated for hypothetical recombinant inbred lines (RILs) across different seasonal patterns of drought. QTL that accelerated leaf elongation caused an increase in crop leaf area and yield in well-watered or preflowering water deficit conditions, but a reduction in yield under terminal stresses (as such “leafy” genotypes prematurely exhausted the water supply). The QTL impact on yield was substantially enhanced by including pleiotropic effects of these QTL on silk elongation and on consequent grain set. The simulations obtained illustrated the difficulty of interpreting the genetic control of yield for genotypes influenced only by the additive effects of QTL associated with leaf and silk growth. The results highlight the potential of integrative simulation modeling for gene-to-phenotype prediction and for exploiting G × E interactions for complex traits such as drought tolerance.

title: QTL analysis and QTL-based prediction of flowering phenology in recombinant inbred lines of barley.
abstract: Combining ecophysiological modelling and genetic mapping has increasingly received attention from researchers who wish to predict complex plant or crop traits under diverse environmental conditions. The potential for using this combined approach to predict flowering time of individual genotypes in a recombinant inbred line (RIL) population of spring barley (Hordeum vulgare L.) was examined. An ecophysiological phenology model predicts preflowering duration as affected by temperature and photoperiod, based on the following four input traits: f(o) (the minimum number of days to flowering at the optimum temperature and photoperiod), theta1 and theta2 (the development stages for the start and the end of the photoperiod-sensitive phase, respectively), and delta (the photoperiod sensitivity). The model-input trait values were obtained from a photoperiod-controlled greenhouse experiment. Assuming additivity of QTL effects, a multiple QTL model was fitted for the model-input traits using composite interval mapping. Four to seven QTL were identified for each trait. Each trait had at least one QTL specific to that trait alone. Other QTL were shared by two or all traits. Values of the model-input traits predicted for the RILs from the QTL model were fed back into the ecophysiological model. This QTL-based ecophysiological model was subsequently used to predict preflowering duration (d) for eight field trial environments. The model accounted for 72% of the observed variation among 94 RILs and 94% of the variation among the two parents across the eight environments, when observations in different environments were pooled. However, due to the low percentage (34-41%) of phenotypic variation accounted for by the identified QTL for three model-input traits (theta1, theta2 and delta), the QTL-based model accounted for somewhat less variation among the RILs than the model using original phenotypic input trait values. Nevertheless, days to flowering as predicted from the QTL-based ecophysiological model were highly correlated with days to flowering as predicted from QTL-models per environment for days to flowering per se. The ecophysiological phenology model was thus capable of extrapolating (QTL) information from one environment to another.

title: A Gene‐Based Model to Simulate Soybean Development and Yield Responses to Environment
abstract: Realizing the potential of agricultural genomics into practical applications requires quantitative predictions for complex traits and different genotypes and environmental conditions. The objective of this study was to develop and test a procedure for quantitative prediction of phenotypes as a function of environment and specific genetic loci in soybean [Glycine max (L.) Merrill]. We combined the ecophysiological model CROPGRO-Soybean with linear models that predict cultivar-specific parameters as functions of E loci. The procedure involved three steps: (i) a field experiment was conducted in Florida in 2001 to obtain phenotypic data for a set of near-isogenic lines (NILs) with known genotypes at six E loci; (ii) we used these data to estimate cultivar-specific parameters for CROPGRO-Soybean, minimizing root mean square error (RMSE) between observed and simulated values; (iii) these parameters were then expressed as linear functions of the (known) E loci. CROPGRO-Soybean predicted various phenological stages for the same NILs grown in 2002 in Florida with a RMSE of about 5 d using the E loci-derived parameters. A second evaluation of the approach used phenotypic data from cultivar trials conducted in Illinois. Cultivars were genotyped at the E loci using microsatellites. The model predicted time to maturity in the Illinois variety trials with RMSE around 7.5 d; it also explained 75% of the time-to-maturity variance and 54% of the yield variance. Our results suggest that gene-based approaches can effectively use agricultural genomics data for cultivar performance prediction. This technology may have multiple uses in plant breeding.

title: Crop model based QTL analysis across environments and QTL based estimation of time to floral induction and flowering in Brassica oleracea
abstract: Studying quantitative traits is complicated due to genotype by environment interactions. One strategy to overcome these difficulties is to combine quantitative trait loci (QTL) and ecophysiological models, e.g. by identifying QTLs for the response curves of adaptive traits to influential environmental factors. A B. oleracea DH-population segregating for time to flowering was cultivated at different temperature regimes. Composite interval mapping was carried out on the three parameters of a model describing time to flowering as a function of temperature, i.e. on the intercept and slope of the response of time to floral induction to temperature and on the duration from transition to flowering. The additive effects of QTLs detected for the parameters have been used to estimate time to floral induction and flowering in the B. oleracea DH-population. The combined QTL and crop model explained 66% of the phenotypic variation for time to floral induction and 56% of the phenotypic variation for time to flowering. Estimation of time to floral induction and flowering based on environment specific QTLs explained 61 and 41% of the phenotypic variation. Results suggest that flowering time can be predicted effectively by coupling QTL and crop models and that using crop modelling tools for QTL analysis increases the power of QTL detection.

title: Linking physiological and genetic analyses of the control of leaf growth under changing environmental conditions
abstract: Decrease in leaf growth rate under water deficit can be seen as an adaptive process. The analysis of its genetic variability is therefore important in the context of drought tolerance. Several mechanisms are widely believed to drive the reduction in leaf growth rate under water deficit, namely leaf carbon balance, incomplete turgor maintenance, and decrease in cell wall plasticity or in cell division rate, with contributions from hormones such as abscisic acid or ethylene. Each of these mechanisms is still controversial, and involves several families of genes. It is argued that gene regulatory networks are not feasible for modelling such complex systems. Leaf growth can be modelled via response curves to environmental conditions, which are considered as ‘meta-mechanisms’ at a higher degree of organisation. Response curves of leaf elongation rate to meristem temperature, atmospheric vapour pressure deficit, and soil water status were established in recombinant inbred lines (RILs) of maize in experiments carried out in the field and in the greenhouse. A quantitative trait locus (QTL) analysis was conducted on the slopes of these responses. Each parameter of the ecophysiological model could then be computed as the sum of QTL effects, allowing calculation of parameters of new RILs, either virtual or existing. Leaf elongation rates of new RILS were simulated and were similar to measurements in a growth chamber experiment. This opens the way to the simulation of virtual genotypes, known only by their alleles, in any climatic scenario. Each genotype is therefore represented by a set of response parameters, valid in a large range of conditions and deduced from the alleles at QTLs.

title: Leaf growth rate per unit thermal time follows QTL-dependent daily patterns in hundreds of maize lines under naturally fluctuating conditions.
abstract: We have analysed daily patterns of leaf elongation rate (LER) in large data sets with 318 genotypes placed in naturally fluctuating temperature and evaporative demand, and examined the effect of targeted alleles on these patterns. The method consisted, firstly, in expressing elongation rate per unit thermal time, so it became temperature independent; secondly, in a joint analysis of diurnal fluctuations of elongation rate and of micrometeorological conditions in several experiments, and finally, in a comparison of daily patterns between groups of genotypes possessing targeted alleles. (1) Conditions for using thermal time at a time step of 15 min were first tested successfully in 318 recombinant inbred lines (RILs) of three mapping populations. (2) An analysis of 1989 time courses revealed a robust daily pattern of LER per unit thermal time (LERth) over several experiments. LERth was constant during the night and was reproducible (for a given RIL) over up to 10 consecutive nights in different experiments. It declined rapidly during the early morning, closely following the daily pattern of transpiration rate. (3) Groups of RILs carrying alleles conferring a high response to temperature had markedly higher night-time plateau of LER than those with low responses. Groups of RILs with high response to evaporative demand had rapid decreases in elongation rate at the transition between night and day, while this decrease was slower in groups of RILs with low response. These results open the way for using kinetics of responses to environmental stimuli as a phenotyping tool in genetic analyses.

title: Evaluation of a Crop Simulation Model that Incorporates Gene Action
abstract: Crop simulation models are receiving increasing use in agricultural research. However, applications to plant breeding have been limited, in part due to the restricted capabilities of models to represent genetic differences. A gene-based simulation model, GeneGro, has been developed that integrates action of seven genes into a common bean (Phaseolus vulgaris L.) model. The genes for physiological traits identified in the model include Ppd, Hr, Fin, Fd, Ssz-1, Ssz-2, and Ssz-3. Evaluation of GeneGro was performed by comparison of measured field data vs. simulated data, and through a sensitivity analysis of the model. The experimental data set for model comparison was comprised of 14 field trials conducted in Canada, the USA, Mexico, and Colombia, representing 213 treatment combinations and including 39 cultivars. GeneGro explained 75% of variation in days to flower, 68% in days to maturity, and 39% in seed mass, but only 11% of variation in seed yield. Most of the variation in simulated seed yield was accounted for by the model when mean effects of site and cultivars were removed through regression analysis. This suggests that the poor simulation of seed yield was partially due to errors in simulating differences among sites rather than from simulating the response of genotypes to sites. Seed yield simulations were made for 96 genotypes that represented all expected phenotypic combinations of the seven genes included in the model. Simulations were conducted using historical weather data from Fargo, ND; Madero, Mexico; and Palmira, Colombia. GeneGro predicted that photoperiod sensitivity, conferred by Ppd and Hr, would result in zero seed yields at Fargo, a slight seed yield increase at Madero, and no effect at Palmira. Testing effects of maturity on seed yield, the genotypes fin and Fd resulted in lower seed yields due to shorter growth cycles, in agreement with field trials. The predicted effects of the three genes related to seed size varied among the sites. These results support the use of genetic information to represent cultivar differences in simulation models. They also emphasize the need for a better understanding of the physiological genetics of traits such as phenology, seed size, and growth habit.

title: Crop modeling, QTL mapping, and their complementary role in plant breeding
abstract: Received for publication May 1, 2001. Crop modelers and geneticists have developed a vision of their roles in plant breeding from their own perspective. However, to improve breeding efficiency, interdisciplinary collaboration becomes increasingly important. The objective of this paper is to explore opportunities for collaboration between modelers and geneticists in ideotype breeding for high crop yield. The advent of molecular markers enables variation of a complex trait to be dissected into the effects of quantitative trait loci (QTL) and assists the transfer of these QTL into desired cultivars or lines. A recent study in which QTL information was linked to crop modeling has shown that QTL analysis removes part of random errors of measured model input parameters and that QTL information can successfully be coupled with crop models to replace measured parameters. The QTL-based modeling overcomes the limitations in designing ideotypes by using models that ignore the inheritance of model input traits. On the other hand, crop modeling can potentially be a powerful tool to resolve genotype x environment interactions and to dissect yield into characters that might be under simpler genetic control. Based on the complementary aspects of crop modeling and QTL mapping, we propose an approach that integrates marker-assisted selection into model-based ideotype framework to support breeding for high crop yield. For this approach to be effective, there is a need to develop crop models that are capable of predicting yield differences among genotypes in a population under various environmental conditions.

title: An overview of APSIM, a model designed for farming systems simulation
abstract: The Agricultural Production Systems Simulator (APSIM) is a modular modelling framework that has been developed by the Agricultural Production Systems Research Unit in Australia. APSIM was developed to simulate biophysical process in farming systems, in particular where there is interest in the economic and ecological outcomes of management practice in the face of climatic risk. The paper outlines APSIM's structure and provides details of the concepts behind the different plant, soil and management modules. These modules include a diverse range of crops, pastures and trees, soil processes including water balance, N and P transformations, soil pH, erosion and a full range of management controls. Reports of APSIM testing in a diverse range of systems and environments are summarised. An example of model performance in a long-term cropping systems trial is provided. APSIM has been used in a broad range of applications, including support for on-farm decision making, farming systems design for production or resource management objectives, assessment of the value of seasonal climate forecasting, analysis of supply chain issues in agribusiness activities, development of waste management guidelines, risk assessment for government policy making and as a guide to research and education activity. An extensive citation list for these model testing and application studies is provided.

title: Development of a generic crop model template in the cropping system model APSIM
abstract: The Agricultural Production Systems slMulator, APSIM, is a cropping system modelling environment that simulates the dynamics of soil-plant-management interactions within a single crop or a cropping system. Adaptation of previously developed crop models has resulted in multiple crop modules in APSIM, which have low scientific transparency and code efficiency. A generic crop model template (GCROP) has been developed to capture unifying physiological principles across crops (plant types) and to provide modular and efficient code for crop modelling. It comprises a standard crop interface to the APSIM engine, a generic crop model structure, a crop process library, and well-structured crop parameter files. The process library contains the major science underpinning the crop models and incorporates generic routines based on physiological principles for growth and development processes that are common across crops. It allows APSIM to simulate different crops using the same set of computer code. The generic model structure and parameter files provide an easy way to test, modify, exchange and compare modelling approaches at process level without necessitating changes in the code. The standard interface generalises the model inputs and outputs, and utilises a standard protocol to communicate with other APSIM modules through the APSIM engine. The crop template serves as a convenient means to test new insights and compare approaches to component modelling, while maintaining a focus on predictive capability. This paper describes and discusses the scientific basis, the design, implementation and future development of the crop template in APSIM. On this basis, we argue that the combination of good software engineering with sound crop science can enhance the rate of advance in crop modelling. Crown Copyright (C) 2002

title: Physiological Determinants of Crop Growth.
abstract: Physiological determinants of crop growth , Physiological determinants of crop growth , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

title: How do crops manipulate water supply and demand?
abstract: The supply of water provided by the root system of a crop stand is defined in terms of the rate at which water is extracted by a root front moving downwards with a constant velocity, the available water per unit soil volume, and a time constant that is inversely proportional to root density. The demand for water, often identified with a potential transpiration rate, is defined in terms of a maximum crop growth rate multiplied by the conservative ratio of transpiration to dry-matter production. From experimental evidence, supported by theory, this ratio is proportional to the mean saturation vapour-pressure deficit. As hypothesized, the root front accelerates during seedling establishment to keep demand and supply in balance. Once a maximum root velocity is reached ( ca. 2-4 cm d-1) transpiration is limited by water supply, except when the soil behind the root front is wetted by rain or irrigation, when it is limited by demand. Irrigation amounts and timing can both be estimated from this scheme.

title: Roots and drought resistance
abstract: Passioura, J.B., 1983. Roots and drought resistance. Agric. Water Manage., 7: 265–280. 
 
The influence of roots on the yield of water-limited crops is analysed with the help of the identity: 
 
yield = water used × water-use efficiency × harvest index 
 
Despite being severely water-stressed, many droughted crops leave substantial amounts of apparently available water in the subsoil at maturity. The factors influencing this amount are outlined, particularly those concerning the morphology of the root system. Prospects for improving yield by extracting the residual water are discussed. 
 
Because roots are difficult to harvest, water-use efficiency is usually defined as above-ground-biomass/water-used. It follows that the more assimilate a plant transfers to its roots the lower will be its water-use efficiency. There is presumably an optimal root/ shoot ratio (in terms of water relations) at which above-ground biomass is maximal for a given water supply. This ratio appears to exceed the optimum in many cases. 
 
For a given biomass, the yield of a grain crop depends in part on the pattern of water use during the season, because harvest index is often related to the proportion of the total water supply that is used after anthesis. For crops relying on a limited supply of stored water, a high axial resistance to flow in the roots may ensure that water in the subsoil is not used so quickly that too little remains at anthesis for the plants to set and fill an adequate number of grains. A breeding program aimed at changing this resistance in wheat roots is described. 
 
Finally, the principles are discussed on which physiological research can be useful in improving drought resistance. The need to dissect water-limited yield into largely independent components is emphasised, for such a dissection greatly improves the focus of the research.

title: Water and nitrogen limitations in soybean grain production I. Model development
abstract: A simple, phenomenological model was developed to describe the carbon, nitrogen, and water budgets of a soybean (Glycine max (L.) Merr) crop from emergence to maturity. Daily meteorological data input to the model were minimum temperature, maximum temperature, solar radiation, and precipitation. Leaves were grown to give a linear function of mean daily temperature. From the calculated leaf area index the daily intercepted solar radiation by the crop was determined. Daily carbon accumulation was calculated as a linear function of intercepted radiation. The daily nitrogen accumulation rate was calculated as a linear function of vegetative biomass. Leaf growth, carbon accumulation and symbiotic-nitrogen fixation rates were all made sensitive to the amount of soil water. Experimental data were collected to develop the empirical relationships between these three physiological processes and the amount of transpirable soil water. These data showed nitrogen fixation rates to be more sensitive to soil dehydration than either leaf growth or leaf gas exchange. Preliminary tests showed that model predictions compared favorably with field observations. An analysis of the model's behavior showed that crop yield was most sensitive to those variables influencing the interception of solar radiation and its conversion to biomass.

title: Development and evaluation of a sorghum model based on CERES-Maize in a semi-arid tropical environment
abstract: Birch, C.J., Carberry, P.S., Muchow, R.C., McCown, R.L. and Hargreaves, J.N.G., 1990. Development and evaluation of a sorghum model based on CERES-Maize in a semi-arid tropical environment. Field Crops Res., 24: 87-104. This paper reports on the development and evaluation of a grain sorghum model (CERESSorghum ( SAT ) ) for use in the semi-arid tropics. The model was developed from a version of CERESMaize, previously adapted for use in this climatic zone. Functions for phenology, leaf growth, leaf senescence, assimilate accumulation and grain growth were modified using a small subset of sorghum data and validated against a much larger field-data set. When tested with cultivar De Kalb DK55 at Katherine, Northern Territory, the model successfully predicted grain-yield with a root mean square deviation of 0.972 to ha- ~ over a range of sowing dates and water regimes resulting in observed yields ranging from 1.56 to 6.28 t ha -~. Deviations of predicted from observed yields were no greater than those of maize predictions by the parent model. Prediction of components of yield and biomass were also satisfactory. Calibration required 28 changes to the CERES-Maize(SAT) model, of which 15 were changes to coefficients in equations rather than substantial changes to the model. Because of the ease of conversion and the time-use efficiency found in these analyses, the techniques used in this paper could have application where locally calibrated models are required.

title: A model to assess nitrogen limitations on the growth and yield of spring wheat
abstract: Under many conditions the availability of soil nitrogen imposes an important constraint on wheat (Triticum aestivum L.) yields. In this paper a simple, mechanistic model of spring-wheat growth and yield was proposed to account for nitrogen uptake and use by the crop. A soil nitrogen balance was developed so that crop nitrogen uptake was restrained when the available mineral nitrogen in the soil was exhausted. The crop nitrogen uptake rate was calculated as a function of cumulative thermal units. Leaf area development and maintenance, radiation-use efficiency, and stem growth were assumed to depend on accumulated nitrogen. Seed growth resulted in nitrogen transfer from leaves and stems to the seeds. The model was compared against data collected in nine years of experimentation at Gilat, Israel. Good agreement between observed and simulated yields was obtained for varying nitrogen fertilizer treatments (r2=0.94) and levels of soil nitrogen following fallow (r2=0.93).

title: A sunflower simulation model: I. Model development
abstract: In dryland farming systems, opportunities to improve sunflower (Helianthus annuus L.) yields are mostly associated with management decisions made at planting. Dynamic crop simulation models can assist in making such decisions. This study reports the structure of QSUN, a simple and mechanistic crop model for sunflower, and how it accounts for the dynamic interaction of the crop with the soil and aerial environment. The model incorporates several recent approaches to simulation of crop growth in dryland conditions. QSUN estimates growth, development, and yield of a sunflower crop. Daily inputs of temperature and photoperiod drive a phenology submodel to predict stages of emergence, bud visibility, 50% anthesis, and maturity [...]

title: Assessing climatic risk to sorghum production in water-limited subtropical environments. I.Development and testing of a simulation model
abstract: Sorghum ( Sorghum bicolor (L.) Moench.) is one of the major summer crops grown in the subtropics. The high rainfall variability and limited planting opportunities in these regions make crop production risky. A robust crop simulation model can assist farmer decision-making via simulation analyses to quantify production risks. Accordingly, we developed a simple, yet mechanistic crop simulation model for sorghum for use in assessing climatic risk to production in water-limited environments. The model simulates grain yield, biomass accumulation, crop leaf area, phenology and soil water balance. The model uses a daily time-step and readily available weather and soil information and assumes no nutrient limitation. The model was tested on numerous data ( n =38) from experiments spanning a broad range of environments in the semi-arid tropics and subtropics. Potential limitations in the model were identified and examined in a novel testing procedure by using combinations of predicted and observed data in various modules of the model. The model performed satisfactorily, accounting for 94% and 64% of the variation in total biomass and grain yield, respectively. The difference in outcome for biomass and yield was caused by limitations in predicting harvest index. The concepts involved, and the limitations encountered, developing a crop model to be simple but consistent with the biophysical rigour required for application to such a diverse range of environments, are discussed.

title: Modelling genotypic and environmental control of leaf area dynamics in grain sorghum. I. Whole plant level
abstract: Leaf area dynamics are controlled by genotypic and environmental influences. In this series of papers, general models of leaf area dynamics of uniculm and tillering sorghum ( Sorghum bicolor (L.) Moench) at the whole plant and individual leaf levels were developed to examine and quantify both genotypic and environmental controls. Green leaf area was modelled by examining leaf area production and senescence separately. Data from field experiments involving broad ranges of hybrids and environments were collated and analysed. Crops were grown with adequate water and nutrient supply. In this paper, a general framework to model leaf area production at the whole plant level is presented. Accumulation of total plant leaf area (TPLA) (without losses due to senescence) was simulated using a logistic function of thermal time (TT) from emergence and it increased to its maximum value (TPLA max ) shortly before flowering. To calculate TT, base optimum and maximum temperatures of 11, 30 and 42° C respectively were derived by examining the effect of temperature on rate of appearance of fully expanded leaves. Hence, TT incorporated the major effect exerted on TPLA by temperature. Most remaining genotypic and environmental variation in TPLA was related to variation in TPLA max . Values of TPLA max were predicted from total leaf number on the main culm (TLN) and fertile tiller number per plant (FTN) by allowing for a curvilinear increase in TPLA max with TLN and a sequential decrease in total leaf area produced by successive surviving tillers relative to that on the main culm. The potential genotypic and environmental controls on TPLA, introduced via factors affecting TLN and FTN, were considered. Frr seven hybrids grown in eight environments (locations and times of planting), this simple general model accounted for 93% of observed variation in TPLA with time, with a root mean square deviation of 664 cm 2 for observed values of TPLA ranging from 161 to 11 302 cm 2 .

title: Modelling genotypic and environmental control of leaf area dynamics in grain sorghum. II. Individual leaf level
abstract: Carberry, P.S., Muchow, R.C. and Hammer, G.L., 1993. Modelling genotypic and environmental control of leaf area dynamics in grain sorghum. II. Individual leaf level. Field Crops Res., 33:311328. Development of leaf area on tiller axes of grain sorghum (Sorghum bicolor (L.) Moench) has previously either been ignored or treated with over-simplifications in crop simulation models. This paper describes a framework to simulate total leaf area of tillering sorghums based on the prediction of the appearance and expansion of individual leaves. Data were collated from experiments on grain sorghum hybrids grown at locations ranging in latitude from 39 ° 11 'N to 27°33'S. A leaf area model was developed which simulated axes within plants independently, such that the production and expansion of individual leaves were simulated on the main culm and each developing tiller. The model simulates total leaf area per plant (TPLA) (without losses due to senescence) using functions to predict: (i) the appearance of successive axes on plants as a function of thermal time from emergence; (ii) a constant rate of mature leaf production per axis per unit of thermal time; (iii) the profile of mature leaf areas for leaves on each axis as a function of total number of leaves produced per axis; and (iv) the leaf area contribution of immature leaves at any time as equivalent to that for a constant number of mature leaves. For seven sorghum hybrids grown at three locations, a general model simulated TPLA over time, accounting for 90% of observed variation with a root mean square deviation of 905 cm 2 for observed values of TPLA ranging from 161 cm 2 to 10584 cm 2.

title: Genotype-by-Environment Interaction in Grain Sorghum. II. Effects of Temperature and Photoperiod on Ontogeny
abstract: (…) Development rate of all hybrids exhibited a curvilinear response to temperature in both phases. Old and new hybrids differed in their temperature responses in GS1 but were similar in GS2. New hybrids had slower rates of development at all temperatures, but the difference was greater at higher temperature (>25 o C). All hybrids had similar short-day photoperiodic response in GS1, with a critical photoperiod 13.2 h. The models were tested on a separate data set covering a similar broad range of environments and performed well

title: Effect of Heat and Drought Stress on Sorghum ( Sorghum Bicolor ). I. Panicle Development and Leaf Appearance
abstract: Seven sorghum lines, flowering from 50 to 87 days after sowing, were subjected to early drought stress, late stress, and both early and late stress in the field during the dry season in India. Panicle initiation was delayed by 2–25 days and flowering by 1–59 days by the drought stress treatments, the greatest effect being in the treatment subjected to both early and late stress. Stress increased the period between panicle initiation and flowering by retarding the rate of panicle development; when stress was severe panicle development stopped. Upon relief of stress following irrigation, panicle development resumed at rates comparable to those in a fully irrigated control. The rate of leaf appearance was affected in a similar manner to panicle development soon after water was withheld. Rate of leaf appearance and panicle development decreased as pre-dawn leaf water potential decreased and ceased at water potentials of −0.55 and −0.7 MPa, respectively

title: Functional dynamics of the nitrogen balance of sorghum: I. N demand of vegetative plant parts
abstract: Stay-green, an important trait for grain yield of sorghum grown under water limitation, has been associated with a high leaf nitrogen content at the start of grain filling. This study quantifies the N demand of leaves and stems and explores effects of N stress on the N balance of vegetative plant parts of three sorghum hybrids differing in potential crop height. The hybrids were grown under well-watered conditions at three levels of N supply. Vertical profiles of biomass and N% of leaves and stems, together with leaf size and number, and specific leaf nitrogen (SLN), were measured at regular intervals. The hybrids had similar minimum but different critical and maximum SLN, associated with differences in leaf size and N partitioning, the latter associated with differences in plant height. N demand of expanding new leaves was represented by critical SLN, and structural stem N demand by minimum stem N%. The fraction of N partitioned to leaf blades increased under N stress. A framework for N dynamics of leaves and stems is developed that captures effects of N stress and genotype on N partitioning and on critical and maximum SLN.

title: Nitrogen Response of Leaf Photosynthesis and Canopy Radiation Use Efficiency in Field-Grown Maize and Sorghum
abstract: The grain yielding capability of maize (Zea mays L.) and sorghum [Sorghum bicolor (L.) Moench] is dependent on the capacity of the crop to assimilate CO 2 . Carbon dioxide assimilation can be measured directly at the leaf level (C A ) and indirectly at the canopy levels by determining radiation use efficiency (RUE). Since leaf N content per unit leaf area (LN) was expected to influence both of these measures of CO 2 assimilation, the primary objective of this study was to obtain field data on C A and RUE in response to differing LN induced by varying the amount of applied N fertilizer [...]

title: Potential yield and water-use efficiency benefits in sorghum from limited maximum transpiration rate.
abstract: Limitations on maximum transpiration rates, which are commonly observed as midday stomatal closure, have been observed even under well-watered conditions. Such limitations may be caused by restricted hydraulic conductance in the plant or by limited supply of water to the plant from uptake by the roots. This behaviour would have the consequences of limiting photosynthetic rate, increasing transpiration efficiency, and conserving soil water. A key question is whether the conservation of water will be rewarded by sustained growth during seed fill and increased grain yield. This simulation analysis was undertaken to examine consequences on sorghum yield over several years when maximum transpiration rate was imposed in a model. Yields were simulated at four locations in the sorghum-growing area of Australia for 115 seasons at each location. Mean yield was increased slightly (5-7%) by setting maximum transpiration rate at 0.4 mm h-1. However, the yield increase was mainly in the dry, low-yielding years in which growers may be more economically vulnerable. In years with yield less than ∼450 g m-2, the maximum transpiration rate trait resulted in yield increases of 9-13%. At higher yield levels, decreased yields were simulated. The yield responses to restricted maximum transpiration rate were associated with an increase in efficiency of water use. This arose because transpiration was reduced at times of the day when atmospheric demand was greatest. Depending on the risk attitude of growers, incorporation of a maximum transpiration rate trait in sorghum cultivars could be desirable to increase yields in dry years and improve water use efficiency and crop yield stability.

title: Can Changes in Canopy and/or Root System Architecture Explain Historical Maize Yield Trends in the U.S. Corn Belt?
abstract: Continuous increase in the yield of maize (Zea mays L.) in the U.S. Corn Be-It has involved an interaction with plant density. A number of contributing traits and mechanisms have been suggested. In this Study we used a modeling approach to examine whether changes in canopy and/or root system architecture might explain the observed trends. A maize crop model was generalized so that changes in canopy and root system architecture could be examined. A layered, diurnal canopy photosynthesis model was introduced to predict consequences of change in canopy architecture. A two-dimensional root exploration model was introduced to predict consequences of change in root system architecture. Field experiments were conducted to derive model parameters for the base hybrid (Pioneer 3394). Simulation studies for various canopy and root system architectures were undertaken for a range of sites, soils, and densities. Simulated responses to density compared well with those found in field experiments. The analysis indicated that (i) change in root system architecture and water capture had a direct effect on biomass accumulation and historical yield trends; and (ii) change in canopy architecture had little direct effect but likely had important indirect effects via leaf area retention and partitioning of carbohydrate to the ear, The study provided plausible explarations and identified testable hypotheses for future research and crop improvement effort.

title: Transpiration-use efficiency of barley
abstract: Transpiration-use efficiency, the ratio of biomass (Y) produced per unit of water transpired (T) by a crop, depends on crop characteristics and on the environment in which crops develop. Transpiration-use efficiency has been described as Y/T = kc/Da, where kc is a crop dependent constant and Da is the daytime air vapor pressure deficit. Our objectives were to determine Y/T and kc of barley grown in Pullman, WA, and to analyze the variation in Y/T and kc of barley (Hordeum vulgare L.) and wheat (Triticum aestivum L.) reported in the literature. Transpiration and biomass accumulation of barley crops were measured in the years 2000 and 2001. The coefficient kc was estimated as the slope of the regression between cumulative values of biomass and T/Da .I t ranged from 6.6 � 0.4 to 6.9 � 0.2 Pa. These figures are greater than 5.8 Pa obtained by applying equations developed by Tanner and Sinclair [Tanner, C.B., Sinclair, T.R., 1983. Efficient water use in crop production: research or re-search.  Taylor, H.M., et al.  Data on kc reported in the literature, although scarce, ranged from 3.0 to 5.9 Pa for barley, and from 2.8 to 6.7 Pa for wheat, with the lower values occurring at low Da (<1 kPa). This variability seems to associate with the response of the internal (leaf) to external (bulk air) CO2 concentration ratio (ci/ca) to changes of the leaf-to-air vapor pressure deficit (Dl), suggesting that kc rather than a constant could be a function of Dl. The evaluation of more field data on kc, the field validation of the response of ci/ca to Dl, and testing this approach for different species and cultivars is needed to improve the understanding of the Y/T determination at the canopy level.

title: On the extent of genetic variation for transpiration efficiency in sorghum
abstract: A glasshouse study examined 49 diverse sorghum lines for variation in transpiration efficiency. Three of the 49 lines grown were Sorghum spp, native to Australia; one was the major weed Johnson grass (Sorghum halepense), and the remaining 45 lines were cultivars of Sorghum bicolor. All plants were grown under non-limiting water and nutrient conditions using a semi-automatic pot watering system designed to facilitate accurate measurement of water use. Plants were harvested 56-58 days after sowing and dry weights of plant parts were determined. Transpiration efficiency differed significantly among cultivars. The 3 Australian native sorghums had much lower transpiration efficiency than the other 46 cultivars, which ranged from 7.7 to 6.0 g/kg. For the 46 diverse cultivars, the ratio of range in transpiration efficiency to its l.s.d. was 2.0, which was similar to that found among more adapted cultivars in a previous study. This is a significant finding as it suggests that there is likely to be little pay-off from pursuing screening of unadapted material for increased variation in transpiration efficiency. It is necessary, however, also to examine absolute levels of transpiration efficiency to determine whether increased levels have been found. The cultivar with greatest transpiration efficiency in this study (IS9710) had a value 9% greater (P < 0.05) than the accepted standard for adapted sorghum cultivars. The potential impact of such an increase in transpiration efficiency warrants continued effort to capture it. Transpiration efficiency has been related theoretically and experimentally to the degree of carbon isotope discrimination in leaf tissue in sorghum, which thus offers a relatively simple selection index. In this study, the variation in transpiration efficiency was not related simply to carbon isotope discrimination. Significant associations of transpiration efficiency with ash content and indices of photosynthetic capacity were found. However, the associations were not strong. These results suggest that a simple screening technique could not be based on any of the measures or indices analysed in this study. A better understanding of the physiological basis of the observed genetic differences in transpiration efficiency may assist in developing reliable selection indices. It was concluded that the potential value of the improvement in transpiration efficiency over the accepted standard and the degree of genetic variation found warrant further study on this subject. It was suggested that screening for genetic variation under water-limiting conditions may provide useful insights and should be pursued.

title: Water extraction by grain sorghum in a sub-humid environment. I. Analysis of the water extraction pattern
abstract: Under water-limiting conditions, water extraction by a dryland crop is limited by the depth of the root system, and by the rate and degree of water extraction. The water extraction pattern of 6 crops of grain sorghum under continous soil drying in a sub-humid sub-tropical environment was analysed in terms of two components: the rate of descent of the extraction front down the soil profile (extraction front velocity), and the time required to extract 90% of the extractable water from each depth after the extraction front arrived (1/kl90). Extractable water content (θa), at each depth, was defined as the difference between the stable water content (θ) at the start of extraction and the lower asymptote of the exponential decay curve of θ versus time (lower limit). The crops varied in genotype, level of evaporative demand, degree of tillering, and plant population density, and were grown on the same soil type over two seasons. The aim of the study was to test the stability of the extraction front velocity, θa and of 1/kl90 under different agronomic and environmental conditions, to assess their usefulness for modelling water extraction of sorghum. Extraction front velocity varied little among the 6 crops with an overall average of 3.43 cm day−1. The extraction front of crops that were grown under long, terminal drying cycles continued to descend until early grain-filling, reaching a maximum depth of 190 cm. The value of 1/kl90 in the upper 100 cm of the profile varied considerably across crops. It is shown that this variation can be explained by variation in root length density and level of evaporative demand. For crops exposed to a long, terminal drying cycle, the actual water extracted below 150 cm depth was less than θa in the soil layers above 150 cm. This was due to both a lower θa below 150 cm, associated with low root length density, and also insufficient time between the arrival of the extraction front and maturity, for the crop to extract all the water above the lower limit.

title: Developing guidelines for replanting grain sorghum: II. Improved methods of simulating caryopsis weight and tiller number
abstract: Enhancing the yield prediction accuracy of SORKAM, a growth model for sorghum [Sorghum bicolor (L.) Moench], requires improving the simulation of grain growth and the relationship between tiller number and minimum temperature. A new grain growth equation, developed from 1990 data collected at Manhattan, KS, relates grainfilling rate to the rate of change of plant dry matter per caryopsis during the effective filling period. Additional functions are specified for the lag and leveling-off phases of caryopsis growth, resulting in a new submodel, which was tested against data from Kansas and two Australian sites. The tiller number calculation was revised using three years of Manhattan data. After incorporating the new submodels, SORKAM outputs were compared with observed yields and yield components in three Kansas regions. The R 2 values for yield increased from 0.27, 0.46, and 0.79 to 0.76, 0.69, and 0.90 for eastern, central, and western Kansas, respectively. Caryopsis weight comparisons showed that the revised model accounted for 48 to 72% of observed variability, up from 15 to 57% for the original model. Tiller number predictions also improved, although modestly.

title: REVIEW Towards an explanation of crop nitrogen demand based on the optimization of leaf nitrogen per unit leaf area
abstract: An area of plant science that is still uncertain is precisely what determines plants' demand for nitrogen (N), that is the amount of N they need to take up from the soil to meet their requirements for potential growth and synthesis of new tissue. A robust and unequivocal physiological basis from which to determine N demand is lacking. Yet N dominates plant nutrition. No nutrient is needed in larger quantities and, in most environments, no nutrient is in such limiting supply. Knowledge of the factors governing N demand is essential to predict the needs of crops under a wide range of field situations, so that growers can be given more reliable fertilizer recommendations (Greenwood 1982; van Keulen et al . 1989). This is important, not just for economic reasons, but because of the risks to the environment that can arise from the over-application of N fertilizers, in particular the problem of nitrate leaching (Addiscott et al . 1991).

title: Leaf Nitrogen, Photosynthesis, and Crop Radiation Use Efficiency: A Review
abstract: Three crop species were considered: solybean (Glycine max [L.] Merr.), rice (Oryza sativa L.), and maize (Zea mays L.). A relationship was developed predicting crop radiation use efficiency (biomass accumulated per unit solar radiation intercepted) for each of the crops as a function of both leaf CO 2 assimilation rate and leaf N content. At the leaf CO 2 assimilation rates typical of a species, the radiation use efficiency was predicted to be about 1.2 g MJ -1 for soybean, 1.4 g MJ -1 for rice, and 1.7 g MJ -1 for maize

title: Patterns of light and nitrogen distribution in relation to whole canopy carbon gain in C3 and C4 mono- and dicotyledonous species
abstract: An analytical model was used to describe the optimal nitrogen distribution. From this model, it was hypothesized that the non-uniformity of the nitrogen distribution increases with the canopy extinction rate for light and the total amount of free nitrogen in the canopy, and that it is independent of the slope of the relation between light saturated photosynthesis (Pm) and leaf nitrogen content (nL). These hypotheses were tested experimentally for plants with inherently different architectures and different photosynthetic modes. A garden experiment was carried out with a C3 monocot [rice, Oryza sativa (L.)], a C3 dicot [soybean, Glycine max (L.) Merr] a C4 monocot [sorghum, Sorghum bicolor (L.) Moensch] and a C4 dicot [amarantus, Amaranthus cruentus (L.)]. Leaf photosynthetic characteristics as well as light and nitrogen distribution in the canopies of dense stands of these species were measured. The dicot stands were found to have higher extinction coefficients for light than the monocot stands. Dicots also had more non-uniform N distribution patterns. The main difference between the C3 and C4 species was that the C4 species were found to have a greater slope value of the leaf-level Pm—nL relation. Patterns of N distribution were similar in stands of the C3 and C4 species. In general, these experimental results were in accordance with the model predictions, in that the pattern of nitrogen allocation in the canopy is mainly determined by the extinction coefficient for light and the total amount of free nitrogen.

title: Functional dynamics of the nitrogen balance of sorghum. II. Grain filling period.
abstract: Maintenance of green leaf area during grain filling can increase grain yield of sorghum grown under terminal water limitation. This 'stay-green' trait has been related to the nitrogen (N) supply-demand balance during grain filling. This study quantifies the N demand of grain and N translocation rates from leaves and stem and explores effects of genotype and N stress on onset and rate of leaf senescence during the grain filling period. Three hybrids differing in potential height were grown at three levels of N supply under well-watered conditions. Vertical profiles of biomass, leaf area, and N% of leaves, stem and grain were measured at regular intervals. Weekly SPAD chlorophyll readings on main shoot leaves were correlated with observed specific leaf nitrogen (SLN) to derive seasonal patterns of leaf N content. For all hybrids, individual grain N demand was sink determined and was initially met through N translocation from the stem and rachis. Only if this was insufficient did leaf N translocation occur. Maximum N translocation rates from leaves and stem were dependent on their N status. However, the supply of N at canopy scale was also related to the amount of leaf area senescing at any one time. This supply-demand framework for N dynamics explained effects of N stress and genotype on the onset and rate of leaf senescence.

title: APSIM's water and nitrogen modules and simulation of the dynamics of water and nitrogen in fallow systems
abstract: is a software system which provides a flexible structure for the simulation of climatic and soil management effects on growth of crops in farming systems and changes in the soil resource. The focus of this paper is the predictive performance of APSIM for simulation of soil water and nitrate nitrogen in contrasting soils (vertisols and alfisols) and environments. The three APSIM modules that determine the dynamics of water, carbon, and nitrogen in the soil system (viz. SOILWAT, SOILN and RESIDUE v.1) are described in terms of the processes represented, with particular emphasis on aspects of their coding that differ from their precursors in CERES and PERFECT. The most fundamental change is in SOILN, which now provides a formal balance of both carbon and nitrogen in the soil and includes a labile soil organic matter pool that decomposes more rapidly than the bulk of the soil organic matter. Model performance, in terms of prediction of soil water and nitrate, is evaluated during fallows, thereby avoiding complications arising from water use and nitrogen uptake by a crop. One data set is from a long-term experiment on a vertisol in southeast Queensland which studied two tillage treatments (conventional and zero tillage) in combination with fertiliser nitrogen inputs for the growth of wheat; soil water and nitrate were measured twice each year (pre-planting and post-harvest). The second comes from experiments at Katherine, Northern Territory, where legume leys growing on alfisols were chemically killed and ensuing changes in soil water and nitrate were measured during a single season. For both datasets, the predictive ability of the model was satisfactory for water and nitrate, in terms of both the total amounts in the whole profile and their distribution with depth. Since neither of these datasets included measurements of the runoff component of the water balance, this aspect of model performance was evaluated, and shown to be generally good, using data from a third source where runoff had been measured from contour bay catchments.

title: Effect of nitrogen supply on the comparative productivity of maize and sorghum in a semi-arid tropical environment II. Radiation interception and biomass accumulation
abstract: Differences in biomass accumulation due to variable nitrogen supply in maize and sorghum grown under irrigation in the semi-arid tropics were associated with differences in both radiation interception and the efficiency with which intercepted radiation was used to produce dry matter. Radiation-use efficiency was more responsive to N supply than was radiation interception. Radiation-use efficiency increased with higher rates of applied N; maximum radiation-use efficiency was greater in maize than in sorghum; and radiation-use efficiency declined during grain filling in maize more than in sorghum. These differences were explained in terms of specific leaf N. A linear relationship, which was similar for both species, was fitted between radiation-use efficiency and specific leaf N. It is concluded that radiation-use efficiency may not be as stable across environments as was previously thought, but rather depends on the balance of leaf growth, N uptake and allocation to leaves, and N mobilization from leaves to grain.

title: From dwarves to giants? Plant height manipulation for biomass yield.
abstract: The increasing demand for lignocellulosic biomass for the production of biofuels provides value to vegetative plant tissue and leads to a paradigm shift for optimizing plant architecture in bioenergy crops. Plant height (PHT) is among the most important biomass yield components and is the focus of this review, with emphasis on the energy grasses maize (Zea mays) and sorghum (Sorghum bicolor). We discuss the scientific advances in the identification of PHT quantitative trait loci (QTLs) and the understanding of pathways and genes controlling PHT, especially gibberellins and brassinosteroids. We consider pleiotropic effects of QTLs or genes affecting PHT on other agronomically important traits and, finally, we discuss strategies for applying this knowledge to the improvement of dual-purpose or dedicated bioenergy crops.

title: Maize Radiation Use Efficiency under Optimal Growth Conditions
abstract: Accurate measurement of crop growth and radiation use efficiency (RUE) under optimal growth conditions is required to predict plant dry matter accumulation and grain yield near the genetic growth potential. Research was conducted to quantify the biomass and leaf area index (LAI) accumulation, extinction coefficient, and RUE of maize (Zea mays L.) under conditions of optimal growth. Maize was grown in two environments over five growing seasons (1998-2002). Total aboveground biomass at maturity ranged from 2257 g m -2 in 1998 to 2916 g m -2 in 2001; values that are considerably greater than the biomass achieved in most previous studies on RUE in maize. Peak LAI ranged from 4.8 to 7.8. Maize extinction coefficients during vegetative growth (k) were within the range of recently published values (0.49 ± 0.03), with no clear pattern of differences in k among years. Seasonal changes in interception of photosynthetically active radiation (PAR) were similar across all but one year. Estimates of RUE were obtained using the short-interval crop growth rate method and the cumulative biomass and absorbed PAR (APAR) method. Values of RUE obtained using the two methods were 3.74 (±0.20) g MJ -1 APAR and 3.84 (±0.08) g MJ -1 APAR, respectively, and did not vary among years. This compares to a published mean RUE for maize of 3.3 g MJ -1 of intercepted PAR (Mitchell et al., 1998). Moreover, RUE did not decline during grain filling. Differences in biomass accumulation among years were attributed in part to differences in observed radiation interception, which varied primarily due to differences in LAI. Maize simulation models that rely on RUE for biomass accumulation should use an RUE of 3.8 g MJ -1 APAR for predicting optimum yields without growth limitations.

title: Heterosis for Leaf CO2 Exchange Rate during the Grain‐Filling Period in Maize
abstract: Heterosis for grain yield in maize (Zea mays L.) manifests itself through its effects on the components of grain yield, dry matter accumulation at maturity, harvest index, and its effects on physiological processes underlying these components, such as leaf CO 2 exchange rate (CER). The objectives of this study were (i) to quantify the pattern of leaf CER throughout the grain-filling period in maize hybrids and their parental inbred lines, and (ii) to determine the mode of inheritance of leaf CER during the grain-filling period. Studies were performed with 12 F 1 hybrids and their seven inbred parents grown hydroponically in the field at the Cambridge Research Station, ON, Canada, in 2002. Data were recorded on leaf CER from silking to maturity, and grain yield, aboveground dry matter, and root dry matter at maturity. Mean leaf CER of hybrids was not different from that of their parental inbred lines at silking. However, significant differences became apparent 2 wk after silking and became increasingly larger as plants advanced toward maturity. In general, leaf CER differed among inbred lines but did not differ among hybrids. Combining ability analysis showed that predominantly additive genetic effects influence the expression of leaf CER late in the season. Finally, the maintenance of leaf CER throughout a plant's life cycle, rather than potential leaf CER, is positively associated with dry matter accumulation during the grain-filling period and grain yield.

title: Ecophysiological traits in maize hybrids and their parental inbred lines: Phenotyping of responses to contrasting nitrogen supply levels
abstract: Maize ( Zea mays L.) breeding based primarily on final grain yield has been successful in improving this trait since the introduction of hybrids. Contrarily, understanding of the variation in ecophysiological processes responsible of this improvement is limited, especially between parental inbred lines and their hybrids. This limitation may hinder future progress in genetic gain, especially in environments where heritability estimation is reduced because grain yield is severely affected by abiotic stresses. The objective of this study was to analyze the genotypic variation between inbred lines and derived hybrids in the physiological determinants of maize grain yield at the crop level, and how differences among hybrids and parental inbreds may effect contrasting responses to N stress. Special emphasis was given to biomass production and partitioning during the critical period for kernel number determination. Phenotyping included the evaluation of 26 morpho-physiological attributes for 6 maize inbred lines and 12 derived hybrids, cropped in the field at contrasting N supply levels (N 0 : no N added; N 400 : 400 kg N ha −1 applied as urea) during three growing seasons. Tested genotypes differed in the response to reduce N supply for most measured traits. Grain yield was always larger for hybrids than for inbreds, but N deficiency affected the former more than the latter (average reduction in grain yield of 40% for hybrids and of 24% for inbreds). We also found (i) a common pattern across genotypes and N levels for the response of kernel number per plant to plant growth rate during the critical period, (ii) a reduced apical ear reproductive capacity (i.e., kernel set per unit of ear growth rate) of inbreds as compared to hybrids, (iii) similar RUE during the critical period and N absorption at maturity at low N levels for both groups of genotypes, but enhanced RUE and N absorption of hybrids at high N supply levels, and (iv) an improved N utilization efficiency of hybrids across all levels of N supply. Results are indicative of a more efficient use of absorbed N by hybrids than by parental inbreds. Larger grain yield of hybrids than of inbreds at N 0 was associated to (i) enhanced dry matter accumulation due to improved light interception during the life cycle and (ii) enhanced biomass partitioning to the grain.

title: Loss of an MDR Transporter in Compact Stalks of Maize br2 and Sorghum dw3 Mutants
abstract: Agriculturally advantageous reduction in plant height is usually achieved by blocking the action or production of gibberellins. Here, we describe a different dwarfing mechanism found in maize brachytic2 (br2) mutants characterized by compact lower stalk internodes. The height reduction in these plants results from the loss of a P-glycoprotein that modulates polar auxin transport in the maize stalk. The sorghum ortholog of br2 is dwarf3 (dw3), an unstable mutant of long-standing commercial interest and concern. A direct duplication within the dw3 gene is responsible for its mutant nature and also for its instability, because it facilitates unequal crossing-over at the locus.

title: Developing guidelines for replanting grain sorghum: I. Validation and sensitivity analysis of the SORKAM sorghum growth model
abstract: Sorghum [Sorghum bicolor (L.) Moench] producers often have difficulty determining when plant stands are low enough to merit replanting. Our objective was to use SORKAM, a sorghum growth model, to develop guidelines for replanting grain sorghum. A necessary first step is validation of the model over an extensive range of management and environmental factors. Validation was accomplished using 19 field data sets representing 11 yr and six Kansas locations. Several nonparametric tests were used to compare observed and simulated yields, yield components, and phenological dates. In addition, sensitivities of yield and yield components were determined in response to yearly climate, planting date, plant population, and maturity class changes. Model sensitivities were compared with sensitivities calculated from field data. While phenological predictions were adequate, SORKAM could capture only 27 to 79% of grain yield variability at the locations tested. Yield predictions from different plant populations within a planting date were particularly inaccurate. The validation and sensitivity analyses showed that the poor yield predictions were the result of improper computation of tiller number and faulty partitioning of biomass to caryopsis weight. Partitioning errors translocated enough assimilate from culm to grain to make yields essentially constant across populations within a planting date. To use SORKAM to generate replant guidelines, improvements must be made in modeling the relationships among yield components and the source-sink relationship that determines caryopsis weight.

title: Determination of grain number in sorghum
abstract: Grain number is an important component of grain yield in sorghum. Research in wheat and maize has indicated a dependency of grain number on the crop or panicle growth rate around anthesis (CGRa and PGRa respectively), but little quantitative information is available for sorghum. The aim of this paper was firstly to quantify the effect of CGRa and PGRa on grain number and secondly, to identify other parameters that could be used as substitutes for PGRa. Analyses included data from a number of experiments, covering a range in nitrogen and drought treatments and including both tall (single dwarf) and short (triple dwarf) hybrids. CGRa and SGRa (stem growth rate) were calculated from the derivative of a curvilinear function fitted to experimental data, and PGRa was obtained by subtraction of SGRa from CGRa. Results indicated a linear relationship between grain number and CGRa, but the slope differed for tall and short hybrids. This was due to a difference in the proportion of dry matter allocated to the reproductive organs around anthesis (Pr), as PGRa was closely related to grain number, irrespective of crop height. Since panicle dry mass at maturity (excluding grain) was closely correlated with reproductive biomass shortly after anthesis, this indicator represents an integration of panicle growth during the critical period for yield determination in sorghum (i.e. flag leaf until start of grain filling). Panicle biomass at maturity (excluding grain) was thus also linearly related to grain number, and the relationship was independent of crop height and of the timing, severity, or type of stress. Our results indicate that panicle mass at maturity could provide an alternative to PGRa for the estimation of grain number.

title: Radiation Use Efficiency
abstract: Publisher Summary This chapter reviews the various aspects of radiation use efficiency (RUE). Topics that are covered include theoretical analyses, experimental determination and measures, and sources of variability. Crop growth rate (dm/dt) could be readily estimated from successive harvests through the growing season. The studies that examined theoretically the nature of RUE will be reviewed. These theoretical studies help to give a background and framework for evaluating potential sources of variation in experimental measures of RUE. Specifically, theoretical studies help to identify variations in the environment and crops that might influence RUE. The various experimental measures of RUE are also discussed. RUE was calculated based on differing leaf photosynthetic rates of various crop species and varying levels of solar radiation. The chapter compares RUE reported for various species and experiments. The focus is particularly on data collected under optimum, usually control conditions, to compare observations on potential RUE from each study. The collection of a baseline of potential RUE data could serve as a useful reference in developing a realistic perspective on the upper limits of RUE that might be reasonably expected for individual crop species.

title: Simulating Seed Number in Grain Sorghum from Increases in Plant Dry Weight
abstract: Simulation of seed number for crop models is important in identifying cultural practices, which enhance yield stability. Field and crop simulation studies examined the relationship between dry weight accumulation and seed number per plant to potentially improve the capability of the grain sorghum [Sorghum bicolor (L.) Moench] model, SORKAM, to simulate seed number. The best estimates of seed numbers were obtained from plant dry weight accumulated during the 360 growing degree day intervals encompassing panicle branch-spikelet formation (PBSI) and panicle elongation through anthesis (EA(I)). Comparison of observed vs. simulated seed numbers using SORKAM's original equations accounted for 57% of the variation in seed number, but it underestimated high seed numbers. Accumulated plant dry weight for the PBSI and EA(I) intervals accounted for 49 and 64% of the variation in seed number, respectively. Simulation of seed numbers improved when the more sensitive water stress coefficient (for leaf area, WATCO(Ie)) was applied to the interval (PBSI or EA(I)) experiencing the highest water stress while the less sensitive water stress coefficient (for dry weight, WATCO(dw)) was applied to the interval experiencing the lowest water stress. The slope from the regression of observed on simulated seed numbers was 0.80 (r(2) = 0.57) for SORKAM with the WATCO(Ie) switch compared with 0.59 (r(2) = 0.57) in the original SORKAM model. Hence, the timing and recovery of water stress during the panicle development period was important in estimating seed number of sorghum.

title: Reproductive partitioning and seed set efficiency in soybean, sunflower and maize
abstract: Seed number per plant (SNP) can be modelled as a function of plant growth rate during the critical period for seed set (PGR C ), the proportion of plant growth partitioned to reproductive organs ( P R ) and the minimum assimilate requirement per seed ( λ ). In comparison to PGR C , less attention has been given to P R and λ . In this paper, we analysed reproductive partitioning and λ in three species of contrasting reproductive strategies, soybean ( Glycine max L. Merrill), sunflower ( Helianthus annuus L.) and maize ( Zea mays L.). To study plant-to-plant variation and to characterise stability of the variables analysed, we focused on individual plants grown under a wide range of plant densities. In soybean and sunflower, reproductive partitioning comprised about 50% of shoot growth, was fairly stable in a wide range of plant growth, and only decreased in a few, very small plants. In comparison, reproductive partitioning in non-prolific maize showed an optimum, was generally below 50% and exhibited a strong variation and instability at plant growth rates ≅2 g/day. Among species, stability of reproductive partitioning correlated inversely with a PGR C threshold for reproductive growth and positively with reproductive plasticity at high PGR C . Consideration of reproductive partitioning improved estimation of seed number, particularly in maize, a species prone to barrenness. Seed number as a function of reproductive growth was adequately described through linear (soybean) and hyperbolic models with x -intercepts (sunflower and maize). Seed set efficiency in terms of seed number per unit of reproductive growth (Ef) was constant only in soybean. In sunflower and maize, Ef increased with decreasing reproductive growth and became highly variable and unstable when reproductive growth was close to the threshold for seed set. In maize, such threshold was higher than in soybean and sunflower possibly as a consequence of a higher minimum combined demand for assimilate, resulting from a higher λ and number of simultaneously developing sinks. Inclusion of parameters assessing (i) stability in reproductive partitioning at low plant growth rates, and (ii) the minimum assimilate requirement per seed might improve seed number estimation.

title: Floret development in near isogenic wheat lines differing in plant height
abstract: The effects of Rht1 and Rht2 alleles on the dynamics of floret development in isogenic lines (dwarf, DD; semi-dwarf, SD and standard height, SH) of spring wheat were investigated. Studies were conducted on wheat grown in the field in each of 4 years and where water and nutrients were non-limiting. The number of grains per spike was significantly greater in the lines with Rht alleles than in the SH lines. Grain number for each line was such that DD>SD>SH. Grains per spike varied with the number of grains per spikelet rather than number of spikelets per spike. Grains per spikelet in turn varied with the number of fertile florets at anthesis. Florets were considered fertile when male and female reproductive organs had developed green anthers and bifidum stigma, respectively. The dwarfing genes had no effect on the percentage of fertile florets setting grain. Increased number of fertile florets per spikelet due to the presence of Rht1 and Rht2 alleles in the genome was a consequence of the higher number of relatively distal primordia, to progress to the stage of fertile floret at anthesis in the DD and SD than in the SH lines. This ability to allow that a greater proportion of distal florets maintain a normal rate of development was related to the fact that Rht alleles produced a more favourable assimilate partitioning to the spike during the pre-anthesis period associated with the reduction in stem growth imposed by Rht alleles. This allowed a higher proportion of the later-initiated floret primordia to produce fertile florets at anthesis.

title: Environmental and genetic control of morphogenesis in crops: towards models simulating phenotypic plasticity
abstract: As molecular biologists are realising the importance of physiology in understanding functional genomics of quantitative traits, and as physiologists are realising the formidable prospects for improving their phenotypic models with information on the underlying gene networks, researchers worldwide are working on linked physiological-genetic models. These efforts are in their early methodological stage despite, or because of, the availability of many different types of models, the problem being to bring together the different ways that scientists see the plant. This paper describes some current efforts to adapt phenotype models to the objective of simulating gene-phene processes at the plant or crop scale. Particular emphasis is given to the models' capacity to simulate genotype x environment interaction and the resulting phenotypic plasticity, assuming that this permits the defining of model parameters that are closer to specific gene action. Three different types of approaches are presented: (1) a generic, mathematical-architectural model called GREENLAB that simulates resource-modulated morphogenesis; (2) an ecophysiological model of peach tree fruit development and filling, parameterised for a mapping population to evaluate the potential of plugging quantitative trait locus (QTL) effects into the model; and (3) the new model Ecomeristem that constructs plant architecture and its phenotypic plasticity from meristem behaviour, the principal hypothesis being that resource limitations and stresses feed back on the meristems. This latter choice is based on the fact that gene expression happens to a large extent in the meristems. The model is evaluated on the basis of preliminary studies on vegetative-stage rice. The different modelling concepts are critically discussed with respect to their ability to simulate phenotypic plasticity and to operate with parameters that approximate specific gene action, particularly in the area of morphogenesis.

title: Dry Matter Partitioning in Tomato: Validation of a Dynamic Simulation Model
abstract: A model for dynamic simulation of dry matter distribution between reproductive and vegetative plant parts and the distribution among individual fruit trusses in glasshouse tomato, is validated. The model is part of the crop growth model TOMSIM and is based on the hypothesis that dry matter distribution is regulated by the sink strengths of the plant organs, quantified by their potential growth rates, i.e. the growth rates at non-limiting assimilate supply. Within the plant, individual fruit trusses are distinguished and sink strength of a truss is described as a function of its development stage. Truss development rate is a function of temperature only. The same potential growth curve, proportional to the number of fruits per truss, is adopted for all trusses. In a simple version of the model, vegetative plant parts are lumped together as one sink with a constant sink strength. In a more detailed version, vegetative sink strength is calculated as the sum of sink strengths of vegetative units (three leaves and stem internodes between two trusses). The model was validated for six glasshouse experiments, covering effects of planting date, plant density, number of fruits per truss (pruning at anthesis), truss removal (every second truss removed at anthesis), single- and double-shoot plants and a temperature experiment conducted in climate rooms at 17, 20 or 23 °C. Daily increase in above-ground dry weight, average daily temperatures and number of set fruits per truss were inputs to the model. Both the simple and the more detailed model showed good agreement between measured and simulated fraction of dry matter partitioned into the fruits over time. For the simple version of the model, the slope of the lines relating simulated to measured fraction partitioned into the fruits (16 data sets), varied between 0.92 and 1.11, on average it was 1.04, implying 4% over-estimation for this fraction. For the detailed model these numbers were slightly better: 0.89, 1.08 and 1.01, respectively. The temperature experiment revealed no important direct influence of temperature on the ratio between generative and vegetative sink strength. Simulated truss growth curves showed reasonable agreement with the measurements, although both models over-estimated (17% on average) final dry weight of the lower trusses (truss 1 –3) on a plant. Modelling dry matter partitioning based on sink strengths of organs is promising, as it is a general, dynamic and flexible approach, showing good agreement between measurements and simulation for a range of conditions. Applicability of the model is, however, still limited as long as the number of fruits per truss (flower and /or fruit abortion) is not simulated, as this is a major feedback mechanism in plant growth.

title: Integrating simulation of architectural development and source-sink behaviour of peach trees by incorporating Markov chains and physiological organ function submodels into L-PEACH.
abstract: L-PEACH is an L-system-based functional-structural model for simulating architectural growth and carbohydrate partitioning among individual organs in peach (Prunus persica (L.) Batsch) trees. The original model provided a prototype for how tree architecture and carbon economy could be integrated, but did not simulate peach tree architecture realistically. Moreover, evaluation of the functional characteristics of the individual organs and the whole tree remained a largely open issue. In the present study, we incorporated Markovian models into L-PEACH to improve the architecture of the simulated trees. The model was also calibrated to grams of carbohydrate, and tools for systematically displaying quantitative outputs and evaluating the behaviour of the model were developed. The use of the Markovian model concept to model tree architecture in L-PEACH reproduced tree behaviour and responses to management practices visually similar to trees in commercial orchards. The new architectural model along with several improvements in the carbohydrate-partitioning algorithms derived from the model evaluation significantly improved the results related to carbon allocation, such as organ growth, carbohydrate assimilation, reserve dynamics and maintenance respiration. The model results are now consistent within the modelled tree structure and are in general agreement with observations of peach trees growing under field conditions.

title: Quantitative genetics and functional-structural plant growth models: simulation of quantitative trait loci detection for model parameters and application to potential yield optimization.
abstract: Prediction of phenotypic traits from new genotypes under untested environmental conditions is crucial to build simulations of breeding strategies to improve target traits. Although the plant response to environmental stresses is characterized by both architectural and functional plasticity, recent attempts to integrate biological knowledge into genetics models have mainly concerned specific physiological processes or crop models without architecture, and thus may prove limited when studying genotype x environment interactions. Consequently, this paper presents a simulation study introducing genetics into a functional-structural growth model, which gives access to more fundamental traits for quantitative trait loci (QTL) detection and thus to promising tools for yield optimization.



The GREENLAB model was selected as a reasonable choice to link growth model parameters to QTL. Virtual genes and virtual chromosomes were defined to build a simple genetic model that drove the settings of the species-specific parameters of the model. The QTL Cartographer software was used to study QTL detection of simulated plant traits. A genetic algorithm was implemented to define the ideotype for yield maximization based on the model parameters and the associated allelic combination.



By keeping the environmental factors constant and using a virtual population with a large number of individuals generated by a Mendelian genetic model, results for an ideal case could be simulated. Virtual QTL detection was compared in the case of phenotypic traits--such as cob weight--and when traits were model parameters, and was found to be more accurate in the latter case. The practical interest of this approach is illustrated by calculating the parameters (and the corresponding genotype) associated with yield optimization of a GREENLAB maize model. The paper discusses the potentials of GREENLAB to represent environment x genotype interactions, in particular through its main state variable, the ratio of biomass supply over demand.

title: Modelling Shoot:Root Relations: the Only Way Forward?
abstract: The basic transport-resistance (TR) model of shoot:root carbon:nitrogen allocation is described. This approach assumes that the two processes of substrate transport and chemical conversion determine allocation. It is suggested thatallallocation models, whether built for the purposes of theoretical investigation or practical application, should start with this irreducible framework. Here it is assumed that the processes operate according to: (a) for substrate sources, dependence on shoot and root sizes with possible product inhibition; (b) for transport, movement down a substrate concentration gradient; and (c) for substrate sinks or utilization, linear bisubstrate kinetics. Some dynamic properties of the model are explored. Failure of this approach to allocation flags the need for additional mechanisms to control the processes. Details of the failure will indicate the modifications needed, which may involve hormones or reflect teleonomy (apparently goal-seeking behaviour), and which are added to the irreducible framework. However, these additions should not replace the irreducible framework of transport and chemical conversions, because they do not in reality. Modifications to the basic model to represent possibilities such as ontogenesis with the transition from exponential growth towards a steady state or with the scaling of within-plant transport resistances with plant size, the influence of hormones, and active transport, are described.

title: Root system architecture: opportunities and constraints for genetic improvement of crops.
abstract: Abiotic stresses increasingly curtail crop yield as a result of global climate change and scarcity of water and nutrients. One way to minimize the negative impact of these factors on yield is to manipulate root system architecture (RSA) towards a distribution of roots in the soil that optimizes water and nutrient uptake. It is now established that most of the genetic variation for RSA is driven by a suite of quantitative trait loci. As we discuss here, marker-assisted selection and quantitative trait loci cloning for RSA are underway, exploiting genomic resources, candidate genes and the knowledge gained from Arabidopsis, rice and other crops. Nonetheless, efficient and accurate phenotyping, modelling and collaboration with breeders remain important challenges, particularly when defining ideal RSA for different crops and target environments.

title: A model-based analysis of the dynamics of carbon balance at the whole-plant level in Arabidopsis thaliana.
abstract: Arabidopsis thaliana (L.) Heynh. is used as a model plant in many research projects. However, few models simulate its growth at the whole-plant scale. The present study describes the first model of Arabidopsis growth integrating organogenesis, morphogenesis and carbon-partitioning processes for aerial and subterranean parts of the plant throughout its development. The objective was to analyse competition among sinks as they emerge from patterns of plant structural development. The model was adapted from the GreenLab model and was used to estimate organ sink strengths by optimisation against biomass measurements. Dry biomass production was calculated by a radiation use efficiency-based approach. Organogenesis processes were parameterised based on experimental data. The potential of this model for growth analysis was assessed using the Columbia ecotype, which was grown in standard environmental conditions. Three phases were observed in the overall time course of trophic competition within the plant. In the vegetative phase, no competition was observed. In the reproductive phase, competition increased with a strong increase when lateral inflorescences developed. Roots and internodes and structures bearing siliques were strong sinks and had a similar impact on competition. The application of the GreenLab model to the growth analysis of A. thaliana provides new insights into source-sink relationships as functions of phenology and morphogenesis.

title: Computational Modeling and Molecular Physiology Experiments Reveal New Insights into Shoot Branching in Pea[C][W]
abstract: Bud outgrowth is regulated by the interplay of multiple hormones, including auxin, cytokinin, strigolactones, and an unidentified long-distance feedback signal that moves from shoot to root. The model of bud outgrowth regulation in pea (Pisum sativum) includes these signals and a network of five RAMOSUS (RMS) genes that operate in a shoot-root-shoot loop to regulate the synthesis of, and response to, strigolactones. The number of components in this network renders the integration of new and existing hypotheses both complex and cumbersome. A hypothesis-driven computational model was therefore developed to help understand regulation of shoot branching. The model evolved in parallel with stepwise laboratory research, helping to define and test key hypotheses. The computational model was used to verify new mechanisms involved in the regulation of shoot branching by confirming that the new hypotheses captured all relevant biological data sets. Based on cytokinin and RMS1 expression analyses, this model is extended to include subtle but important differences in the function of RMS3 and RMS4 genes in the shoot and rootstock. Additionally, this research indicates that a branch-derived signal upregulates RMS1 expression independent of the other feedback signal. Furthermore, we propose xylem-sap cytokinin promotes sustained bud outgrowth, rather than acting at the earlier stage of bud release.

title: Stay‐green: A consequence of the balance between supply and demand for nitrogen during grain filling?
abstract: Retention of green leaf area in grain sorghum under post-anthesis drought, known as stay-green, is associated with greater biomass production, lodging resistance and yield. The stay-green phenomenon can be examined at a cell, leaf, or whole plant level. At a cell level, the retention of chloroplast proteins such as LHCP2, OEC33 and Rubisco until late in senescence has been reported in sorghum containing the KS19 source of stay-green, indicating that photosynthesis may be maintained for longer during senescence in these genotypes. At a leaf level, longevity of photosynthetic apparatus is intimately related to nitrogen (N) status. At a whole plant level, stay-green can be viewed as a consequence of the balance between N demand by the grain and N supply during grain filling. To examine some of these concepts, nine hybrids varying in the B35 and KS19 sources of stay-green were grown under a postanthesis water deficit. Genotypic variation in delayed onset and reduced rate of leaf senescence were explained by differences in specific leaf nitrogen (SLN) and N uptake during grain filling. Matching N supply from age-related senescence and N uptake during grain tilling with grain N demand found that the shortfall in N supply for grain filling was greater in the senescent than stay-green hybrids, resulting in more accelerated leaf senescence in the former. We hypothesise that increased N uptake by stay-green hybrids is a result of greater biomass accumulation during grain filling in response to increased sink demand (higher grain numbers) which, in turn, is the result of increased radiation use efficiency and transpiration efficiency due to higher SLN. Delayed leaf senescence resulting from higher SLN should, in turn, allow snore carbon and nitrogen to be allocated to the roots of stay-green hybrids during grain filling, thereby maintaining a greater capacity to extract N from the soil compared with senescent hybrids.

title: Flowering time control: gene network modelling and the link to quantitative genetics
abstract: Flowering is a key stage in plant development that initiates grain production and is vulnerable to stress. The genes controlling flowering time in the model plant Arabidopsis thaliana are reviewed. Interactions between these genes have been described previously by qualitative network diagrams. We mathematically relate environmentally dependent transcription, RNA processing, translation, and protein–protein interaction rates to resultant phenotypes. We have developed models (reported elsewhere) based on these concepts that simulate flowering times for novel A. thaliana genotype–environment combinations. Here we draw 12 contrasts between genetic network (GN) models of this type and quantitative genetics (QG), showing that both have equal contributions to make to an ideal theory. Physiological dominance and additivity are examined as emergent properties in the context of feed-forwards networks, an instance of which is the signal-integration portion of the A. thaliana flowering time network. Additivity is seen to be a complex, multi-gene property with contributions from mass balance in transcript production, the feed-forwards structure itself, and downstream promoter reaction thermodynamics. Higher level emergent properties are exemplified by critical short daylength (CSDL), which we relate to gene expression dynamics in rice (Oryza sativa). Next to be discussed are synergies between QG and GN relating to the quantitative trait locus (QTL) mapping of model coefficients. This suggests a new verification test useful in GN model development and in identifying needed updates to existing crop models. Finally, the utility of simple models is evinced by 80 years of QG theory and mathematical ecology.

title: Developmental and physiological traits associated with high yield and stay-green phenotype in wheat
abstract: Water availability is a key limiting factor in wheat production in the northern grain belt of Australia. Varieties with improved adaptation to such conditions are actively sought. The CIMMYT wheat line SeriM82 has shown a significant yield advantage in multi-environment screening trials in this region. The objective of this study was to identify the physiological basis of the adaptive traits underpinning this advantage. Six detailed experiments were conducted to compare the growth, development, and yield of SeriM82 with that of the adapted cultivar, Hartog. The experiments were undertaken in field environments that represented the range of moisture availability conditions commonly encountered by winter crops grown on the deep Vertosol soils of this region. The yield of SeriM82 was 6-28% greater than that of Hartog, and SeriM82 exhibited a stay-green phenotype by maintaining green leaf area longer during the grain-filling period in all environments where yield was significantly greater than Hartog. However, where the availability of deep soil moisture was limited, SeriM82 failed to exhibit significantly greater yield or to express the stay-green phenotype. Thus, the stay-green phenotype was closely associated with the yield advantage of SeriM82. SeriM82 also exhibited higher mean grain mass than Hartog in all environments. It is suggested that small differences in water use before anthesis, or greater water extraction from depth after anthesis, could underlie the stay-green phenotype. The inability of SeriM82 to exhibit stay-green and higher yield where deep soil moisture was depleted indicates that extraction of deep soil moisture is important.

title: Evaluating Plant Breeding Strategies by Simulating Gene Action and Dryland Environment Effects
abstract: In quantitative genetics, computer simulation is commonly used to evaluate alternative plant breeding strateFunctional genomics is the systematic study of genome-wide effects gies on the basis of stochastic descriptions of gene action of gene expression on organism growth and development with the ultimate aim of understanding how networks of genes influence traits. and interaction (e.g., Hospital et al., 1997; Podlich and Here, we use a dynamic biophysical cropping systems model (APSIMCooper, 1998). Our aim is to demonstrate how linkages Sorg) to generate a state space of genotype performance based on between gene action and crop performance in dryland 15 genes controlling four adaptive traits and then search this space environments can be investigated by combining the biousing a quantitative genetics model of a plant breeding program (QUphysical response simulation of the of crops to the moisGENE) to simulate recurrent selection. Complex epistatic and gene ture environment with the quantitative genetics simulaenvironment effects were generated for yield even though gene action tion of plant breeding programs. A review of present at the trait level had been defined as simple additive effects. Given research will reveal that substantial resources are being alternative breeding strategies that restricted either the cultivar matuinvested into the cellular and molecular basis for adaptarity type or the drought environment type, the positive ( ) alleles tion to dry environments while plant breeding compafor 15 genes associated with the four adaptive traits were accumulated at different rates over cycles of selection. While early maturing genonies and public programs continue to make advances in types were favored in the Severe-Terminal drought environment type, yield through conventional means. Exploitation of the late genotypes were favored in the Mild-Terminal and Midseason investment in the former requires the integration of drought environment types. In the Severe-Terminal environment, knowledge from agronomy and cellular, plant, and crop there was an interaction of the stay-green (SG) trait with other traits: physiology as well as plant breeding and quantitative Selection for alleles of the SG genes was delayed until alleles genetics. For those less familiar with the breeding and for genes associated with the transpiration efficiency and osmotic quantitative genetics, there are some useful background adjustment traits had been fixed. Given limitations in our current texts (e.g., Hallauer et al., 1988; Falconer and Mackay, understanding of trait interaction and genetic control, the results are 1996) in addition to Podlich and Cooper (1998) and not conclusive. However, they demonstrate how the per se complexity Chapman et al. (2002a). of gene gene environment interactions will challenge the application of genomics and marker-assisted selection in crop improvement In combining gene sequencing, gene cloning, and for dryland adaptation. plant transformation with biochemical and genome databases, scientists in private and public industry have identified and constructed genes that control relatively linear pathways like herbicide tolerance, disease resisW this paper focuses on the simulation of plant tance, and product quality (Somerville and Somerville, breeding programs from an understanding of gene 1999; Mazur et al., 1999). Molecular biology is beginning action, it is useful to begin with a description of how to investigate the role of the other genes that relate to connections between crop modeling, genomics (the unadaptation to the abiotic environment. For these genoderstanding of how multiple genes function together), type–environment systems, thousands of genes interact and plant breeding are developing. Crop simulation in complex ways to generate crop responses to the enmodels have been used to integrate physiological undervironment via mediation of responses over both short standing and evaluate alternative strategies of system time scales (e.g., cellular response to environment shocks management to account for the soil, climate, and agrolike frost) and long time scales (e.g., morphological nomic technologies available. The principal objective of growth responses of crop development and morphola plant-breeding program is the generation and selection ogy). Some pathways for abiotic adaptation are comparof new gene combinations to create genotypes with trait atively straightforward, e.g., direct cellular tolerance of performance that is superior to current genotypes, withsalt stresses (see review by Hasegawa et al., 2000). Howin the target population of environments (TPE) (Comever, it will be some time ( 20 yr?) before we understock, 1977). This objective applies equally to conventional, molecular, and combined approaches. stand how the interactions of developmental and signaling genes control yield of crops as a function of responses at the biochemical, cellular, plant, and canopy or crop S. Chapman, CSIRO Plant Industry, Long Pocket Lab., 120 Meiers Rd., Indooroopilly, 4068, QLD, Australia; M. Cooper and D. Podlich, levels of organization. Until then, we need to deal with School of Land and Food Sci., The University of Queensland, Brisadaptive traits at a more integrative level (i.e., traits bane, 4072, QLD, Australia; and G. Hammer,  observable at the plant or crop level) while beginning Unit, Queensland Dep. of Primary Industries, P.O. Box 102, Toowoomba, QLD, 4350, Australia. M. Cooper and D. Podlich, current address: Pioneer Hi-Bred Int., 7300 N.W. 62nd Ave., P.O. Box 1004,  G E, genotype environment; MET, multienvironJohnston, IA 50131.  May 2001. Corresponding author ment trial; OA, osmotic adjustment; PH, flowering time; QTLs, quan(scott.chapman@csiro.au). titative trait loci; SG, stay-green; TE, transpiration efficiency; TPE, target population of environments.  (2003).

title: Physiology and modelling of traits in crop plants: implications for genetic improvement
abstract: Crop growth models have excellent potential for evaluating genetic improvement, for analyzing past genetic improvement from experimental data, and for proposing plant ideotypes for target environments. Crop models used for these plant breeding applications should be sufficiently mechanistic that processes can be investigated in a manner familiar to crop physiologists and plant breeders. In addition, the crop models must consider a sufficient number of cultivar-specific traits descriptive of life cycle phases, vegetative traits, and reproductive growth attributes. In this paper, we discuss how crop models consider genetic variability within a species (cultivar variation), how varietal characteristics can be determined from variety trial or other data, how crop models can be used to evaluate past genetic improvement, and how crop models can be used to hypothesize ideotypes for specific environments. We conclude that crop growth models can partially reproduce genotype by environment interactions when considered across broad ranges of weather and sites, and that crop models can be used to help plant breeders target cultivar improvement for specific environments. However, more physiological insight into primary processes such as source–sink relationships and morphological development will be needed for enhanced application of the models in breeding programmes.

title: Genotype by environment interactions affecting grain sorghum. II. Frequencies of different seasonal patterns of drought stress are related to location effects on hybrid yields.
abstract: Genotype × environment (G×E) interactions due to variation in soil moisture and rainfall complicate the interpretation of sorghum hybrid performance trials over locations (L) and years (Y). This paper aims to use pattern analysis to explain measures of the G×L interaction for yield, and whether these can, in turn, be explained using simulation models to determine the occurrence of environment types (within-season patterns of drought). The aim of this work is to simplify the analysis of G×E by explaining it in terms of interactions of genotypes with envi- ronment types (ET) that are not 'fixed' to locations and years. In a sequential analysis of 17 seasons, 18 locations were separated into groups that tended to represent either the northern (i.e. central Queensland, CQ) or southern Queensland (SQ) regions. For a subset of 6 locations, ordination partially explained differences among locations as being related to latitude (r = 0.88) and rainfall (r = -0.46), but they were better related (r > 0.9) to the frequencies of 3 stress ETs as determined by long-term crop simulations. These 3 environment types were: (1) low stress (occurring in 33% of seasons); (2) severe terminal stress with an early-season (9%) or midseason time (29%) of onset; and (3) intermediate terminal stress with a midseason (9%) or late-season (20%) time of onset. Low stress ETs were more common in two SQ locations than in CQ. Stress ETs as defined by simulation models and pattern analysis had more consistent relationships with simulated yields than did the fixed descriptors of locations and years. Sorghum hybrid trials for broad adaptation in Queensland should include locations at least from each of the 2 regions and the results should be interpreted in the context of the season in which they are conducted. To match the long-term patterns in the 6 locations of the analysis, trial yields would need to sample from at least 3 yield ranges: 3.5 t/ha. Additional seasons of testing are likely to be required when the locations used during a season do not adequately represent the target population of environments over all locations and years.

title: Computer simulation of a selection strategy to accommodate genotype environment interactions in a wheat recurrent selection programme
abstract: Multi-environment trials (METs) are used in plant breeding programmes to evaluate genotypes (lines/families) as a basis for selection on expected performance (yield and/or quality) in a target population of environments (TPE). When a large component of the genotype-environment (G x E) interactions results from crossover interactions, samples of environments in METs that deviate From the TPE provide a suboptimal basis for selection of genotypes on performance expected in the TPE. To adjust for the negative effects of these deviations, a selection strategy that weights the data from the MET according to their expected frequency of occurrence in the TPE (i.e. a weighted selection strategy)was investigated. Computer simulation methodology was used to obtain preliminary information on the weighted selection strategy and compare it to the traditional unweighted selection strategy For a range of MET scenarios and G x E interaction models. The evaluation of the weighted selection strategy was conducted in context with the germplasm enhancement programme (GEP) of the Northern Wheat Improvement Programme in Australia. The results indicated that when the environments sampled in the MET matched those expected in the TPE, the unweighted and weighted selection strategies achieved a similar response to selection in the TPE. However. when the environments sampled in the MET did not match the expectations in the TPE and a large component of the G x E interactions resulted from crossover interactions, the weighted selection strategy achieved a greater response to selection in the TPE. The advantage of the weighted strategy increased as the amount of crossover G x E interaction increased or fewer environments were sampled in the METs.

title: Use of crop models to understand genotype by environment interactions for drought in real-world and simulated plant breeding trials
abstract: Crop simulation models of plant processes capture the biological interactions between the sensing of signals at an organ level (e.g. drought affecting roots), the response of the plant at a biochemical level (e.g. change in development rate) and the result at the organ (or crop) level (e.g. reduced growth). In dissecting the complex control of phenotypes like yield, simulation models have several roles. Models have been used to generate an index of the climatic environment (e.g. of drought stress) for breeding programme trials. In wheat and sorghum grown in northern Australia, this has shown that mid-season drought generates large genotype by environment interaction. By defining gene action to calculate the value of input trait parameters to crop models, simulated multi-environment trials estimate the yield of ‘synthetic’ sorghum cultivars grown in historical or artificial climates with current or potential management regimes. In this way, the biological interactions among traits constrain the crop yields to only those that are biologically possible in the given set of environments. This allows the construction of datasets that are more ‘realistic’ representations of gene by trait by environment interaction than is possible using only the statistical attributes (e.g. means, variances and correlations) of real-world trait datasets. This approach has an additional advantage in that ‘biological and experimental noise’ can be manipulated separately. These ‘testbeds’ for statistical techniques can be extended to the interpretation of a crossing and selection programme where the processes of chromosomal recombination are simulated using a quantitative genetics model and applied to the trait parameters. Statisticians are challenged to develop improved methods for the resulting simulated phenotype datasets, with the objective of revealing the (known) underlying genetic and environment structure that was input to the simulations. These improved methods can then be applied to existing plant breeding programmes.

title: Detection and use of QTL for complex traits in multiple environments.
abstract: QTL mapping methods for complex traits are challenged by new developments in marker technology, phenotyping platforms, and breeding methods. In meeting these challenges, QTL mapping approaches will need to also acknowledge the central roles of QTL by environment interactions (QEI) and QTL by trait interactions in the expression of complex traits like yield. This paper presents an overview of mixed model QTL methodology that is suitable for many types of populations and that allows predictive modeling of QEI, both for environmental and developmental gradients. Attention is also given to multi-trait QTL models which are essential to interpret the genetic basis of trait correlations. Biophysical (crop growth) model simulations are proposed as a complement to statistical QTL mapping for the interpretation of the nature of QEI and to investigate better methods for the dissection of complex traits into component traits and their genetic controls.

title: QU-GENE: a simulation platform for quantitative analysis of genetic models
abstract: Classical quantitative genetics theory makes a number of simplifying assumptions in order to develop mathematical expressions that describe the mean and variation (genetic and phenotypic) within and among populations, and to predict how these are expected to change under the influence of external forces. These assumptions are often necessary to render the development of many aspects of the theory mathematically tractable. The availability of high-speed computers today provides opportunity for the use of computer simulation methodology to investigate the implications of relaxing many of the assumptions that are commonly made.



QU-GENE (QUantitative-GENEtics) was developed as a flexible computer simulation platform for the quantitative analysis of genetic models. Three features of the QU-GENE software that contribute to its flexibility are (i) the core E(N:K) genetic model, where E is the number of types of environment, N is the number of genes, K indicates the level of epistasis and the parentheses indicate that different N:K genetic models can be nested within types of environments, (ii) the use of a two-stage architecture that separates the definition of the genetic model and genotype-environment system from the detail of the individual simulation experiments and (iii) the use of a series of interactive graphical windows that monitor the progress of the simulation experiments. The E(N:K) framework enables the generation of families of genetic models that incorporate the effects of genotype-by-environment (G x E) interactions and epistasis. By the design of appropriate application modules, many different simulation experiments can be conducted for any genotype-environment system. The structure of the QU-GENE simulation software is explained and demonstrated by way of two examples. The first concentrates on some aspects of the influence of G x E interactions on response to selection in plant breeding, and the second considers the influence of multiple-peak epistasis on the evolution of a four-gene epistatic network.


AVAILABILITY
QU-GENE is available over the Internet at (http://pig.ag.uq.edu.au/qu-gene/)


CONTACT
m.cooper@mailbox.uq.edu.