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Intimate relationships exist between form and function of plants, determining many processes governing their growth and development. However, in most crop simulation models that have been created to simulate plant growth and, for example, predict biomass production, plant structure has been neglected. In this study, a detailed simulation model of growth and development of spring wheat (Triticum aestivum) is presented, which integrates degree of tillering and canopy architecture with organ-level light interception, photosynthesis, and dry-matter partitioning. An existing spatially explicit 3D architectural model of wheat development was extended with routines for organ-level microclimate, photosynthesis, assimilate distribution within the plant structure according to organ demands, and organ growth and development. Outgrowth of tiller buds was made dependent on the ratio between assimilate supply and demand of the plants. Organ-level photosynthesis, biomass production, and bud outgrowth were simulated satisfactorily. However, to improve crop simulation results more efforts are needed mechanistically to model other major plant physiological processes such as nitrogen uptake and distribution, tiller death, and leaf senescence. Nevertheless, the work presented here is a significant step forwards towards a mechanistic functional–structural plant model, which integrates plant architecture with key plant processes.

BACKGROUND: Modelling plant growth allows us to test hypotheses and carry out virtual experiments concerning plant growth processes that could otherwise take years in field conditions. The visualization of growth simulations allows us to see directly and vividly the outcome of a given model and provides us with an instructive tool useful for agronomists and foresters, as well as for teaching. Functional-structural (FS) plant growth models are nowadays particularly important for integrating biological processes with environmental conditions in 3-D virtual plants, and provide the basis for more advanced research in plant sciences. SCOPE: In this viewpoint paper, we ask the following questions. Are we modelling the correct processes that drive plant growth, and is growth driven mostly by sink or source activity? In current models, is the importance of soil resources (nutrients, water, temperature and their interaction with meristematic activity) considered adequately? Do classic models account for architectural adjustment as well as integrating the fundamental principles of development? Whilst answering these questions with the available data in the literature, we put forward the opinion that plant architecture and sink activity must be pushed to the centre of plant growth models. In natural conditions, sinks will more often drive growth than source activity, because sink activity is often controlled by finite soil resources or developmental constraints. PMA06: This viewpoint paper also serves as an introduction to this Special Issue devoted to plant growth modelling, which includes new research covering areas stretching from cell growth to biomechanics. All papers were presented at the Second International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA06), held in Beijing, China, from 13-17 November, 2006. Although a large number of papers are devoted to FS models of agricultural and forest crop species, physiological and genetic processes have recently been included and point the way to a new direction in plant modelling research.

Summary • Plants respond to environmental change through alterations in organ size, number and biomass. However, different phenotypes are rarely integrated in a single model, and the prediction of plant responses to environmental conditions is challenging. The aim of this study was to simulate and predict plant phenotypic plasticity in development and growth using an organ‐level functional–structural plant model, GreenLab. • Chrysanthemum plants were grown in climate chambers in 16 different environmental regimes: four different temperatures (15, 18, 21 and 24°C) combined with four different light intensities (40%, 51%, 65% and 100%, where 100% is 340 μmol m−2 s−1). Measurements included plant height, flower number and major organ dry mass (main and side‐shoot stems, main and side‐shoot leaves and flowers). To describe the basipetal flowering sequence, a position‐dependent growth delay function was introduced into the model. • The model was calibrated on eight treatments. It was capable of simulating multiple plant phenotypes (flower number, organ biomass, plant height) with visual output. Furthermore, it predicted well the phenotypes of the other eight treatments (validation) through parameter interpolation. • This model could potentially serve to bridge models of different scales, and to link energy input to crop output in glasshouses.

Growing glasshouse plant canopies are exposed to natural fluctuations in light quantity, and the dynamically changing canopy architecture induces local variations in light quality. This modelling study aimed to analyse the importance of both light signals for an accurate prediction of individual internodel lengths. We conceptualized two model approaches for estimating final internode lengths (FILs). The first one is only photosynthetically active radiation (PAR)-sensitive and ignores canopy architecture, whereas the second approach uses a functional-structural growth model for considering variations in both PAR and red: far-red (R: FR) ratio (L-Cucumber). Internode lengths measured in three experiments were used for model parameterization and evaluation. The overall trends for the simulated FILs using the exclusively PAR-sensitive model approach were already in line with the measured FILs, but they underestimated FILs at higher ranks. L-Cucumber provided considerably better FIL predictions under various light conditions and canopy architectures. Both light signals are needed for an accurate estimation of the FILs, and only L-Cucumber is able to consider R: FR signals from the growing canopy. Yet this study highlights the significance of the PAR signal for predicting FILs as neighbour effects increase, which indicates a potential role of photosynthate signalling in internode elongation.

Background and Aims: Plant population density (PPD) influences plant growth greatly. Functional-structural plant models such as GREENLAB can be used to simulate plant development and growth and PPD effects on plant functioning and architectural behaviour can be investigated. This study aims to evaluate the ability of GREENLAB to predict maize growth and development at different PPDs. Methods:Two field experiments were conducted on irrigated fields in the North China Plain with a block design of four replications. Each experiment included three PPDs: 2{middle dot}8, 5{middle dot}6 and 11{middle dot}1 plants m-2. Detailed observations were made on the dimensions and fresh biomass of above-ground plant organs for each phytomer throughout the seasons. Growth stage-specific target files (a description of plant organ weight and dimension according to plant topological structure) were established from the measured data required for GREENLAB parameterization. Parameter optimization was conducted using a generalized least square method for the entire growth cycles for all PPDs and years. Data from in situ plant digitization were used to establish geometrical symbol files for organs that were then applied to translate model output directly into 3-D representation for each time step of the model execution. Key Results:The analysis indicated that the parameter values of organ sink variation function, and the values of most of the relative sink strength parameters varied little among years and PPDs, but the biomass production parameter, computed plant projection surface and internode relative sink strength varied with PPD. Simulations of maize plant growth based on the fitted parameters were reasonably good as indicated by the linearity and slopes similar to unity for the comparison of simulated and observed values. Based on the parameter values fitted from different PPDs, shoot (including vegetative and reproductive parts of the plant) and cob fresh biomass for other PPDs were simulated. Three-dimensional representation of individual plant and plant stand from the model output with two contrasting PPDs were presented with which the PPD effect on plant growth can be easily recognized. Conclusions: This study showed that GREENLAB model has the ability to capture plant plasticity induced by PPD. The relatively stable parameter values strengthened the hypothesis that one set of equations can govern dynamic organ growth. With further validation, this model can be used for agronomic applications such as yield optimization.

The shade avoidance syndrome (SAS) is one of the best-studied forms of plant phenotypic plasticity. The suite of SAS responses enables plants to accurately match their phenotype to the light conditions determined by neighbouring plants, especially the decrease in the ratio of red (R) and far red (FR) light intensity (R : FR) (Ballar e et al., 1990). In recent years, significant progress has been made in understanding the physiological and molecular regulation of SAS (among others reviewed in Casal, 2013; Gommers et al., 2013; Pierik & de Wit, 2014). In addition, several studies have shown that SAS is adaptive because inappropriate elongation resulting from inaccurate estimation of neighbour proximity or deficiency in the capacity to respond to neighbour presence is disadvantageous for fitness (Dudley & Schmitt, 1995, 1996; Weinig, 2000; Pierik et al., 2003; Weijschede et al., 2008; Keuskamp et al., 2010). However, it is difficult to assess the consequences of detailed physiological and molecular regulations of SAS for whole-plant and whole-vegetation performance. Furthermore, the wide variety of different cues involved in plant–plant interactions, including light quality and quantity (Ballar e et al., 1990; Smith, 2000), mechanical interaction (i.e. touch and wind shielding; Anten et al., 2005; de Wit et al., 2012) and various volatiles (Pierik et al., 2003; Kegge et al., 2013), poses questions about their relative importance for plant performance. Here, we argue that the consequences of physiological regulations and the complexity of natural systems can be addressed by using virtual plant simulation modelling in combination with experimental studies. So-called functional–structural plant (FSP) models have been applied in a broad range of research questions in the field of plant sciences (reviewed in Vos et al., 2010; DeJong et al., 2011; Guo et al., 2011; Prusinkiewicz & Runions, 2012) and simulate plant development over time in three dimensions (the principles are outlined in Box 1). These models can include responses to environmental conditions such as light (Fig. 1) and can be used to study how the interplay among physiology, architecture and environment scale from plant organ to wholeplant performance. FSP models can generate and test hypotheses about the influence of different environmental components on plant growth and development by including one component at a time. By comparing model predictions with naturally developed vegetation stands, the contribution of the different components of environmental factors to plant performance can be assessed. In this Letter, we outline the way in which FSP models can improve experimental designs and how data collected from these experiments can, in turn, improve the mechanistic description of regulation of shade avoidance in the model. Ultimately, this feedback process results in a modelling tool that can scale up from plant organ responses to whole-plant performance and address ecologically relevant questions such as the adaptive significance of variation in SAS.

Background and Aims :The dynamical system of plant growth GreenLab was originally developed for individual plants, without explicitly taking into account inter-plant competition for light. Inspired by the competition models developed in the context of forest science, we propose to adapt the method of crown projection onto the x-y plane to GreenLab, in order to study the effects of density on resource acquisition and on architectural development. Materials and methods : The empirical production equation of GreenLab is extrapolated to the stand level by computing the exposed photosynthetic foliage area of each plant. The computation is based on the combination of Poisson models of leaf distribution for all the neighbour plants, in the overlapping crown projection surfaces. To study the effects of density on architectural development, we link the proposed competition model to the model of interaction between functional growth and structural development introduced by Mathieu (2006). Key Results and Conclusions : The model is applied to determine the production of field crops according to density and its validity is discussed by comparing it to the classical equation of field crop production given by Howell and Musick (1985). The application of the model to trees leads us to derive a new general equation of resource acquisition. It is used to illustrate the expression of plant plasticity in response to competition for light. Density strongly impacts tree architectural development through interactions with the source-sink balances during the growth. Well-known properties of forest stands are reproduced concerning the effects of density on tree height and radial growth.

OpenSimRoot is an open-source, functional–structural plant model and mathematical description of root growth and function. We describe OpenSimRoot and its functionality to broaden the benefits of root modeling to the plant science community. OpenSimRoot is an extended version of SimRoot, established to simulate root system architecture, nutrient acquisition and plant growth. OpenSimRoot has a plugin, modular infrastructure, coupling single plant and crop stands to soil nutrient and water transport models. It estimates the value of root traits for water and nutrient acquisition in environments and plant species. The flexible OpenSimRoot design allows upscaling from root anatomy to plant community to estimate the following: resource costs of developmental and anatomical traits; trait synergisms; and (interspecies) root competition. OpenSimRoot can model three-dimensional images from magnetic resonance imaging (MRI) and X-ray computed tomography (CT) of roots in soil. New modules include: soil water-dependent water uptake and xylem flow; tiller formation; evapotranspiration; simultaneous simulation of mobile solutes; mesh refinement; and root growth plasticity. OpenSimRoot integrates plant phenotypic data with environmental metadata to support experimental designs and to gain a mechanistic understanding at system scales.

Vegetation stands have a heterogeneous distribution of light quality, including the red/far-red light ratio (R/FR) that informs plants about proximity of neighbors. Adequate responses to changes in R/FR are important for competitive success. How the detection and response to R/FR are spatially linked and how this spatial coordination between detection and response affects plant performance remains unresolved. We show in Arabidopsis thaliana and Brassica nigra that localized FR enrichment at the lamina tip induces upward leaf movement (hyponasty) from the petiole base. Using a combination of organ-level transcriptome analysis, molecular reporters, and physiology, we show that PIF-dependent spatial auxin dynamics are key to this remote response to localized FR enrichment. Using computational 3D modeling, we show that remote signaling of R/FR for hyponasty has an adaptive advantage over local signaling in the petiole, because it optimizes the timing of leaf movement in response to neighbors and prevents hyponasty caused by self-shading.

This article presents an overview of Helios, a new three-dimensional (3D) plant and environmental modeling framework. Helios is a model coupling framework designed to provide maximum flexibility in integrating and running arbitrary 3D environmental system models. Users interact with Helios through a well-documented open-source C++ API. Version 1.0 comes with model plug-ins for radiation transport, the surface energy balance, stomatal conductance, photosynthesis, solar position, and procedural tree generation. Additional plug-ins are also available for visualizing model geometry and data and for processing and integrating LiDAR scanning data. Many of the plug-ins perform calculations on the graphics processing unit, which allows for efficient simulation of very large domains with high detail. An example modeling study is presented in which leaf-level heterogeneity in water usage and photosynthesis of an orchard is examined to understand how this leaf-scale variability contributes to whole-tree and -canopy fluxes.