Stronger wind, smaller tree: Testing tree growth plasticity through a modeling approach.

Plants exhibit plasticity in response to various external conditions, characterized by changes in physiological and morphological features. Although being non-negligible, compared to the other environmental factors, the effect of wind on plant growth is less extensively studied, either experimentally or computationally. This study aims to propose a modeling approach that can simulate the impact of wind on plant growth, which brings a biomechanical feedback to growth and biomass distribution into a functional-structural plant model (FSPM). Tree reaction to the wind is simulated based on the hypothesis that plants tend to fit in the environment best. This is interpreted as an optimization problem of finding the best growth-regulation sink parameter giving the maximal plant fitness (usually seed weight, but expressed as plant biomass and size). To test this hypothesis in silico, a functional-structural plant model, which simulates both the primary and secondary growth of stems, is coupled with a biomechanical model which computes forces, moments of forces, and breakage location in stems caused by both wind and self-weight increment during plant growth. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is adopted to maximize the multi-objective function (stem biomass and tree height) by determining the key parameter value controlling the biomass allocation to the secondary growth. The digital trees show considerable phenotypic plasticity under different wind speeds, whose behavior, as an emergent property, is in accordance with experimental results from works of literature: the height and leaf area of individual trees decreased with wind speed, and the diameter at the breast height (DBH) increased at low-speed wind but declined at higher-speed wind. Stronger wind results in a smaller tree. Such response of trees to the wind is realistically simulated, giving a deeper understanding of tree behavior. The result shows that the challenging task of modeling plant plasticity may be solved by optimizing the plant fitness function. Adding a biomechanical model enriches FSPMs and opens a wider application of plant models.

Functional-Structural Plant Models Mission in Advancing Crop Science: Opportunities and Prospects.

Functional-structural plant models (FSPMs) have been evolving for over 2 decades and their future development, to some extent, depends on the value of potential applications in crop science. To date, stabilizing crop production by identifying valuable traits for novel cultivars adapted to adverse environments is topical in crop science. Thus, this study will examine how FSPMs are able to address new challenges in crop science for sustainable crop production. FSPMs developed to simulate organogenesis, morphogenesis, and physiological activities under various environments and are amenable to downscale to the tissue, cellular, and molecular level or upscale to the whole plant and ecological level. In a modeling framework with independent and interactive modules, advanced algorithms provide morphophysiological details at various scales. FSPMs are shown to be able to: (i) provide crop ideotypes efficiently for optimizing the resource distribution and use for greater productivity and less disease risk, (ii) guide molecular design breeding via linking molecular basis to plant phenotypes as well as enrich crop models with an additional architectural dimension to assist breeding, and (iii) interact with plant phenotyping for molecular breeding in embracing three-dimensional (3D) architectural traits. This study illustrates that FSPMs have great prospects in speeding up precision breeding for specific environments due to the capacity for guiding and integrating ideotypes, phenotyping, molecular design, and linking molecular basis to target phenotypes. Consequently, the promising great applications of FSPMs in crop science will, in turn, accelerate their evolution and vice versa.

Two decades of research with the GreenLab model in agronomy.

BACKGROUND: With up to 200 published contributions, the GreenLab mathematical model of plant growth, developed since 2000 under Sino-French co-operation for agronomic applications, is descended from the structural models developed in the AMAP unit that characterize the development of plants and encompass them in a conceptual mathematical framework. The model also incorporates widely recognized crop model concepts (thermal time, light use efficiency and light interception), adapting them to the level of the individual plant. SCOPE: Such long-term research work calls for an overview at some point. That is the objective of this review paper, which retraces the main history of the model's development and its current status, highlighting three aspects. (1) What are the key features of the GreenLab model? (2) How can the model be a guide for defining relevant measurement strategies and experimental protocols? (3) What kind of applications can such a model address? This last question is answered using case studies as illustrations, and through the Discussion. CONCLUSIONS: The results obtained over several decades illustrate a key feature of the GreenLab model: owing to its concise mathematical formulation based on the factorization of plant structure, it comes along with dedicated methods and experimental protocols for its parameter estimation, in the deterministic or stochastic cases, at single-plant or population levels. Besides providing a reliable statistical framework, this intense and long-term research effort has provided new insights into the internal trophic regulations of many plant species and new guidelines for genetic improvement or optimization of crop systems.

Internal trophic pressure, a regulator of plant development? Insights from a stochastic functional-structural plant growth model applied to Coffea trees.

BACKGROUND AND AIMS: Using internal trophic pressure as a regulating variable to model the complex interaction loops between organogenesis, production of assimilates and partitioning in functional-structural models of plant growth has attracted increasing interest in recent years. However, this approach is hampered by the fact that internal trophic pressure is a non-measurable quantity that can be assessed only through model parametric estimation, for which the methodology is not straightforward, especially when the model is stochastic. METHODS: A stochastic GreenLab model of plant growth (called 'GL4') is developed with a feedback effect of internal trophic competition, represented by the ratio of biomass supply to demand (Q/D), on organogenesis. A methodology for its parameter estimation is presented and applied to a dataset of 15 two-year-old Coffea canephora trees. Based on the fitting results, variations in Q/D are reconstructed and analysed in relation to the estimated variations in organogenesis parameters. KEY RESULTS: Our stochastic retroactive model was able to simulate realistically the progressive set-up of young plant architecture and the branch pruning effect. Parameter estimation using real data for Coffea trees provided access to the internal trophic dynamics. These dynamics correlated with the organogenesis probabilities during the establishment phase. CONCLUSIONS: The model can satisfactorily reproduce the measured data, thus opening up promising avenues for further applying this original procedure to other experimental data. The framework developed can serve as a model-based toolkit to reconstruct the hidden internal trophic dynamics of plant growth.

Estimating Sink Parameters of Stochastic Functional-Structural Plant Models Using Organic Series-Continuous and Rhythmic Development.

Functional-structural plant models (FSPMs) generally simulate plant development and growth at the level of individual organs (leaves, flowers, internodes, etc.). Parameters that are not directly measurable, such as the sink strength of organs, can be estimated inversely by fitting the weights of organs along an axis (organic series) with the corresponding model output. To accommodate intracanopy variability among individual plants, stochastic FSPMs have been built by introducing the randomness in plant development; this presents a challenge in comparing model output and experimental data in parameter estimation since the plant axis contains individual organs with different amounts and weights. To achieve model calibration, the interaction between plant development and growth is disentangled by first computing the occurrence probabilities of each potential site of phytomer, as defined in the developmental model (potential structure). On this basis, the mean organic series is computed analytically to fit the organ-level target data. This process is applied for plants with continuous and rhythmic development simulated with different development parameter sets. The results are verified by Monte-Carlo simulation. Calibration tests are performed both in silico and on real plants. The analytical organic series are obtained for both continuous and rhythmic cases, and they match well with the results from Monte-Carlo simulation, and vice versa. This fitting process works well for both the simulated and real data sets; thus, the proposed method can solve the source-sink functions of stochastic plant architectures through a simplified approach to plant sampling. This work presents a generic method for estimating the sink parameters of a stochastic FSPM using statistical organ-level data, and it provides a method for sampling stems. The current work breaks a bottleneck in the application of FSPMs to real plants, creating the opportunity for broad applications.

Stochastic modelling of tree architecture and biomass allocation: application to teak (Tectona grandis L. f.), a tree species with polycyclic growth and leaf neoformation.

Background and aims: For a given genotype, the observed variability of tree forms results from the stochasticity of meristem functioning and from changing and heterogeneous environmental factors affecting biomass formation and allocation. In response to climate change, trees adapt their architecture by adjusting growth processes such as pre- and neoformation, as well as polycyclic growth. This is the case for the teak tree. The aim of this work was to adapt the plant model, GreenLab, in order to take into consideration both these processes using existing data on this tree species. Methods: This work adopted GreenLab formalism based on source-sink relationships at organ level that drive biomass production and partitioning within the whole plant over time. The stochastic aspect of phytomer production can be modelled by a Bernoulli process. The teak model was designed, parameterized and analysed using the architectural data from 2- to 5-year-old teak trees in open field stands. Key results: Growth and development parameters were identified, fitting the observed compound organic series with the theoretical series, using generalized least squares methods. Phytomer distributions of growth units and branching pattern varied depending on their axis category, i.e. their physiological age. These emerging properties were in accordance with the observed growth patterns and biomass allocation dynamics during a growing season marked by a short dry season. Conclusions: Annual growth patterns observed on teak, including shoot pre- and neoformation and polycyclism, were reproduced by the new version of the GreenLab model. However, further updating is discussed in order to ensure better consideration of radial variation in basic specific gravity of wood. Such upgrading of the model will enable teak ideotypes to be defined for improving wood production in terms of both volume and quality.

Multiscale digital Arabidopsis predicts individual organ and whole-organism growth.

Understanding how dynamic molecular networks affect whole-organism physiology, analogous to mapping genotype to phenotype, remains a key challenge in biology. Quantitative models that represent processes at multiple scales and link understanding from several research domains can help to tackle this problem. Such integrated models are more common in crop science and ecophysiology than in the research communities that elucidate molecular networks. Several laboratories have modeled particular aspects of growth in Arabidopsis thaliana, but it was unclear whether these existing models could productively be combined. We test this approach by constructing a multiscale model of Arabidopsis rosette growth. Four existing models were integrated with minimal parameter modification (leaf water content and one flowering parameter used measured data). The resulting framework model links genetic regulation and biochemical dynamics to events at the organ and whole-plant levels, helping to understand the combined effects of endogenous and environmental regulators on Arabidopsis growth. The framework model was validated and tested with metabolic, physiological, and biomass data from two laboratories, for five photoperiods, three accessions, and a transgenic line, highlighting the plasticity of plant growth strategies. The model was extended to include stochastic development. Model simulations gave insight into the developmental control of leaf production and provided a quantitative explanation for the pleiotropic developmental phenotype caused by overexpression of miR156, which was an open question. Modular, multiscale models, assembling knowledge from systems biology to ecophysiology, will help to understand and to engineer plant behavior from the genome to the field.

A functional and structural Mongolian Scots pine (Pinus sylvestris var. mongolica) model integrating architecture, biomass and effects of precipitation.

Mongolian Scots pine (Pinus sylvestris var. mongolica) is one of the principal tree species in the network of Three-North Shelterbelt for windbreak and sand stabilisation in China. The functions of shelterbelts are highly correlated with the architecture and eco-physiological processes of individual tree. Thus, model-assisted analysis of canopy architecture and function dynamic in Mongolian Scots pine is of value for better understanding its role and behaviour within shelterbelt ecosystems in these arid and semiarid regions. We present here a single-tree functional and structural model, derived from the GreenLab model, which is adapted for young Mongolian Scots pines by incorporation of plant biomass production, allocation, allometric rules and soil water dynamics. The model is calibrated and validated based on experimental measurements taken on Mongolian Scots pines in 2007 and 2006 under local meteorological conditions. Measurements include plant biomass, topology and geometry, as well as soil attributes and standard meteorological data. After calibration, the model allows reconstruction of three-dimensional (3D) canopy architecture and biomass dynamics for trees from one- to six-year-old at the same site using meteorological data for the six years from 2001 to 2006. Sensitivity analysis indicates that rainfall variation has more influence on biomass increment than on architecture, and the internode and needle compartments and the aboveground biomass respond linearly to increases in precipitation. Sensitivity analysis also shows that the balance between internode and needle growth varies only slightly within the range of precipitations considered here. The model is expected to be used to investigate the growth of Mongolian Scots pines in other regions with different soils and climates.

A virtual plant that responds to the environment like a real one: the case for chrysanthemum.

• 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.

A stochastic model of tree architecture and biomass partitioning: application to Mongolian Scots pines.

BACKGROUND AND AIMS: Mongolian Scots pine (Pinus sylvestris var. mongolica) is one of the principal species used for windbreak and sand stabilization in arid and semi-arid areas in northern China. A model-assisted analysis of its canopy architectural development and functions is valuable for better understanding its behaviour and roles in fragile ecosystems. However, due to the intrinsic complexity and variability of trees, the parametric identification of such models is currently a major obstacle to their evaluation and their validation with respect to real data. The aim of this paper was to present the mathematical framework of a stochastic functional-structural model (GL2) and its parameterization for Mongolian Scots pines, taking into account inter-plant variability in terms of topological development and biomass partitioning. METHODS: In GL2, plant organogenesis is determined by the realization of random variables representing the behaviour of axillary or apical buds. The associated probabilities are calibrated for Mongolian Scots pines using experimental data including means and variances of the numbers of organs per plant in each order-based class. The functional part of the model relies on the principles of source-sink regulation and is parameterized by direct observations of living trees and the inversion method using measured data for organ mass and dimensions. KEY RESULTS: The final calibration accuracy satisfies both organogenetic and morphogenetic processes. Our hypothesis for the number of organs following a binomial distribution is found to be consistent with the real data. Based on the calibrated parameters, stochastic simulations of the growth of Mongolian Scots pines in plantations are generated by the Monte Carlo method, allowing analysis of the inter-individual variability of the number of organs and biomass partitioning. Three-dimensional (3D) architectures of young Mongolian Scots pines were simulated for 4-, 6- and 8-year-old trees. CONCLUSIONS: This work provides a new method for characterizing tree structures and biomass allocation that can be used to build a 3D virtual Mongolian Scots pine forest. The work paves the way for bridging the gap between a single-plant model and a stand model.

Correlation between dynamic tomato fruit-set and source-sink ratio: a common relationship for different plant densities and seasons?

BACKGROUND AND AIMS: It is widely accepted that fruit-set in plants is related to source-sink ratio. Despite its critical importance to yield, prediction of fruit-set remains an ongoing problem in crop models. Functional-structural plant models are potentially able to simulate organ-level plasticity of plants. To predict fruit-set, the quantitative link between source-sink ratio and fruit-set probability is analysed here via a functional-structural plant model, GreenLab. METHODS: Two experiments, each with four plant densities, were carried out in a solar greenhouse during two growth seasons (started in spring and autumn). Dynamic fruit-set probability was estimated by frequent observation on inflorescences. Source and sink parameter values were obtained by fitting GreenLab outputs for the biomass of plant parts (lamina, petiole, internode, fruit), at both organ and plant level, to corresponding destructive measurements at six dates from real plants. The dynamic source-sink ratio was calculated as the ratio between biomass production and plant demand (sum of all organ sink strength) per growth cycle, both being outputs of the model. KEY RESULTS AND CONCLUSIONS: Most sink parameters were stable over multiple planting densities and seasons. From planting, source-sink ratio increased in the vegetative stage and reached a peak after fruit-set commenced, followed by a decrease of leaf appearance rate. Fruit-set probability was correlated with the source-sink ratio after the appearance of flower buds. The relationship between fruit-set probability and the most correlated source-sink ratio could be quantified by a single regression line for both experiments. The current work paves the way to predicting dynamic fruit-set using a functional structure model.

Characterization of the interactions between architecture and source-sink relationships in winter oilseed rape (Brassica napus) using the GreenLab model.

BACKGROUND AND AIMS: This study aimed to characterize the interaction between architecture and source-sink relationships in winter oilseed rape (WOSR): do the costs of ramification compromise the source-sink ratio during seed filling? The GreenLab model is a good candidate to address this question because it has been already used to describe interactions between source-sink relationships and architecture for other species. However, its adaptation to WOSR is a challenge because of the complexity of its developmental scheme, especially during the reproductive phase. METHODS: Equations were added in GreenLab to compute expansion delays for ramification, flowering of each axis and photosynthesis of pods including the energetic cost of oil synthesis. Experimental field data were used to estimate morphological parameters while source-sink parameters of the model were estimated by adjustment of model outputs to the data. Ecophysiological outputs were used to assess the sources/sink relationships during the whole growth cycle. KEY RESULTS: First results indicated that, at the plant scale, the model correctly simulates the dynamics of organ growth. However, at the organ scale, errors were observed that could be explained either by secondary growth that was not incorporated or by uncertainties in morphological parameters (durations of expansion and life). Ecophysiological outputs highlighted the dramatic negative impact of ramification on the source-sink ratio, as well as the decrease in this ratio during seed filling despite pod envelope photosynthesis that allowed significant biomass production to be maintained. CONCLUSIONS: This work is a promising first step in the construction of a structure-function model for a plant as complex as WOSR. Once tested for other environments and/or genotypes, the model can be used for studies on WOSR architectural plasticity.

Does the structure-function model GREENLAB deal with crop phenotypic plasticity induced by plant spacing? A case study on tomato.

BACKGROUND AND AIMS: Plant growth models able to simulate phenotypic plasticity are increasingly required because (1) they should enable better predictions of the observed variations in crop production, yield and quality, and (2) their parameters are expected to have a more robust genetic basis, with possible implications for selection of quantitative traits such as growth- and allocation-related processes. The structure-function plant model, GREENLAB, simulates resource-dependent plasticity of plant architecture. Evidence for its generality has been previously reported, but always for plants grown in a limited range of environments. This paper aims to test the model concept to its limits by using plant spacing as a means to generate a gradient of competition for light, and by using a new crop species, tomato, known to exhibit a strong photomorphogenetic response. METHODS: A greenhouse experiment was carried out with three homogeneous planting densities (plant spacing = 0.3, 0.6 and 1 m). Detailed records of plant development, plant architecture and organ growth were made throughout the growing period. Model calibration was performed for each situation using a statistical optimization procedure (multi-fitting). KEY RESULTS AND CONCLUSIONS: Obvious limitations of the present version of the model appeared to account fully for the plant plasticity induced by inter-plant competition for light. A lack of stability was identified for some model parameters at very high planting density. In particular, those parameters characterizing organ sink strengths and governing light interception proved to be environment-dependent. Remarkably, however, responses of the parameter values concerned were consistent with actual growth measurements and with previously reported results. Furthermore, modifications of total biomass production and of allocation patterns induced by the planting-density treatments were accurately simulated using the sets of optimized parameters. These results demonstrate that the overall model structure is potentially able to reproduce the observed plant plasticity and suggest that sound biologically based adaptations could overcome the present model limitations. Potential options for model improvement are proposed, and the possibility of using the kernel algorithm currently available as a fitting tool to build up more sophisticated model versions is advocated.

The derivation of sink functions of wheat organs using the GREENLAB model.

BACKGROUND AND AIMS: In traditional crop growth models assimilate production and partitioning are described with empirical equations. In the GREENLAB functional-structural model, however, allocation of carbon to different kinds of organs depends on the number and relative sink strengths of growing organs present in the crop architecture. The aim of this study is to generate sink functions of wheat (Triticum aestivum) organs by calibrating the GREENLAB model using a dedicated data set, consisting of time series on the mass of individual organs (the 'target data'). METHODS: An experiment was conducted on spring wheat (Triticum aestivum, 'Minaret'), in a growth chamber from, 2004 to, 2005. Four harvests were made of six plants each to determine the size and mass of individual organs, including the root system, leaf blades, sheaths, internodes and ears of the main stem and different tillers. Leaf status (appearance, expansion, maturity and death) of these 24 plants was recorded. With the structures and mass of organs of four individual sample plants, the GREENLAB model was calibrated using a non-linear least-square-root fitting method, the aim of which was to minimize the difference in mass of the organs between measured data and model output, and to provide the parameter values of the model (the sink strengths of organs of each type, age and tiller order, and two empirical parameters linked to biomass production). KEY RESULTS AND CONCLUSIONS: The masses of all measured organs from one plant from each harvest were fitted simultaneously. With estimated parameters for sink and source functions, the model predicted the mass and size of individual organs at each position of the wheat structure in a mechanistic way. In addition, there was close agreement between experimentally observed and simulated values of leaf area index.

Computing competition for light in the GREENLAB model of plant growth: a contribution to the study of the effects of density on resource acquisition and architectural development.

BACKGROUND AND AIMS: The dynamical system of plant growth GREENLAB was originally developed for individual plants, without explicitly taking into account interplant competition for light. Inspired by the competition models developed in the context of forest science for mono-specific stands, 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. METHODS: The empirical production equation of GREENLAB is extrapolated to stands 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 neighbouring plants whose crown projection surfaces overlap. 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, PhD Thesis, Ecole Centrale de Paris, France). KEY RESULTS AND CONCLUSIONS: The model is applied to mono-specific field crops and forest stands. For high-density crops at full cover, the model is shown to be equivalent to the classical equation of field crop production (Howell and Musick, 1985, in Les besoins en eau des cultures; Paris: INRA Editions). However, our method is more accurate at the early stages of growth (before cover) or in the case of intermediate densities. It may potentially account for local effects, such as uneven spacing, variation in the time of plant emergence or variation in seed biomass. The application of the model to trees illustrates the expression of plant plasticity in response to competition for light. Density strongly impacts on tree architectural development through interactions with the source-sink balances during growth. The effects of density on tree height and radial growth that are commonly observed in real stands appear as emerging properties of the model.

Parametric identification of a functional-structural tree growth model and application to beech trees (Fagus sylvatica).

Functional-structural models provide detailed representations of tree growth and their application to forestry seems full of prospects. However, owing to the complexity of tree architecture, parametric identification of such models remains a critical issue. We present the GreenLab approach for modelling tree growth. It simulates tree growth plasticity in response to changes of their internal level of trophic competition, especially topological development and cambial growth. The model includes a simplified representation of tree architecture, based on a species-specific description of branching patterns. We study whether those simplifications allow enough flexibility to reproduce with the same set of parameters the growth of two observed understorey beech trees (Fagus sylvatica L.) of different ages in different environmental conditions. The parametric identification of the model is global, i.e. all parameters are estimated simultaneously, potentially providing a better description of interactions between sub-processes. As a result, the source-sink dynamics throughout tree development is retrieved. Simulated and measured trees were compared for their trunk profiles (fresh masses and dimensions of every growth units, ring diameters at different heights) and compartment masses of their order 2 branches. Possible improvements of this method by including topological criteria are discussed.

A model-based analysis of the dynamics of carbon balance at the whole-plant level in Arabidopsis thaliana.

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.

Parameter optimization and field validation of the functional-structural model GREENLAB for maize at different population densities.

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: 2.8, 5.6 and 11.1 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.

AmapSim: a structural whole-plant simulator based on botanical knowledge and designed to host external functional models.

BACKGROUND AND AIMS: AmapSim is a tool that implements a structural plant growth model based on a botanical theory and simulates plant morphogenesis to produce accurate, complex and detailed plant architectures. This software is the result of more than a decade of research and development devoted to plant architecture. New advances in the software development have yielded plug-in external functions that open up the simulator to functional processes. METHODS: The simulation of plant topology is based on the growth of a set of virtual buds whose activity is modelled using stochastic processes. The geometry of the resulting axes is modelled by simple descriptive functions. The potential growth of each bud is represented by means of a numerical value called physiological age, which controls the value for each parameter in the model. The set of possible values for physiological ages is called the reference axis. In order to mimic morphological and architectural metamorphosis, the value allocated for the physiological age of buds evolves along this reference axis according to an oriented finite state automaton whose occupation and transition law follows a semi-Markovian function. KEY RESULTS: Simulations were performed on tomato plants to demonstrate how the AmapSim simulator can interface external modules, e.g. a GREENLAB growth model and a radiosity model. CONCLUSIONS: The algorithmic ability provided by AmapSim, e.g. the reference axis, enables unified control to be exercised over plant development parameter values, depending on the biological process target: how to affect the local pertinent process, i.e. the pertinent parameter(s), while keeping the rest unchanged. This opening up to external functions also offers a broadened field of applications and thus allows feedback between plant growth and the physical environment.

Quantitative genetics and functional-structural plant growth models: simulation of quantitative trait loci detection for model parameters and application to potential yield optimization.

BACKGROUND AND AIMS: 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. METHODS: 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. KEY RESULTS AND CONCLUSIONS: 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.