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.

Crop/Plant Modeling Supports Plant Breeding: II. Guidance of Functional Plant Phenotyping for Trait Discovery.

Observable morphological traits are widely employed in plant phenotyping for breeding use, which are often the external phenotypes driven by a chain of functional actions in plants. Identifying and phenotyping inherently functional traits for crop improvement toward high yields or adaptation to harsh environments remains a major challenge. Prediction of whole-plant performance in functional-structural plant models (FSPMs) is driven by plant growth algorithms based on organ scale wrapped up with micro-environments. In particular, the models are flexible for scaling down or up through specific functions at the organ nexus, allowing the prediction of crop system behaviors from the genome to the field. As such, by virtue of FSPMs, model parameters that determine organogenesis, development, biomass production, allocation, and morphogenesis from a molecular to the whole plant level can be profiled systematically and made readily available for phenotyping. FSPMs can provide rich functional traits representing biological regulatory mechanisms at various scales in a dynamic system, e.g., Rubisco carboxylation rate, mesophyll conductance, specific leaf nitrogen, radiation use efficiency, and source-sink ratio apart from morphological traits. High-throughput phenotyping such traits is also discussed, which provides an unprecedented opportunity to evolve FSPMs. This will accelerate the co-evolution of FSPMs and plant phenomics, and thus improving breeding efficiency. To expand the great promise of FSPMs in crop science, FSPMs still need more effort in multiscale, mechanistic, reproductive organ, and root system modeling. In summary, this study demonstrates that FSPMs are invaluable tools in guiding functional trait phenotyping at various scales and can thus provide abundant functional targets for phenotyping toward crop improvement.

Machine learning versus crop growth models: an ally, not a rival.

The rapid increases of the global population and climate change pose major challenges to a sustainable production of food to meet consumer demands. Process-based models (PBMs) have long been used in agricultural crop production for predicting yield and understanding the environmental regulation of plant physiological processes and its consequences for crop growth and development. In recent years, with the increasing use of sensor and communication technologies for data acquisition in agriculture, machine learning (ML) has become a popular tool in yield prediction (especially on a large scale) and phenotyping. Both PBMs and ML are frequently used in studies on major challenges in crop production and each has its own advantages and drawbacks. We propose to combine PBMs and ML given their intrinsic complementarity, to develop knowledge- and data-driven modelling (KDDM) with high prediction accuracy as well as good interpretability. Parallel, serial and modular structures are three main modes can be adopted to develop KDDM for agricultural applications. The KDDM approach helps to simplify model parameterization by making use of sensor data and improves the accuracy of yield prediction. Furthermore, the KDDM approach has great potential to expand the boundary of current crop models to allow upscaling towards a farm, regional or global level and downscaling to the gene-to-cell level. The KDDM approach is a promising way of combining simulation models in agriculture with the fast developments in data science while mechanisms of many genetic and physiological processes are still under investigation, especially at the nexus of increasing food production, mitigating climate change and achieving sustainability.

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.

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.

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.

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.

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.

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.

Managing Traditional Solar Greenhouse With CPSS: A Just-for-Fit Philosophy.

The profit of greenhouse production is influenced by management activities (e.g., environmental control and plantation scheduling) as well as social conditions (e.g., price fluctuation). In China, the prevailing horticultural facility is the traditional solar greenhouse. The key existing problem is the lack of knowledge of growers, which in turn leads to inefficient management, low production, or unsalable products. To secure effective greenhouse management, the production planning system must account for the crop growing environment, grower's activities, and the market. This paper presents an agricultural cyber-physical-social system (CPSS) serving agricultural production management, with a case study on the solar greenhouse. The system inputs are derived from social and physical sensors, with the former collecting the price of agricultural products in a wholesale market, and the latter collecting the necessary environmental data in the solar greenhouse. Decision support for the cropping plan is provided by the artificial system, computational experiment, and parallel execution-based method, with description intelligence for estimating the crop development and harvest time, prediction intelligence for optimizing the planting time and area according to the expected targets (stable production or maximum gross profit), and prescription intelligence for online system training. The presented system fits the current technical and economic situation of horticulture in China. The application of agricultural CPSS could decrease waste in labor or fertilizer and support sustainable agricultural production.