Mengzhen Kang

Structural Factorization of Plants to Compute Their Functional and Architectural Growth

Numerical simulation of plant growth has been facing a bottleneck due to the cumbersome computation implied by the complex plant topological structure. In this article, the authors present a new mathematical model for plant growth, GreenLab, overcoming these difficulties. GreenLab is based on a powerful factorization of the plant structure. Fast simulation algorithms are derived for deterministic and stochastic trees. The computation time no longer depends on the number of organs and grows at most quadratically with the age of the plant. This factorization finds applications to build trees very efficiently, in the context of geometric models, and to compute biomass production and distribution, in the context of functional structural 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.

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.

Stochastic modelling of tree annual shoot dynamics

Abstract• ContextModelling annual shoot development processes is a key step towards functional–structural modelling of trees. Various patterns of meristem activity can be distinguished in tree shoots, with active periods of phytomer production followed by rest periods. This approach has seldom been integrated in functional–structural tree models.• AimsThis paper presents theoretical research work on modelling and computation of the dynamics of tree annual shoots using stochastic processes with various development patterns: continuous or rhythmic, monocyclic or polycyclic, “seasonal” or “a-seasonal”, with preformation or neoformation produced from meristem functioning.• MethodsThe renewal theory is used to compute stochastic aspects of phytomer production, resulting from meristem extension or rest periods and meristem mortality.• ResultsContinuous development can be modelled with a Bernoulli process, while rhythmic development is modelled by alternation between extension and rest periods, the duration of each period following specific distributions.• ConclusionThe application of such stochastic modelling is the estimation of organ production during tree development as a component of the demand in functional–architectural tree models, used for computing biomass production and partitioning.

Original article: An optimal control methodology for plant growth-Case study of a water supply problem of sunflower

An optimal control methodology is proposed for plant growth. This methodology is demonstrated by solving a water supply problem for optimal sunflower fruit filling. The functional-structural sunflower growth is described by a dynamical system given soil water conditions. Numerical solutions are obtained through an iterative optimization procedure, in which the gradients of the objective function, i.e. the sunflower fruit weight, are calculated efficiently either with adjoint modeling or by differentiation algorithms. Further improvements in sunflower yield have been found compared to those obtained using genetic algorithms in our previous studies. The optimal water supplies adapt to the fruit filling. For instance, during the mid-season growth, the supply frequency condenses and the supply amplitude peaks. By contrast, much less supplies are needed during the early and ending growth stages. The supply frequency is a determining factor, whereas the sunflower growth is less sensitive to the time and amount of one specific irrigation. These optimization results agree with common qualitative agronomic practices. Moreover they provide more precise quantitative control for sunflower growth.

A Stochastic Language for Plant Topology

The article describes a stochastic formal language adapted to the botanical concepts underlying the GreenLab organogenesis model. It is based on stochastic L-systems (parallel rewriting grammars) and on multi-type branching processes: stochastic processes control bud productions and at each growth cycle, each new growth unit is the result of a random variable. This formalism allows determining inductively the generating functions of the resulting plant structures and of the numbers of organs, which fully characterizes the plant development resulting from the elementary stochastic processes of bud productions. The moments of the stochastic distributions of the numbers of organs are also explicitly deduced.

Functional tree models reacting to the environment

Visually realistic tree images competing for light and space have been created previously [Paubicki et al. 2009]. Here we present a method of generating tree forms reacting to the environment based on several biological hypothesis. In this method, a tree is composed of functional organs playing roles of sources and/or sinks of biomass. Each tree is a stand-alone artificial life with internal feedback between its structure and functioning.

Calibration of Topological Development in the Procedure of Parametric Identification: Application of the Stochastic GreenLab Model for Pinus sylvestris var. mongolica

Climate, biophysical conditions and human activities all contribute to the occurrences of ecosystem and environment problems, i.e. water scarcity, desertification, salinization, in arid and semiarid zone of North China. Mongolian Scots pine tree (Pinus sylvestris var. mongolica) is one of the principal species of the windbreak and sand-fixing forest in this area. In this paper, we presented the calibration process of stochastic GreenLab model based on experiment data. Specific plant topology and sink–source parameters were estimated for Mongolian Scots pine trees through optimizing procedure. The fitting results showed that the calibration process were reasonable and acceptable. The model produced a variety of three-dimensional visual representations of Mongolian Scots pine trees with different topological structures simulated by Monte Carlo methods. This model can be used to describe the plant development and growth in a stand level, taking into accounts the variations in plant topology and biomass.

From parallel plants to smart plants: intelligent control and management for plant growth

Precision management of agricultural systems, aiming at optimizing profitability, productivity and sustainability, comprises a set of technologies including sensors, information systems, and informed management, etc. Expert systems are expected to aid farmers in plant management or environment control, but they are mostly based on the offline and static information, deviated from the actual situation. Parallel management, achieved by virtual/artificial agricultural system, computational experiment and parallel execution, provides a generic framework of solution for online decision support. In this paper, we present the three steps toward the parallel management of plant: growth description U+0028 the crop model U+0029, prediction, and prescription. This approach can update the expert system by adding learning ability and the adaption of knowledge database according to the descriptive and predictive model. The possibilities of passing the knowledge of experienced farmers to younger generation, as well as the application to the parallel breeding of plant through such system, are discussed.