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1.  Plant growth and architectural modelling and its applications 
Annals of Botany  2011;107(5):723-727.
Over the last decade, a growing number of scientists around the world have invested in research on plant growth and architectural modelling and applications (often abbreviated to plant modelling and applications, PMA). By combining physical and biological processes, spatially explicit models have shown their ability to help in understanding plant–environment interactions. This Special Issue on plant growth modelling presents new information within this topic, which are summarized in this preface. Research results for a variety of plant species growing in the field, in greenhouses and in natural environments are presented. Various models and simulation platforms are developed in this field of research, opening new features to a wider community of researchers and end users. New modelling technologies relating to the structure and function of plant shoots and root systems are explored from the cellular to the whole-plant and plant-community levels.
PMCID: PMC3077987  PMID: 21638797
Plant morphology; architecture; functional–structural plant model; FSPM; source and sink; root system; photosynthesis; simulation; plasticity; computational plants
2.  Three-dimensional distribution of vessels, passage cells and lateral roots along the root axis of winter wheat (Triticum aestivum) 
Annals of Botany  2011;107(5):843-853.
Background and Aims
The capacity of a plant to absorb and transport water and nutrients depends on anatomical structures within the roots and their co-ordination. However, most descriptions of root anatomical structure are limited to 2-D cross-sections, providing little information on 3-D spatial relationships and hardly anything on their temporal evolution. Three-dimensional reconstruction and visualization of root anatomical structures can illustrate spatial co-ordination among cells and tissues and provide new insights and understanding of the interrelation between structure and function.
Classical paraffin serial-section methods, image processing, computer-aided 3-D reconstruction and 3-D visualization techniques were combined to analyse spatial relationships among metaxylem vessels, passage cells and lateral roots in nodal roots of winter wheat (Triticum aestivum).
Key Results
3-D reconstruction demonstrated that metaxylem vessels were neither parallel, nor did they run directly along the root axis from the root base to the root tip; rather they underwent substitution and transition. Most vessels were connected to pre-existent or newly formed vessels by pits on their lateral walls. The spatial distributions of both passage cells and lateral roots exhibited similar position-dependent patterns. In the transverse plane, the passage cells occurred opposite the poles of the protoxylem and the lateral roots opposite those of the protophloem. Along the axis of a young root segment, the passage cells were arranged in short and discontinuous longitudinal files, thus as the tissues mature, the sequence in which the passage cells lose their transport function is not basipetal. In older segments, passage cells decreased drastically in number and coexisted with lateral roots. The spatial distribution of lateral roots was similar to that of the passage cells, mirroring their similar functions as lateral pathways for water and nutrient transport to the stele.
With the 3-D reconstruction and visualization techniques developed here, the spatial relationships between vessels, passage cells and lateral roots and the temporal evolution of these relationships can be described. The technique helps to illustrate synchronization and spatial co-ordination among the root's radial and axial pathways for water and nutrient transport and the interdependence of structure and function in the root.
PMCID: PMC3077985  PMID: 21289027
Winter wheat; Triticum aestivum; metaxylem vessel; passage cell; lateral root; 3-D reconstruction; 3-D visualization; spatial co-ordination; positional relationship
3.  A stochastic model of tree architecture and biomass partitioning: application to Mongolian Scots pines 
Annals of Botany  2010;107(5):781-792.
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.
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.
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.
PMCID: PMC3077980  PMID: 21062760
Pinus sylvestris var. mongolica; functional–structural plant model; canopy architecture; three-dimensional; forest canopy; virtual plant; GreenLab, parameterization
4.  Parameter Optimization and Field Validation of the Functional–Structural Model GREENLAB for Maize at Different Population Densities 
Annals of Botany  2007;101(8):1185-1194.
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.
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.
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.
PMCID: PMC2710275  PMID: 17921525
Functional–structural plant model; GREENLAB; plant architecture; source–sink relationship; plant population density; maize (Zea mays); model parameterization
5.  Parameter Stability of the Functional–Structural Plant Model GREENLAB as Affected by Variation within Populations, among Seasons and among Growth Stages 
Annals of Botany  2006;99(1):61-73.
Background and Aims
It is increasingly accepted that crop models, if they are to simulate genotype-specific behaviour accurately, should simulate the morphogenetic process generating plant architecture. A functional–structural plant model, GREENLAB, was previously presented and validated for maize. The model is based on a recursive mathematical process, with parameters whose values cannot be measured directly and need to be optimized statistically. This study aims at evaluating the stability of GREENLAB parameters in response to three types of phenotype variability: (1) among individuals from a common population; (2) among populations subjected to different environments (seasons); and (3) among different development stages of the same plants.
Five field experiments were conducted in the course of 4 years on irrigated fields near Beijing, China. Detailed observations were conducted throughout the seasons on the dimensions and fresh biomass of all above-ground plant organs for each metamer. Growth stage-specific target files were assembled from the data for GREENLAB parameter optimization. Optimization was conducted for specific developmental stages or the entire growth cycle, for individual plants (replicates), and for different seasons. Parameter stability was evaluated by comparing their CV with that of phenotype observation for the different sources of variability. A reduced data set was developed for easier model parameterization using one season, and validated for the four other seasons.
Key Results and Conclusions
The analysis of parameter stability among plants sharing the same environment and among populations grown in different environments indicated that the model explains some of the inter-seasonal variability of phenotype (parameters varied less than the phenotype itself), but not inter-plant variability (parameter and phenotype variability were similar). Parameter variability among developmental stages was small, indicating that parameter values were largely development-stage independent. The authors suggest that the high level of parameter stability observed in GREENLAB can be used to conduct comparisons among genotypes and, ultimately, genetic analyses.
PMCID: PMC2802986  PMID: 17158141
Plant architecture; functional–structural models; crop simulation; parameter stability; allometric relationships; sink capacity; Zea mays

Results 1-5 (5)