基于植株拓扑结构的生物量分配的玉米虚拟模型

依据植物结构—功能相互作用机理,建立了能模拟玉米生长发育与形态结构建成的虚拟模型。该模型的重要部分为基于植株拓扑结构的生物量分配模块。叙述了该模块的构建原理,以2000年田间试验数据提取了玉米的发育、生物量生产和生物量分配参数。模型模拟了2001年的玉米生长发育与生物量分配过程,模拟结果与田间试验结果比较吻合。应用该模型模拟了2001年玉米不同生育阶段植株的生物量分配和各器官生物量积累动态。     

Parameter optimization and field validation of the functional-structural model GREENLAB for maize

BACKGROUND AND AIMS: There are three reasons for the increasing demand for crop models that build the plant on the basis of architectural principles and organogenetic processes: (1) realistic concepts for developing new crops need to be guided by such models; (2) there is an increasing interest in crop phenotypic plasticity, based on variable architecture and morphology; and (3) engineering of mechanized cropping systems requires information on crop architecture. The functional-structural model GREENLAB was recently presented that simulates resource-dependent plasticity of plant architecture. This study introduces a new methodology for crop parameter optimization against measured data called multi-fitting, validates the calibrated model for maize with independent field data, and describes a technique for 3D visualization of outputs. METHODS: Maize was grown near Beijing during the 2000, 2001 and 2003 (two sowing dates) summer seasons in a block design with four to five replications. Detailed morphological and topological observations were made on the plant architecture throughout the development of the four crops. Data obtained in 2000 was used to establish target files for parameter optimization using the generalized least square method, and parameter accuracy was evaluated by coefficient of variance. In situ plant digitization was used to establish 3D symbol files for organs that were then used to translate model outputs directly into 3D representations for each time step of model execution. KEY RESULTS AND CONCLUSIONS: Multi-fitting against several target files obtained at different growth stages gave better parameter accuracy than single fitting at maturity only, and permitted extracting generic organ expansion kinetics from the static observations. The 2000 model gave excellent predictions of plant architecture and vegetative growth for the other three seasons having different temperature regimes, but predictions of inter-seasonal variability of biomass partitioning during grain filling were less accurate. This was probably due to insufficient consideration of processes governing cob sink size and terminal leaf senescence. Further perspectives for model improvement are discussed.     

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.     

Parameter stability of the functional-structural plant model GREENLAB as affected by variation within populations, among seasons and among growth stages

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. METHODS: 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.     

A dynamic, architectural plant model simulating resource-dependent growth

BACKGROUND AND AIMS: Physiological and architectural plant models have originally been developed for different purposes and therefore have little in common, thus making combined applications difficult. There is, however, an increasing demand for crop models that simulate the genetic and resource-dependent variability of plant geometry and architecture, because man is increasingly able to transform plant production systems through combined genetic and environmental engineering. MODEL: GREENLAB is presented, a mathematical plant model that simulates interactions between plant structure and function. Dual-scale automaton is used to simulate plant organogenesis from germination to maturity on the basis of organogenetic growth cycles that have constant thermal time. Plant fresh biomass production is computed from transpiration, assuming transpiration efficiency to be constant and atmospheric demand to be the driving force, under non-limiting water supply. The fresh biomass is then distributed among expanding organs according to their relative demand. Demand for organ growth is estimated from allometric relationships (e.g. leaf surface to weight ratios) and kinetics of potential growth rate for each organ type. These are obtained through parameter optimization against empirical, morphological data sets by running the model in inverted mode. Potential growth rates are then used as estimates of relative sink strength in the model. These and other 'hidden' plant parameters are calibrated using the non-linear, least-square method. KEY RESULTS AND CONCLUSIONS: The model reproduced accurately the dynamics of plant growth, architecture and geometry of various annual and woody plants, enabling 3D visualization. It was also able to simulate the variability of leaf size on the plant and compensatory growth following pruning, as a result of internal competition for resources. The potential of the model's underlying concepts to predict the plant's phenotypic plasticity is discussed.     

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.     

基于器官生物量构建植株形态的玉米虚拟模型

探讨了基于玉米器官生物量模拟其形态的方法,并应用2000年田间试验数据提取了玉米节间、叶鞘和叶片的形态构建参数。基于玉米虚拟模型生物量分配模块模拟的器官生物量积累和建立的形态构建方法与提取的参数,模拟了2001年玉米不同生长阶段的器官形态,模拟结果与田间试验数据吻合较好。应用本模型实现了玉米生长过程中植株各个器官形态变化以及植株高度、叶面积动态的模拟,并实现了植株形态的可视化。     

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.     

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.     

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.     

Response of maize biomass and soil water fluxes on elevated CO2 and drought—From field experiments to process‐based simulations

The rising concentration of atmospheric carbon dioxide (CO₂) is known to increase the total aboveground biomass of several C3 crops, whereas C4 crops are reported to be hardly affected when water supply is sufficient. However, a free‐air carbon enrichment (FACE) experiment in Braunschweig, Germany, in 2007 and 2008 resulted in a 25% increased biomass of the C4 crop maize under restricted water conditions and elevated CO₂ (550 ppm). To project future yields of maize under climate change, an accurate representation of the effects of eCO₂ and drought on biomass and soil water conditions is essential. Current crop growth models reveal limitations in simulations of maize biomass under eCO₂ and limited water supply. We use the coupled process‐based hydrological‐plant growth model Catchment Modeling Framework‐Plant growth Modeling Framework to overcome this limitation. We apply the coupled model to the maize‐based FACE experiment in Braunschweig that provides robust data for the investigation of combined CO₂ and drought effects. We approve hypothesis I that CO₂ enrichment has a small direct‐fertilizing effect with regard to the total aboveground biomass of maize and hypothesis II that CO₂ enrichment decreases water stress and leads to higher yields of maize under restricted water conditions. Hypothesis III could partly be approved showing that CO₂ enrichment decreases the transpiration of maize, but does not raise soil moisture, while increasing evaporation. We emphasize the importance of plant‐specific CO₂ response factors derived by use of comprehensive FACE data. By now, only one FACE experiment on maize is accomplished applying different water levels. For the rigorous testing of plant growth models and their applicability in climate change studies, we call for datasets that go beyond single criteria (only yield response) and single effects (only elevated CO₂).     

Rhythms and alternating patterns in plants as emergent properties of a model of interaction between development and functioning

BACKGROUND AND AIMS: To model plasticity of plants in their environment, a new version of the functional-structural model GREENLAB has been developed with full interactions between architecture and functioning. Emergent properties of this model were revealed by simulations, in particular the automatic generation of rhythms in plant development. Such behaviour can be observed in natural phenomena such as the appearance of fruit (cucumber or capsicum plants, for example) or branch formation in trees. METHODS: In the model, a single variable, the source-sink ratio controls different events in plant architecture. In particular, the number of fruits and branch formation are determined as increasing functions of this ratio. For some sets of well-chosen parameters of the model, the dynamical evolution of the ratio during plant growth generates rhythms. KEY RESULTS AND CONCLUSIONS: Cyclic patterns in branch formation or fruit appearance emerge without being forced by the model. The model is based on the theory of discrete dynamical systems. The mathematical formalism helps us to explain rhythm generation and to control the behaviour of the system. Rhythms can appear during both the exponential and stabilized phases of growth, but the causes are different as shown by an analytical study of the system. Simulated plant behaviours are very close to those observed on real plants. With a small number of parameters, the model gives very interesting results from a qualitative point of view. It will soon be subjected to experimental data to estimate the model parameters.     

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.     

Characterization of the effects of inter-tree competition on source–sink balance in Chinese pine trees with the GreenLab model

We investigate the characteristics of individual tree response to competition on source–sink balance through the functional–structural plant model GreenLab. Four Chinese pine (Pinus tabulaeformis Carr.) trees were destructively sampled and were divided into two groups: high-density group and low-density group. First, the effects of density on organ dimensions and on organ relative mass were analysed based on experimental measurements. These were primary indicators of the plant response to competition. Second, the hidden parameters of the GreenLab model, as well as a tree-specific characteristic surface, were estimated using the data of total tree biomass for needle and wood compartments, for each of the four trees in parallel. The quality of the fitting is finally validated using data of individual organ mass at shoot level for the sampled branches. The Mann–Whitney Student’s t test showed that there were significant differences between the shoot attributes of the two groups for shoot diameter, shoot biomass and needle biomass. No significant difference was found for current year shoot lengths of the two groups. The parametric identification of the model allowed estimating and comparing the amount of biomass that was allocated to primary growth and to secondary growth in the two density conditions. It showed that biomass allocated to secondary growth (ring compartment) was the most strongly affected by density, and that the organ demand satisfaction ratio profiles of each of these trees were a relevant, integrated indicator of the tree state.     

Perennial rhizomatous grasses as bioenergy feedstock in SWAT: parameter development and model improvement

The Soil and Water Assessment Tool (SWAT) is increasingly used to quantify h y drologic and water quality impacts of bioenergy production, but crop‐growth parameters for candidate perennial rhizomatous grasses (PRG) Miscanthus × giganteus and upland ecotypes of Panicum virgatum (switchgrass) are limited by the availability of field data. Crop‐growth parameter ranges and suggested values were developed in this study using agronomic and weather data collected at the Purdue University Water Quality Field Station in northwestern Indiana. During the process of parameterization, the comparison of measured data with conceptual representation of PRG growth in the model led to three changes in the SWAT 2009 code: the harvest algorithm was modified to maintain belowground biomass over winter, plant respiration was extended via modified‐DLAI to better reflect maturity and leaf senescence, and nutrient uptake algorithms were revised to respond to temperature, water, and nutrient stress. Parameter values and changes to the model resulted in simulated biomass yield and leaf area index consistent with reported values for the region. Code changes in the SWAT model improved nutrient storage during dormancy period and nitrogen and phosphorus uptake by both switchgrass and Miscanthus.     

基于光合产物动态分配的玉米生物量模拟

光合产物分配是作物生长发育及生物量形成的关键环节,也是作物生长模拟的重要内容.本研究依据光合产物分配机理,结合玉米不同生长阶段的光合产物分配特点,构建了玉米光合产物分配模型.与WOFOST模型的CO₂同化模块相结合,实现了对玉米各器官生物量动态的逐日模拟.利用锦州农田生态系统野外观测站5年的春玉米大田试验资料对模拟效果进行了验证.结果表明: 模型能解释总生物量变化的95.4%;对营养器官生物量变化的解释率达87.0%;对叶、根、茎生物量变化的解释率分别达85.3%,67.9%和76.5%;对穗生物量变化的解释率达87.5%.模型可实现玉米各器官的生物量动态的准确模拟.     

基于GreenLab的油松结构-功能模型

 植物结构-功能模型(Functional-structural models, FSMs)将结构模型与过程模型结合起来, 用以描述环境机制驱动的植物生长, 输出植物的三维结构。GreenLab是一个近年来不断发展着的基于源-汇关系的通用植物结构-功能模型, 它多应用于农作物, 在树木方面的应用还很少。该文以幼龄油松(Pinus tabulaeformis)为研究对象, 首次将GreenLab模型应用到虚拟树木生长的研究中。采用破坏性取样, 实测了9株油松幼树的形态结构、拓扑结构和器官生物量信息, 根据拓扑编码体系组织数据。模型的直接参数是通过实测数据获得的, 隐含参数是利用非线性最小二乘法拟合反求获得的。对模型的假设进行了验证, 并对模型的模拟效果进行了评估, 结果表明: 节间总鲜质量、树木叶总鲜质量、节间鲜质量、节间长度观测值和模型模拟值建立的回归方程的决定系数在0.78~0.91之间, 因此该模型较真实地反映了油松的结构和生长过程。提出的树木结构和生物量测量及编码方法, 可作为针叶树建立结构-功能模型的参照。     

棉花蕾花铃生物量、氮累积特征及临界氮浓度稀释模型

在大田栽培条件下,于河南安阳（黄河流域黄淮棉区）和江苏南京（长江流域下游棉区）设置了棉花氮素水平试验,对不同氮素水平条件下棉花蕾花铃的生物量、氮素累积及氮浓度的动态变化进行分析,并依据Justes的临界氮浓度稀释模型确定方法,研究棉花蕾花铃临界氮浓度稀释模型。结果表明：棉花蕾花铃的生物量增长和氮吸收累积均受氮素水平的影响,其动态变化符合S型曲线,氮累积的快速起始时间较生物量早1～5d;氮浓度过高或过低均不利于产量形成,蕾花铃等器官存在氮奢侈消费现象;氮浓度随施氮量的增加而升高、随生育进程的推移而降低,其生物量累积量与氮浓度间符合幂函数关系,两试点蕾花铃氮稀释曲线模型形式相同,但模型参数a不同,不同生态区存在独立的临界氮稀释曲线模型。由于临界稀释模型具有明确的生物学意义,可以作为定量诊断蕾花铃氮营养动态变化的指标之一。