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1.  Correlation between dynamic tomato fruit-set and source–sink ratio: a common relationship for different plant densities and seasons? 
Annals of Botany  2010;107(5):805-815.
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.
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.
PMCID: PMC3077983  PMID: 21183453
Tomato; Solanum lycopersicum; fruit-set probability; time step; source–sink ratio; sink strength; functional–structural plant model; inverse modelling; plant plasticity
2.  Floral bud damage compensation by branching and biomass allocation in genotypes of Brassica napus with different architecture and branching potential 
Plant branching is a key process in the yield elaboration of winter oilseed rape (WOSR). It is also involved in plant tolerance to flower damage because it allows the setting of new fertile inflorescences. Here we characterize the changes in the branching and distribution of the number of pods between primary and secondary inflorescences in response to floral bud clippings. Then we investigate the impacts of the modifications in branching on the biomass allocation and its consequence on the crop productivity (harvest index). These issues were addressed on plants with contrasted architecture and branching potential, using three genotypes (Exocet, Pollen, and Gamin) grown under two levels of nitrogen fertilization. Clipping treatments of increasing intensities were applied to either inflorescences or flower buds. We were able to show that restoration of the number of pods after clipping is the main lever for the compensation. Genotypes presented different behaviors in branching and biomass allocation as a function of clipping treatments. The number of fertile ramifications increased for the high intensities of clipping. In particular, the growth of secondary ramifications carried by branches developed before clipping has been observed. The proportions of yield and of number of pods carried by these secondary axes increased and became almost equivalent to the proportion carried by primary inflorescences. In terms of biomass allocation, variations have also been evidenced in the relationship between pod dry mass on a given axis and the number of pods set, while the shoot/root ratio was not modified. The harvest index presented different responses: it decreased after flower buds clipping, while it was maintained after the clipping of the whole inflorescences. The results are discussed relative to their implications regarding the identification of interesting traits to be target in breeding programs in order to improve WOSR tolerance.
PMCID: PMC4338677  PMID: 25759703
winter oilseed rape; Brassica napus; architecture; biomass allocation; harvest index; allometry; plasticity; plant resilience
3.  A dynamic model of plant growth with interactions between development and functional mechanisms to study plant structural plasticity related to trophic competition 
Annals of Botany  2009;103(8):1173-1186.
Background and Aims
The strong influence of environment and functioning on plant organogenesis has been well documented by botanists but is poorly reproduced in most functional–structural models. In this context, a model of interactions is proposed between plant organogenesis and plant functional mechanisms.
The GreenLab model derived from AMAP models was used. Organogenetic rules give the plant architecture, which defines an interconnected network of organs. The plant is considered as a collection of interacting ‘sinks’ that compete for the allocation of photosynthates coming from ‘sources’. A single variable characteristic of the balance between sources and sinks during plant growth controls different events in plant development, such as the number of branches or the fruit load.
Key Results
Variations in the environmental parameters related to light and density induce changes in plant morphogenesis. Architecture appears as the dynamic result of this balance, and plant plasticity expresses itself very simply at different levels: appearance of branches and reiteration, number of organs, fructification and adaptation of ecophysiological characteristics.
The modelling framework serves as a tool for theoretical botany to explore the emergence of specific morphological and architectural patterns and can help to understand plant phenotypic plasticity and its strategy in response to environmental changes.
PMCID: PMC2685317  PMID: 19297366
Trophic plasticity; plant growth; functional–structural models; dynamic system; interactions; GreenLab
4.  The Derivation of Sink Functions of Wheat Organs using the GREENLAB Model 
Annals of Botany  2007;101(8):1099-1108.
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’).
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.
PMCID: PMC2710274  PMID: 18045794
Wheat; Triticum aestivum ‘Minaret’; tiller; GREENLAB; organ mass; functional–structural model; model calibration; multi-fitting; source–sink
5.  Simulation of fruit-set and trophic competition and optimization of yield advantages in six Capsicum cultivars using functional–structural plant modelling 
Annals of Botany  2010;107(5):793-803.
Background and aims
Many indeterminate plants can have wide fluctuations in the pattern of fruit-set and harvest. Fruit-set in these types of plants depends largely on the balance between source (assimilate supply) and sink strength (assimilate demand) within the plant. This study aims to evaluate the ability of functional–structural plant models to simulate different fruit-set patterns among Capsicum cultivars through source–sink relationships.
A greenhouse experiment of six Capsicum cultivars characterized with different fruit weight and fruit-set was conducted. Fruit-set patterns and potential fruit sink strength were determined through measurement. Source and sink strength of other organs were determined via the GREENLAB model, with a description of plant organ weight and dimensions according to plant topological structure established from the measured data as inputs. Parameter optimization was determined using a generalized least squares method for the entire growth cycle.
Key Results and Conclusions
Fruit sink strength differed among cultivars. Vegetative sink strength was generally lower for large-fruited cultivars than for small-fruited ones. The larger the size of the fruit, the larger variation there was in fruit-set and fruit yield. Large-fruited cultivars need a higher source–sink ratio for fruit-set, which means higher demand for assimilates. Temporal heterogeneity of fruit-set affected both number and yield of fruit. The simulation study showed that reducing heterogeneity of fruit-set was obtained by different approaches: for example, increasing source strength; decreasing vegetative sink strength, source–sink ratio for fruit-set and flower appearance rate; and harvesting individual fruits earlier before full ripeness. Simulation results showed that, when we increased source strength or decreased vegetative sink strength, fruit-set and fruit weight increased. However, no significant differences were found between large-fruited and small-fruited groups of cultivars regarding the effects of source and vegetative sink strength on fruit-set and fruit weight. When the source–sink ratio at fruit-set decreased, the number of fruit retained on the plant increased competition for assimilates with vegetative organs. Therefore, total plant and vegetative dry weights decreased, especially for large-fruited cultivars. Optimization study showed that temporal heterogeneity of fruit-set and ripening was predicted to be reduced when fruits were harvested earlier. Furthermore, there was a 20 % increase in the number of extra fruit set.
PMCID: PMC3077981  PMID: 21097946
Source–sink relationship; fruit-set pattern; functional–structural models; Capsicum annuum
6.  Modelling fungal sink competitiveness with grains for assimilates in wheat infected by a biotrophic pathogen 
Annals of Botany  2012;110(1):113-123.
Background and Aims
Experiments have shown that biotrophic fungi divert assimilates for their growth. However, no attempt has been made either to account for this additional sink or to predict to what extent it competes with both grain filling and plant reserve metabolism for carbon. Fungal sink competitiveness with grains was quantified by a mixed experimental–modelling approach based on winter wheat infected by Puccinia triticina.
One week after anthesis, plants grown under controlled conditions were inoculated with varying loads. Sporulation was recorded while plants underwent varying degrees of shading, ensuring a range of both fungal sink and host source levels. Inoculation load significantly increased both sporulating area and rate. Shading significantly affected net assimilation, reserve mobilization and sporulating area, but not grain filling or sporulation rates. An existing carbon partitioning (source–sink) model for wheat during the grain filling period was then enhanced, in which two parameters characterize every sink: carriage capacity and substrate affinity. Fungal sink competitiveness with host sources and sinks was modelled by representing spore production as another sink in diseased wheat during grain filling.
Key Results
Data from the experiment were fitted to the model to provide the fungal sink parameters. Fungal carriage capacity was 0·56 ± 0·01 µg dry matter °Cd−1 per lesion, much less than grain filling capacity, even in highly infected plants; however, fungal sporulation had a competitive priority for assimilates over grain filling. Simulation with virtual crops accounted for the importance of the relative contribution of photosynthesis loss, anticipated reserve depletion and spore production when light level and disease severity vary. The grain filling rate was less reduced than photosynthesis; however, over the long term, yield loss could double because the earlier reserve depletion observed here would shorten the duration of grain filling.
Source–sink modelling holds the promise of accounting for plant–pathogen interactions over time under fluctuating climatic/lighting conditions in a robust way.
PMCID: PMC3380591  PMID: 22589327
Triticum aestivum; Puccinia triticina; source–sink model; dry mass partitioning; spore production; reserve balance; environmentally linked disease damage; tolerance to disease
7.  Persistence of seeds from crops of conventional and herbicide tolerant oilseed rape (Brassica napus) 
A series of rotation experiments at five sites over four years has explored the environmental and agronomic implications of growing herbicide tolerant oilseed rape and sugar beet. This paper reports on the population dynamics of volunteer rape (Brassica napus). The experiments compared four winter oilseed rape (WOSR) cultivars: a conventional cultivar (Apex) and three developmental cultivars either genetically modified (GM) to be tolerant to glyphosate or glufosinate, or conventionally bred to be tolerant to herbicides of the imidazolinone group. Seed losses at harvest averaged 3575 seeds m−2 but ranged from less than 2000 up to more than 10 000 seeds m−2. There was a rapid decline in seed numbers during the first few months after harvest, resulting in a mean loss of seeds of 60%. In subsequent seasons, the seedbank declined much more slowly at four of the five sites (ca 20% per year) and the models predicted 95% seed loss after approximately 9 years. Seed decline was much faster at the fifth site. There were no clear differences between the four cultivars in either the numbers of seeds shed at harvest or in their subsequent persistence. The importance of the persistence of GM rape seeds, in the context of the coexistence of GM and non-GM crops and the role of good management practices that minimize seed persistence, are discussed.
PMCID: PMC1559884  PMID: 16191596
genetically modified crops; herbicide tolerant crops; oilseed rape; Brassica napus; seed persistence
8.  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
9.  Parameter Optimization and Field Validation of the Functional–Structural Model GREENLAB for Maize 
Annals of Botany  2006;97(2):217-230.
• 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.
PMCID: PMC2803369  PMID: 16390847
Plant architecture; competition among sinks; source–sink relationships; functional–structural models; Zea mays; model parameterization
10.  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 
Annals of Botany  2007;101(8):1207-1219.
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.
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.
PMCID: PMC2710279  PMID: 18037666
Functional–structural plant models; GREENLAB; competition for light; Beer–Lambert Law; plant plasticity; dynamical system
11.  Quantifying the source–sink balance and carbohydrate content in three tomato cultivars 
Supplementary lighting is frequently applied in the winter season for crop production in greenhouses. The effect of supplementary lighting on plant growth depends on the balance between assimilate production in source leaves and the overall capacity of the plants to use assimilates. This study aims at quantifying the source–sink balance and carbohydrate content of three tomato cultivars differing in fruit size, and to investigate to what extent the source/sink ratio correlates with the potential fruit size. Cultivars Komeet (large size), Capricia (medium size), and Sunstream (small size, cherry tomato) were grown from 16 August to 21 November, at similar crop management as in commercial practice. Supplementary lighting (High Pressure Sodium lamps, photosynthetic active radiation at 1 m below lamps was 162 μmol photons m-2 s-1; maximum 10 h per day depending on solar irradiance level) was applied from 19 September onward. Source strength was estimated from total plant growth rate using periodic destructive plant harvests in combination with the crop growth model TOMSIM. Sink strength was estimated from potential fruit growth rate which was determined from non-destructively measuring the fruit growth rate at non-limiting assimilate supply, growing only one fruit on each truss. Carbohydrate content in leaves and stems were periodically determined. During the early growth stage, ‘Komeet’ and ‘Capricia’ showed sink limitation and ‘Sunstream’ was close to sink limitation. During this stage reproductive organs had hardly formed or were still small and natural irradiance was high (early September) compared to winter months. Subsequently, during the fully fruiting stage all three cultivars were strongly source-limited as indicated by the low source/sink ratio (average source/sink ratio from 50 days after planting onward was 0.17, 0.22, and 0.33 for ‘Komeet,’ ‘Capricia,’ and ‘Sunstream,’ respectively). This was further confirmed by the fact that pruning half of the fruits hardly influenced net leaf photosynthesis rates. Carbohydrate content in leaves and stems increased linearly with the source/sink ratio. We conclude that during the early growth stage under high irradiance, tomato plants are sink-limited and that the level of sink limitation differs between cultivars but it is not correlated with their potential fruit size. During the fully fruiting stage tomato plants are source-limited and the extent of source limitation of a cultivar is positively correlated with its potential fruit size.
PMCID: PMC4456573  PMID: 26097485
source–sink balance; plant development stage; carbohydrate content; quantification; tomato cultivars; Solanum lycopersicum
12.  Genetic differences in fruit-set patterns are determined by differences in fruit sink strength and a source : sink threshold for fruit set 
Annals of Botany  2009;104(5):957-964.
Background and Aims
Fruit set in indeterminate plant species largely depends on the balance between source and sink strength. Plants of these species show fluctuations in fruit set during the growing season. It was tested whether differences in fruit sink strength among the cultivars explained the differences in fruit-set patterns.
Capsicum was chosen as a model plant. Six cultivars with differences in fruit set, fruit size and plant growth were evaluated in a greenhouse experiment. Fruit-set patterns, generative and vegetative sink strength, source strength and the source : sink ratio at fruit set were determined. Sink strength was quantified as potential growth rate. Fruit set was related to total fruit sink strength and the source : sink ratio. The effect of differences observed in above-mentioned parameters on fruit-set patterns was examined using a simple simulation model.
Key Results
Sink strengths of individual fruits differed greatly among cultivars. Week-to-week fruit set in large-fruited cultivars fluctuated due to large fluctuations in total fruit sink strength, but in small-fruited cultivars, total fruit sink strength and fruit set were relatively constant. Large variations in week-to-week fruit set were correlated with a low fruit-set percentage. The source : sink threshold for fruit set was higher in large-fruited cultivars. Simulations showed that within the range of parameter values found in the experiment, fruit sink strength and source : sink threshold for fruit set had the largest impact on fruit set: an increase in these parameters decreased the average percentage fruit set and increased variation in weekly fruit set. Both were needed to explain the fruit-set patterns observed. The differences observed in the other parameters (e.g. source strength) had a lower effect on fruit set.
Both individual fruit sink strength and the source : sink threshold for fruit set were needed to explain the differences observed between fruit-set patterns of the six cultivars.
PMCID: PMC2749527  PMID: 19643909
Fruit-set patterns; fruit sink strength; source : sink ratio; threshold for fruit set; Capsicum annuum; cultivars
13.  Rhythms and Alternating Patterns in Plants as Emergent Properties of a Model of Interaction between Development and Functioning 
Annals of Botany  2007;101(8):1233-1242.
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.
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.
PMCID: PMC2710268  PMID: 17715304
Rhythms; plasticity; plant growth model; GREENLAB; interactions; branching system; fructification; emergent properties
14.  Effects on weed and invertebrate abundance and diversity of herbicide management in genetically modified herbicide-tolerant winter-sown oilseed rape 
We evaluated the effects of the herbicide management associated with genetically modified herbicide-tolerant (GMHT) winter oilseed rape (WOSR) on weed and invertebrate abundance and diversity by testing the null hypothesis that there is no difference between the effects of herbicide management of GMHT WOSR and that of comparable conventional varieties. For total weeds there were few treatment differences between GMHT and conventional cropping, but large and opposite treatment effects were observed for dicots and monocots. In the GMHT treatment, there were fewer dicots and more monocots than in conventional crops. At harvest, dicot biomass and seed rain in the GMHT treatment were one-third of that in the conventional, while monocot biomass was threefold greater and monocot seed rain almost fivefold greater in the GMHT treatment than in the conventional. These differential effects persisted into the following two years of the rotation. Bees and butterflies that forage and select for dicot weeds were less abundant in GMHT WOSR management in July. Year totals for Collembola were greater under GMHT management. There were few other treatment effects on invertebrates, despite the marked effects of herbicide management on the weeds.
PMCID: PMC1578713  PMID: 15799941
genetically modified crops; biodiversity; oilseed rape; canola; herbicide management
15.  Dynamics of Nitrogen Uptake and Mobilization in Field-grown Winter Oilseed Rape (Brassica napus) from Stem Extension to Harvest 
Annals of Botany  2005;95(5):853-861.
• Background and Aims Despite its high capacity to take up nitrate from the soil, winter oilseed rape (Brassica napus) is characterized by a very low N recovery in the reproductive tissues under field conditions. A significant part of the N taken up is lost to the soil in dead leaves during the growth cycle. An accurate description of N dynamics at the whole plant level in each compartment under field conditions should lead to a better understanding of N allocation in B. napus and improvements in the nitrogen harvest index.
• Methods An experiment was conducted in field conditions using sequential weekly 15N labelling to follow N uptake, partitioning and mobilization. Nitrogen labelling (2·5 kg N ha−1; 10 % excess) was analysed weekly (from stem extension to harvest) to distinguish between uptake of new N (labelled) and mobilized N (unlabelled) in the different plant components.
• Key Results and Conclusions N requirements for seed filling were satisfied mainly by N mobilized from vegetative parts (about 73 % of the total N in pods). Determination of the endogenous N flow showed that there was net transfer of N to the pods by leaves (36 %), stem (34 %), inflorescences (22 %) and taproot (8 %). Precise study of N flow from leaves at different nodes revealed the existence of two main groups of leaves in terms of their apparent capacity to mobilize N; 30–60 % and 70–80 % of peak N content occurring during flowering and pod filling, respectively. Moreover, the latter group was found to be the main source of endogenous N from leaves. The mobilization of endogenous N from these leaves was prolonged and concomitant with N accumulation in the pods. A complex pattern of N mobilization from the leaves, to vegetative or reproductive tissues, was revealed. These results will be used to model N partitioning during the growth cycle.
PMCID: PMC4246740  PMID: 15701662
Brassica napus; leaf nodes; 15N labelling; dynamics; uptake; partitioning; mobilization
16.  Thiourea, a ROS Scavenger, Regulates Source-to-Sink Relationship to Enhance Crop Yield and Oil Content in Brassica juncea (L.) 
PLoS ONE  2013;8(9):e73921.
In the present agricultural scenario, the major thrust is to increase crop productivity so as to ensure sustainability. In an earlier study, foliar application of thiourea (TU; a non physiological thiol based ROS scavenger) has been demonstrated to enhance the stress tolerance and yield of different crops under field condition. Towards this endeavor, present work deals with the effect of TU on photosynthetic efficiency and source-to-sink relationship of Indian mustard (Brassica juncea) for understanding its mode of action. The application of TU increased the efficiency of both PSI and PSII photosystems and vegetative growth of plant. The comparative analysis of sucrose to starch ratio and expression level of sugar transporters confirmed the higher source and sink strength in response to TU treatment. The biochemical evidence in support of this was derived from higher activities of sucrose phosphate synthase and fructose-1,6-bis-phosphatase at source; and sucrose synthase and different classes of invertases at both source and sink. This indicated an overall increase in photoassimilate level at sink. An additional contribution through pod photosynthesis was confirmed through the analysis of phosphoenol pyruvate carboxylase enzyme activity and level of organic acids. The increased photoassimilate level was also co-ordinated with acetyl coA carboxylase mediated oil biosynthesis. All these changes were ultimately reflected in the form of 10 and 20% increase in total yield and oil content, respectively under TU treatment as compared to control. Additionally, no change was observed in oil composition of seeds derived from TU treated plants. The study thus signifies the co-ordinated regulation of key steps of photosynthesis and source-to-sink relationship through the external application of TU resulting in increased crop yield and oil content.
PMCID: PMC3776803  PMID: 24058504
17.  A Dynamic, Architectural Plant Model Simulating Resource‐dependent Growth 
Annals of Botany  2004;93(5):591-602.
• 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.
PMCID: PMC4242319  PMID: 15056562
Plant architecture; phenotypic plasticity; demand functions; competition among sinks; source–sink relationships; structural‐functional models
18.  Is the remobilization of S and N reserves for seed filling of winter oilseed rape modulated by sulphate restrictions occurring at different growth stages? 
Journal of Experimental Botany  2010;61(15):4313-4324.
How the remobilization of S and N reserves can meet the needs of seeds of oilseed rape subject to limitation of S fertilization remains largely unclear. Thus, this survey aims to determine the incidence of sulphate restriction [low S (LS)] applied at bolting [growth stage (GS) 32], visible bud (GS 53), and start of pod filling (GS 70) on source–sink relationships for S and N, and on the dynamics of endogenous/exogenous S and N contributing to seed yield and quality. Sulphate restrictions applied at GS 32, GS 53, and GS 70 were annotated LS32, LS53, and LS70. Long-term 34SO42− and 15NO3− labelling was used to explore S and N partitioning at the whole-plant level. In LS53, the sulphur remobilization efficiency (SRE) to seeds increased, but not enough to maintain seed quality. In LS32, an early S remobilization from leaves provided S for root, stem, and pod growth, but the subsequent demand for seed development was not met adequately and the N utilization efficiency (NUtE) was reduced when compared with high S (HS). The highest SRE (65±1.2% of the remobilized S) associated with an efficient foliar S mobilization (with minimal residual S concentrations of 0.1–0.2% dry matter) was observed under LS70 treatment, which did not affect yield components.
PMCID: PMC2955745  PMID: 20693411
Oilseed rape; sulphate restriction; 34S and 15N labelling; S remobilization efficiency; S utilization efficiency
19.  Response of Bean (Vicia faba L.) Plants to Low Sink Demand by Measuring the Gas Exchange Rates and Chlorophyll a Fluorescence Kinetics 
PLoS ONE  2013;8(12):e80770.
The decline of photosynthesis in plants under low sink demand is well known. Previous studies focused on the relationship between stomatal conductance (gs) and net photosynthetic rate (Pn). These studies investigated the effect of changes in Photosystem II (PSII) function on the Pn decline under low sink demand. However, little is known about its effects on different limiting steps of electron transport chain in PSII under this condition.
Methodology/Principal Finding
Two-month-old bean plants were processed by removing pods and flowers (low sink demand). On the 1st day after low sink demand treatment, a decline of Pn was accompanied by a decrease in gs and internal-to-ambient CO2 concentration ratio (Ci/Ca). From the 3rd to 9th day, Pn and gs declined continuously while Ci/Ca ratio remained stable in the treatment. Moreover, these values were lower than that of control. Wk (a parameter reflecting the damage to oxygen evolving complex of the donor side of PSII) values in the treatment were significantly higher than their corresponding control values. However, RCQA (a parameter reflecting the number of active RCs per excited cross-section of PSII) values in the treatment were significantly lower than control from the 5th day. From the 11th to 21st day, Pn and gs of the treatment continued to decline and were lower than control. This was accompanied by a decrease of RCQA, and an increase of Wk. Furthermore, the quantum yield parameters φPo, φEo and ψEo in the treatment were lower than in control; however, Ci/Ca values in the treatment gradually increased and were significantly higher than control on the 21st day.
Stomatal limitation during the early stage, whereas a combination of stomatal and non-stomatal limitation during the middle stage might be responsible for the reduction of Pn under low sink demand. Non-stomatal limitation during the late stages after the removal of the sink of roots and pods may also cause Pn reduction. The non-stomatal limitation was associated with the inhibition of PSII electron transport chain. Our data suggests that the donor side of PSII was the most sensitive to low sink demand followed by the reaction center of PSII. The acceptor side of PSII may be the least sensitive.
PMCID: PMC3851463  PMID: 24324626
20.  Dynamics of Nitrogen Uptake and Mobilization in Field-grown Winter Oilseed Rape (Brassica napus) From Stem Extension to Harvest. II. An 15N-labelling-based Simulation Model of N Partitioning Between Vegetative and Reproductive Tissues 
Annals of Botany  2005;95(7):1187-1198.
• Background and Aims Oilseed rape (Brassica napus) has often been used as a catch crop to deal with the issue of N leaching, but for this to be effective, prediction of the crop's N uptake capability and N partitioning is required. The aim of this work was to build a compartmental model of N dynamics in oilseed rape, based on the kinetic description of N uptake, partitioning and mobilization in each organ.
• Model In this study, logistic and exponential equations were fitted to the N relations of each compartment, especially the leaf at each node. Data previously obtained from an 15N-labelling field experiment was used to quantify the partitioning of total N content, the allocation of N taken up and subsequent changes in the sink/source status for endogenous N in each tissue throughout the growth cycle.
• Key Results and Conclusions This modelling approach provides a unique tool for the quantitative estimation of cycling of endogenous N in relation to changes in N uptake at the whole-plant level. Furthermore, as oilseed rape is known to release large amounts of N to the soil during spring through leaf loss, this model was used to identify potential methods for improving the N harvest index of the crop. Simulations showed that N content or yield could be improved by 15 % by optimizing N transfer from vegetative to reproductive tissues and by reducing the residual %N (DW) in abscised leaves.
PMCID: PMC4246903  PMID: 15802311
Brassica napus L.; field conditions; 15N labelling; N uptake; N dynamics; mobilization; cycling N pool; modelling
21.  Phenology, growth and physiological adjustments of oil palm (Elaeis guineensis) to sink limitation induced by fruit pruning 
Annals of Botany  2009;104(6):1183-1194.
Background and Aims
Despite its simple architecture and small phenotypic plasticity, oil palm has complex phenology and source–sink interactions. Phytomers appear in regular succession but their development takes years, involving long lag periods between environmental influences and their effects on sinks. Plant adjustments to resulting source–sink imbalances are poorly understood. This study investigated oil palm adjustments to imbalances caused by severe fruit pruning.
An experiment with two treatments (control and complete fruit pruning) during 22 months in 2006–2008) and six replications per treatment was conducted in Indonesia. Phenology, growth of above-ground vegetative and reproductive organs, leaf morphology, inflorescence sex differentiation, dynamics of non-structural carbohydrate reserves and light-saturated net photosynthesis (Amax) were monitored.
Key Results
Artificial sink limitation by complete fruit pruning accelerated development rate, resulting in higher phytomer, leaf and inflorescence numbers. Leaf size and morphology remained unchanged. Complete fruit pruning also suppressed the abortion of male inflorescences, estimated to be triggered at about 16 months before bunch maturity. The number of female inflorescences increased after an estimated lag of 24–26 months, corresponding to time from sex differentiation to bunch maturity. The most important adjustment process was increased assimilate storage in the stem, attaining nearly 50 % of dry weight in the stem top, mainly as starch, whereas glucose, which in controls was the most abundant non-structural carbohydrate stored in oil palm, decreased.
The development rate of oil palm is in part controlled by source–sink relationships. Although increased rate of development and proportion of female inflorescences constituted observed adjustments to sink limitation, the low plasticity of plant architecture (constant leaf size, absence of branching) limited compensatory growth. Non-structural carbohydrate storage was thus the main adjustment process.
PMCID: PMC2766206  PMID: 19748908
Carbon allocation; non-structural carbohydrates; source–sink relationships; Elaeis guineensis; phenotypic plasticity; photosynthesis
22.  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
23.  Are the common assimilate pool and trophic relationships appropriate for dealing with the observed plasticity of grapevine development? 
Annals of Botany  2009;105(2):233-247.
Background and Aims
Models based on the consideration of plant development as the result of source–sink relationships between organs suffer from an inherent lack of quantification of the effect of trophic competition on organ growth processes. The ‘common assimilate pool theory’ underlying many such models is highly debatable.
Six experiments were carried out in a greenhouse and outdoors with two grapevine cultivars and with 12 management systems, resulting in different types of plant architecture. Ten variables were used to quantify the impact of variations in assimilate supply and topological distances between sources and sinks on organogenesis, morphogenesis and biomass growth.
Key Results
A hierarchy of the responses of these processes to variations in assimilate supply was identified. Organ size seemed to be independent of assimilate supply, whereas both organogenesis and biomass growth were affected by variations in assimilate supply. Lower levels of organ biomass growth in response to the depletion of assimilate supplies seemed to be the principal mechanism underlying the plasticity of plant development in different environments. Defoliation or axis ablation resulted in changes in the relationship between growth processes and assimilate supply, highlighting the influence of non-trophic determinants. The findings cast doubt on the relevance of ‘the common assimilate pool theory’ for modelling the development of grapevine.
The results of this study suggest new formalisms for increasing the ability of models to take plant plasticity into account. The combination of an ecophysiological model for morphogenesis taking environmental signals into account and a biomass driven model for organogenesis and biomass allocation taking the topological distances between the sources and the sinks into account appears to be a promising approach. Moreover, in order to simulate the impact of agronomic practices, it will be necessary to take into account the non-trophic determinants of plant development such as hormonal signaletics.
PMCID: PMC2814752  PMID: 19946042
Biomass growth; branching system; common assimilate pool; morphogenesis; organogenesis; source–sink; grapevine; Vitis vinifera
24.  Biochemical and molecular characteristics of leaf photosynthesis and relative seed yield of two contrasting rice cultivars in response to elevated [CO2] 
Journal of Experimental Botany  2014;65(20):6049-6056.
The basis for differential responses of rice yield to rising CO2 levels may be associated with temporal changes in photosynthetic capacity that sustain carbon assimilation rates during grain filling.
Understanding the basis for intraspecific yield variability may be important in elucidating biological mechanisms that are associated with superior yield performance in response to projected increases in carbon dioxide concentration, [CO2]. Using a free-air CO2 enrichment (FACE) facility, two rice lines, S63 and W14, which differed consistently in their enhancement of seed yield when grown at elevated [CO2] in multiple field trials, were examined. To determine if the different cultivar responses were linked to changes in photosynthetic characteristics at elevated [CO2], spatial and temporal changes in photosynthetic stimulation and the occurrence of down-regulation, or acclimation, in relation to panicle sink development were quantified for the uppermost canopy leaves. Changes in photosynthetic capacity were determined by quantifying changes in the sink:source ratio, leaf nitrogen (N) content, the concentration and mRNA expression of the large Rubisco subunit, and changes in V c,max, the maximum ribulose bisphosphate (RuBP)-saturated rate of carboxylation. For the W14 cultivar, significant reductions in photosynthesis at the elevated, relative to ambient [CO2], signalling photosynthetic acclimation, were observed following panicle initiation. The observance of photosynthetic acclimation was consistent with significant reductions in N, Rubisco content and expression, and V c,max. In contrast, for the cultivar S63, elevated [CO2] resulted in increased spikelet number and grain weight, increased sink:source ratios, and continued stimulation of photosynthesis up to grain maturity. Overall, these data suggest that the greater response of the S63 line to elevated [CO2] may be associated with enhanced carbon sinks relative to sources, and the ability to maintain photosynthetic capacity during grain development.
PMCID: PMC4203138  PMID: 25180108
Elevated CO2; panicle; photosynthetic capacity; rice; sink; source.
25.  Quantitative Genetics and Functional–Structural Plant Growth Models: Simulation of Quantitative Trait Loci Detection for Model Parameters and Application to Potential Yield Optimization 
Annals of Botany  2007;101(8):1243-1254.
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 × 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.
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 × genotype interactions, in particular through its main state variable, the ratio of biomass supply over demand.
PMCID: PMC2710265  PMID: 17766844
Plant growth model; GREENLAB; genetics; QTL; breeding; yield optimization; genetic algorithm; Zea mays

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