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1.  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
2.  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
3.  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
4.  Characterization of the interactions between architecture and source–sink relationships in winter oilseed rape (Brassica napus) using the GreenLab model 
Annals of Botany  2010;107(5):765-779.
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.
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.
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.
PMCID: PMC3077979  PMID: 20980324
Biological system modelling; source–sink relationships; ramification; GreenLab model; energetic cost; oleaginous seeds; Brassica napus; winter oilseed rape
5.  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
6.  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
7.  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
8.  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
9.  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
10.  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
11.  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
12.  Does the Structure–Function Model GREENLAB Deal with Crop Phenotypic Plasticity Induced by Plant Spacing? A Case Study on Tomato 
Annals of Botany  2008;101(8):1195-1206.
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.
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.
PMCID: PMC2710282  PMID: 18199575
Functional–structural models; GREENLAB; phenotypic plasticity; planting density; competition; source–sink relationship; parameter stability; Solanum lycopersicum
13.  Hormonal and metabolic regulation of tomato fruit sink activity and yield under salinity 
Journal of Experimental Botany  2014;65(20):6081-6095.
Cytokinins and cell wall invertase are positive players in regulating fruit sink strength, growth, and yield under salinity as components of the same signalling cascade establishing and developing sink organs.
Salinization of water and soil has a negative impact on tomato (Solanum lycopersicum L.) productivity by reducing growth of sink organs and by inducing senescence in source leaves. It has been hypothesized that yield stability implies the maintenance or increase of sink activity in the reproductive structures, thus contributing to the transport of assimilates from the source leaves through changes in sucrolytic enzymes and their regulation by phytohormones. In this study, classical and functional physiological approaches have been integrated to study the influence of metabolic and hormonal factors on tomato fruit sink activity, growth, and yield: (i) exogenous hormones were applied to plants, and (ii) transgenic plants overexpressing the cell wall invertase (cwInv) gene CIN1 in the fruits and de novo cytokinin (CK) biosynthesis gene IPT in the roots were constructed. Although salinity reduces fruit growth, sink activity, and trans-zeatin (tZ) concentrations, it increases the ethylene precursor 1-aminocyclopropane-1-carboxylic acid (ACC) during the actively growing period (25 days after anthesis). Indeed, exogenous application of the CK analogue kinetin to salinized actively growing fruits recovered sucrolytic activities (mainly cwInv and sucrose synthase), sink strength, and fruit weight, whereas the ethylene-releasing compound ethephon had a negative effect in equivalent non-stressed fruits. Fruit yield was increased by both the constitutive expression of CIN1 in the fruits (up to 4-fold) or IPT in the root (up to 30%), owing to an increase in the fruit number (lower flower abortion) and in fruit weight. This is possibly related to a recovery of sink activity in reproductive tissues due to both (i) increase in sucrolytic activities (cwInv, sucrose synthase, and vacuolar and cytoplasmic invertases) and tZ concentration, and (ii) a decrease in the ACC levels and the activity of the invertase inhibitor. This study provides new functional evidences about the role of metabolic and hormonal inter-regulation of local sink processes in controlling tomato fruit sink activity, growth, and yield under salinity.
PMCID: PMC4203140  PMID: 25170099
Cell wall invertase; cytokinins; fruit; salinity; sink activity; tomato.
14.  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
15.  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
16.  Night temperature and source–sink effects on overall growth, cell number and cell size in bell pepper ovaries 
Annals of Botany  2012;110(5):987-994.
Background and Aims
Ovary swelling, and resultant fruit malformation, in bell pepper flowers is favoured by low night temperature or a high source–sink ratio. However, the interaction between night temperature and source–sink ratio on ovary swelling and the contribution of cell size and cell number to ovary swelling are unknown. The present research examined the interactive effects of night temperature and source–sink ratio on ovary size, cell number and cell size at anthesis in bell pepper flowers.
Bell pepper plants were grown in growth chambers at night temperatures of either 20 °C (HNT) or 12 °C (LNT). Within each temperature treatment, plants bore either 0 (non-fruiting) or two developing fruits per plant. Ovary fresh weight, cell size and cell number were measured.
Key Results
Ovary fresh weights in non-fruiting plants grown at LNT were the largest, while fresh weights were smallest in plants grown at HNT with fruits. In general, mesocarp cell size in ovaries was largest in non-fruiting plants grown at either LNT or HNT and smallest in fruiting plants at HNT. Mesocarp cell number was greater in non-fruiting plants under LNT than in the rest of the night temperature/fruiting treatments. These responses were more marked in ovaries sampled after 18 d of treatment compared with those sampled after 40 d of treatment.
Ovary fresh weight of flowers at anthesis increased 65 % in non-fruiting plants grown under LNT compared with fruiting plants grown under HNT. This increase was due primarily to increases in mesocarp cell number and size. These results indicate that the combined effects of LNT and high source–sink ratio on ovary swelling are additive. Furthermore, the combined effects of LNT and low source–sink ratio or HNT and high source–sink ratio can partially overcome the detrimental effects of LNT and high source–sink ratio.
PMCID: PMC3448427  PMID: 22933415
Capsicum annuum; fruit quality; pepper ovary swelling; source–sink effects
17.  Partitioning of 13C-photosynthate from Spur Leaves during Fruit Growth of Three Japanese Pear (Pyrus pyrifolia) Cultivars Differing in Maturation Date 
Annals of Botany  2005;95(4):685-693.
• Background and Aims In fruit crops, fruit size at harvest is an important aspect of quality. With Japanese pears (Pyrus pyrifolia), later maturing cultivars usually have larger fruits than earlier maturing cultivars. It is considered that the supply of photosynthate during fruit development is a critical determinant of size. To assess the interaction of assimilate supply and early/late maturity of cultivars and its effect on final fruit size, the pattern of carbon assimilate partitioning from spur leaves (source) to fruit and other organs (sinks) during fruit growth was investigated using three genotypes differing in maturation date.
• Methods Partitioning of photosynthate from spur leaves during fruit growth was investigated by exposure of spurs to 13CO2 and measurement of the change in 13C abundance in dry matter with time. Leaf number and leaf area per spur, fresh fruit weight, cell number and cell size of the mesocarp were measured and used to model the development of the spur leaf and fruit.
• Key Results Compared with the earlier-maturing cultivars ‘Shinsui’ and ‘Kousui’, the larger-fruited, later-maturing cultivar ‘Shinsetsu’ had a greater total leaf area per spur, greater source strength (source weight × source specific activity), with more 13C assimilated per spur and allocated to fruit, smaller loss of 13C in respiration and export over the season, and longer duration of cell division and enlargement. Histology shows that cultivar differences in final fruit size were mainly attributable to the number of cells in the mesocarp.
• Conclusions Assimilate availability during the period of cell division was crucial for early fruit growth and closely correlated with final fruit size. Early fruit growth of the earlier-maturing cultivars, but not the later-maturing ones, was severely restrained by assimilate supply rather than by sink limitation.
PMCID: PMC4246860  PMID: 15655106
13C labelling; fruit growth; sink strength; spur leaves; pear; Pyrus pyrifolia Nakai
18.  Linking ascorbic acid production in Ribes nigrum with fruit development and changes in sources and sinks 
Annals of Botany  2013;111(4):703-712.
Background and Aims
Understanding the synthesis of ascorbic acid (l-AsA) in green tissues in model species has advanced considerably; here we focus on its production and accumulation in fruit. In particular, our aim is to understand the links between organs which may be sources of l-AsA (leaves) and those which accumulate it (fruits). The work presented here tests the idea that changes in leaf and fruit number influence the accumulation of l-AsA. The aim was to understand the importance of leaf tissue in the production of l-AsA and to determine how this might provide routes for the manipulation of fruit tissue l-AsA.
The experiments used Ribes nigrum (blackcurrant), predominantly in field experiments, where the source–sink relationship was manipulated to alter potential leaf l-AsA production and fruit growth and accumulation of l-AsA. These manipulations included reductions in reproductive capacity, by raceme removal, and the availability of assimilates by leaf removal and branch phloem girdling. Natural variation in fruit growth and fruit abscission is also described as this influences subsequent experimental design and the interpretation of l-AsA data.
Key Results
Results show that fruit l-AsA concentration is conserved but total yield of l-AsA per plant is dependent on a number of innate factors many of which relate to raceme attributes. Leaf removal and phloem girdling reduced fruit weight, and a combination of both reduced fruit yields further. It appears that around 50 % of assimilates utilized for fruit growth came from apical leaves, while between 20 and 30 % came from raceme leaves, with the remainder from ‘storage’.
Despite being able to manipulate leaf area and therefore assimilate availability and stored carbohydrates, along with fruit yields, rarely were effects on fruit l-AsA concentration seen, indicating fruit l-AsA production in Ribes was not directly coupled to assimilate supply. There was no supporting evidence that l-AsA production occurred predominantly in green leaf tissue followed by its transfer to developing fruits. It is concluded that l-AsA production occurs predominantly in the fruit of Ribes nigrum.
PMCID: PMC3605959  PMID: 23419248
l-Ascorbic acid; blackcurrant; fruit; Ribes nigrum; source sinks; vitamin C
19.  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
20.  Reproductive investment within inflorescences of Stylidium armeria varies with the strength of early resource commitment 
Annals of Botany  2010;105(5):697-705.
Background and Aims
Resource allocation to flowers, fruits and seeds can vary greatly within an inflorescence. For example, distal fruits are often smaller and produce fewer and smaller fruits and seeds than more basal fruits. To assess the causes and functional significance of intra-inflorescence variation, pollen and resources were manipulated to test whether such patterns could be altered within racemes of Stylidum armeria, a perennial Australian herb.
Pollen and resource levels were manipulated over two flowering seasons. How the number of ovules, fertilized ovules and seeds, the probability of fruit set, and the biomass of floral and fruiting structures varied with their position on the raceme were analysed.
Key Results
Most plants showed a decline in ovule and seed number toward the distal positions on the raceme, but plants differed in their pattern of intra-inflorescence allocation: racemes with greater investment in basal fruits displayed a stronger trade-off with distal investment than did racemes that made smaller initial investments. This trade-off was (a) much stronger for ovule number than for seed number, (b) ameliorated but not erased by resource addition, and (c) exacerbated by resource reduction. There was large and seemingly erratic variation across fruit positions in ovule fertilization and seed set following both natural and supplemental pollination.
In S. armeria, allocation to reproductive traits within the inflorescence is influenced by dynamic trade-offs in resource allocation between early and late fruits, and may also be subject to inherent architectural effects. Large, unpredictable variation among fruits in fertilization success and seed set may influence the evolution of inflorescence size, ovule number and floral dimorphism.
PMCID: PMC2859907  PMID: 20375201
Architectural effects; floral biomass; intra-inflorescence; pollen limitation; resource pre-emption; Stylidium armeria
21.  Dry matter partitioning models for the simulation of individual fruit growth in greenhouse cucumber canopies 
Annals of Botany  2011;108(6):1075-1084.
Background and Aims
Growth imbalances between individual fruits are common in indeterminate plants such as cucumber (Cucumis sativus). In this species, these imbalances can be related to differences in two growth characteristics, fruit growth duration until reaching a given size and fruit abortion. Both are related to distribution, and environmental factors as well as canopy architecture play a key role in their differentiation. Furthermore, events leading to a fruit reaching its harvestable size before or simultaneously with a prior fruit can be observed. Functional–structural plant models (FSPMs) allow for interactions between environmental factors, canopy architecture and physiological processes. Here, we tested hypotheses which account for these interactions by introducing dominance and abortion thresholds for the partitioning of assimilates between growing fruits.
Using the L-System formalism, an FSPM was developed which combined a model for architectural development, a biochemical model of photosynthesis and a model for assimilate partitioning, the last including a fruit growth model based on a size-related potential growth rate (RP). Starting from a distribution proportional to RP, the model was extended by including abortion and dominance. Abortion was related to source strength and dominance to sink strength. Both thresholds were varied to test their influence on fruit growth characteristics. Simulations were conducted for a dense row and a sparse isometric canopy.
Key Results
The simple partitioning models failed to simulate individual fruit growth realistically. The introduction of abortion and dominance thresholds gave the best results. Simulations of fruit growth durations and abortion rates were in line with measurements, and events in which a fruit was harvestable earlier than an older fruit were reproduced.
Dominance and abortion events need to be considered when simulating typical fruit growth traits. By integrating environmental factors, the FSPM can be a valuable tool to analyse and improve existing knowledge about the dynamics of assimilates partitioning.
PMCID: PMC3189842  PMID: 21715366
Modelling; individual fruit growth; functional–structural plant model; L-System; Cucumis sativus; cucumber; plant architecture; assimilate distribution
22.  Using plant growth modeling to analyze C source–sink relations under drought: inter- and intraspecific comparison 
The ability to assimilate C and allocate non-structural carbohydrates (NSCs) to the most appropriate organs is crucial to maximize plant ecological or agronomic performance. Such C source and sink activities are differentially affected by environmental constraints. Under drought, plant growth is generally more sink than source limited as organ expansion or appearance rate is earlier and stronger affected than C assimilation. This favors plant survival and recovery but not always agronomic performance as NSC are stored rather than used for growth due to a modified metabolism in source and sink leaves. Such interactions between plant C and water balance are complex and plant modeling can help analyzing their impact on plant phenotype. This paper addresses the impact of trade-offs between C sink and source activities and plant production under drought, combining experimental and modeling approaches. Two contrasted monocotyledonous species (rice, oil palm) were studied. Experimentally, the sink limitation of plant growth under moderate drought was confirmed as well as the modifications in NSC metabolism in source and sink organs. Under severe stress, when C source became limiting, plant NSC concentration decreased. Two plant models dedicated to oil palm and rice morphogenesis were used to perform a sensitivity analysis and further explore how to optimize C sink and source drought sensitivity to maximize plant growth. Modeling results highlighted that optimal drought sensitivity depends both on drought type and species and that modeling is a great opportunity to analyze such complex processes. Further modeling needs and more generally the challenge of using models to support complex trait breeding are discussed.
PMCID: PMC3817663  PMID: 24204372
drought; plant biomass accumulation; non-structural carbohydrate; source and sink regulation; functional structural plant model; rice; oil palm
23.  Peach Water Relations, Gas Exchange, Growth and Shoot Mortality under Water Deficit in Semi-Arid Weather Conditions 
PLoS ONE  2015;10(4):e0120246.
In this study the sensitivity of peach tree (Prunus persica L.) to three water stress levels from mid-pit hardening until harvest was assessed. Seasonal patterns of shoot and fruit growth, gas exchange (leaf photosynthesis, stomatal conductance and transpiration) as well as carbon (C) storage/mobilization were evaluated in relation to plant water status. A simple C balance model was also developed to investigate sink-source relationship in relation to plant water status at the tree level. The C source was estimated through the leaf area dynamics and leaf photosynthesis rate along the season. The C sink was estimated for maintenance respiration and growth of shoots and fruits. Water stress significantly reduced gas exchange, and fruit, and shoot growth, but increased fruit dry matter concentration. Growth was more affected by water deficit than photosynthesis, and shoot growth was more sensitive to water deficit than fruit growth. Reduction of shoot growth was associated with a decrease of shoot elongation, emergence, and high shoot mortality. Water scarcity affected tree C assimilation due to two interacting factors: (i) reduction in leaf photosynthesis (-23% and -50% under moderate (MS) and severe (SS) water stress compared to low (LS) stress during growth season) and (ii) reduction in total leaf area (-57% and -79% under MS and SS compared to LS at harvest). Our field data analysis suggested a Ψstem threshold of -1.5 MPa below which daily net C gain became negative, i.e. C assimilation became lower than C needed for respiration and growth. Negative C balance under MS and SS associated with decline of trunk carbohydrate reserves – may have led to drought-induced vegetative mortality.
PMCID: PMC4382189  PMID: 25830350
24.  Carbon fluxes in ecosystems of Yellowstone National Park predicted from remote sensing data and simulation modeling 
A simulation model based on remote sensing data for spatial vegetation properties has been used to estimate ecosystem carbon fluxes across Yellowstone National Park (YNP). The CASA (Carnegie Ames Stanford Approach) model was applied at a regional scale to estimate seasonal and annual carbon fluxes as net primary production (NPP) and soil respiration components. Predicted net ecosystem production (NEP) flux of CO2 is estimated from the model for carbon sinks and sources over multi-year periods that varied in climate and (wildfire) disturbance histories. Monthly Enhanced Vegetation Index (EVI) image coverages from the NASA Moderate Resolution Imaging Spectroradiometer (MODIS) instrument (from 2000 to 2006) were direct inputs to the model. New map products have been added to CASA from airborne remote sensing of coarse woody debris (CWD) in areas burned by wildfires over the past two decades.
Model results indicated that relatively cooler and wetter summer growing seasons were the most favorable for annual plant production and net ecosystem carbon gains in representative landscapes of YNP. When summed across vegetation class areas, the predominance of evergreen forest and shrubland (sagebrush) cover was evident, with these two classes together accounting for 88% of the total annual NPP flux of 2.5 Tg C yr-1 (1 Tg = 1012 g) for the entire Yellowstone study area from 2000-2006. Most vegetation classes were estimated as net ecosystem sinks of atmospheric CO2 on annual basis, making the entire study area a moderate net sink of about +0.13 Tg C yr-1. This average sink value for forested lands nonetheless masks the contribution of areas burned during the 1988 wildfires, which were estimated as net sources of CO2 to the atmosphere, totaling to a NEP flux of -0.04 Tg C yr-1 for the entire burned area. Several areas burned in the 1988 wildfires were estimated to be among the lowest in overall yearly NPP, namely the Hellroaring Fire, Mink Fire, and Falls Fire areas.
Rates of recovery for burned forest areas to pre-1988 biomass levels were estimated from a unique combination of remote sensing and CASA model predictions. Ecosystem production and carbon fluxes in the Greater Yellowstone Ecosystem (GYE) result from complex interactions between climate, forest age structure, and disturbance-recovery patterns of the landscape.
PMCID: PMC3177874  PMID: 21835025
25.  Carbon allocation during fruiting in Rubus chamaemorus 
Annals of Botany  2009;104(4):703-713.
Background and Aims
Rubus chamaemorus (cloudberry) is a herbaceous clonal peatland plant that produces an extensive underground rhizome system with distant ramets. Most of these ramets are non-floral. The main objectives of this study were to determine: (a) if plant growth was source limited in cloudberry; (b) if the non-floral ramets translocated carbon (C) to the fruit; and (c) if there was competition between fruit, leaves and rhizomes for C during fruit development.
Floral and non-floral ramet activities were monitored during the period of flower and fruit development using three approaches: gas exchange measurements, 14CO2 labelling and dry mass accumulation in the different organs. Source and sink activity were manipulated by eliminating leaves or flowers or by reducing rhizome length.
Key Results
Photosynthetic rates were lower in floral than in deflowered ramets. Autoradiographs and 14C labelling data clearly indicated that fruit is a very strong sink for the floral ramet, whereas non-floral ramets translocated C toward the rhizome but not toward floral ramets. Nevertheless, rhizomes received some C from the floral ramet throughout the fruiting period. Ramets with shorter rhizomes produced smaller leaves and smaller fruits, and defoliated ramets produced very small fruits.
Plant growth appears to be source-limited in cloudberry since a reduction in sink strength did not induce a reduction in photosynthetic activity. Non-floral ramets did not participate directly to fruit development. Developing leaves appear to compete with the developing fruit but the intensity of this competition could vary with the specific timing of the two organs. The rhizome appears to act both as a source but also potentially as a sink during fruit development. Further studies are needed to characterize better the complex role played by the rhizome in fruit C nutrition.
PMCID: PMC2729635  PMID: 19520701
Allocation pattern; 14C labelling; carbon translocation; carbon reserves; cloudberry; defoliation; fruit production; gas exchange; Rubus chamaemorus; source–sink relationship; flowering

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