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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.
Methods
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.
doi:10.1093/aob/mcq223
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.
Methods
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.
Conclusions
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.
doi:10.1093/aob/mcp181
PMCID: PMC2749527  PMID: 19643909
Fruit-set patterns; fruit sink strength; source : sink ratio; threshold for fruit set; Capsicum annuum; cultivars
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.
Methods
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.
Conclusions
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.
doi:10.1093/aob/mcp054
PMCID: PMC2685317  PMID: 19297366
Trophic plasticity; plant growth; functional–structural models; dynamic system; interactions; GreenLab
4.  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.
Methods
In the model, a single variable, the source–sink ratio controls different events in plant architecture. In particular, the number of fruits and branch formation are determined as increasing functions of this ratio. For some sets of well-chosen parameters of the model, the dynamical evolution of the ratio during plant growth generates rhythms.
Key Results and Conclusions
Cyclic patterns in branch formation or fruit appearance emerge without being forced by the model. The model is based on the theory of discrete dynamical systems. The mathematical formalism helps us to explain rhythm generation and to control the behaviour of the system. Rhythms can appear during both the exponential and stabilized phases of growth, but the causes are different as shown by an analytical study of the system. Simulated plant behaviours are very close to those observed on real plants. With a small number of parameters, the model gives very interesting results from a qualitative point of view. It will soon be subjected to experimental data to estimate the model parameters.
doi:10.1093/aob/mcm171
PMCID: PMC2710268  PMID: 17715304
Rhythms; plasticity; plant growth model; GREENLAB; interactions; branching system; fructification; emergent properties
5.  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.
Methods
Equations were added in GreenLab to compute expansion delays for ramification, flowering of each axis and photosynthesis of pods including the energetic cost of oil synthesis. Experimental field data were used to estimate morphological parameters while source–sink parameters of the model were estimated by adjustment of model outputs to the data. Ecophysiological outputs were used to assess the sources/sink relationships during the whole growth cycle.
Key Results
First results indicated that, at the plant scale, the model correctly simulates the dynamics of organ growth. However, at the organ scale, errors were observed that could be explained either by secondary growth that was not incorporated or by uncertainties in morphological parameters (durations of expansion and life). Ecophysiological outputs highlighted the dramatic negative impact of ramification on the source–sink ratio, as well as the decrease in this ratio during seed filling despite pod envelope photosynthesis that allowed significant biomass production to be maintained.
Conclusions
This work is a promising first step in the construction of a structure–function model for a plant as complex as WOSR. Once tested for other environments and/or genotypes, the model can be used for studies on WOSR architectural plasticity.
doi:10.1093/aob/mcq205
PMCID: PMC3077979  PMID: 20980324
Biological system modelling; source–sink relationships; ramification; GreenLab model; energetic cost; oleaginous seeds; Brassica napus; winter oilseed rape
6.  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’).
Methods
An experiment was conducted on spring wheat (Triticum aestivum, ‘Minaret’), in a growth chamber from, 2004 to, 2005. Four harvests were made of six plants each to determine the size and mass of individual organs, including the root system, leaf blades, sheaths, internodes and ears of the main stem and different tillers. Leaf status (appearance, expansion, maturity and death) of these 24 plants was recorded. With the structures and mass of organs of four individual sample plants, the GREENLAB model was calibrated using a non-linear least-square-root fitting method, the aim of which was to minimize the difference in mass of the organs between measured data and model output, and to provide the parameter values of the model (the sink strengths of organs of each type, age and tiller order, and two empirical parameters linked to biomass production).
Key Results and Conclusions
The masses of all measured organs from one plant from each harvest were fitted simultaneously. With estimated parameters for sink and source functions, the model predicted the mass and size of individual organs at each position of the wheat structure in a mechanistic way. In addition, there was close agreement between experimentally observed and simulated values of leaf area index.
doi:10.1093/aob/mcm212
PMCID: PMC2710274  PMID: 18045794
Wheat; Triticum aestivum ‘Minaret’; tiller; GREENLAB; organ mass; functional–structural model; model calibration; multi-fitting; source–sink
7.  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.
Methods
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.
Conclusions
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.
doi:10.1093/aob/mcm233
PMCID: PMC2710275  PMID: 17921525
Functional–structural plant model; GREENLAB; plant architecture; source–sink relationship; plant population density; maize (Zea mays); model parameterization
8.  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.
Methods
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.
Conclusions
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.
doi:10.1093/aob/mcp216
PMCID: PMC2766206  PMID: 19748908
Carbon allocation; non-structural carbohydrates; source–sink relationships; Elaeis guineensis; phenotypic plasticity; photosynthesis
9.  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.
Methods
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.
Conclusions
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.
doi:10.1093/aob/mcq026
PMCID: PMC2859907  PMID: 20375201
Architectural effects; floral biomass; intra-inflorescence; pollen limitation; resource pre-emption; Stylidium armeria
10.  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.
Methods
A greenhouse experiment was carried out with three homogeneous planting densities (plant spacing = 0·3, 0·6 and 1 m). Detailed records of plant development, plant architecture and organ growth were made throughout the growing period. Model calibration was performed for each situation using a statistical optimization procedure (multi-fitting).
Key Results and Conclusions
Obvious limitations of the present version of the model appeared to account fully for the plant plasticity induced by inter-plant competition for light. A lack of stability was identified for some model parameters at very high planting density. In particular, those parameters characterizing organ sink strengths and governing light interception proved to be environment-dependent. Remarkably, however, responses of the parameter values concerned were consistent with actual growth measurements and with previously reported results. Furthermore, modifications of total biomass production and of allocation patterns induced by the planting-density treatments were accurately simulated using the sets of optimized parameters. These results demonstrate that the overall model structure is potentially able to reproduce the observed plant plasticity and suggest that sound biologically based adaptations could overcome the present model limitations. Potential options for model improvement are proposed, and the possibility of using the kernel algorithm currently available as a fitting tool to build up more sophisticated model versions is advocated.
doi:10.1093/aob/mcm317
PMCID: PMC2710282  PMID: 18199575
Functional–structural models; GREENLAB; phenotypic plasticity; planting density; competition; source–sink relationship; parameter stability; Solanum lycopersicum
11.  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.
Methods
The empirical production equation of GREENLAB is extrapolated to stands by computing the exposed photosynthetic foliage area of each plant. The computation is based on the combination of Poisson models of leaf distribution for all the neighbouring plants whose crown projection surfaces overlap. To study the effects of density on architectural development, we link the proposed competition model to the model of interaction between functional growth and structural development introduced by Mathieu (2006, PhD Thesis, Ecole Centrale de Paris, France).
Key Results and Conclusions
The model is applied to mono-specific field crops and forest stands. For high-density crops at full cover, the model is shown to be equivalent to the classical equation of field crop production ( Howell and Musick, 1985, in Les besoins en eau des cultures; Paris: INRA Editions). However, our method is more accurate at the early stages of growth (before cover) or in the case of intermediate densities. It may potentially account for local effects, such as uneven spacing, variation in the time of plant emergence or variation in seed biomass. The application of the model to trees illustrates the expression of plant plasticity in response to competition for light. Density strongly impacts on tree architectural development through interactions with the source–sink balances during growth. The effects of density on tree height and radial growth that are commonly observed in real stands appear as emerging properties of the model.
doi:10.1093/aob/mcm272
PMCID: PMC2710279  PMID: 18037666
Functional–structural plant models; GREENLAB; competition for light; Beer–Lambert Law; plant plasticity; dynamical system
12.  A Functional and Structural Mongolian Scots Pine (Pinus sylvestris var. mongolica) Model Integrating Architecture, Biomass and Effects of Precipitation 
PLoS ONE  2012;7(8):e43531.
Mongolian Scots pine (Pinus sylvestris var. mongolica) is one of the principal tree species in the network of Three-North Shelterbelt for windbreak and sand stabilisation in China. The functions of shelterbelts are highly correlated with the architecture and eco-physiological processes of individual tree. Thus, model-assisted analysis of canopy architecture and function dynamic in Mongolian Scots pine is of value for better understanding its role and behaviour within shelterbelt ecosystems in these arid and semiarid regions. We present here a single-tree functional and structural model, derived from the GreenLab model, which is adapted for young Mongolian Scots pines by incorporation of plant biomass production, allocation, allometric rules and soil water dynamics. The model is calibrated and validated based on experimental measurements taken on Mongolian Scots pines in 2007 and 2006 under local meteorological conditions. Measurements include plant biomass, topology and geometry, as well as soil attributes and standard meteorological data. After calibration, the model allows reconstruction of three-dimensional (3D) canopy architecture and biomass dynamics for trees from one- to six-year-old at the same site using meteorological data for the six years from 2001 to 2006. Sensitivity analysis indicates that rainfall variation has more influence on biomass increment than on architecture, and the internode and needle compartments and the aboveground biomass respond linearly to increases in precipitation. Sensitivity analysis also shows that the balance between internode and needle growth varies only slightly within the range of precipitations considered here. The model is expected to be used to investigate the growth of Mongolian Scots pines in other regions with different soils and climates.
doi:10.1371/journal.pone.0043531
PMCID: PMC3425476  PMID: 22927982
13.  In-silico analysis of water and carbon relations under stress conditions. A multi-scale perspective centered on fruit 
Fruit development, from its early stages, is the result of a complex network of interacting processes, on different scales. These include cell division, cell expansion but also nutrient transport from the plant, and exchanges with the environment. In the presence of nutrient limitation, in particular, the plant reacts as a whole, by modifying its architecture, metabolism, and reproductive strategy, determining the resources available for fruit development, which in turn affects the overall source-sink balance of the system. Here, we present an integrated model of tomato that explicitly accounts for early developmental changes (from cell division to harvest), and use it to investigate the impact of water deficit and carbon limitation on nutrient fluxes and fruit growth, in both dry and fresh mass. Variability in fruit response is analyzed on two different scales: among trusses at plant level, and within cell populations at fruit level. Results show that the effect of stress on individual cells strongly depends on their age, size, and uptake capabilities, and that the timing of stress application, together with the fruit position on the plant, is crucial in determining the final phenotypic outcome. Water deficit and carbon depletion impacted either source size, source activity, or sink strength with contrasted effects on fruit growth. An important prediction of the model is the major role of symplasmic transport of carbon in the early stage of fruit development, as a catalyst for cell and fruit growth.
doi:10.3389/fpls.2013.00495
PMCID: PMC3856696  PMID: 24367372
model; development; cell division; cell expansion; symplasm; plant architecture; tomato; stress
14.  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.
Methods
Five field experiments were conducted in the course of 4 years on irrigated fields near Beijing, China. Detailed observations were conducted throughout the seasons on the dimensions and fresh biomass of all above-ground plant organs for each metamer. Growth stage-specific target files were assembled from the data for GREENLAB parameter optimization. Optimization was conducted for specific developmental stages or the entire growth cycle, for individual plants (replicates), and for different seasons. Parameter stability was evaluated by comparing their CV with that of phenotype observation for the different sources of variability. A reduced data set was developed for easier model parameterization using one season, and validated for the four other seasons.
Key Results and Conclusions
The analysis of parameter stability among plants sharing the same environment and among populations grown in different environments indicated that the model explains some of the inter-seasonal variability of phenotype (parameters varied less than the phenotype itself), but not inter-plant variability (parameter and phenotype variability were similar). Parameter variability among developmental stages was small, indicating that parameter values were largely development-stage independent. The authors suggest that the high level of parameter stability observed in GREENLAB can be used to conduct comparisons among genotypes and, ultimately, genetic analyses.
doi:10.1093/aob/mcl245
PMCID: PMC2802986  PMID: 17158141
Plant architecture; functional–structural models; crop simulation; parameter stability; allometric relationships; sink capacity; Zea mays
15.  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.
Methods
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.
Conclusions
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.
doi:10.1093/aob/mcs173
PMCID: PMC3448427  PMID: 22933415
Capsicum annuum; fruit quality; pepper ovary swelling; source–sink effects
16.  Competition for Assimilates and Fruit Position Affect Fruit Set in Indeterminate Greenhouse Tomato 
Annals of Botany  1995;75(1):55-65.
Localization and characterization of fruit set in winter tomato crops was investigated to determine the main internal and external controlling factors and to establish a quantitative relationship between fruit set and competition for assimilates. Individual fruit growth and development was assessed on a beef tomato cultivar during the reproductive period (first nine inflorescences). A non-destructive photograph technique was used to measure fruit growth from very early stages of their development and then calliper measurements were made on big fruits. From these measurements we determined the precise developmental stage at which fruit growth stopped. Fruit potential growth, which is defined as the growth achieved in non-limiting conditions for assimilate supply, was also assessed by this method on plants thinned to one flower per inflorescence. The latter was used to calculate the ratio between actual and potential growth, which was found to be a good index of the competition for assimilates.
Time lags of fruit set were observed mainly on distal organs. When more than three flowers were left on each inflorescence, distal organs developed at the same time as proximal organs of the following inflorescence. Consequently they were submitted to a double competition within one inflorescence and among inflorescences. It was shown that, what is commonly named ‘fruit set failure’, is not an irreversible death of the organ and that a small fruit could resume growth after a delay of several weeks as soon as the first fruits ripened and thus ceased to compete for assimilates. In that case proximal fruits resumed growth before distal ones. The delayed fruits contained only few seeds but a germination test confirmed that fertilization took place before fruit set failed.
Competition for assimilates was calculated during plant development by the ratio between actual and potential fruit growth. Potential growth of proximal fruits was strongly dependent on the position of the inflorescence on the stem, whereas potential growth of distal fruits was lower than or equal to that of proximal fruits of the same inflorescence and it was independent on the inflorescence position. We took into account both inflorescence and fruit positions to establish a quantitative relationship between fruit set of individual inflorescences and the ratio between actual and potential fruit growth.
doi:10.1016/S0305-7364(05)80009-5
PMCID: PMC3023665  PMID: 21247913
Tomato; Lycopersicon esculentum Mill.; fruit set; competition for assimilates; potential growth; fruit sink strength
17.  Gene Regulatory Networks Elucidating Huanglongbing Disease Mechanisms 
PLoS ONE  2013;8(9):e74256.
Next-generation sequencing was exploited to gain deeper insight into the response to infection by Candidatus liberibacter asiaticus (CaLas), especially the immune disregulation and metabolic dysfunction caused by source-sink disruption. Previous fruit transcriptome data were compared with additional RNA-Seq data in three tissues: immature fruit, and young and mature leaves. Four categories of orchard trees were studied: symptomatic, asymptomatic, apparently healthy, and healthy. Principal component analysis found distinct expression patterns between immature and mature fruits and leaf samples for all four categories of trees. A predicted protein – protein interaction network identified HLB-regulated genes for sugar transporters playing key roles in the overall plant responses. Gene set and pathway enrichment analyses highlight the role of sucrose and starch metabolism in disease symptom development in all tissues. HLB-regulated genes (glucose-phosphate-transporter, invertase, starch-related genes) would likely determine the source-sink relationship disruption. In infected leaves, transcriptomic changes were observed for light reactions genes (downregulation), sucrose metabolism (upregulation), and starch biosynthesis (upregulation). In parallel, symptomatic fruits over-expressed genes involved in photosynthesis, sucrose and raffinose metabolism, and downregulated starch biosynthesis. We visualized gene networks between tissues inducing a source-sink shift. CaLas alters the hormone crosstalk, resulting in weak and ineffective tissue-specific plant immune responses necessary for bacterial clearance. Accordingly, expression of WRKYs (including WRKY70) was higher in fruits than in leaves. Systemic acquired responses were inadequately activated in young leaves, generally considered the sites where most new infections occur.
doi:10.1371/journal.pone.0074256
PMCID: PMC3783430  PMID: 24086326
18.  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.
doi:10.3389/fpls.2013.00437
PMCID: PMC3817663  PMID: 24204372
drought; plant biomass accumulation; non-structural carbohydrate; source and sink regulation; functional structural plant model; rice; oil palm
19.  Fruit transpiration in kiwifruit: environmental drivers and predictive model 
AoB Plants  2012;2012:pls036.
Seasonal and regional variations in kiwifruit storage quality imply a weather effect. This is perhaps mediated via fruit transpiration and fruit mineral nutrition. Concurrent measurements of fruit transpiration and weather are modelled to predict cumulative fruit transpiration throughout the season.
Background and aims
In most fruit crops, storage quality varies greatly between regions and seasons, causing significant commercial loss. Understanding the sources of this variability will contribute to the knowledge of fruit developmental physiology and may also benefit commercial fruit production via altered managements that reduce it or forecasts that predict it. A causal-chain relationship is proposed to help elucidate the sources of variability in fruit storage quality: the weather →(i)→ fruit transpiration →(ii)→ fruit calcium →(iii)→ fruit storage quality. This paper explores the first link of this hypothesis, →(i)→, for Hayward kiwifruit using field measurements of fruit transpiration rate and concurrent meteorological recordings. The aims are to identify the key environmental variables driving fruit transpiration and develop a predictive fruit transpiration model.
Methodology
Fruit transpiration was determined hourly over several 24-h periods by recording weight loss of detached fruit, on Days 23, 35, 49, 65, 94 and 140 after full bloom. Meteorological records were made every 15 min throughout the season at an adjacent regional weather station. A model of fruit transpiration was developed in which the usual meteorological variables (radiation, temperature, windspeed and relative humidity) were incorporated in a Fick's Law transpiration flux equation.
Principal results
Fruit transpiration rate (i.e. the molar flux density, mmol cm−2 h−1) varied diurnally and decreased during the season. The dominant fruit variable governing transpiration rate was skin conductance and the dominant environmental variables were relative humidity and temperature. Radiation and windspeed were not significantly influential.
Conclusions
The model provides a good fit to the fruit transpiration rate measurements regardless of the time of day/night or the stage of fruit development. The model allows reasonably accurate and continuous predictions of fruit transpiration rate throughout fruit development based on standard meteorological recordings. It also allows estimates of cumulative fruit transpiration throughout the season.
doi:10.1093/aobpla/pls036
PMCID: PMC3491587  PMID: 23136639
20.  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.
Methods
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.
Conclusions
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.
doi:10.1093/aob/mcp278
PMCID: PMC2814752  PMID: 19946042
Biomass growth; branching system; common assimilate pool; morphogenesis; organogenesis; source–sink; grapevine; Vitis vinifera
21.  Accumulation of Biomass and Mineral Elements with Calendar Time by Cotton: Application of the Expanded Growth Model 
PLoS ONE  2013;8(9):e72810.
Accumulation of plant biomass (Mg ha−1) with calendar time (wk) occurs as a result of photosynthesis for green land-based plants. A corresponding accumulation of mineral elements (kg ha−1) such as nitrogen, phosphorus, and potassium occurs from the soil through plant roots. Field data from literature for the warm-season annual cotton (Gossypium hirsutum L.) are used in this analysis. The expanded growth model is used to describe accumulation of biomass and mineral elements with calendar time. The growth model predicts a simple linear relationship between biomass yield and the growth quantifier, which is confirmed with the data. The growth quantifier incorporates the unit processes of distribution of solar energy which drives biomass accumulation by photosynthesis, partitioning of biomass between light-gathering and structural components of the plants, and an aging function. A hyperbolic relationship between plant nutrient uptake and biomass yield is assumed, and is confirmed for the mineral elements nitrogen, phosphorus, and potassium. It is concluded that the rate limiting process in the system is biomass accumulation by photosynthesis and that nutrient accumulation occurs in virtual equilibrium with biomass accumulation. The expanded growth model describes field data from California and Alabama rather well. Furthermore, all model parameters were common for the two sites with the exception of the yield factor A which accounts for differences in soil types, environmental conditions, fertilizer levels, and plant population.
doi:10.1371/journal.pone.0072810
PMCID: PMC3767794  PMID: 24039802
22.  The defH9-iaaM auxin-synthesizing gene increases plant fecundity and fruit production in strawberry and raspberry 
BMC Biotechnology  2004;4:4.
Background
The DefH9-iaaM gene fusion which is expressed specifically in placenta/ovules and promotes auxin-synthesis confers parthenocarpic fruit development to eggplant, tomato and tobacco. Transgenic DefH9-iaaM eggplants and tomatoes show increased fruit production due mainly to an improved fruit set. However, the weight of the fruits is also frequently increased.
Results
DefH9-iaaM strawberry and raspberry plants grown under standard cultivation conditions show a significant increase in fruit number and size and fruit yield. In all three Rosaceae species tested, Fragaria vesca, Fragaria x ananassa and Rubus idaeus, DefH9-iaaM plants have an increased number of flowers per inflorescence and an increased number of inflorescences per plant. This results in an increased number of fruits per plant. Moreover, the weight and size of transgenic fruits was also increased. The increase in fruit yield was approximately 180% in cultivated strawberry, 140% in wild strawberry, and 100% in raspberry. The DefH9-iaaM gene is expressed in the flower buds of all three species. The total IAA (auxin) content of young flower buds of strawberry and raspberry expressing the DefH9-iaaM gene is increased in comparison to untransformed flower buds. The DefH9-iaaM gene promotes parthenocarpy in emasculated flowers of both strawberry and raspberry.
Conclusions
The DefH9-iaaM gene is expressed and biologically active in Rosaceae. The DefH9-iaaM gene can be used, under cultivation conditions that allow pollination and fertilization, to increase fruit productivity significantly in Rosaceae species. The finding that the DefH9-iaaM auxin-synthesizing gene increases the number of inflorescences per plant and the number of flowers per inflorescence indicates that auxin plays a role in plant fecundity in these three perennial Rosaceae species.
doi:10.1186/1472-6750-4-4
PMCID: PMC394336  PMID: 15113427
DefH9-iaaM; Flower; Fruit; Inflorescence; Raspberry; Strawberry
23.  Carbon-use efficiency in green sinks is increased when a blend of apoplastic fructose and glucose is available for uptake 
Journal of Experimental Botany  2011;62(6):2013-2022.
Understanding how green sink strength is regulated in planta poses a difficult problem because non-structural carbohydrate (NSC) levels can have integrated, simultaneous feedback effects on photosynthesis, sugar uptake, and respiration that depend on specific NSC moieties. Photosynthetic gametophytes of the fern Ceratopteris richardii provide a simple land plant model to assess how different NSCs imported from the apoplast of intact plants affect green sink strength. Sink strength was quantified as the amount of exogenous sugar that plants grown in low light depleted from their liquid media, and the relative contributions of carbon assimilation by photosynthesis and sugar uptake was estimated from stable isotope analysis of plant dry mass. Gametophytes absorbed fructose and glucose with equal affinity when cultured on either hexose alone, or in the presence of an equimolar blend of both sugars. Plants also depleted sucrose from the surrounding media, although a portion of this disaccharide that was hydrolysed into fructose and glucose by putative cell wall invertase activity remained in the media. The δ13C in plant dry masses harvested from sugar treatments were all close to –18‰, indicating that 25–39% of total plant carbon was from C3 photosynthesis (δ13C=–29‰) and 61–75% was from uptake of exogenous sugars (δ13C=–11‰). Carbon-use efficiency (i.e. carbon accumulated/carbon depleted) was significantly improved when plants had a blend of exogenous sugars available compared with plants grown in a single hexose alone. Plants avoided complete down-regulation of photosynthesis even though a large excess of exogenous carbon fluxed through their cells.
doi:10.1093/jxb/erq407
PMCID: PMC3060692  PMID: 21350040
disaccharide; fern gametophyte; hexose; mixotrophy; monosaccharide transporter
24.  Contribution of Doñana Wetlands to Carbon Sequestration 
PLoS ONE  2013;8(8):e71456.
Inland and transitional aquatic systems play an important role in global carbon (C) cycling. Yet, the C dynamics of wetlands and floodplains are poorly defined and field data is scarce. Air-water fluxes in the wetlands of Doñana Natural Area (SW Spain) were examined by measuring alkalinity, pH and other physiochemical parameters in a range of water bodies during 2010–2011. Areal fluxes were calculated and, using remote sensing, an estimate of the contribution of aquatic habitats to gaseous transport was derived. Semi-permanent ponds adjacent to the large Guadalquivir estuary acted as mild sinks, whilst temporal wetlands were strong sources of (−0.8 and 36.3 ). Fluxes in semi-permanent streams and ponds changed seasonally; acting as sources in spring-winter and mild sinks in autumn (16.7 and −1.2 ). Overall, Doñana's water bodies were a net annual source of (5.2 ). Up–scaling clarified the overwhelming contribution of seasonal flooding and allochthonous organic matter inputs in determining regional air-water gaseous transport (13.1 ). Nevertheless, this estimate is about 6 times < local marsh net primary production, suggesting the system acts as an annual net sink. Initial indications suggest longer hydroperiods may favour autochthonous C capture by phytoplankton. Direct anthropogenic impacts have reduced the hydroperiod in Doñana and this maybe exacerbated by climate change (less rainfall and more evaporation), suggesting potential for the modification of C sequestration.
doi:10.1371/journal.pone.0071456
PMCID: PMC3747241  PMID: 23977044
25.  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.
Methods
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’.
Conclusions
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.
doi:10.1093/aob/mct026
PMCID: PMC3605959  PMID: 23419248
l-Ascorbic acid; blackcurrant; fruit; Ribes nigrum; source sinks; vitamin C

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