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1.  Correlation between dynamic tomato fruit-set and source–sink ratio: a common relationship for different plant densities and seasons? 
Annals of Botany  2010;107(5):805-815.
Background and Aims
It is widely accepted that fruit-set in plants is related to source–sink ratio. Despite its critical importance to yield, prediction of fruit-set remains an ongoing problem in crop models. Functional–structural plant models are potentially able to simulate organ-level plasticity of plants. To predict fruit-set, the quantitative link between source–sink ratio and fruit-set probability is analysed here via a functional–structural plant model, GreenLab.
Two experiments, each with four plant densities, were carried out in a solar greenhouse during two growth seasons (started in spring and autumn). Dynamic fruit-set probability was estimated by frequent observation on inflorescences. Source and sink parameter values were obtained by fitting GreenLab outputs for the biomass of plant parts (lamina, petiole, internode, fruit), at both organ and plant level, to corresponding destructive measurements at six dates from real plants. The dynamic source–sink ratio was calculated as the ratio between biomass production and plant demand (sum of all organ sink strength) per growth cycle, both being outputs of the model.
Key Results and Conclusions
Most sink parameters were stable over multiple planting densities and seasons. From planting, source–sink ratio increased in the vegetative stage and reached a peak after fruit-set commenced, followed by a decrease of leaf appearance rate. Fruit-set probability was correlated with the source–sink ratio after the appearance of flower buds. The relationship between fruit-set probability and the most correlated source–sink ratio could be quantified by a single regression line for both experiments. The current work paves the way to predicting dynamic fruit-set using a functional structure model.
PMCID: PMC3077983  PMID: 21183453
Tomato; Solanum lycopersicum; fruit-set probability; time step; source–sink ratio; sink strength; functional–structural plant model; inverse modelling; plant plasticity
2.  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
3.  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
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.
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
5.  Persistence of seeds from crops of conventional and herbicide tolerant oilseed rape (Brassica napus) 
A series of rotation experiments at five sites over four years has explored the environmental and agronomic implications of growing herbicide tolerant oilseed rape and sugar beet. This paper reports on the population dynamics of volunteer rape (Brassica napus). The experiments compared four winter oilseed rape (WOSR) cultivars: a conventional cultivar (Apex) and three developmental cultivars either genetically modified (GM) to be tolerant to glyphosate or glufosinate, or conventionally bred to be tolerant to herbicides of the imidazolinone group. Seed losses at harvest averaged 3575 seeds m−2 but ranged from less than 2000 up to more than 10 000 seeds m−2. There was a rapid decline in seed numbers during the first few months after harvest, resulting in a mean loss of seeds of 60%. In subsequent seasons, the seedbank declined much more slowly at four of the five sites (ca 20% per year) and the models predicted 95% seed loss after approximately 9 years. Seed decline was much faster at the fifth site. There were no clear differences between the four cultivars in either the numbers of seeds shed at harvest or in their subsequent persistence. The importance of the persistence of GM rape seeds, in the context of the coexistence of GM and non-GM crops and the role of good management practices that minimize seed persistence, are discussed.
PMCID: PMC1559884  PMID: 16191596
genetically modified crops; herbicide tolerant crops; oilseed rape; Brassica napus; seed persistence
6.  Effects on weed and invertebrate abundance and diversity of herbicide management in genetically modified herbicide-tolerant winter-sown oilseed rape 
We evaluated the effects of the herbicide management associated with genetically modified herbicide-tolerant (GMHT) winter oilseed rape (WOSR) on weed and invertebrate abundance and diversity by testing the null hypothesis that there is no difference between the effects of herbicide management of GMHT WOSR and that of comparable conventional varieties. For total weeds there were few treatment differences between GMHT and conventional cropping, but large and opposite treatment effects were observed for dicots and monocots. In the GMHT treatment, there were fewer dicots and more monocots than in conventional crops. At harvest, dicot biomass and seed rain in the GMHT treatment were one-third of that in the conventional, while monocot biomass was threefold greater and monocot seed rain almost fivefold greater in the GMHT treatment than in the conventional. These differential effects persisted into the following two years of the rotation. Bees and butterflies that forage and select for dicot weeds were less abundant in GMHT WOSR management in July. Year totals for Collembola were greater under GMHT management. There were few other treatment effects on invertebrates, despite the marked effects of herbicide management on the weeds.
PMCID: PMC1578713  PMID: 15799941
genetically modified crops; biodiversity; oilseed rape; canola; herbicide management
7.  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
8.  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
9.  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
10.  Extending the rapeseed gene pool with resynthesized Brassica napus II: Heterosis 
Hybrid breeding relies on the combination of parents from two differing heterotic groups. However, the genetic diversity in adapted oilseed rape breeding material is rather limited. Therefore, the use of resynthesized Brassica napus as a distant gene pool was investigated. Hybrids were derived from crosses between 44 resynthesized lines with a diverse genetic background and two male sterile winter oilseed rape tester lines. The hybrids were evaluated together with their parents and check cultivars in 2 years and five locations in Germany. Yield, plant height, seed oil, and protein content were monitored, and genetic distances were estimated with molecular markers (127 polymorphic RFLP fragments). Resynthesized lines varied in yield between 40.9 dt/ha and 21.5 dt/ha, or between 85.1 and 44.6% of check cultivar yields. Relative to check cultivars, hybrids varied from 91.6 to 116.6% in yield and from 94.5 to 103.3% in seed oil content. Mid-parent heterosis varied from −3.5 to 47.2% for yield. The genetic distance of parental lines was not significantly correlated with heterosis or hybrid yield. Although resynthesized lines do not meet the elite rapeseed standards, they are a valuable source for hybrid breeding due to their large distance from present breeding material and their high heterosis when combined with European winter oilseed rape.
Electronic supplementary material
The online version of this article (doi:10.1007/s00122-011-1765-7) contains supplementary material, which is available to authorized users.
PMCID: PMC3304059  PMID: 22159759
11.  Application of glutathione to roots selectively inhibits cadmium transport from roots to shoots in oilseed rape 
Journal of Experimental Botany  2013;64(4):1073-1081.
Glutathione is a tripeptide involved in various aspects of plant metabolism. This study investigated the effects of the reduced form of glutathione (GSH) applied to specific organs (source leaves, sink leaves, and roots) on cadmium (Cd) distribution and behaviour in the roots of oilseed rape plants (Brassica napus) cultured hydroponically. The translocation ratio of Cd from roots to shoots was significantly lower in plants that had root treatment of GSH than in control plants. GSH applied to roots reduced the Cd concentration in the symplast sap of root cells and inhibited root-to-shoot Cd translocation via xylem vessels significantly. GSH applied to roots also activated Cd efflux from root cells to the hydroponic solution. Inhibition of root-to-shoot translocation of Cd was visualized, and the activation of Cd efflux from root cells was also shown by using a positron-emitting tracer imaging system (PETIS). This study investigated a similar inhibitory effect on root-to-shoot translocation of Cd by the oxidized form of glutathione, GSSG. Inhibition of Cd accumulation by GSH was abolished by a low-temperature treatment. Root cells of plants exposed to GSH in the root zone had less Cd available for xylem loading by actively excluding Cd from the roots. Consequently, root-to-shoot translocation of Cd was suppressed and Cd accumulation in the shoot decreased.
PMCID: PMC3580817  PMID: 23364937
Cadmium (Cd); glutathione; oilseed rape (Brassica napus); oxidized form of glutathione (GSSG); positron-emitting tracer imaging system (PETIS); reduced form of glutathione; transport; xylem.
12.  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
13.  Non-Uniform Dispersion of the Source-Sink Relationship Alters Wavefront Curvature 
PLoS ONE  2013;8(11):e78328.
The distribution of cellular source-sink relationships plays an important role in cardiac propagation. It can lead to conduction slowing and block as well as wave fractionation. It is of great interest to unravel the mechanisms underlying evolution in wavefront geometry. Our goal is to investigate the role of the source-sink relationship on wavefront geometry using computer simulations. We analyzed the role of variability in the microscopic source-sink relationship in driving changes in wavefront geometry. The electrophysiological activity of a homogeneous isotropic tissue was simulated using the ten Tusscher and Panfilov 2006 action potential model and the source-sink relationship was characterized using an improved version of the Romero et al. safety factor formulation (SFm2). Our simulations reveal that non-uniform dispersion of the cellular source-sink relationship (dispersion along the wavefront) leads to alterations in curvature. To better understand the role of the source-sink relationship in the process of wave formation, the electrophysiological activity at the initiation of excitation waves in a 1D strand was examined and the source-sink relationship was characterized using the two recently updated safety factor formulations: the SFm2 and the Boyle-Vigmond (SFVB) definitions. The electrophysiological activity at the initiation of excitation waves was intimately related to the SFm2 profiles, while the SFVB led to several counterintuitive observations. Importantly, with the SFm2 characterization, a critical source-sink relationship for initiation of excitation waves was identified, which was independent of the size of the electrode of excitation, membrane excitability, or tissue conductivity. In conclusion, our work suggests that non-uniform dispersion of the source-sink relationship alters wavefront curvature and a critical source-sink relationship profile separates wave expansion from collapse. Our study reinforces the idea that the safety factor represents a powerful tool to study the mechanisms of cardiac propagation in silico, providing a better understanding of cardiac arrhythmias and their therapy.
PMCID: PMC3817246  PMID: 24223791
14.  Is the remobilization of S and N reserves for seed filling of winter oilseed rape modulated by sulphate restrictions occurring at different growth stages? 
Journal of Experimental Botany  2010;61(15):4313-4324.
How the remobilization of S and N reserves can meet the needs of seeds of oilseed rape subject to limitation of S fertilization remains largely unclear. Thus, this survey aims to determine the incidence of sulphate restriction [low S (LS)] applied at bolting [growth stage (GS) 32], visible bud (GS 53), and start of pod filling (GS 70) on source–sink relationships for S and N, and on the dynamics of endogenous/exogenous S and N contributing to seed yield and quality. Sulphate restrictions applied at GS 32, GS 53, and GS 70 were annotated LS32, LS53, and LS70. Long-term 34SO42− and 15NO3− labelling was used to explore S and N partitioning at the whole-plant level. In LS53, the sulphur remobilization efficiency (SRE) to seeds increased, but not enough to maintain seed quality. In LS32, an early S remobilization from leaves provided S for root, stem, and pod growth, but the subsequent demand for seed development was not met adequately and the N utilization efficiency (NUtE) was reduced when compared with high S (HS). The highest SRE (65±1.2% of the remobilized S) associated with an efficient foliar S mobilization (with minimal residual S concentrations of 0.1–0.2% dry matter) was observed under LS70 treatment, which did not affect yield components.
PMCID: PMC2955745  PMID: 20693411
Oilseed rape; sulphate restriction; 34S and 15N labelling; S remobilization efficiency; S utilization efficiency
15.  Brassica orthologs from BANYULS belong to a small multigene family, which is involved in procyanidin accumulation in the seed 
Planta  2009;230(6):1167-1183.
As part of a research programme focused on flavonoid biosynthesis in the seed coat of Brassica napus L. (oilseed rape), orthologs of the BANYULS gene that encoded anthocyanidin reductase were cloned in B. napus as well as in the related species Brassica rapa and Brassica oleracea. B. napus genome contained four functional copies of BAN, two originating from each diploid progenitor. Amino acid sequences were highly conserved between the Brassicaceae including B. napus, B. rapa, B. oleracea as well as the model plant Arabidopsis thaliana. Along the 200 bp in 5′ of the ATG codon, Bna.BAN promoters (ProBna.BAN) were conserved with AtANR promoter and contained putative cis-acting elements. In addition, transgenic Arabidopsis and oilseed rape plants carrying the first 230 bp of ProBna.BAN fused to the UidA reporter gene were generated. In the two Brassicaceae backgrounds, ProBna.BAN activity was restricted to the seed coat. In B. napus seed, ProBna.BAN was activated in procyanidin-accumulating cells, namely the innermost layer of the inner integument and the micropyle-chalaza area. At the transcriptional level, the four Bna.BAN genes were expressed in the seed. Laser microdissection assays of the seed integuments showed that Bna.BAN expression was restricted to the inner integument, which was consistent with the activation profile of ProBna.BAN. Finally, Bna.BAN genes were mapped onto oilseed rape genetic maps and potential co-localisations with seed colour quantitative trait loci are discussed.
PMCID: PMC2764081  PMID: 19760260
Anthocyanidin reductase; BANYULS genes; Brassica; Flavonoid metabolism; Seed coat-specific promoter
16.  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.
PMCID: PMC3060692  PMID: 21350040
disaccharide; fern gametophyte; hexose; mixotrophy; monosaccharide transporter
17.  Quantitative Genetics and Functional–Structural Plant Growth Models: Simulation of Quantitative Trait Loci Detection for Model Parameters and Application to Potential Yield Optimization 
Annals of Botany  2007;101(8):1243-1254.
Background and Aims
Prediction of phenotypic traits from new genotypes under untested environmental conditions is crucial to build simulations of breeding strategies to improve target traits. Although the plant response to environmental stresses is characterized by both architectural and functional plasticity, recent attempts to integrate biological knowledge into genetics models have mainly concerned specific physiological processes or crop models without architecture, and thus may prove limited when studying genotype × environment interactions. Consequently, this paper presents a simulation study introducing genetics into a functional–structural growth model, which gives access to more fundamental traits for quantitative trait loci (QTL) detection and thus to promising tools for yield optimization.
The GREENLAB model was selected as a reasonable choice to link growth model parameters to QTL. Virtual genes and virtual chromosomes were defined to build a simple genetic model that drove the settings of the species-specific parameters of the model. The QTL Cartographer software was used to study QTL detection of simulated plant traits. A genetic algorithm was implemented to define the ideotype for yield maximization based on the model parameters and the associated allelic combination.
Key Results and Conclusions
By keeping the environmental factors constant and using a virtual population with a large number of individuals generated by a Mendelian genetic model, results for an ideal case could be simulated. Virtual QTL detection was compared in the case of phenotypic traits – such as cob weight – and when traits were model parameters, and was found to be more accurate in the latter case. The practical interest of this approach is illustrated by calculating the parameters (and the corresponding genotype) associated with yield optimization of a GREENLAB maize model. The paper discusses the potentials of GREENLAB to represent environment × genotype interactions, in particular through its main state variable, the ratio of biomass supply over demand.
PMCID: PMC2710265  PMID: 17766844
Plant growth model; GREENLAB; genetics; QTL; breeding; yield optimization; genetic algorithm; Zea mays
18.  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.
PMCID: PMC3425476  PMID: 22927982
19.  QTL for Yield Traits and Their Association with Functional Genes in Response to Phosphorus Deficiency in Brassica napus 
PLoS ONE  2013;8(1):e54559.
Oilseed rape (Brassica napus L.) is one of the most important oil crops. A primary limitation to the cultivation of this crop is the lack of available phosphorus (P) in soils. To elucidate the genetic control of P deficiency tolerance in Brassica napus, quantitative trait locus (QTL) for seed yield and yield related-traits in response to P deficiency were identified using a double haploid mapping population (TN DH) derived from a cross between a P-efficient cultivar, Ningyou 7 and a P-inefficient cultivar, Tapidor.
Three field trials were conducted to determine seed yield (SY), plant height (PH), number of primary branches (BN), height to the first primary branch (FBH), relative first primary branch height (RBH), pod number per plant (PN), seed number per pod (SN) and seed weight of 1,000 seeds (SW) in 188 lines of TN DH population exposed to low P (LP) and optimal P (OP) conditions. P deficiency decreased PH, BN, SN, PN and SY, and increased FBH and RBH with no effect on SW. Three reproducible LP-specific QTL regions were identified on chromosomes A2, A3 and A5 that controlled SN, PN and SW respectively. In addition, six reproducible constitutive regions were also mapped with two each for SY-LP on A2, and FBH-LP on C6 and one each for PH-LP and SW-LP on A3. About 30 markers derived from 19 orthologous genes involved in Arabidopsis P homeostasis were mapped on 24 QTL regions by comparative mapping between Arabidopsis and Brassica napus. Among these genes, GPT1, MGD2 and SIZ1 were associated with two major loci regulating SY-LP and other yield-related traits on A2 between 77.1 and 95.0 cM.
The stable QTLs detected under LP conditions and their candidate genes may provide useful information for marker-assisted selection in breeding high-yield B. napus varieties with improved P efficiency.
PMCID: PMC3557265  PMID: 23382913
20.  Response of Bean (Vicia faba L.) Plants to Low Sink Demand by Measuring the Gas Exchange Rates and Chlorophyll a Fluorescence Kinetics 
PLoS ONE  2013;8(12):e80770.
The decline of photosynthesis in plants under low sink demand is well known. Previous studies focused on the relationship between stomatal conductance (gs) and net photosynthetic rate (Pn). These studies investigated the effect of changes in Photosystem II (PSII) function on the Pn decline under low sink demand. However, little is known about its effects on different limiting steps of electron transport chain in PSII under this condition.
Methodology/Principal Finding
Two-month-old bean plants were processed by removing pods and flowers (low sink demand). On the 1st day after low sink demand treatment, a decline of Pn was accompanied by a decrease in gs and internal-to-ambient CO2 concentration ratio (Ci/Ca). From the 3rd to 9th day, Pn and gs declined continuously while Ci/Ca ratio remained stable in the treatment. Moreover, these values were lower than that of control. Wk (a parameter reflecting the damage to oxygen evolving complex of the donor side of PSII) values in the treatment were significantly higher than their corresponding control values. However, RCQA (a parameter reflecting the number of active RCs per excited cross-section of PSII) values in the treatment were significantly lower than control from the 5th day. From the 11th to 21st day, Pn and gs of the treatment continued to decline and were lower than control. This was accompanied by a decrease of RCQA, and an increase of Wk. Furthermore, the quantum yield parameters φPo, φEo and ψEo in the treatment were lower than in control; however, Ci/Ca values in the treatment gradually increased and were significantly higher than control on the 21st day.
Stomatal limitation during the early stage, whereas a combination of stomatal and non-stomatal limitation during the middle stage might be responsible for the reduction of Pn under low sink demand. Non-stomatal limitation during the late stages after the removal of the sink of roots and pods may also cause Pn reduction. The non-stomatal limitation was associated with the inhibition of PSII electron transport chain. Our data suggests that the donor side of PSII was the most sensitive to low sink demand followed by the reaction center of PSII. The acceptor side of PSII may be the least sensitive.
PMCID: PMC3851463  PMID: 24324626
21.  Towards the theory of pollinator-mediated gene flow. 
I present a new exposition of a model of gene flow by animal-mediated pollination between a source population and a sink population. The model's parameters describe two elements: (i) the expected portion of the source's paternity that extends to the sink population; and (ii) the dilution of this portion by within-sink pollinations. The model is termed the portion-dilution model (PDM). The PDM is a parametric restatement of the conventional view of animal-mediated pollination. In principle, it can be applied to plant species in general. I formulate a theoretical value of the portion parameter that maximizes gene flow and prescribe this as a benchmark against which to judge the performance of real systems. Existing foraging theory can be used in solving part of the PDM, but a theory for source-to-sink transitions by pollinators is currently elusive.
PMCID: PMC1693199  PMID: 12831465
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.  Are the common assimilate pool and trophic relationships appropriate for dealing with the observed plasticity of grapevine development? 
Annals of Botany  2009;105(2):233-247.
Background and Aims
Models based on the consideration of plant development as the result of source–sink relationships between organs suffer from an inherent lack of quantification of the effect of trophic competition on organ growth processes. The ‘common assimilate pool theory’ underlying many such models is highly debatable.
Six experiments were carried out in a greenhouse and outdoors with two grapevine cultivars and with 12 management systems, resulting in different types of plant architecture. Ten variables were used to quantify the impact of variations in assimilate supply and topological distances between sources and sinks on organogenesis, morphogenesis and biomass growth.
Key Results
A hierarchy of the responses of these processes to variations in assimilate supply was identified. Organ size seemed to be independent of assimilate supply, whereas both organogenesis and biomass growth were affected by variations in assimilate supply. Lower levels of organ biomass growth in response to the depletion of assimilate supplies seemed to be the principal mechanism underlying the plasticity of plant development in different environments. Defoliation or axis ablation resulted in changes in the relationship between growth processes and assimilate supply, highlighting the influence of non-trophic determinants. The findings cast doubt on the relevance of ‘the common assimilate pool theory’ for modelling the development of grapevine.
The results of this study suggest new formalisms for increasing the ability of models to take plant plasticity into account. The combination of an ecophysiological model for morphogenesis taking environmental signals into account and a biomass driven model for organogenesis and biomass allocation taking the topological distances between the sources and the sinks into account appears to be a promising approach. Moreover, in order to simulate the impact of agronomic practices, it will be necessary to take into account the non-trophic determinants of plant development such as hormonal signaletics.
PMCID: PMC2814752  PMID: 19946042
Biomass growth; branching system; common assimilate pool; morphogenesis; organogenesis; source–sink; grapevine; Vitis vinifera
24.  North–South divide: contrasting impacts of climate change on crop yields in Scotland and England 
Effects of climate change on productivity of agricultural crops in relation to diseases that attack them are difficult to predict because they are complex and nonlinear. To investigate these crop–disease–climate interactions, UKCIP02 scenarios predicting UK temperature and rainfall under high- and low-CO2 emission scenarios for the 2020s and 2050s were combined with a crop-simulation model predicting yield of fungicide-treated winter oilseed rape and with a weather-based regression model predicting severity of phoma stem canker epidemics. The combination of climate scenarios and crop model predicted that climate change will increase yield of fungicide-treated oilseed rape crops in Scotland by up to 0.5 t ha−1 (15%). In contrast, in southern England the combination of climate scenarios, crop, disease and yield loss models predicted that climate change will increase yield losses from phoma stem canker epidemics to up to 50 per cent (1.5 t ha−1) and greatly decrease yield of untreated winter oilseed rape. The size of losses is predicted to be greater for winter oilseed rape cultivars that are susceptible than for those that are resistant to the phoma stem canker pathogen Leptosphaeria maculans. Such predictions illustrate the unexpected, contrasting impacts of aspects of climate change on crop–disease interactions in agricultural systems in different regions.
PMCID: PMC2839380  PMID: 19447817
climate scenarios; crop simulation model; resistance to Leptosphaeria maculans; phoma stem canker; stochastic weather generator; weather-based disease forecast model
25.  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

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