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Depending on the questions to be answered, water flow in the xylem can be modelled following different approaches with varying spatial and temporal resolution. When focussing on the influence of hydraulic architecture upon flow dynamics, distribution of water potentials in a tree crown or questions of vulnerability of the hydraulic system, functional-structural plant models, which link representations of morphological structure with simulated processes and with a virtual environment, can be a promising tool. Such a model will then include a network of idealized xylem segments, each representing the conducting part of a stem or branch segment, and a numerical machinery suitable for solving a system of differential equations on it reflecting the hydrodynamic laws, which are the basis of the broadly accepted cohesion-tension theory of water flow in plants. We will discuss functional-structural plant models, the simplifications that are useful for hydraulic simulations within this framework, the deduction of the used differential equations from basic physical conservation laws, and their numerical solution, as well as additional necessary models of radiation, photosynthesis, and stomatal conductance. In some supplementary notes, we are shortly addressing some related questions, for example, about root systems or about the relation between macro-scale hydraulic parameters and fine-grained (anatomical) xylem structure., (© 2024. The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature.)

Photosynthetic light response curve parameters help us understand the interspecific variation in photosynthetic traits, leaf acclimation status, carbon uptake, and plant productivity in specific environments. These parameters are also influenced by leaf traits which rely on species and growth environment. In accessions of four amaranth species (Amaranthus. hybridus, A. dubius, A. hypochondriacus, and A. cruentus), we determined variations in the net photosynthetic light response curves and leaf traits, and analysed the relationships between maximum gross photosynthetic rate, leaf traits, and whole-plant productivity. Non-rectangular hyperbolae were used for the net photosynthesis light response curves. Maximum gross photosynthetic rate (Pgmax) was the only variant parameter among the species, ranging from 22.29 to 34.21 μmol m-2 s-1. Interspecific variation existed for all the leaf traits except leaf mass per area and leaf inclination angle. Stomatal conductance, nitrogen, chlorophyll, and carotenoid contents, as well as leaf area correlated with Pgmax. Stomatal conductance and leaf nitrogen explained much of the variation in Pgmax at the leaf level. At the plant level, the slope between absolute growth rate and leaf area showed a strong linear relationship with Pgmax. Overall, A. hybridus and A. cruentus exhibited higher Pgmax at the leaf level and light use efficiency at the whole-plant level than A. dubius, and A. hypochondriacus. Thus, A. hybridus and A. cruentus tended to be more efficient with respect to carbon assimilation. These findings highlight the correlation between leaf photosynthetic characteristics, other leaf traits, and whole plant productivity in amaranths. Future studies may explore more species and accessions of Amaranthus at different locations or light environments., Competing Interests: The authors have declared that no competing interests exist.

How to increase crop yield is the most important issue in agricultural production. Many studies have been devoted to optimizing spatial distribution of crops, to improve light interception and increase photosynthetic assimilation. However, finding an optimal solution based on field experiments is almost impossible since the large number of combinations of factors that are related, and the cost in terms of finances and time are prohibitive. A new optimization strategy was proposed in this study, integrating a Functional-Structural Model of rice with a workflow based on a Mixed Particle Swarm Optimization (MPSO) algorithm. The 3D modelling platform GroIMP was used to implement the model and optimization workflow. MPSO is a new Particle Swarm Optimization-based algorithm with multistage disturbances, which has improved abilities to get rid of local optima and to explore solution space. Spacing between plants was used as optimization target in the first example. An optimal plant spacing was obtained within the model framework of current environmental settings together with the functional and structural modules. Simulation results indicate that the optimized plant spacing could increase rice yield, and that the optimization results remain stable., Competing Interests: The authors have declared that no competing interests exist.

Apple skin color is an important trait for organoleptic quality. In fact, it has a major influence on consumer choice. Skin color is, thus, one of the most important criteria taken into account by breeders. For apples, most novel varieties are so-called "mutants" or "sports" that have been identified in clonal populations. Indeed, many "sports" exist that show distinct phenotypic differences compared to the varieties from which they originated. These differences affect a limited number of traits of economic importance, including skin color. Until recently, the detailed genetic or epigenetic changes resulting in heritable phenotypic changes in sports was largely unknown. Recent technological advances and the availability of several high-quality apple genomes now provide the bases to understand the exact nature of the underlying molecular changes that are responsible for the observed phenotypic changes observed in sports. The present review investigates the molecular nature of sports affected in apple skin color giving arguments in favor of the genetic or epigenetic explanatory models.

Apple fruit growth is the result of several factors: inherent demand (relative sink strength) of the fruit (defined by the demands for cell division and expansion growth, etc.), carbon assimilation by the source leaves (source strength), and the resulting allocation to the organ in question. It is thus a complex process involving source-sink interactions. In the present study, we designed an experimental system in which parts of fruit-bearing branches of two apple cultivars ("Fuji" and "Ariane") were isolated from the rest of the tree by girdling and then subjected to specific pruning and fruit removal treatments to create a wide range of global (branch-level) source-sink ratios. We monitored not only fruit kinetics but also photosynthesis as a response to light in leaves of the three different shoot types (i.e., the rosette, the bourse, and the vegetative shoots) to 1) study the impact of source-sink distance on carbon partitioning between fruits within the same branch and 2) to investigate the impact of source/sink ratio on fruit growth and leaf photosynthetic activity. Our results indicate 1) no significant differences among lateral fruits belonging to different ranks, and this independent of source availability; 2) that a modification of the source/sink ratio seems to be compensated by an alteration of the photosynthetic rate of leaves, with stronger and weaker values obtained for lower and higher ratios, respectively. Moreover, our results seem to suggest that two growing sinks together will upregulate photosynthesis rate more strongly than one growing sink does on its own, and this with the same leaf area per fruit. These results are discussed, and some hypotheses are put forward to explain them.

Background and Aims: Several studies have found seasonal and temporal variability in leaf photosynthesis parameters in different crops. This variability depends upon the environment, the developmental stage of the plant and the presence or absence of sinks. Girdling involves the removal of the bark and phloem down to the youngest xylem all around the stem and prevents export of photoassimilates out of the stem. The load of developing fruits has often been reported to influence the individual net leaf photosynthesis rate (Pn) in tree crops. In this study, we chose (1) to model the key parameters of photosynthesis models of leaves (Pgmax, Rd, α and θ) as a function of time and using these two means (girdling and low fruit load) to alter the source-sink balance and (2) to compare three models: the rectangular and non-rectangular hyperbola model by Thornley, as well as the non-rectangular hyperbola model by Marshall and Biscoe., Methods: Six-year-old fruit-bearing branches of 10-year-old apple trees were used to study and model the seasonal variation of photosynthetic parameters in leaves of vegetative shoots, as a function of global fruit load (at the branch level), with or without girdling, during the growing season of 2015. Three treatments were applied: control, low load (LL) or low load + girdling (LLG). For each fruit-bearing branch, light-response curves of Pn for two leaves of vegetative shoots were measured at two different positions, proximal and distal., Key Results: The model of Marshall and Biscoe was the most accurate for the simulation of Pn in fruit-bearing branches of apple trees with time (season) and the three treatments applied., Conclusion: The present study proposed a way to model the photosynthesis rate by temporal and environmental variables only. A proper validation of this model will be necessary to extend its utilization and appreciate its predictive capacity fully.

Functional-structural plant modeling (FSPM) is a fast and dynamic method to predict plant growth under varying environmental conditions. Temperature is a primary factor affecting the rate of plant development. In the present study, we used three different temperature treatments (10/14°C, 18/22°C, and 26/30°C) to test the effect of temperature on growth and development of rapeseed ( Brassica napus L.) seedlings. Plants were sampled at regular intervals (every 3 days) to obtain growth data during the length of the experiment (1 month in total). Total leaf dry mass, leaf area, leaf mass per area (LMA), width-length ratio, and the ratio of petiole length to leaf blade length (PBR), were determined and statistically analyzed, and contributed to a morphometric database. LMA under high temperature was significantly smaller than LMA under medium and low temperature, while leaves at high temperature were significantly broader. An FSPM of rapeseed seedlings featuring a growth function used for leaf extension and biomass accumulation was implemented by combining measurement with literature data. The model delivered new insights into growth and development dynamics of winter oilseed rape seedlings. The present version of the model mainly focuses on the growth of plant leaves. However, future extensions of the model could be used in practice to better predict plant growth in spring and potential cold damage of the crop.

In apple, the first-order branch of a tree has a characteristic architecture constituting three shoot types: bourses (rosettes), bourse shoots, and vegetative shoots. Its overall architecture as well as that of each shoot thus determines the distribution of sources (leaves) and sinks (fruits) and could have an influence on the amount of sugar allocated to fruits. Knowledge of architecture, in particular the position and area of leaves helps to quantify source strength. In order to reconstruct this initial architecture, rules equipped with allometric relations could be used: these allow predicting model parameters that are difficult to measure from simple traits that can be determined easily, non-destructively and directly in the orchard. Once such allometric relations are established they can be used routinely to recreate initial structures. Models based on allometric relations have been established in this study in order to predict the leaf areas of the three different shoot types of three apple cultivars with different branch architectures: "Fuji," "Ariane," and "Rome Beauty." The allometric relations derived from experimental data allowed us to model the total shoot leaf area as well as the individual leaf area for each leaf rank, for each shoot type and each genotype. This was achieved using two easily measurable input variables: total leaf number per shoot and the length of the biggest leaf on the shoot. The models were tested using a different data set, and they were able to accurately predict leaf area of all shoot types and genotypes. Additional focus on internode lengths on spurs contributed to refine the models.

Background and Aims: Maximizing photosynthesis at the canopy level is important for enhancing crop yield, and this requires insights into the limiting factors of photosynthesis. Using greenhouse cucumber (Cucumis sativus) as an example, this study provides a novel approach to quantify different components of photosynthetic limitations at the leaf level and to upscale these limitations to different canopy layers and the whole plant., Methods: A static virtual three-dimensional canopy structure was constructed using digitized plant data in GroIMP. Light interception of the leaves was simulated by a ray-tracer and used to compute leaf photosynthesis. Different components of photosynthetic limitations, namely stomatal (S(L)), mesophyll (M(L)), biochemical (B(L)) and light (L(L)) limitations, were calculated by a quantitative limitation analysis of photosynthesis under different light regimes., Key Results: In the virtual cucumber canopy, B(L) and L(L) were the most prominent factors limiting whole-plant photosynthesis. Diffusional limitations (S(L) + M(L)) contributed <15% to total limitation. Photosynthesis in the lower canopy was more limited by the biochemical capacity, and the upper canopy was more sensitive to light than other canopy parts. Although leaves in the upper canopy received more light, their photosynthesis was more light restricted than in the leaves of the lower canopy, especially when the light condition above the canopy was poor. An increase in whole-plant photosynthesis under diffuse light did not result from an improvement of light use efficiency but from an increase in light interception. Diffuse light increased the photosynthesis of leaves that were directly shaded by other leaves in the canopy by up to 55%., Conclusions: Based on the results, maintaining biochemical capacity of the middle-lower canopy and increasing the leaf area of the upper canopy would be promising strategies to improve canopy photosynthesis in a high-wire cucumber cropping system. Further analyses using the approach described in this study can be expected to provide insights into the influences of horticultural practices on canopy photosynthesis and the design of optimal crop canopies.

Understanding the role of branch architecture in carbon production and allocation is essential to gain more insight into the complex process of assimilate partitioning in fruit trees. This mini review reports on the current knowledge of the role of branch architecture in carbohydrate production and partitioning in apple. The first-order carrier branch of apple illustrates the complexity of branch structure emerging from bud activity events and encountered in many fruit trees. Branch architecture influences carbon production by determining leaf exposure to light and by affecting leaf internal characteristics related to leaf photosynthetic capacity. The dynamics of assimilate partitioning between branch organs depends on the stage of development of sources and sinks. The sink strength of various branch organs and their relative positioning on the branch also affect partitioning. Vascular connections between branch organs determine major pathways for branch assimilate transport. We propose directions for employing a modeling approach to further elucidate the role of branch architecture on assimilate partitioning.

Reduction of energy use for assimilation lighting is one of the most urgent goals of current greenhouse horticulture in the Netherlands. In recent years numerous lighting systems have been tested in greenhouses, yet their efficiency has been very difficult to measure in practice. This simulation study evaluated a number of lighting strategies using a 3D light model for natural and artificial light in combination with a 3D model of tomato. The modeling platform GroIMP was used for the simulation study. The crop was represented by 3D virtual plants of tomato with fixed architecture. Detailed data on greenhouse architecture and lamp emission patterns of different light sources were incorporated in the model. A number of illumination strategies were modeled with the calibrated model. Results were compared to the standard configuration. Moreover, adaptation of leaf angles was incorporated for testing their effect on light use efficiency (LUE). A Farquhar photosynthesis model was used to translate the absorbed light for each leaf into a produced amount of carbohydrates. The carbohydrates produced by the crop per unit emitted light from sun or high pressure sodium lamps was the highest for horizontal leaf angles or slightly downward pointing leaves, and was less for more upward leaf orientations. The simulated leaf angles did not affect light absorption from inter-lighting LED modules, but the scenario with LEDs shining slightly upward (20(°)) increased light absorption and LUE relative to default horizontal beaming LEDs. Furthermore, the model showed that leaf orientation more perpendicular to the string of LEDs increased LED light interception. The combination of a ray tracer and a 3D crop model could compute optimal lighting of leaves by quantification of light fluxes and illustration by rendered lighting patterns. Results indicate that illumination efficiency increases when the lamp light is directed at most to leaves that have a high photosynthetic potential.

Background and Aims: The production system of cut-rose (Rosa × hybrida) involves a complex combination of plant material, management practice and environment. Plant structure is determined by bud break and shoot development while having an effect on local light climate. The aim of the present study is to cover selected aspects of the cut-rose system using functional-structural plant modelling (FSPM), in order to better understand processes contributing to produce quality and quantity., Methods: The model describes the production system in three dimensions, including a virtual greenhouse environment with the crop, light sources (diffuse and direct sun light and lamps) and photosynthetically active radiation (PAR) sensors. The crop model is designed as a multiscaled FSPM with plant organs (axillary buds, leaves, internodes, flowers) as basic units, and local light interception and photosynthesis within each leaf. A Monte-Carlo light model was used to compute the local light climate for leaf photosynthesis, the latter described using a biochemical rate model., Key Results: The model was able to reproduce PAR measurements taken at different canopy positions, different times of the day and different light regimes. Simulated incident and absorbed PAR as well as net assimilation rate in upright and bent shoots showed characteristic spatial and diurnal dynamics for different common cultivation scenarios., Conclusions: The model of cut-rose presented allowed the creation of a range of initial structures thanks to interactive rules for pruning, cutting and bending. These static structures can be regarded as departure points for the dynamic simulation of production of flower canes. Furthermore, the model was able to predict local (per leaf) light absorption and photosynthesis. It can be used to investigate the physiology of ornamental plants, and provide support for the decisions of growers and consultants.

Background and Aims: Although quantitative trait loci (QTL) analysis of yield-related traits for rice has developed rapidly, crop models using genotype information have been proposed only relatively recently. As a first step towards a generic genotype-phenotype model, we present here a three-dimensional functional-structural plant model (FSPM) of rice, in which some model parameters are controlled by functions describing the effect of main-effect and epistatic QTLs., Methods: The model simulates the growth and development of rice based on selected ecophysiological processes, such as photosynthesis (source process) and organ formation, growth and extension (sink processes). It was devised using GroIMP, an interactive modelling platform based on the Relational Growth Grammar formalism (RGG). RGG rules describe the course of organ initiation and extension resulting in final morphology. The link between the phenotype (as represented by the simulated rice plant) and the QTL genotype was implemented via a data interface between the rice FSPM and the QTLNetwork software, which computes predictions of QTLs from map data and measured trait data., Key Results: Using plant height and grain yield, it is shown how QTL information for a given trait can be used in an FSPM, computing and visualizing the phenotypes of different lines of a mapping population. Furthermore, we demonstrate how modification of a particular trait feeds back on the entire plant phenotype via the physiological processes considered., Conclusions: We linked a rice FSPM to a quantitative genetic model, thereby employing QTL information to refine model parameters and visualizing the dynamics of development of the entire phenotype as a result of ecophysiological processes, including the trait(s) for which genetic information is available. Possibilities for further extension of the model, for example for the purposes of ideotype breeding, are discussed.

In the present paper, we based a search for candidates underlying different levels of salinity tolerance during germination in the Oregon Wolfe Barley mapping population (DOM x REC) by proteomic profiling of the mature grain of lines showing differing levels of salinity tolerance. By contrasting the parents DOM and REC, displaying divergent stress responses, and two tolerant and two sensitive segregants, six protein spots were identified that showed a differential abundance between the tolerant and the sensitive lines. The tolerant lines expressed a higher level of 6-phosphogluconate dehydrogenase and glucose/ribitol dehydrogenase (Glc/RibDH). Both proteins were heterologously over-expressed in an osmo-sensitive yeast strain and over-expression of Glc/RibDH resulted in an enhanced ability of yeast transformants to grow on salt containing media. A quantitative trait locus (QTL) analysis of the population germinating at different salt concentrations led to the identification of two chromosome regions on 5H and one on 7H associated with salt stress response. A dense barley transcript map was employed to map the genomic region of all identified proteins. Two of these, heat-shock protein 70 and Glc/RibDH, co-localized with the identified QTL on chromosome 5H. The putative functional role of the candidates is discussed.

The programming language XL ('eXtended L-system language') is an extension of Java, which supports the specification and execution of relational growth grammars, a variant of parallel graph grammars. XL is a powerful generalisation of the well-known L-system approach to functional-structural plant modelling. Some features of XL are discussed that are particularly useful for combining structure and function and for querying plant architectural data, and an exemplary functional-structural plant model of young beech trees is presented that is implemented in XL and includes PAR distribution, assimilate allocation and morphological plasticity. Together with a simpler model of spruce trees, this beech model is included in a virtual landscape with a mixed-species forest stand where competition for light occurs. The open-source platform GroIMP was used for the complete model development process and for visualising the results.

Background and Aims: Functional-structural plant models (FSPM) constitute a paradigm in plant modelling that combines 3D structural and graphical modelling with the simulation of plant processes. While structural aspects of plant development could so far be represented using rule-based formalisms such as Lindenmayer systems, process models were traditionally written using a procedural code. The faithful representation of structures interacting with functions across scales, however, requires a new modelling formalism. Therefore relational growth grammars (RGG) were developed on the basis of Lindenmayer systems., Methods: In order to implement and test RGG, a new modelling language, the eXtended L-system language (XL) was created. Models using XL are interpreted by the interactive, Java-based modelling platform GroIMP. Three models, a semi-quantitative gibberellic acid (GA) signal transduction model, and a phytochrome-based shade detection and object avoidance model, both coupled to an existing morphogenetic structural model of barley (Hordeum vulgare L.), serve as examples to demonstrate the versatility and suitability of RGG and XL to represent the interaction of diverse biological processes across hierarchical scales., Key Results: The dynamics of the concentrations in the signal transduction network could be modelled qualitatively and the phenotypes of GA-response mutants faithfully reproduced. The light model used here was simple to use yet effective enough to carry out local measurement of red:far-red ratios. Suppression of tillering at low red:far-red ratios could be simulated., Conclusions: The RGG formalism is suitable for implementation of multi-scaled FSPM of plants interacting with their environment via hormonal control. However, their ensuing complexity requires careful design. On the positive side, such an FSPM displays knowledge gaps better thereby guiding future experimental design.

The effect of elevated CO2 concentrations on the levels of secondary metabolites was investigated in tobacco plants grown under two nitrogen supply (5 and 8 mM NH4NO3) and CO2 conditions (350 and 1000 p.p.m.) each. High CO2 resulted in a dramatic increase of phenylpropanoids in the leaves, including the major carbon-rich compound chlorogenic acid (CGA) and the coumarins scopolin and scopoletin at both nitrogen fertilizations. This was accompanied by increased PAL activity in leaves and roots, which was even higher at the lower nitrogen supply. Hardly any change was observed for the structural phenolic polymer lignin and the sesquiterpenoid capsidiol. In contrast, elevated CO2 led to clearly decreased levels of the main nitrogen-rich constituent nicotine at the lower N-supply (5 mM NH4NO3) but not when plants were grown at the higher N-supply (8 mM NH4NO3). Inoculation experiments with potato virus Y (PVY) were used to evaluate possible ecological consequences of elevated CO2. The titre of viral coat-protein was markedly reduced in leaves under these conditions at both nitrogen levels. Since PR-gene expression and free salicylic acid (SA) levels remained unchanged at elevated CO2, we suggest that the accumulation of phenylpropanoids, for example, the major compound CGA and the coumarins scopolin and scopoletin may result in an earlier confinement of the virus at high CO2. Based on our results two final conclusions emerge. First, elevated CO2 leads to a shift in secondary metabolite composition that is dependent on the availability of nitrogen. Second, changes in the pool of secondary metabolites have important consequences for plant-pathogen interactions as shown for PVY as a test organism.

A multiscaled ecophysiological model of barley (Hordeum vulgare) development is presented here. The model is based on the new formalism of relational growth grammars (RGG), an extension of L-systems, and implemented using the new modelling language XL. It is executable in the interactive modelling platform GroIMP. The model consists of a set of morphogenetic rules, combined with a metabolic regulatory network, which simulates the biosynthesis of gibberellic acid (GA1). GA1 and two of its metabolic precursors are transported along the developing simulated structure. Local concentrations of GA1 determine internode elongation. Furthermore, virtual barley individuals are chosen interactively from a population, based on genotype, and (sexual or asexual) reproduction is simulated. Genotype and phenotype of the population are visualized. Seven Mendelian genes have been implemented in the model so far; some of these directly influence the GA-regulation network. The model exemplifies and validates the new formalism and modelling language. RGG have the capability to represent genetic, metabolic and morphological aspects of plant development and reproduction, all within the same framework.

We present the high-level language of relational growth grammars (RGGs) as a formalism designed for the specification of ALife models. RGGs can be seen as an extension of the well-known parametric Lindenmayer systems and contain rule-based, procedural, and object-oriented features. They are defined as rewriting systems operating on graphs with the edges coming from a set of user-defined relations, whereas the nodes can be associated with objects. We demonstrate their ability to represent genes, regulatory networks of metabolites, and morphologically structured organisms, as well as developmental aspects of these entities, in a common formal framework. Mutation, crossing over, selection, and the dynamics of a network of gene regulation can all be represented with simple graph rewriting rules. This is demonstrated in some detail on the classical example of Dawkins' biomorphs and the ABC model of flower morphogenesis: other applications are briefly sketched. An interactive program was implemented, enabling the execution of the formalism and the visualization of the results.

Ninety-nine different lines of the Doubled-Haploid F2 winter barley population W766 ('Angora' x 'W704/137') were genetically fingerprinted using AFLP, microsatellite, morphological and resistance markers. A preliminary map consisting of seven linkage groups is presented. The map contains a highly distorted region on the long arm of chromosome 3H reflecting preselection of the genotypes for resistance against barley mild mosaic virus. QTL analysis of morphological and phenological traits yielded 99 significant QTL, with most traits (66.3%) being represented by a single QTL. The distribution of significant QTL over the chromosomes was very uneven, the bulk being placed on the long arm of chromosome 3H and no QTL being found on chromosome 4H. This possibly points to the presence of a strong pleiotropic gene on 3H or of a group of related genes that mask weaker effects that were found on other linkage groups as subsignificant QTL. Using two examples of detected QTL (for tillering and grain number), it is shown how the findings of the QTL analysis could be incorporated into an existing morphological simulation model of barley using simple statistical methods.