A 3-D functional-structural grapevine model that couples the dynamics of water transport with leaf gas exchange

Crop/Plant Modeling Supports Plant Breeding: II. Guidance of Functional Plant Phenotyping for Trait Discovery

Observable morphological traits are widely employed in plant phenotyping for breeding use, which are often the external phenotypes driven by a chain of functional actions in plants. Identifying and phenotyping inherently functional traits for crop improvement toward high yields or adaptation to harsh environments remains a major challenge. Prediction of whole-plant performance in functional-structural plant models (FSPMs) is driven by plant growth algorithms based on organ scale wrapped up with micro-environments. In particular, the models are flexible for scaling down or up through specific functions at the organ nexus, allowing the prediction of crop system behaviors from the genome to the field. As such, by virtue of FSPMs, model parameters that determine organogenesis, development, biomass production, allocation, and morphogenesis from a molecular to the whole plant level can be profiled systematically and made readily available for phenotyping. FSPMs can provide rich functional traits representing biological regulatory mechanisms at various scales in a dynamic system, e.g., Rubisco carboxylation rate, mesophyll conductance, specific leaf nitrogen, radiation use efficiency, and source-sink ratio apart from morphological traits. High-throughput phenotyping such traits is also discussed, which provides an unprecedented opportunity to evolve FSPMs. This will accelerate the co-evolution of FSPMs and plant phenomics, and thus improving breeding efficiency. To expand the great promise of FSPMs in crop science, FSPMs still need more effort in multiscale, mechanistic, reproductive organ, and root system modeling. In summary, this study demonstrates that FSPMs are invaluable tools in guiding functional trait phenotyping at various scales and can thus provide abundant functional targets for phenotyping toward crop improvement.

GrapevineXL reliably predicts multi-annual dynamics of vine water status, berry growth, and sugar accumulation in vineyards

Climate and water availability greatly affect each season's grape yield and quality. Using models to accurately predict environment impacts on fruit productivity and quality is a huge challenge. We calibrated and validated the functional-structural model, GrapevineXL, with a data set including grapevine seasonal midday stem water potential (Ψ_xylem), berry dry weight (DW), fresh weight (FW), and sugar concentration per volume ([Sugar]) for a wine grape cultivar (Vitis vinifera cv. Cabernet Franc) in field conditions over 13 years in Bordeaux, France. Our results showed that the model could make a fair prediction of seasonal Ψ_xylem and good-to-excellent predictions of berry DW, FW, [Sugar] and leaf gas exchange responses to predawn and midday leaf water potentials under diverse environmental conditions with 14 key parameters. By running virtual experiments to mimic climate change, an advanced veraison (i.e. the onset of ripening) of 14 and 28 days led to significant decreases of berry FW by 2.70% and 3.22%, clear increases of berry [Sugar] by 2.90% and 4.29%, and shortened ripening duration in 8 out of 13 simulated years, respectively. Moreover, the impact of the advanced veraison varied with seasonal patterns of climate and soil water availability. Overall, the results showed that the GrapevineXL model can predict plant water use and berry growth in field conditions and could serve as a valuable tool for designing sustainable vineyard management strategies to cope with climate change.

Integrated model simulates bigger, sweeter tomatoes under changing climate under reduced nitrogen and water input

When simulating the response of fruit growth and quality to environmental factors and cultivation practices, the interactions between the mother plant and fruit need to be considered as a whole system. Here, we developed the integrative Tomato plant and fruit Growth and Fruit Sugar metabolism (TGFS) model by coupling equations describing the biophysical processes of leaf gas exchange, water transport, carbon allocation, organ growth and fruit sugar metabolism. The model also accounts for effects of soil nitrogen and atmospheric CO₂ concentration on gaseous exchange of water and carbon by the leaf. With different nitrogen and water input values, TGFS performed well at simulating the dry mass of the tomato leaf, stem, root, and fruit, and the concentrations of soluble sugar and starch in fruit. TGFS simulations showed that increasing air temperature and CO₂ concentration has positive effects on fruit growth, but not on sugar concentrations. Further model-based analyses of cultivation scenarios suggest that, in the context of climate change, decreasing N by 15%-25% and decreasing irrigation by 10%-20% relative to current levels would increase tomato fresh weight by 27.8%-36.4% while increasing soluble sugar concentration by up to 10%. TGFS provides a promising tool to optimise N and water inputs for sustainable high-quality tomatoes.

Towards grapevine root architectural models to adapt viticulture to drought

To sustainably adapt viticultural production to drought, the planting of rootstock genotypes adapted to a changing climate is a promising means. Rootstocks contribute to the regulation of scion vigor and water consumption, modulate scion phenological development and determine resource availability by root system architecture development. There is, however, a lack of knowledge on spatio-temporal root system development of rootstock genotypes and its interactions with environment and management that prevents efficient knowledge transfer into practice. Hence, winegrowers take only limited advantage of the large variability of existing rootstock genotypes. Models of vineyard water balance combined with root architectural models, using both static and dynamic representations of the root system, seem promising tools to match rootstock genotypes to frequently occurring future drought stress scenarios and address scientific knowledge gaps. In this perspective, we discuss how current developments in vineyard water balance modeling may provide the background for a better understanding of the interplay of rootstock genotypes, environment and management. We argue that root architecture traits are key drivers of this interplay, but our knowledge on rootstock architectures in the field remains limited both qualitatively and quantitatively. We propose phenotyping methods to help close current knowledge gaps and discuss approaches to integrate phenotyping data into different models to advance our understanding of rootstock x environment x management interactions and predict rootstock genotype performance in a changing climate. This could also provide a valuable basis for optimizing breeding efforts to develop new grapevine rootstock cultivars with optimal trait configurations for future growing conditions.

Space farming: Horticulture systems on spacecraft and outlook to planetary space exploration

Successful human space exploration requires more products than can be taken as payload. There is a need, therefore, for in-space circular manufacturing. Requirements for this include limited resource inflow, from either Earth or other planets and the generation of minimal waste. The provision of nutritious food is a clear need for human survival on the Moon or Mars and is one of the most complex to solve. Demand in large quantities, constant and reliable provision of food requires the development of specialist agricultural technologies. Here, we first review the history of space farming over the past five decades. This survey assesses the technologies which have been tested under the harsh conditions of space, identifying which modern horticultural components are applicable for in-space plant growth. We then outline which plants have been grown and under what conditions, and speculate upon the types of plants that could be selected to best nourish astronauts. Current systems are focussed on experimentation and exploration, but do not yet provide turn-key solutions for efficient food production within a long-term space exploration scenario. With that take, this review aims to provide a perspective on how an engineered closed circular environmental life-support system (ECCLES) might be constructed. To exemplify the latter, nutrient auto accumulation by biofortification is proposed through the integration of space farming and space mining, which is uncharted on Earth.

Model-assisted ideotyping reveals trait syndromes to adapt viticulture to a drier climate

Climate change is challenging the resilience of grapevine (Vitis), one of the most important crops worldwide. Adapting viticulture to a hotter and drier future will require a multifaceted approach including the breeding of more drought-tolerant genotypes. In this study, we focused on plant hydraulics as a multi-trait system that allows the plant to maintain hydraulic integrity and gas exchange rates longer under drought. We quantified a broad range of drought-related traits within and across Vitis species, created in silico libraries of trait combinations, and then identified drought tolerant trait syndromes. By modeling the maintenance of hydraulic integrity of current cultivars and the drought tolerant trait syndromes, we identified elite ideotypes that increased the amount of time they could experience drought without leaf hydraulic failure. Generally, elites exhibited a trait syndrome with lower stomatal conductance, earlier stomatal closure, and a larger hydraulic safety margin. We demonstrated that, when compared with current cultivars, elite ideotypes have the potential to decrease the risk of hydraulic failure across wine regions under future climate scenarios. This study reveals the syndrome of traits that can be leveraged to protect grapevine from experiencing hydraulic failure under drought and increase drought tolerance.

Fruit tree crop models: an update

Functional structural plant models of tree crops are useful tools that were introduced more than two decades ago. They can represent the growth and development of a plant through the in silico simulation of the 3D architecture in connection with physiological processes. In tree crops, physiological processes such as photosynthesis, carbon allocation and growth are usually integrated into these models, although other functions such as water and nutrient uptake are often disregarded. The implementation of the 3D architecture involves different techniques such as L-system frameworks, pipe model concepts and Markovian models to simulate branching processes, bud fates and elongation of stems based on the production of metamers. The simulation of root architecture is still a challenge for researchers due to a limited amount of information and experimental issues in dealing with roots, because root development is not based on the production of metamers. This review aims to focus on functional-structural models of fruit tree crops, highlighting their physiological components. The potential and limits of these tools are reviewed to point out the topics that still need more attention.

Analyzing the Impact of Greenhouse Planting Strategy and Plant Architecture on Tomato Plant Physiology and Estimated Dry Matter

Determine the level of significance of planting strategy and plant architecture and how they affect plant physiology and dry matter accumulation within greenhouses is essential to actual greenhouse plant management and breeding. We thus analyzed four planting strategies (plant spacing, furrow distance, row orientation, planting pattern) and eight different plant architectural traits (internode length, leaf azimuth angle, leaf elevation angle, leaf length, leaflet curve, leaflet elevation, leaflet number/area ratio, leaflet length/width ratio) with the same plant leaf area using a formerly developed functional-structural model for a Chinese Liaoshen-solar greenhouse and tomato plant, which used to simulate the plant physiology of light interception, temperature, stomatal conductance, photosynthesis, and dry matter. Our study led to the conclusion that the planting strategies have a more significant impact overall on plant radiation, temperature, photosynthesis, and dry matter compared to plant architecture changes. According to our findings, increasing the plant spacing will have the most significant impact to increase light interception. E-W orientation has better total light interception but yet weaker light uniformity. Changes in planting patterns have limited influence on the overall canopy physiology. Increasing the plant leaflet area by leaflet N/A ratio from what we could observe for a rose the total dry matter by 6.6%, which is significantly better than all the other plant architecture traits. An ideal tomato plant architecture which combined all the above optimal architectural traits was also designed to provide guidance on phenotypic traits selection of breeding process. The combined analysis approach described herein established the causal relationship between investigated traits, which could directly apply to provide management and breeding insights on other plant species with different solar greenhouse structures.

Innovation in grapevine water status monitoring and drought adaptation: leaf angle and temperature regulation

Increase of frequency, duration, and intensity of drought and heatwave and related water and heat crops stress are among the principal effects of climate change. This paper reports: (i) the effect of calcite particle film (CaPF) as a mitigation strategy against heat stress in well-watered (WW) or in drought-stress (D) conditions; and (ii) response of leaf angle variation to stomatal conductance changes induced by drought stress of Aleatico grapevine cultivar. Results have showed that CaPF, under WW conditions, reduced leaf temperature, and increased gas exchange, but, under very severe water stress, CaPF treatment was ineffective. Leaf angle ranged from 70° (WW vines) to 100° (drought stressed vines) and showed a good fit (R2 =0.81) with stomatal conductance within the range of 0.25 – 0.05 mol m-2 s–1 proving it might be a reliable proxy of vine water status.

Integrating terrestrial laser scanning with functional-structural plant models to investigate ecological and evolutionary processes of forest communities

BACKGROUND

Woody plants (trees and shrubs) play an important role in terrestrial ecosystems, but their size and longevity make them difficult subjects for traditional experiments. In the last 20 years functional-structural plant models (FSPMs) have evolved: they consider the interplay between plant modular structure, the immediate environment and internal functioning. However, computational constraints and data deficiency have long been limiting factors in a broader application of FSPMs, particularly at the scale of forest communities. Recently, terrestrial laser scanning (TLS), has emerged as an invaluable tool for capturing the 3-D structure of forest communities, thus opening up exciting opportunities to explore and predict forest dynamics with FSPMs.

SCOPE

The potential synergies between TLS-derived data and FSPMs have yet to be fully explored. Here, we summarize recent developments in FSPM and TLS research, with a specific focus on woody plants. We then evaluate the emerging opportunities for applying FSPMs in an ecological and evolutionary context, in light of TLS-derived data, with particular consideration of the challenges posed by scaling up from individual trees to whole forests. Finally, we propose guidelines for incorporating TLS data into the FSPM workflow to encourage overlap of practice amongst researchers.

CONCLUSIONS

We conclude that TLS is a feasible tool to help shift FSPMs from an individual-level modelling technique to a community-level one. The ability to scan multiple trees, of multiple species, in a short amount of time, is paramount to gathering the detailed structural information required for parameterizing FSPMs for forest communities. Conventional techniques, such as repeated manual forest surveys, have their limitations in explaining the driving mechanisms behind observed patterns in 3-D forest structure and dynamics. Therefore, other techniques are valuable to explore how forests might respond to environmental change. A robust synthesis between TLS and FSPMs provides the opportunity to virtually explore the spatial and temporal dynamics of forest communities.

Missing Links in Predicting Berry Sunburn in Future Vineyards

Sunburn in grapevine berries is known as a recurring disorder causing severe yield losses and a decline in berry quality. The transition from healthy to sunburnt along a temporal trajectory is not fully understood. It is driven by light-boosted local heat impact and modulated by, e.g., past environments of the berry and its developmental state. Events of berry sunburn are often associated with heatwaves, indicating a link to climate change. In addition, the sensitivity of grapevine architecture to changing environmental condition indicates an urgent need to investigate and adapt mitigation strategies of berry sunburn in future vineyards. In this perspective, we want to identify missing links in predicting berry sunburn in vineyards and propose a modeling framework that may help us to investigate berry sunburn in future vineyards. For this, we propose to address open issues in both developing a model of berry sunburn and considering dynamic canopy growth, and canopy interaction with the environment and plant management such as shoot positioning or leaf removal. Because local environmental conditions drive sunburn, we aim at showing that identifying sunburn-reducing strategies in a vineyard under future environmental conditions can be supported by a modeling approach that integrates effects of management practices over time and takes grapevine architecture explicitly into account. We argue that functional-structural plant models may address such complex tasks. Once open issues are solved, they might be a promising tool to advance our knowledge on reducing risks of berry sunburn in silico.

Optimization of Vineyard Water Management: Challenges, Strategies, and Perspectives

Water availability is endangering the production, quality, and economic viability of growing wine grapes worldwide. Climate change projections reveal warming and drying trends for the upcoming decades, constraining the sustainability of viticulture. In this context, a great research effort over the last years has been devoted to understanding the effects of water stress on grapevine performance. Moreover, irrigation scheduling and other management practices have been tested in order to alleviate the deleterious effects of water stress on wine production. The current manuscript provides a comprehensive overview of the advances in the research on optimizing water management in vineyards, including the use of novel technologies (modeling, remote sensing). In addition, methods for assessing vine water status are summarized. Moreover, the manuscript will focus on the interactions between grapevine water status and biotic stressors. Finally, future perspectives for research are provided. These include the performance of multifactorial studies accounting for the interrelations between water availability and other stressors, the development of a cost-effective and easy-to-use tool for assessing vine water status, and the study of less-known cultivars under different soil and climate conditions.

Nighttime transpiration represents a negligible part of water loss and does not increase the risk of water stress in grapevine

Nighttime transpiration has been previously reported as a significant source of water loss in many species; however, there is a need to determine if this trait plays a key role in the response to drought. This study aimed to determine the magnitude, regulation and relative contribution to whole plant water-use, of nighttime stomatal conductance (g_night ) and transpiration (E_night ) in grapevine (Vitis vinifera L.). Our results showed that nighttime water loss was relatively low compared to daytime transpiration, and that decreases in soil and plant water potentials were mainly explained by daytime stomatal conductance (g_day ) and transpiration (E_day ). Contrary to E_day , E_night did not respond to VPD and possible effects of an innate circadian regulation were observed. Plants with higher g_night also exhibited higher daytime transpiration and carbon assimilation at midday, and total leaf area, suggesting that increased g_night may be linked with daytime behaviors that promote productivity. Modeling simulations indicated that g_night was not a significant factor in reaching critical hydraulic thresholds under scenarios of either extreme drought, or time to 20% of soil relative water content. Overall, this study suggests that g_night is not significant in exacerbating the risk of water stress and hydraulic failure in grapevine.

Modeling vegetative vigour in grapevine: unraveling underlying mechanisms

Mechanistic modeling constitutes a powerful tool to unravel complex biological phenomena. This study describes the construction of a mechanistic, dynamic model for grapevine plant growth and canopy biomass (vigor). To parametrize and validate the model, the progeny from a cross of Ramsey (Vitis champinii) × Riparia Gloire (V. riparia) was evaluated. Plants with different vigor were grown in a greenhouse during the summer of 2014 and 2015. One set of plants was grafted with Cabernet Sauvignon. Shoot growth rate (b), leaf area (LA), dry biomass, whole plant and root specific hydraulic conductance (k_H and L_pr), stomatal conductance (g_s), and water potential (Ψ) were measured. Partitioning indices and specific leaf area (SLA) were calculated. The model includes an empirical fit of a purported seasonal pattern of bioactive GAs based on published seasonal evolutionary levels and reference values. The model provided a good fit of the experimental data, with R = 0.85. Simulation of single trait variations defined the individual effect of each variable on vigor determination. The model predicts, with acceptable accuracy, the vigor of a young plant through the measurement of L_pr and SLA. The model also permits further understanding of the functional traits that govern vigor, and, ultimately, could be considered useful for growers, breeders and those studying climate change.

Parameter estimation for functional-structural plant models when data are scarce: using multiple patterns for rejecting unsuitable parameter sets

BACKGROUND AND AIMS

Functional-structural plant (FSP) models provide insights into the complex interactions between plant architecture and underlying developmental mechanisms. However, parameter estimation of FSP models remains challenging. We therefore used pattern-oriented modelling (POM) to test whether parameterization of FSP models can be made more efficient, systematic and powerful. With POM, a set of weak patterns is used to determine uncertain parameter values, instead of measuring them in experiments or observations, which often is infeasible.

METHODS

We used an existing FSP model of avocado (Persea americana 'Hass') and tested whether POM parameterization would converge to an existing manual parameterization. The model was run for 10 000 parameter sets and model outputs were compared with verification patterns. Each verification pattern served as a filter for rejecting unrealistic parameter sets. The model was then validated by running it with the surviving parameter sets that passed all filters and then comparing their pooled model outputs with additional validation patterns that were not used for parameterization.

KEY RESULTS

POM calibration led to 22 surviving parameter sets. Within these sets, most individual parameters varied over a large range. One of the resulting sets was similar to the manually parameterized set. Using the entire suite of surviving parameter sets, the model successfully predicted all validation patterns. However, two of the surviving parameter sets could not make the model predict all validation patterns.

CONCLUSIONS

Our findings suggest strong interactions among model parameters and their corresponding processes, respectively. Using all surviving parameter sets takes these interactions into account fully, thereby improving model performance regarding validation and model output uncertainty. We conclude that POM calibration allows FSP models to be developed in a timely manner without having to rely on field or laboratory experiments, or on cumbersome manual parameterization. POM also increases the predictive power of FSP models.

A functional-structural plant model that simulates whole- canopy gas exchange of grapevine plants (Vitis vinifera L.) under different training systems

BACKGROUND AND AIMS

Scaling from single-leaf to whole-canopy photosynthesis faces several complexities related to variations in light interception and leaf properties. To evaluate the impact of canopy strucuture on gas exchange, we developed a functional-structural plant model to upscale leaf processes to the whole canopy based on leaf N content. The model integrates different models that calculate intercepted radiation, leaf traits and gas exchange for each leaf in the canopy. Our main objectives were (1) to introduce the gas exchange model developed at the plant level by integrating the leaf-level responses related to canopy structure, (2) to test the model against an independent canopy gas exchange dataset recorded on different plant architectures, and (3) to quantify the impact of intra-canopy N distribution on crop photosynthesis.

METHODS

The model combined a 3D reconstruction of grapevine (Vitis vinifera) canopy architecture, a light interception model, and a coupled photosynthesis and stomatal conductance model that considers light-driven variations in N distribution. A portable chamber device was constructed to measure whole-plant gas exchange to validate the model outputs with data collected on different training systems. Finally, a sensitivity analysis was performed to evaluate the impact on C assimilation of different N content distributions within the canopy.

KEY RESULTS

By considering a non-uniform leaf N distribution within the canopy, our model accurately reproduced the daily pattern of gas exchange of different canopy architectures. The gain in photosynthesis permitted by the non-uniform compared with a theoretical uniform N distribution was about 18 %, thereby contributing to the maximization of C assimilation. By contrast, considering a maximal N content for all leaves in the canopy overestimated net CO2 exchange by 28 % when compared with the non-uniform distribution.

CONCLUSIONS

The model reproduced the gas exchange of plants under different training systems with a low error (10 %). It appears to be a reliable tool to evaluate the impact of a grapevine training system on water use efficiency at the plant level.

The physiology of drought stress in grapevine: towards an integrative definition of drought tolerance

Water availability is arguably the most important environmental factor limiting crop growth and productivity. Erratic precipitation patterns and increased temperatures resulting from climate change will likely make drought events more frequent in many regions, increasing the demand on freshwater resources and creating major challenges for agriculture. Addressing these challenges through increased irrigation is not always a sustainable solution so there is a growing need to identify and/or breed drought-tolerant crop varieties in order to maintain sustainability in the context of climate change. Grapevine (Vitis vinifera), a major fruit crop of economic importance, has emerged as a model perennial fruit crop for the study of drought tolerance. This review synthesizes the most recent results on grapevine drought responses, the impact of water deficit on fruit yield and composition, and the identification of drought-tolerant varieties. Given the existing gaps in our knowledge of the mechanisms underlying grapevine drought responses, we aim to answer the following question: how can we move towards a more integrative definition of grapevine drought tolerance?

Image-Based Assessment of Drought Response in Grapevines

Many plants can modify their leaf profile rapidly in response to environmental stress. Image-based data are increasingly used to retrieve reliable information on plant water status in a non-contact manner that has the potential to be scaled to high-throughput and repeated through time. This paper examined the variation of leaf angle as measured by both 3D images and goniometer in progressively drought stressed grapevine. Grapevines, grown in pots, were subjected to a 21-day period of drought stress receiving 100% (CTRL), 60% (IRR 60%) and 30% (IRR 30%) of maximum soil available water capacity. Leaf angle was (i) measured manually (goniometer) and (ii) computed by a 3D reconstruction method (multi-view stereo and structure from motion). Stomatal conductance, leaf water potential, fluorescence (F v /F m ), leaf area and 2D RGB data were simultaneously collected during drought imposition. Throughout the experiment, values of leaf water potential ranged from -0.4 (CTRL) to -1.1 MPa (IRR 30%) and it linearly influenced the leaf angle when measured manually (R 2 = 0.86) and with 3D image (R 2 = 0.73). Drought was negatively related to stomatal conductance and leaf area growth particularly in IRR 30% while photosynthetic parameters (i.e., F v /F m ) were not impaired by water restriction. A model for leaf area estimation based on the number of pixels of 2D RGB images developed at a different phenotyping robotized platform in a closely related experiment was successfully employed (R 2 = 0.78). At the end of the experiment, top view 2D RGB images showed a ∼50% reduction of greener fraction (GGF) in CTRL and IRR 60% vines compared to initial values, while GGF in IRR 30% increased by approximately 20%.

Modelling grape growth in relation to whole-plant carbon and water fluxes

The growth of fleshy fruits is still poorly understood as a result of the complex integration of water and solute fluxes, cell structural properties, and the regulation of whole plant source-sink relationships. To unravel the contribution of these processes to berry growth, a biophysical grape (Vitis vinifera L.) berry growth module was developed and integrated with a whole-plant functional-structural model, and was calibrated on two varieties, Cabernet Sauvignon and Sangiovese. The model captured well the variations in growth and sugar accumulation caused by environmental conditions, changes in leaf-to-fruit ratio, plant water status, and varietal differences, with obvious future application in predicting yield and maturity under a variety of production contexts and regional climates. Our analyses illustrated that grapevines strive to maintain proper ripening by partially compensating for a reduced source-sink ratio, and that under drought an enhanced berry sucrose uptake capacity can reverse berry shrinkage. Sensitivity analysis highlighted the importance of phloem hydraulic conductance, sugar uptake, and surface transpiration on growth, while suggesting that cell wall extensibility and the turgor threshold for cell expansion had minor effects. This study demonstrates that this integrated model is a useful tool in understanding the integration and relative importance of different processes in driving fleshy fruit growth.

Estimating Sink Parameters of Stochastic Functional-Structural Plant Models Using Organic Series-Continuous and Rhythmic Development

Functional-structural plant models (FSPMs) generally simulate plant development and growth at the level of individual organs (leaves, flowers, internodes, etc.). Parameters that are not directly measurable, such as the sink strength of organs, can be estimated inversely by fitting the weights of organs along an axis (organic series) with the corresponding model output. To accommodate intracanopy variability among individual plants, stochastic FSPMs have been built by introducing the randomness in plant development; this presents a challenge in comparing model output and experimental data in parameter estimation since the plant axis contains individual organs with different amounts and weights. To achieve model calibration, the interaction between plant development and growth is disentangled by first computing the occurrence probabilities of each potential site of phytomer, as defined in the developmental model (potential structure). On this basis, the mean organic series is computed analytically to fit the organ-level target data. This process is applied for plants with continuous and rhythmic development simulated with different development parameter sets. The results are verified by Monte-Carlo simulation. Calibration tests are performed both in silico and on real plants. The analytical organic series are obtained for both continuous and rhythmic cases, and they match well with the results from Monte-Carlo simulation, and vice versa. This fitting process works well for both the simulated and real data sets; thus, the proposed method can solve the source-sink functions of stochastic plant architectures through a simplified approach to plant sampling. This work presents a generic method for estimating the sink parameters of a stochastic FSPM using statistical organ-level data, and it provides a method for sampling stems. The current work breaks a bottleneck in the application of FSPMs to real plants, creating the opportunity for broad applications.

Computational botany: advancing plant science through functional–structural plant modelling

The need to integrate the ever-expanding body of knowledge in the plant sciences has led to the development of sophisticated modelling approaches. This special issue focuses on functional–structural plant (FSP) models, which are the result of cross-fertilization between the domains of plant science, computer science and mathematics. FSP models simulate growth and morphology of individual plants that interact with their environment, from which complex plant community properties emerge. FSP models can be used for a broad range of research questions across disciplines related to plant science. This special issue presents the latest developments in FSP modelling, including the novel incorporation of plant ecophysiological concepts and the application of FSP models to address new scientific questions. Additionally, it illustrates the breadth of model evaluation approaches that are performed. FSP modelling is a very active domain of plant research which brings together a wide range of scientific disciplines. It offers the opportunity to address questions in complex plant systems that cannot be addressed by empirical approaches alone, including questions on fundamental concepts related to plant development such as regulation of morphogenesis, as well as on applied concepts such as the relationship between crop performance and plant competition for resources.