Using functional–structural plant models to study, understand and integrate plant development and ecophysiology

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.

Towards a Stochastic Model to Simulate Grapevine Architecture: A Case Study on Digitized Riesling Vines Considering Effects of Elevated CO2

Modeling plant growth, in particular with functional-structural plant models, can provide tools to study impacts of changing environments in silico. Simulation studies can be used as pilot studies for reducing the on-field experimental effort when predictive capabilities are given. Robust model calibration leads to less fragile predictions, while introducing uncertainties in predictions allows accounting for natural variability, resulting in stochastic plant growth models. In this study, stochastic model components that can be implemented into the functional-structural plant model Virtual Riesling are developed relying on Bayesian model calibration with the goal to enhance the model towards a fully stochastic model. In this first step, model development targeting phenology, in particular budburst variability, phytomer development rate and internode growth are presented in detail. Multi-objective optimization is applied to estimate a single set of cardinal temperatures, which is used in phenology and growth modeling based on a development days approach. Measurements from two seasons of grapevines grown in a vineyard with free-air carbon dioxide enrichment (FACE) are used; thus, model building and selection are coupled with an investigation as to whether including effects of elevated CO2 conditions to be expected in 2050 would improve the models. The results show how natural variability complicates the detection of possible treatment effects, but demonstrate that Bayesian calibration in combination with mixed models can realistically recover natural shoot growth variability in predictions. We expect these and further stochastic model extensions to result in more realistic virtual plant simulations to study effects, which are used to conduct in silico studies of canopy microclimate and its effects on grape health and quality.

Functional-Structural Plant Models Mission in Advancing Crop Science: Opportunities and Prospects

Functional-structural plant models (FSPMs) have been evolving for over 2 decades and their future development, to some extent, depends on the value of potential applications in crop science. To date, stabilizing crop production by identifying valuable traits for novel cultivars adapted to adverse environments is topical in crop science. Thus, this study will examine how FSPMs are able to address new challenges in crop science for sustainable crop production. FSPMs developed to simulate organogenesis, morphogenesis, and physiological activities under various environments and are amenable to downscale to the tissue, cellular, and molecular level or upscale to the whole plant and ecological level. In a modeling framework with independent and interactive modules, advanced algorithms provide morphophysiological details at various scales. FSPMs are shown to be able to: (i) provide crop ideotypes efficiently for optimizing the resource distribution and use for greater productivity and less disease risk, (ii) guide molecular design breeding via linking molecular basis to plant phenotypes as well as enrich crop models with an additional architectural dimension to assist breeding, and (iii) interact with plant phenotyping for molecular breeding in embracing three-dimensional (3D) architectural traits. This study illustrates that FSPMs have great prospects in speeding up precision breeding for specific environments due to the capacity for guiding and integrating ideotypes, phenotyping, molecular design, and linking molecular basis to target phenotypes. Consequently, the promising great applications of FSPMs in crop science will, in turn, accelerate their evolution and vice versa.

Interactions Between Environment and Genetic Diversity in Perennial Grass Phenology: A Review of Processes at Plant Scale and Modeling

In perennial grasses, the reproductive development consists of major phenological stages which highly determine the seasonal variations of grassland biomass production in terms of quantity and quality. The reproductive development is regulated by climatic conditions through complex interactions subjected to high genetic diversity. Understanding these interactions and their impact on plant development and growth is essential to optimize grassland management and identify the potential consequences of climate change. Here, we review the main stages of reproductive development, from floral induction to heading, i.e., spike emergence, considering the effect of the environmental conditions and the genetic diversity observed in perennial grasses. We first describe the determinants and consequences of reproductive development at individual tiller scale before examining the interactions between plant tillers and their impact on grassland perenniality. Then, we review the available grassland models through their ability to account for the complexity of reproductive development and genetic × environmental interactions. This review shows that (1) The reproductive development of perennial grasses is characterized by a large intraspecific diversity which has the same order of magnitude as the diversity observed between species or environmental conditions. (2) The reproductive development is determined by complex interactions between the processes of floral induction and morphogenesis of the tiller. (3) The perenniality of a plant is dependent on the reproductive behavior of each tiller. (4) Published models only partly explain the complex interactions between morphogenesis and climate on reproductive development. (5) Introducing more explicitly the underlying processes involved in reproductive development in models would improve our ability to anticipate grassland behavior in future growth conditions.

Three-Dimensional Reconstruction Method of Rapeseed Plants in the Whole Growth Period Using RGB-D Camera

The three-dimensional reconstruction method using RGB-D camera has a good balance in hardware cost and point cloud quality. However, due to the limitation of inherent structure and imaging principle, the acquired point cloud has problems such as a lot of noise and difficult registration. This paper proposes a 3D reconstruction method using Azure Kinect to solve these inherent problems. Shoot color images, depth images and near-infrared images of the target from six perspectives by Azure Kinect sensor with black background. Multiply the binarization result of the 8-bit infrared image with the RGB-D image alignment result provided by Microsoft corporation, which can remove ghosting and most of the background noise. A neighborhood extreme filtering method is proposed to filter out the abrupt points in the depth image, by which the floating noise point and most of the outlier noise will be removed before generating the point cloud, and then using the pass-through filter eliminate rest of the outlier noise. An improved method based on the classic iterative closest point (ICP) algorithm is presented to merge multiple-views point clouds. By continuously reducing both the size of the down-sampling grid and the distance threshold between the corresponding points, the point clouds of each view are continuously registered three times, until get the integral color point cloud. Many experiments on rapeseed plants show that the success rate of cloud registration is 92.5% and the point cloud accuracy obtained by this method is 0.789 mm, the time consuming of a integral scanning is 302 s, and with a good color restoration. Compared with a laser scanner, the proposed method has considerable reconstruction accuracy and a significantly ahead of the reconstruction speed, but the hardware cost is much lower when building a automatic scanning system. This research shows a low-cost, high-precision 3D reconstruction technology, which has the potential to be widely used for non-destructive measurement of rapeseed and other crops phenotype.

Optimization of 3D Point Clouds of Oilseed Rape Plants Based on Time-of-Flight Cameras

Three-dimensional (3D) structure is an important morphological trait of plants for describing their growth and biotic/abiotic stress responses. Various methods have been developed for obtaining 3D plant data, but the data quality and equipment costs are the main factors limiting their development. Here, we propose a method to improve the quality of 3D plant data using the time-of-flight (TOF) camera Kinect V2. A K-dimension (k-d) tree was applied to spatial topological relationships for searching points. Background noise points were then removed with a minimum oriented bounding box (MOBB) with a pass-through filter, while outliers and flying pixel points were removed based on viewpoints and surface normals. After being smoothed with the bilateral filter, the 3D plant data were registered and meshed. We adjusted the mesh patches to eliminate layered points. The results showed that the patches were closer. The average distance between the patches was 1.88 × 10-3 m, and the average angle was 17.64°, which were 54.97% and 48.33% of those values before optimization. The proposed method performed better in reducing noise and the local layered-points phenomenon, and it could help to more accurately determine 3D structure parameters from point clouds and mesh models.

A functional structural model of grass development based on metabolic regulation and coordination rules

Shoot architecture is a key component of the interactions between plants and their environment. We present a novel model of grass, which fully integrates shoot morphogenesis and the metabolism of carbon (C) and nitrogen (N) at organ scale, within a three-dimensional representation of plant architecture. Plant morphogenesis is seen as a self-regulated system driven by two main mechanisms. First, the rate of organ extension and the establishment of architectural traits are regulated by concentrations of C and N metabolites in the growth zones and the temperature. Second, the timing of extension is regulated by rules coordinating successive phytomers instead of a thermal time schedule. Local concentrations are calculated from a model of C and N metabolism at organ scale. The three-dimensional representation allows the accurate calculation of light and temperature distribution within the architecture. The model was calibrated for wheat (Triticum aestivum) and evaluated for early vegetative stages. This approach allowed the simulation of realistic patterns of leaf dimensions, extension dynamics, and organ mass and composition. The model simulated, as emergent properties, plant and agronomic traits. Metabolic activities of growing leaves were investigated in relation to whole-plant functioning and environmental conditions. The current model is an important step towards a better understanding of the plasticity of plant phenotype in different environments.

An overview of agent-based models in plant biology and ecology

Agent-based modelling (ABM) has become an established methodology in many areas of biology, ranging from the cellular to the ecological population and community levels. In plant science, two different scales have predominated in their use of ABM. One is the scale of populations and communities, through the modelling of collections of agents representing individual plants, interacting with each other and with the environment. The other is the scale of the individual plant, through the modelling, by functional-structural plant models (FSPMs), of agents representing plant building blocks, or metamers, to describe the development of plant architecture and functions within individual plants. The purpose of this review is to show key results and parallels in ABM for growth, mortality, carbon allocation, competition and reproduction across the scales from the plant organ to populations and communities on a range of spatial scales to the whole landscape. Several areas of application of ABMs are reviewed, showing that some issues are addressed by both population-level ABMs and FSPMs. Continued increase in the relevance of ABM to environmental science and management will be helped by greater integration of ABMs across these two scales.

Two decades of functional-structural plant modelling: now addressing fundamental questions in systems biology and predictive ecology

BACKGROUND

Functional-structural plant models (FSPMs) explore and integrate relationships between a plant's structure and processes that underlie its growth and development. In the last 20 years, scientists interested in functional-structural plant modelling have expanded greatly the range of topics covered and now handle dynamical models of growth and development occurring from the microscopic scale, and involving cell division in plant meristems, to the macroscopic scales of whole plants and plant communities.

SCOPE

The FSPM approach occupies a central position in plant science; it is at the crossroads of fundamental questions in systems biology and predictive ecology. This special issue of Annals of Botany features selected papers on critical areas covered by FSPMs and examples of comprehensive models that are used to solve theoretical and applied questions, ranging from developmental biology to plant phenotyping and management of plants for agronomic purposes. Altogether, they offer an opportunity to assess the progress, gaps and bottlenecks along the research path originally foreseen for FSPMs two decades ago. This review also allows discussion of current challenges of FSPMs regarding (1) integration of multidisciplinary knowledge, (2) methods for handling complex models, (3) standards to achieve interoperability and greater genericity and (4) understanding of plant functioning across scales.

CONCLUSIONS

This approach has demonstrated considerable progress, but has yet to reach its full potential in terms of integration and heuristic knowledge production. The research agenda of functional-structural plant modellers in the coming years should place a greater emphasis on explaining robust emergent patterns, and on the causes of possible deviation from it. Modelling such patterns could indeed fuel both generic integration across scales and transdisciplinary transfer. In particular, it could be beneficial to emergent fields of research such as model-assisted phenotyping and predictive ecology in managed ecosystems.

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.

WALTer: a three-dimensional wheat model to study competition for light through the prediction of tillering dynamics

BACKGROUND AND AIMS

Branching is a main morphogenetic process involved in the adaptation of plants to the environment. In grasses, tillering is divided into three phases: tiller emergence, cessation of tillering and tiller regression. Understanding and prediction of the tillering process is a major challenge to better control cereal yields. In this paper, we present and evaluate WALTer, an individual-based model of wheat built on simple self-adaptive rules for predicting the tillering dynamics at contrasting sowing densities.

METHODS

WALTer simulates the three-dimensional (3-D) development of the aerial architecture of winter wheat. Tillering was modelled using two main hypotheses: (H1) a plant ceases to initiate new tillers when a critical Green Area Index (GAIc) is reached, and (H2) the regression of a tiller occurs if its interception of light is below a threshold (PARt). The development of vegetative organs follows descriptive rules adapted from the literature. A sensitivity analysis was performed to evaluate the impact of each parameter on tillering and GAI dynamics. WALTer was parameterized and evaluated using an initial dataset providing an extensive description of GAI dynamics, and another dataset describing tillering dynamics under a wide range of sowing densities.

KEY RESULTS

Sensitivity analysis indicated the predominant importance of GAIc and PARt. Tillering and GAI dynamics of expt 1 were well fit by WALTer. Once calibrated based on the agronomic density of expt 2, tillering parameters allowed an adequate prediction of tillering dynamics at contrasting sowing densities.

CONCLUSIONS

Using simple rules and a small number of parameters, WALTer efficiently simulated the wheat tillering dynamics observed at contrasting densities in experimental data. These results show that the definition of a critical GAI and a threshold of PAR is a relevant way to represent, respectively, cessation of tillering and tiller regression under competition for light.

A generic individual-based model can predict yield, nitrogen content, and species abundance in experimental grassland communities

Functional-structural plant models are increasingly being used to analyse relationships between plant functioning and the topological and spatial organisation of their modular structure. In this study, the performance of an individual-based model accounting for the the architecture and population dynamics of forage legumes in multi-species grasslands was assessed. Morphogenetic shoot and root parameters were calibrated for seven widely used species. Other model parameters concerning C and N metabolism were obtained from the literature. The model was evaluated using a series of independent experiments combining the seven species in binary mixtures that were subject to regular defoliation. For all the species, the model could accurately simulate phytomer demography, leaf area dynamics, and root growth under conditions of weak competition. In addition, the plastic changes induced by competition for light and N in terms of plant development, leaf area, N uptake, and total plant biomass were correctly predicted. The different species displayed contrasting sensitivities to defoliation, and the model was able to predict the superior ability of creeping species to sustain regular defoliation. As a result of competition and management, the balance between species changed over time and was strongly dependent on the pair of species used. The model proved able to capture these differences in community dynamics. Overall, the results demonstrate that integrating the individual components of population dynamics in a process-based model can provide good predictive capacity regarding mixtures of cultivated species.

Investigation of complex canopies with a functional-structural plant model as exemplified by leaf inclination effect on the functioning of pure and mixed stands of wheat during grain filling

BACKGROUND AND AIMS

Because functional-structural plant models (FSPMs) take plant architecture explicitly into consideration, they constitute a promising approach for unravelling plant-plant interactions in complex canopies. However, existing FSPMs mainly address competition for light. The aim of the present work was to develop a comprehensive FSPM accounting for the interactions between plant architecture, environmental factors and the metabolism of carbon (C) and nitrogen (N).

METHODS

We developed an original FSPM by coupling models of (1) 3-D wheat architecture, (2) light distribution within canopies and (3) C and N metabolism. Model behaviour was evaluated by simulating the functioning of theoretical canopies consisting of wheat plants of contrasting leaf inclination, arranged in pure and mixed stands and considering four culm densities and three sky conditions.

KEY RESULTS

As an emergent property of the detailed description of metabolism, the model predicted a linear relationship between absorbed light and C assimilation, and a curvilinear relationship between grain mass and C assimilation, applying to both pure stands and each component of mixtures. Over the whole post-anthesis period, planophile plants tended to absorb more light than erectophile plants, resulting in a slightly higher grain mass. This difference was enhanced at low plant density and in mixtures, where the erectophile behaviour resulted in a loss of competitiveness.

CONCLUSION

The present work demonstrates that FSPMs provide a framework allowing the analysis of complex canopies such as studying the impact of particular plant traits, which would hardly be feasible experimentally. The present FSPM can help in interpreting complex interactions by providing access to critical variables such as resource acquisition and allocation, internal metabolic concentrations, leaf life span and grain filling. Simulations were based on canopies identically initialized at flowering; extending the model to the whole cycle is thus required so that all consequences of a trait can be evaluated.

A generic individual-based model to simulate morphogenesis, C-N acquisition and population dynamics in contrasting forage legumes

Background and Aims

Individual-based models (IBMs) are promising tools to disentangle plant interactions in multi-species grasslands and foster innovative species mixtures. This study describes an IBM dealing with the morphogenesis, growth and C-N acquisition of forage legumes that integrates plastic responses from functional-structural plant models.

Methods

A generic model was developed to account for herbaceous legume species with contrasting above- and below-ground morphogenetic syndromes and to integrate the responses of plants to light, water and N. Through coupling with a radiative transfer model and a three-dimensional virtual soil, the model allows dynamic resolution of competition for multiple resources at individual plant level within a plant community. The behaviour of the model was assessed on a range of monospecific stands grown along gradients of light, water and N availability.

Key Results

The model proved able to capture the diversity of morphologies encountered among the forage legumes. The main density-dependent features known about even-age plant populations were correctly anticipated. The model predicted (1) the 'reciprocal yield' law relating average plant mass to density, (2) a self-thinning pattern close to that measured for herbaceous species and (3) consistent changes in the size structure of plant populations with time and pedo-climatic conditions. In addition, plastic changes in the partitioning of dry matter, the N acquisition mode and in the architecture of shoots and roots emerged from the integration of plant responses to their local environment. This resulted in taller plants and thinner roots when competition was dominated by light, and shorter plants with relatively more developed root systems when competition was dominated by soil resources.

Conclusions

A population dynamic model considering growth and morphogenesis responses to multiple resources heterogeneously distributed in the environment was presented. It should allow scaling plant-plant interactions from individual to community levels without the inconvenience of average plant models.

The role of biomass allocation between lamina and petioles in a game of light competition in a dense stand of an annual plant

BACKGROUND AND AIMS

Models of plant three-dimensional (3-D) architecture have been used to find optimal morphological characteristics for light capture or carbon assimilation of a solitary plant. However, optimality theory is not necessarily useful to predict the advantageous strategy of an individual in dense stands, where light capture of an individual is influenced not only by its architecture but also by the architecture of its neighbours. Here, we analysed optimal and evolutionarily stable biomass allocation between the lamina and petiole (evolutionarily stable strategy; ESS) under various neighbour conditions using a 3-D simulation model based on the game theory.

METHODS

We obtained 3-D information of every leaf of actual Xanthium canadense plants grown in a dense stand using a ruler and a protractor. We calculated light capture and carbon assimilation of an individual plant when it stands alone and when it is surrounded by neighbours in the stand. We considered three trade-offs in petiole length and lamina area: biomass allocation, biomechanical constraints and photosynthesis. Optimal and evolutionarily stable biomass allocation between petiole and lamina were calculated under various neighbour conditions.

KEY RESULTS

Optimal petiole length varied depending on the presence of neighbours and on the architecture of neighbours. The evolutionarily stable petiole length of plants in the stand tended to be longer than the optimal length of solitary plants. The mean of evolutionarily stable petiole length in the stand was similar to the real one. Trade-offs of biomechanical constraint and photosynthesis had minor effects on optimal and evolutionarily stable petiole length.

CONCLUSION

Actual plants realize evolutionarily stable architecture in dense stands. Interestingly, there were multiple evolutionarily stable petiole lengths even in one stand, suggesting that plants with different architectures can coexist across plant communities.

A functional-structural model of ephemeral seagrass growth influenced by environment

Background and Aims

Ephemeral seagrasses that respond rapidly to environmental changes are important marine habitats. However, they are under threat due to human activity and are logistically difficult and expensive to study. This study aimed to develop a new functional-structural environmentally dependent model of ephemeral seagrass, able to integrate our understanding of ephemeral seagrass growth dynamics and assess options for potential management interventions, such as seagrass transplantation.

Methods

A functional-structural plant model was developed in which growth and senescence rates are mechanistically linked to environmental variables. The model was parameterized and validated for a population of Halophila stipulacea in the Persian Gulf.

Key Results

There was a good match between empirical and simulated results for the number of apices, net rhizome length or net number of internodes using a 330 d simulation. Simulated data were more variable than empirical data. Simulated structural patterns of seagrass rhizome growth qualitatively matched empirical observations.

Conclusions

This new model successfully simulates the environmentally dependent growth and senescence rates of our case-study ephemeral seagrass species. It produces numerical and visual outputs that help synthesize our understanding of how the influence of environmental variables on plant functional processes affects overall growth patterns. The model can also be used to assess the potential outcomes of management interventions like seagrass transplantation, thus providing a useful management tool. It is freely available and easily adapted for new species and locations, although validation with more species and environments is required.

Pattern-oriented modelling as a novel way to verify and validate functional-structural plant models: a demonstration with the annual growth module of avocado

Background and Aims

Functional-structural plant (FSP) models have been widely used to understand the complex interactions between plant architecture and underlying developmental mechanisms. However, to obtain evidence that a model captures these mechanisms correctly, a clear distinction must be made between model outputs used for calibration and thus verification, and outputs used for validation. In pattern-oriented modelling (POM), multiple verification patterns are used as filters for rejecting unrealistic model structures and parameter combinations, while a second, independent set of patterns is used for validation.

Methods

To test the potential of POM for FSP modelling, a model of avocado (Persea americana 'Hass') was developed. The model of shoot growth is based on a conceptual model, the annual growth module (AGM), and simulates photosynthesis and adaptive carbon allocation at the organ level. The model was first calibrated using a set of observed patterns from a published article. Then, for validation, model predictions were compared with a different set of empirical patterns from various field studies that were not used for calibration.

Key Results

After calibration, our model simultaneously reproduced multiple observed architectural patterns. The model then successfully predicted, without further calibration, the validation patterns. The model supports the hypothesis that carbon allocation can be modelled as being dependent on current organ biomass and sink strength of each organ type, and also predicted the observed developmental timing of the leaf sink-source transition stage.

Conclusions

These findings suggest that POM can help to improve the 'structural realism' of FSP models, i.e. the likelihood that a model reproduces observed patterns for the right reasons. Structural realism increases predictive power so that the response of an AGM to changing environmental conditions can be predicted. Accordingly, our FSP model provides a better but still parsimonious understanding of the mechanisms underlying known patterns of AGM growth.

Virtual Plants Need Water Too: Functional-Structural Root System Models in the Context of Drought Tolerance Breeding

Developing a sustainable agricultural model is one of the great challenges of the coming years. The agricultural practices inherited from the Green Revolution of the 1960s show their limits today, and new paradigms need to be explored to counter rising issues such as the multiplication of climate-change related drought episodes. Two such new paradigms are the use of functional-structural plant models to complement and rationalize breeding approaches and a renewed focus on root systems as untapped sources of plant amelioration. Since the late 1980s, numerous functional and structural models of root systems were developed and used to investigate the properties of root systems in soil or lab-conditions. In this review, we focus on the conception and use of such root models in the broader context of research on root-driven drought tolerance, on the basis of root system architecture (RSA) phenotyping. Such models result from the integration of architectural, physiological and environmental data. Here, we consider the different phenotyping techniques allowing for root architectural and physiological study and their limits. We discuss how QTL and breeding studies support the manipulation of RSA as a way to improve drought resistance. We then go over the integration of the generated data within architectural models, how those architectural models can be coupled with functional hydraulic models, and how functional parameters can be measured to feed those models. We then consider the assessment and validation of those hydraulic models through confrontation of simulations to experimentations. Finally, we discuss the up and coming challenges facing root systems functional-structural modeling approaches in the context of breeding.

Using numerical plant models and phenotypic correlation space to design achievable ideotypes

Numerical plant models can predict the outcome of plant traits modifications resulting from genetic variations, on plant performance, by simulating physiological processes and their interaction with the environment. Optimization methods complement those models to design ideotypes, that is, ideal values of a set of plant traits, resulting in optimal adaptation for given combinations of environment and management, mainly through the maximization of performance criteria (e.g. yield and light interception). As use of simulation models gains momentum in plant breeding, numerical experiments must be carefully engineered to provide accurate and attainable results, rooting them in biological reality. Here, we propose a multi-objective optimization formulation that includes a metric of performance, returned by the numerical model, and a metric of feasibility, accounting for correlations between traits based on field observations. We applied this approach to two contrasting models: a process-based crop model of sunflower and a functional-structural plant model of apple trees. In both cases, the method successfully characterized key plant traits and identified a continuum of optimal solutions, ranging from the most feasible to the most efficient. The present study thus provides successful proof of concept for this enhanced modelling approach, which identified paths for desirable trait modification, including direction and intensity.

Image-based 3D canopy reconstruction to determine potential productivity in complex multi-species crop systems

Background and Aims

Intercropping systems contain two or more species simultaneously in close proximity. Due to contrasting features of the component crops, quantification of the light environment and photosynthetic productivity is extremely difficult. However it is an essential component of productivity. Here, a low-tech but high-resolution method is presented that can be applied to single- and multi-species cropping systems to facilitate characterization of the light environment. Different row layouts of an intercrop consisting of Bambara groundnut ( Vigna subterranea ) and proso millet ( Panicum miliaceum ) have been used as an example and the new opportunities presented by this approach have been analysed.

Methods

Three-dimensional plant reconstruction, based on stereo cameras, combined with ray tracing was implemented to explore the light environment within the Bambara groundnut-proso millet intercropping system and associated monocrops. Gas exchange data were used to predict the total carbon gain of each component crop.

Key Results

The shading influence of the tall proso millet on the shorter Bambara groundnut results in a reduction in total canopy light interception and carbon gain. However, the increased leaf area index (LAI) of proso millet, higher photosynthetic potential due to the C4 pathway and sub-optimal photosynthetic acclimation of Bambara groundnut to shade means that increasing the number of rows of millet will lead to greater light interception and carbon gain per unit ground area, despite Bambara groundnut intercepting more light per unit leaf area.

Conclusions

Three-dimensional reconstruction combined with ray tracing provides a novel, accurate method of exploring the light environment within an intercrop that does not require difficult measurements of light interception and data-intensive manual reconstruction, especially for such systems with inherently high spatial possibilities. It provides new opportunities for calculating potential productivity within multi-species cropping systems, enables the quantification of dynamic physiological differences between crops grown as monoculture and those within intercrops, and enables the prediction of new productive combinations of previously untested crops.

Combining Genome-Wide Information with a Functional Structural Plant Model to Simulate 1-Year-Old Apple Tree Architecture

In crops, optimizing target traits in breeding programs can be fostered by selecting appropriate combinations of architectural traits which determine light interception and carbon acquisition. In apple tree, architectural traits were observed to be under genetic control. However, architectural traits also result from many organogenetic and morphological processes interacting with the environment. The present study aimed at combining a FSPM built for apple tree, MAppleT, with genetic determinisms of architectural traits, previously described in a bi-parental population. We focused on parameters related to organogenesis (phyllochron and immediate branching) and morphogenesis processes (internode length and leaf area) during the first year of tree growth. Two independent datasets collected in 2004 and 2007 on 116 genotypes, issued from a 'Starkrimson' × 'Granny Smith' cross, were used. The phyllochron was estimated as a function of thermal time and sylleptic branching was modeled subsequently depending on phyllochron. From a genetic map built with SNPs, marker effects were estimated on four MAppleT parameters with rrBLUP, using 2007 data. These effects were then considered in MAppleT to simulate tree development in the two climatic conditions. The genome wide prediction model gave consistent estimations of parameter values with correlation coefficients between observed values and estimated values from SNP markers ranging from 0.79 to 0.96. However, the accuracy of the prediction model following cross validation schemas was lower. Three integrative traits (the number of leaves, trunk length, and number of sylleptic laterals) were considered for validating MAppleT simulations. In 2007 climatic conditions, simulated values were close to observations, highlighting the correct simulation of genetic variability. However, in 2004 conditions which were not used for model calibration, the simulations differed from observations. This study demonstrates the possibility of integrating genome-based information in a FSPM for a perennial fruit tree. It also showed that further improvements are required for improving the prediction ability. Especially temperature effect should be extended and other factors taken into account for modeling GxE interactions. Improvements could also be expected by considering larger populations and by testing other genome wide prediction models. Despite these limitations, this study opens new possibilities for supporting plant breeding by in silico evaluations of the impact of genotypic polymorphisms on plant integrative phenotypes.

CN-Wheat, a functional-structural model of carbon and nitrogen metabolism in wheat culms after anthesis. II. Model evaluation

Background and Aims Simulating resource allocation in crops requires an integrated view of plant functioning and the formalization of interactions between carbon (C) and nitrogen (N) metabolisms. This study evaluates the functional-structural model CN-Wheat developed for winter wheat after anthesis. Methods In CN-Wheat the acquisition and allocation of resources between photosynthetic organs, roots and grains are emergent properties of sink and source activities and transfers of mobile metabolites. CN-Wheat was calibrated for field plants under three N fertilizations at anthesis. Model parameters were taken from the literature or calibrated on the experimental data. Key Results The model was able to predict the temporal variations and the distribution of resources in the culm. Thus, CN-Wheat accurately predicted the post-anthesis kinetics of dry masses and N content of photosynthetic organs and grains in response to N fertilization. In our simulations, when soil nitrates were non-limiting, N in grains was ultimately determined by availability of C for root activity. Dry matter accumulation in grains was mostly affected by photosynthetic organ lifespan, which was regulated by protein turnover and C-regulated root activity. Conclusions The present study illustrates that the hypotheses implemented in the model were able to predict realistic dynamics and spatial patterns of C and N. CN-Wheat provided insights into the interplay of C and N metabolism and how the depletion of mobile metabolites due to grain filling ultimately results in the cessation of resource capture. This enabled us to identify processes that limit grain mass and protein content and are potential targets for plant breeding.

Simulation of carbon allocation and organ growth variability in apple tree by connecting architectural and source-sink models

BACKGROUND AND AIMS

Plant growth depends on carbon availability and allocation among organs. QualiTree has been designed to simulate carbon allocation and partitioning in the peach tree (Prunus persica), whereas MappleT is dedicated to the simulation of apple tree (Malus × domestica) architecture. The objective of this study was to couple both models and adapt QualiTree to apple trees to simulate organ growth traits and their within-tree variability.

METHODS

MappleT was used to generate architectures corresponding to the 'Fuji' cultivar, accounting for the variability within and among individuals. These architectures were input into QualiTree to simulate shoot and fruit growth during a growth cycle. We modified QualiTree to account for the observed shoot polymorphism in apple trees, i.e. different classes (long, medium and short) that were characterized by different growth function parameters. Model outputs were compared with observed 3D tree geometries, considering shoot and final fruit size and growth dynamics.

KEY RESULTS

The modelling approach connecting MappleT and QualiTree was appropriate to the simulation of growth and architectural characteristics at the tree scale (plant leaf area, shoot number and types, fruit weight at harvest). At the shoot scale, mean fruit weight and its variability within trees was accurately simulated, whereas the model tended to overestimate individual shoot leaf area and underestimate its variability for each shoot type. Varying the parameter related to the intensity of carbon exchange between shoots revealed that behaviour intermediate between shoot autonomy and a common assimilate pool was required to properly simulate within-tree fruit growth variability. Moreover, the model correctly dealt with the crop load effect on organ growth.

CONCLUSIONS

This study provides understanding of the integration of shoot ontogenetic properties, carbon supply and transport between entities for simulating organ growth in trees. Further improvements regarding the integration of retroaction loops between carbon allocation and the resulting plant architecture are expected to allow multi-year simulations.

Linking ice accretion and crown structure: towards a model of the effect of freezing rain on tree canopies

BACKGROUND AND AIMS

Despite a longstanding interest in variation in tree species vulnerability to ice storm damage, quantitative analyses of the influence of crown structure on within-crown variation in ice accretion are rare. In particular, the effect of prior interception by higher branches on lower branch accumulation remains unstudied. The aim of this study was to test the hypothesis that intra-crown ice accretion can be predicted by a measure of the degree of sheltering by neighbouring branches.

METHODS

Freezing rain was artificially applied to Acer platanoides L., and in situ branch-ice thickness was measured directly and from LiDAR point clouds. Two models of freezing rain interception were developed: 'IceCube', which uses point clouds to relate ice accretion to a voxel-based index (sheltering factor; SF) of the sheltering effect of branch elements above a measurement point; and 'IceTree', a simulation model for in silico evaluation of the interception pattern of freezing rain in virtual tree crowns.

KEY RESULTS

Intra-crown radial ice accretion varied strongly, declining from the tips to the bases of branches and from the top to the base of the crown. SF for branches varied strongly within the crown, and differences among branches were consistent for a range of model parameters. Intra-crown variation in ice accretion on branches was related to SF (R(2) = 0·46), with in silico results from IceTree supporting empirical relationships from IceCube.

CONCLUSIONS

Empirical results and simulations confirmed a key role for crown architecture in determining intra-crown patterns of ice accretion. As suspected, the concentration of freezing rain droplets is attenuated by passage through the upper crown, and thus higher branches accumulate more ice than lower branches. This is the first step in developing a model that can provide a quantitative basis for investigating intra-crown and inter-specific variation in freezing rain damage.

High temperature and vapor pressure deficit aggravate architectural effects but ameliorate non-architectural effects of salinity on dry mass production of tomato

Tomato (Solanum lycopersicum L.) is an important vegetable crop and often cultivated in regions exposed to salinity and high temperatures (HT) which change plant architecture, decrease canopy light interception and disturb physiological functions. However, the long-term effects of salinity and HT combination (S+HT) on plant growth are still unclear. A dynamic functional-structural plant model (FSPM) of tomato was parameterized and evaluated for different levels of S+HT combinations. The evaluated model was used to quantify the contributions of morphological changes (architectural effects) and physiological disturbances (non-architectural effects) on the reduction of shoot dry mass under S+HT. The model predicted architectural variables with high accuracy (>85%), which ensured the reliability of the model analyses. HT enhanced architectural effects but reduced non-architectural effects of salinity on dry mass production. The stronger architectural effects of salinity under HT could not be counterbalanced by the smaller non-architectural effects. Therefore, long-term influences of HT on shoot dry mass under salinity were negative at the whole plant level. Our model analysis highlights the importance of plant architecture at canopy level in studying the plant responses to the environments and shows the merits of dynamic FSPMs as heuristic tools.

Sex-related differences in stress tolerance in dioecious plants: a critical appraisal in a physiological context

Sex-related differences in reproductive effort can lead to differences in vegetative growth and stress tolerance. However, do all dioecious plants show sex-related differences in stress tolerance? To what extent can the environmental context and modularity mask sex-related differences in stress tolerance? Finally, to what extent can physiological measurements help us understand secondary sexual dimorphism? This opinion paper aims to answer these three basic questions with special emphasis on developments in research in this area over the last decade. Compelling evidence indicates that dimorphic species do not always show differences in stress tolerance between sexes; and when sex-related differences do occur, they seem to be highly species-specific, with greater stress tolerance in females than males in some species, and the opposite in others. The causes of such sex-related species-specific differences are still poorly understood, and more physiological studies and diversity of plant species that allow comparative analyses are needed. Furthermore, studies performed thus far demonstrate that the expression of dioecy can lead to sex-related differences in physiological traits-from leaf gas exchange to gene expression-but the biological significance of modularity and sectoriality governing such differences has been poorly investigated. Future studies that consider the importance of modularity and sectoriality are essential for unravelling the mechanisms underlying stress adaptation in male and female plants growing in their natural habitat.

Quantification of the effects of architectural traits on dry mass production and light interception of tomato canopy under different temperature regimes using a dynamic functional-structural plant model

There is increasing interest in evaluating the environmental effects on crop architectural traits and yield improvement. However, crop models describing the dynamic changes in canopy structure with environmental conditions and the complex interactions between canopy structure, light interception, and dry mass production are only gradually emerging. Using tomato (Solanum lycopersicum L.) as a model crop, a dynamic functional-structural plant model (FSPM) was constructed, parameterized, and evaluated to analyse the effects of temperature on architectural traits, which strongly influence canopy light interception and shoot dry mass. The FSPM predicted the organ growth, organ size, and shoot dry mass over time with high accuracy (>85%). Analyses of this FSPM showed that, in comparison with the reference canopy, shoot dry mass may be affected by leaf angle by as much as 20%, leaf curvature by up to 7%, the leaf length:width ratio by up to 5%, internode length by up to 9%, and curvature ratios and leaf arrangement by up to 6%. Tomato canopies at low temperature had higher canopy density and were more clumped due to higher leaf area and shorter internodes. Interestingly, dry mass production and light interception of the clumped canopy were more sensitive to changes in architectural traits. The complex interactions between architectural traits, canopy light interception, dry mass production, and environmental conditions can be studied by the dynamic FSPM, which may serve as a tool for designing a canopy structure which is 'ideal' in a given environment.

What is the most prominent factor limiting photosynthesis in different layers of a greenhouse cucumber canopy?

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.

Cross-scale modelling of transpiration from stomata via the leaf boundary layer

BACKGROUND AND AIMS

Leaf transpiration is a key parameter for understanding land surface-climate interactions, plant stress and plant structure–function relationships. Transpiration takes place at the microscale level, namely via stomata that are distributed discretely over the leaf surface with a very low surface coverage (approx. 0·2-5%). The present study aims to shed more light on the dependency of the leaf boundary-layer conductance (BLC) on stomatal surface coverage and air speed.

METHODS

An innovative three-dimensional cross-scale modelling approach was applied to investigate convective mass transport from leaves, using computational fluid dynamics. The gap between stomatal and leaf scale was bridged by including all these scales in the same computational model (10⁻⁵-10⁻¹ m), which implies explicitly modelling individual stomata.

KEY RESULTS

BLC was strongly dependent on stomatal surface coverage and air speed. Leaf BLC at low surface coverage ratios (CR), typical for stomata, was still relatively high, compared with BLC of a fully wet leaf (hypothetical CR of 100%). Nevertheless, these conventional BLCs (CR of 100%), as obtained from experiments or simulations on leaf models, were found to overpredict the convective exchange. In addition, small variations in stomatal CR were found to result in large variations in BLCs. Furthermore, stomata of a certain size exhibited a higher mass transfer rate at lower CRs.

CONCLUSIONS

The proposed cross-scale modelling approach allows us to increase our understanding of transpiration at the sub-leaf level as well as the boundary-layer microclimate in a way currently not feasible experimentally. The influence of stomatal size, aperture and surface density, and also flow-field parameters can be studied using the model, and prospects for further improvement of the model are presented. An important conclusion of the study is that existing measures of conductances (e.g. from artificial leaves) can be significantly erroneous because they do not account for microscopic stomata, but instead assume a uniform distribution of evaporation such as found for a fully-wet leaf. The model output can be used to correct or upgrade existing BLCs or to feed into higher-scale models, for example within a multiscale framework.

Functional-structural plant models: a growing paradigm for plant studies

A number of research groups in various areas of plant biology as well as computer science and applied mathematics have addressed modelling the spatiotemporal dynamics of growth and development of plants. This has resulted in development of functional-structural plant models (FSPMs). In FSPMs, the plant structure is always explicitly represented in terms of a network of elementary units. In this respect, FSPMs are different from more abstract models in which a simplified representation of the plant structure is frequently used (e.g. spatial density of leaves, total biomass, etc.). This key feature makes it possible to build modular models and creates avenues for efficient exchange of model components and experimental data. They are being used to deal with the complex 3-D structure of plants and to simulate growth and development occurring at spatial scales from cells to forest areas, and temporal scales from seconds to decades and many plant generations. The plant types studied also cover a broad spectrum, from algae to trees. This special issue of Annals of Botany features selected papers on FSPM topics such as models of morphological development, models of physical and biological processes, integrated models predicting dynamics of plants and plant communities, modelling platforms, methods for acquiring the 3-D structures of plants using automated measurements, and practical applications for agronomic purposes.

Assessing the effects of architectural variations on light partitioning within virtual wheat-pea mixtures

BACKGROUND AND AIMS

Predicting light partitioning in crop mixtures is a critical step in improving the productivity of such complex systems, and light interception has been shown to be closely linked to plant architecture. The aim of the present work was to analyse the relationships between plant architecture and light partitioning within wheat-pea (Triticum aestivum-Pisum sativum) mixtures. An existing model for wheat was utilized and a new model for pea morphogenesis was developed. Both models were then used to assess the effects of architectural variations in light partitioning.

METHODS

First, a deterministic model (L-Pea) was developed in order to obtain dynamic reconstructions of pea architecture. The L-Pea model is based on L-systems formalism and consists of modules for 'vegetative development' and 'organ extension'. A tripartite simulator was then built up from pea and wheat models interfaced with a radiative transfer model. Architectural parameters from both plant models, selected on the basis of their contribution to leaf area index (LAI), height and leaf geometry, were then modified in order to generate contrasting architectures of wheat and pea.

KEY RESULTS

By scaling down the analysis to the organ level, it could be shown that the number of branches/tillers and length of internodes significantly determined the partitioning of light within mixtures. Temporal relationships between light partitioning and the LAI and height of the different species showed that light capture was mainly related to the architectural traits involved in plant LAI during the early stages of development, and in plant height during the onset of interspecific competition.

CONCLUSIONS

In silico experiments enabled the study of the intrinsic effects of architectural parameters on the partitioning of light in crop mixtures of wheat and pea. The findings show that plant architecture is an important criterion for the identification/breeding of plant ideotypes, particularly with respect to light partitioning.

Comparison of the morphogenesis of three genotypes of pea (Pisum sativum) grown in pure stands and wheat-based intercrops

Cereal-legume intercrops represent a promising way of combining high productivity and agriculture sustainability. The benefits of cereal-legume mixtures are highly affected by species morphology and functioning, which determine the balance between competition and complementarity for resource acquisition. Studying species morphogenesis, which controls plant architecture, is therefore of major interest. The morphogenesis of cultivated species has been mainly described in mono-specific growing conditions, although morphogenetic plasticity can occur in multi-specific stands. The aim of the present study was therefore to characterize the variability of the morphogenesis of pea plants grown either in pure stands or mixed with wheat. This was achieved through a field experiment that included three pea cultivars with contrasting earliness (hr and HR type) and branching patterns. Results show that most of the assessed parameters of pea morphogenesis (phenology, branching, final number of vegetative organs and their kinetics of appearance) were mainly dependent on the considered genotype, which highlights the importance of the choice of cultivars in intercropping systems. There was however a low variability of pea morphogenesis between sole and mixed stands except for plant height and branching of the long-cycle cultivar. The information provided in the present study at stand and plant scale can be used to build up structural-functional models. These models can contribute to improving the understanding of the functioning of cereal-legume intercrops and also to the definition of plant ideotypes adapted to the growth in intercrops.

PypeTree: a tool for reconstructing tree perennial tissues from point clouds

The reconstruction of trees from point clouds that were acquired with terrestrial LiDAR scanning (TLS) may become a significant breakthrough in the study and modelling of tree development. Here, we develop an efficient method and a tool based on extensive modifications to the skeletal extraction method that was first introduced by Verroust and Lazarus in 2000. PypeTree, a user-friendly and open-source visual modelling environment, incorporates a number of improvements into the original skeletal extraction technique, making it better adapted to tackle the challenge of tree perennial tissue reconstruction. Within PypeTree, we also introduce the idea of using semi-supervised adjustment tools to address methodological challenges that are associated with imperfect point cloud datasets and which further improve reconstruction accuracy. The performance of these automatic and semi-supervised approaches was tested with the help of synthetic models and subsequently validated on real trees. Accuracy of automatic reconstruction greatly varied in terms of axis detection because small (length < 3.5 cm) branches were difficult to detect. However, as small branches account for little in terms of total skeleton length, mean reconstruction error for cumulated skeleton length only reached 5.1% and 1.8% with automatic or semi-supervised reconstruction, respectively. In some cases, using the supervised tools, a perfect reconstruction of the perennial tissue could be achieved.

Assessing the potential of low-cost 3D cameras for the rapid measurement of plant woody structure

Detailed 3D plant architectural data have numerous applications in plant science, but many existing approaches for 3D data collection are time-consuming and/or require costly equipment. Recently, there has been rapid growth in the availability of low-cost, 3D cameras and related open source software applications. 3D cameras may provide measurements of key components of plant architecture such as stem diameters and lengths, however, few tests of 3D cameras for the measurement of plant architecture have been conducted. Here, we measured Salix branch segments ranging from 2-13 mm in diameter with an Asus Xtion camera to quantify the limits and accuracy of branch diameter measurement with a 3D camera. By scanning at a variety of distances we also quantified the effect of scanning distance. In addition, we also test the sensitivity of the program KinFu for continuous 3D object scanning and modeling as well as other similar software to accurately record stem diameters and capture plant form (<3 m in height). Given its ability to accurately capture the diameter of branches >6 mm, Asus Xtion may provide a novel method for the collection of 3D data on the branching architecture of woody plants. Improvements in camera measurement accuracy and available software are likely to further improve the utility of 3D cameras for plant sciences in the future.

Modeling branching in cereals

Cereals and grasses adapt their structural development to environmental conditions and the resources available. The primary adaptive response is a variable degree of branching, called tillering in cereals. Especially for heterogeneous plant configurations the degree of tillering varies per plant. Functional-structural plant modeling (FSPM) is a modeling approach allowing simulation of the architectural development of individual plants, culminating in the emergent behavior at the canopy level. This paper introduces the principles of modeling tillering in FSPM, using (I) a probability approach, forcing the dynamics of tillering to correspond to measured probabilities. Such models are particularly suitable to evaluate the effect structural variables on system performance. (II) Dose-response curves, representing a measured or assumed response of tillering to an environmental cue. (III) Mechanistic approaches to tillering including control by carbohydrates, hormones, and nutrients. Tiller senescence is equally important for the structural development of cereals as tiller appearance. Little study has been made of tiller senescence, though similar concepts seem to apply as for tiller appearance.

Physiological mechanisms in plant growth models: do we need a supra-cellular systems biology approach?

In the first part of this paper, we review the extent to which various types of plant growth models incorporate ecophysiological mechanisms. Many growth models have a central role for the process of photosynthesis; and often implicitly assume C-gain to be the rate-limiting step for biomass accumulation. We subsequently explore the extent to which this assumption actually holds and under what condition constraints on growth due to a limited sink strength are likely to occur. By using generalized dose-response curves for growth with respect to light and CO₂, models can be tested against a benchmark for their overall performance. In the final part, a call for a systems approach at the supra-cellular level is made. This will enable a better understanding of feedbacks and trade-offs acting on plant growth and its component processes. Mechanistic growth models form an indispensable element of such an approach and will, in the end, provide the link with the (sub-)cellular approaches that are yet developing. Improved insight will be gained if model output for the various physiological processes and morphological variables ('virtual profiling') is compared with measured correlation networks among these processes and variables. Two examples of these correlation networks are presented.

Root-shoot allometry of tropical forest trees determined in a large-scale aeroponic system

BACKGROUND AND AIMS

This study is a first step in a multi-stage project aimed at determining allometric relationships among the tropical tree organs, and carbon fluxes between the various tree parts and their environment. Information on canopy-root interrelationships is needed to improve understanding of above- and below-ground processes and for modelling of the regional and global carbon cycle. Allometric relationships between the sizes of different plant parts will be determined.

METHODS

Two tropical forest species were used in this study: Ceiba pentandra (kapok), a fast-growing tree native to South and Central America and to Western Africa, and Khaya anthotheca (African mahogany), a slower-growing tree native to Central and Eastern Africa. Growth and allometric parameters of 12-month-old saplings grown in a large-scale aeroponic system and in 50-L soil containers were compared. The main advantage of growing plants in aeroponics is that their root systems are fully accessible throughout the plant life, and can be fully recovered for harvesting.

KEY RESULTS

The expected differences in shoot and root size between the fast-growing C. pentandra and the slower-growing K. anthotheca were evident in both growth systems. Roots were recovered from the aeroponically grown saplings only, and their distribution among various diameter classes followed the patterns expected from the literature. Stem, branch and leaf allometric parameters were similar for saplings of each species grown in the two systems.

CONCLUSIONS

The aeroponic tree growth system can be utilized for determining the basic allometric relationships between root and shoot components of these trees, and hence can be used to study carbon allocation and fluxes of whole above- and below-ground tree parts.

Elements of a dynamic systems model of canopy photosynthesis

Improving photosynthesis throughout the full canopy rather than photosynthesis of only the top leaves of the canopy is central to improving crop yields. Many canopy photosynthesis models have been developed from physiological and ecological perspectives, however most do not consider heterogeneities of microclimatic factors inside a canopy, canopy dynamics and associated energetics, or competition among different plants, and most models lack a direct linkage to molecular processes. Here we described the rationale, elements, and approaches necessary to build a dynamic systems model of canopy photosynthesis. A systems model should integrate metabolic processes including photosynthesis, respiration, nitrogen metabolism, resource re-mobilization and photosynthate partitioning with canopy level light, CO(2), water vapor distributions and heat exchange processes. In so doing a systems-based canopy photosynthesis model will enable studies of molecular ecology and dramatically improve our insight into engineering crops for improved canopy photosynthetic CO(2) uptake, resource use efficiencies and yields.

L-py: an L-system simulation framework for modeling plant architecture development based on a dynamic language

The study of plant development requires increasingly powerful modeling tools to help understand and simulate the growth and functioning of plants. In the last decade, the formalism of L-systems has emerged as a major paradigm for modeling plant development. Previous implementations of this formalism were made based on static languages, i.e., languages that require explicit definition of variable types before using them. These languages are often efficient but involve quite a lot of syntactic overhead, thus restricting the flexibility of use for modelers. In this work, we present an adaptation of L-systems to the Python language, a popular and powerful open-license dynamic language. We show that the use of dynamic language properties makes it possible to enhance the development of plant growth models: (i) by keeping a simple syntax while allowing for high-level programming constructs, (ii) by making code execution easy and avoiding compilation overhead, (iii) by allowing a high-level of model reusability and the building of complex modular models, and (iv) by providing powerful solutions to integrate MTG data-structures (that are a common way to represent plants at several scales) into L-systems and thus enabling to use a wide spectrum of computer tools based on MTGs developed for plant architecture. We then illustrate the use of L-Py in real applications to build complex models or to teach plant modeling in the classroom.