Towards virtual modeling environments for functional structural plant models based on Jupyter notebooks: Application to the modeling of mango tree growth and development

Functional-Structural Plant Models (FSPMs) are powerful tools to explore the complex interplays between plant growth, underlying physiological processes and the environment. Various modeling platforms dedicated to FSPMs have been developed with limited support for collaborative and distributed model design, reproducibility and dissemination. With the objective to alleviate these problems, we used the Jupyter project, an open-source computational notebook ecosystem, to create virtual modeling environments for plant models. These environments combined Python scientific modules, L-systems formalism, multidimensional arrays and 3D plant architecture visualization in Jupyter notebooks. As a case study, we present an application of such an environment by reimplementing V-Mango, a model of mango tree development and fruit production built on interrelated processes of architectural development and fruit growth that are affected by temporal, structural and environmental factors. This new implementation increased model modularity, with modules representing single processes and the workflows between them. The model modularity allowed us to run simulations for a subset of processes only, on simulated or empirical architectures. The exploration of carbohydrate source-sink relationships on a measured mango branch architecture illustrates this possibility. We also proposed solutions for visualization, distant distributed computation and parallel simulations of several independent mango trees during a growing season. The development of models on locations far from computational resources makes collaborative and distributed model design and implementation possible, and demonstrates the usefulness and efficiency of a customizable virtual modeling environment.

L-system models for image-based phenomics: case studies of maize and canola

Artificial neural networks that recognize and quantify relevant aspects of crop plants show great promise in image-based phenomics, but their training requires many annotated images. The acquisition of these images is comparatively simple, but their manual annotation is time-consuming. Realistic plant models, which can be annotated automatically, thus present an attractive alternative to real plant images for training purposes. Here we show how such models can be constructed and calibrated quickly, using maize and canola as case studies.

Measuring hidden phenotype: Quantifying the shape of barley seeds using the Euler Characteristic Transform

Shape plays a fundamental role in biology. Traditional phenotypic analysis methods measure some features but fail to measure the information embedded in shape comprehensively. To extract, compare, and analyze this information embedded in a robust and concise way, we turn to Topological Data Analysis (TDA), specifically the Euler Characteristic Transform. TDA measures shape comprehensively using mathematical representations based on algebraic topology features. To study its use, we compute both traditional and topological shape descriptors to quantify the morphology of 3121 barley seeds scanned with X-ray Computed Tomography (CT) technology at 127 micron resolution. The Euler Characteristic Transform measures shape by analyzing topological features of an object at thresholds across a number of directional axes. A Kruskal-Wallis analysis of the information encoded by the topological signature reveals that the Euler Characteristic Transform picks up successfully the shape of the crease and bottom of the seeds. Moreover, while traditional shape descriptors can cluster the seeds based on their accession, topological shape descriptors can cluster them further based on their panicle. We then successfully train a support vector machine (SVM) to classify 28 different accessions of barley based exclusively on the shape of their grains. We observe that combining both traditional and topological descriptors classifies barley seeds better than using just traditional descriptors alone. This improvement suggests that TDA is thus a powerful complement to traditional morphometrics to comprehensively describe a multitude of “hidden” shape nuances which are otherwise not detected.

Soybean-BioCro: A semi-mechanistic model of soybean growth

Soybean is a major global source of protein and oil. Understanding how soybean crops will respond to the changing climate and identifying the responsible molecular machinery, are important for facilitating bioengineering and breeding to meet the growing global food demand. The BioCro family of crop models are semi-mechanistic models scaling from biochemistry to whole crop growth and yield. BioCro was previously parameterized and proved effective for the biomass crops miscanthus, coppice willow, and Brazilian sugarcane. Here, we present Soybean-BioCro, the first food crop to be parameterized for BioCro. Two new module sets were incorporated into the BioCro framework describing the rate of soybean development and carbon partitioning and senescence. The model was parameterized using field measurements collected over the 2002 and 2005 growing seasons at the open air [CO2] enrichment (SoyFACE) facility under ambient atmospheric [CO2]. We demonstrate that Soybean-BioCro successfully predicted how elevated [CO2] impacted field-grown soybean growth without a need for re-parameterization, by predicting soybean growth under elevated atmospheric [CO2] during the 2002 and 2005 growing seasons, and under both ambient and elevated [CO2] for the 2004 and 2006 growing seasons. Soybean-BioCro provides a useful foundational framework for incorporating additional primary and secondary metabolic processes or gene regulatory mechanisms that can further aid our understanding of how future soybean growth will be impacted by climate change.

Exploring complementarities between modelling approaches that enable upscaling from plant community functioning to ecosystem services as a way to support agroecological transition

Promoting plant diversity through crop mixtures is a mainstay of the agroecological transition. Modelling this transition requires considering both plant-plant interactions and plants’ interactions with abiotic and biotic environments. Modelling crop mixtures enables designing ways to use plant diversity to provide ecosystem services, as long as they include crop management as input. A single modelling approach is not sufficient, however, and complementarities between models may be critical to consider the multiple processes and system components involved at different and relevant spatial and temporal scales. In this article, we present different modelling solutions implemented in a variety of examples to upscale models from local interactions to ecosystem services. We highlight that modelling solutions (i.e. coupling, metamodelling, inverse or hybrid modelling) are built according to modelling objectives (e.g. understand the relative contributions of primary ecological processes to crop mixtures, quantify impacts of the environment and agricultural practices, assess the resulting ecosystem services) rather than to the scales of integration. Many outcomes of multispecies agroecosystems remain to be explored, both experimentally and through the heuristic use of modelling. Combining models to address plant diversity and predict ecosystem services at different scales remains rare but is critical to support the spatial and temporal prediction of the many systems that could be designed.

Modelling the functional dependency between root and shoot compartments to predict the impact of the environment on the architecture of the whole plant. Methodology for model fitting on simulated data using Deep Learning techniques

Tree structural and biomass growth studies mainly focus on the shoot compartment. Tree roots usually have to be taken apart due to the difficulties involved in measuring and observing this compartment, particularly root growth. In the context of climate change, the study of tree structural plasticity has become crucial and both shoot and root systems need to be considered simultaneously as they play a joint role in adapting traits to climate change (water availability for roots and light or carbon availability for shoots). We developed a botanically accurate whole-plant model and its simulator (RoCoCau) with a linkable external module (TOY) to represent shoot and root compartment dependencies and hence tree structural plasticity in different air and soil environments. This paper describes a new deep neural network calibration trained on simulated datasets computed from a set of more than 360 000 random TOY parameter values and random climate values. These datasets were used for training and for validation. For this purpose, we chose Voxnet, a convolutional neural network designed to classify 3D objects represented as a voxelized scene. We recommend further improvements for Voxnet inputs, outputs, and training. We were able to teach the network to predict the value of environment data well (mean error < 2%), and to predict the value of TOY parameters for plants under water stress conditions (mean error < 5% for all parameters), and for any environmental growing conditions (mean error < 20%).

How does structure matter? Comparison of canopy photosynthesis using one- and three-dimensional light models: a case study using greenhouse cucumber canopies

One-dimensional light models using the Beer-Lambert equation (BL) with the light extinction coefficient k are simple and robust tools for estimating light interception of homogeneous canopies. Functional-structural plant models (FSPMs) are powerful to capture light-plant interactions in heterogeneous canopies, but they are also more complex due to explicit descriptions of three-dimensional plant architecture and light models. For choosing an appropriate modelling approach, the trade-offs between simplicity and accuracy need to be considered when canopies with spatial heterogeneity are concerned. We compared two light modelling approaches, one following BL and another using ray tracing (RT), based on a framework of a dynamic FSPM of greenhouse cucumber. Resolutions of hourly-step (HS) and daily-step (DS) were applied to simulate light interception, leaf-level photosynthetic acclimation and plant-level dry matter production over growth periods of two to five weeks. Results showed that BL-HS was comparable to RT-HS in predicting shoot dry matter and photosynthetic parameters. The k used in the BL approach was simulated using an empirical relationship between k and leaf area index established with the assistance of RT, which showed variation up to 0.2 in k depending on canopy geometry under the same plant density. When a constant k value was used instead, a difference of 0.2 in k resulted in up to 27% loss in accuracy for shoot dry matter. These results suggested that, with the assistance of RT in k estimation, the simple approach BL-HS provided efficient estimation for long-term processes.

Polar auxin transport dynamics of primary and secondary vein patterning in dicot leaves

The growth regulator auxin plays a central role in the phyllotaxy, shape, and venation patterns of leaves. The auxin spatial localization underlying these phenomena involves polar auxin transport (PAT) at the cellular level, particularly the preferential allocation of PIN efflux proteins to certain areas of the plasma membrane. Two general mechanisms have been studied: an up-the-gradient (UTG) allocation dependent on neighbouring-cell auxin concentrations, and a with-the-flux (WTF) allocation dependent on the flow of auxin across walls. We have developed a combined UTG+WTF model to quantify the observed auxin flows both towards (UTG) and away from (WTF) auxin maxima during primary and secondary vein patterning in leaves. The model simulates intracellular and membrane kinetics and intercellular transport, and is solved for a 2D leaf of several hundred cells. In addition to normal development, modelling of increasing PAT inhibition generates, as observed experimentally: a switch from several distinct vein initiation sites to many less-distinct sites; a delay in vein canalization; inhibited connection of new veins to old; and finally loss of patterning in the margin, loss of vein extension, and confinement of auxin to the margin. The model generates the observed formation of discrete auxin maxima at leaf vein sources and shows the dependence of secondary vein patterning on the efficacy of auxin flux through cells. Simulations of vein patterning and leaf growth further indicate that growth itself may bridge the spatial scale from the cell-cell resolution of the PIN-auxin dynamics to vein patterns on the whole-leaf scale.

Simulating rhizodeposition patterns around growing and exuding root systems

In this study, we developed a novel model approach to compute the spatio-temporal distribution patterns of rhizodeposits around growing root systems in three dimensions. This model approach allows us to study the evolution of rhizodeposition patterns around complex three-dimensional root systems. Root systems were generated using the root architecture model CPlantBox. The concentration of rhizodeposits at a given location in the soil domain was computed analytically. To simulate the spread of rhizodeposits in the soil, we considered rhizodeposit release from the roots, rhizodeposit diffusion into the soil, rhizodeposit sorption to soil particles, and rhizodeposit degradation by microorganisms. To demonstrate the capabilities of our new model approach, we performed simulations for the two example rhizodeposits mucilage and citrate and the example root system Vicia faba. The rhizodeposition model was parameterized using values from the literature. Our simulations showed that the rhizosphere soil volume with rhizodeposit concentrations above a defined threshold value (i.e., the rhizodeposit hotspot volume), exhibited a maximum at intermediate root growth rates. Root branching allowed the rhizospheres of individual roots to overlap, resulting in a greater volume of rhizodeposit hotspots. This was particularly important in the case of citrate, where overlap of rhizodeposition zones accounted for more than half of the total rhizodeposit hotspot volumes. Coupling a root architecture model with a rhizodeposition model allowed us to get a better understanding of the influence of root architecture as well as rhizodeposit properties on the evolution of the spatio-temporal distribution patterns of rhizodeposits around growing root systems.

Detailed reconstruction of trees from terrestrial laser scans for remote sensing and radiative transfer modelling applications

This study presents a method for three-dimensional (3D) reconstruction of forest tree species that are, for instance, required for simulations of 3D canopies in radiative transfer modelling. We selected three forest species of different architecture: Norway spruce (Picea abies) and European beech (Fagus sylvatica), representatives of European production forests, and white peppermint (Eucalyptus pulchella), a common forest species of Tasmania. Each species has a specific crown structure and foliage distribution. Our algorithm for 3D model construction of a single tree is based on terrestrial laser scanning (TLS) and ancillary field measurements of leaf angle distribution, percentage of current-year and older leaves, and other parameters that could not be derived from TLS data. The algorithm comprises four main steps: i) segmentation of a TLS tree point cloud separating wooden parts from foliage, ii) reconstruction of wooden parts (trunks and branches) from TLS data, iii) biologically genuine distribution of foliage within the tree crown, and iv) separation of foliage into two age categories (for spruce trees only). The reconstructed 3D models of the tree species were used to build virtual forest scenes in the DART model and to simulate canopy optical signals, specifically: angularly anisotropic top-of-canopy reflectance (for retrieval of leaf biochemical compounds from nadir canopy reflectance signatures captured in airborne imaging spectroscopy data) and solar-induced chlorophyll fluorescence signal (for experimentally unfeasible sensitivity analyses).