Connecting the dots between computational tools to analyse soil-root water relations

Plant water uptake modelling: added value of cross-disciplinary approaches

In recent years, research interest in plant water uptake strategies has rapidly increased in many disciplines, such as hydrology, plant ecology and ecophysiology. Quantitative modelling approaches to estimate plant water uptake and spatiotemporal dynamics have significantly advanced through different disciplines across scales. Despite this progress, major limitations, for example, predicting plant water uptake under drought or drought impact at large scales, remain. These are less attributed to limitations in process understanding, but rather to a lack of implementation of cross-disciplinary insights into plant water uptake model structure. The main goal of this review is to highlight how the four dominant model approaches, that is, Feddes approach, hydrodynamic approach, optimality and statistical approaches, can be and have been used to create interdisciplinary hybrid models enabling a holistic system understanding that, among other things, embeds plant water uptake plasticity into a broader conceptual view of soil-plant feedbacks of water, nutrient and carbon cycling, or reflects observed drought responses of plant-soil feedbacks and their dynamics under, that is, drought. Specifically, we provide examples of how integration of Bayesian and hydrodynamic approaches might overcome challenges in interpreting plant water uptake related to different travel and residence times of different plant water sources or trade-offs between root system optimization to forage for water and nutrients during different seasons and phenological stages.

Root water uptake depth determines the hydraulic vulnerability of temperate European tree species during the extreme 2018 drought

We took advantage of the European 2018 drought and assessed the mechanisms causing differences in drought vulnerability among mature individuals of nine co-occurring tree species at the Swiss Canopy Crane II site in Switzerland. Throughout the drought we monitored leaf water status and determined native embolism formation in the canopy of the trees as indicators of drought vulnerability. We also determined hydraulic vulnerability thresholds (Ψ₁₂ -, Ψ₅₀ - and Ψ₈₈ -values), corresponding hydraulic safety margins (HSMs) and carbohydrate reserves for all species as well as total average leaf area per tree, and used stable isotopes to assess differences in root water uptake depth among the nine species as variables predicting differences in drought vulnerability among species. Marked differences in drought vulnerability were observed among the nine tree species. Six species maintained their water potentials above hydraulic thresholds, while three species, Fagus sylvatica, Carpinus betulus and Picea abies, were pushed beyond their hydraulic thresholds and showed loss of hydraulic conductivity in their canopies at the end of the drought. Embolism resistance thresholds and associated HSMs did not explain why the co-existing species differed in their drought vulnerability, neither did their degree of isohydry, nor their regulation of carbohydrate reserves. Instead, differences in structural-morphological traits, in particular root water uptake depth, were associated with the risk of reaching hydraulic vulnerability thresholds and embolism formation among the nine species. Our study shows that structural-morphological traits, such as root water uptake depth, determine how quickly different species approach hydraulic vulnerability thresholds during a drought event and can thus explain species differences in drought vulnerability among mature field-grown trees.

Forest system hydraulic conductance: partitioning tree and soil components

Soil-leaf hydraulic conductance determines canopy-atmosphere coupling in vegetation models, but it is typically derived from ex-situ measurements of stem segments and soil samples. Using a novel approach, we derive robust in-situ estimates for whole-tree conductance (k_tree ), 'functional' soil conductance (k_soil ), and 'system' conductance (k_system , water table to canopy), at two climatically different tropical rainforest sites. Hydraulic 'functional rooting depth', determined for each tree using profiles of soil water potential (Ψ_soil ) and sap flux data, enabled a robust determination of k_tree and k_soil . k_tree was compared across species, size classes, seasons, height above nearest drainage (HAND), two field sites, and to alternative representations of k_tree ; k_soil was analysed with respect to variations in site, season and HAND. k_tree was lower and changed seasonally at the site with higher vapour pressure deficit (VPD) and rainfall; k_tree differed little across species but scaled with tree circumference; r_soil (1/k_soil ) ranged from 0 in the wet season to 10× less than r_tree (1/k_tree ) in the dry season. VPD and not rainfall may influence plot-level k; leaf water potentials and sap flux can be used to determine k_tree , k_soil and k_system ; Ψ_soil profiles can provide mechanistic insights into ecosystem-level water fluxes.

How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach

This article presents a qualitative mathematical model to simulate the relationship between supplied water and plant growth. A novel aspect of the construction of this phenomenological model is the consideration of a structure of three phases: (1) The soil water availability, (2) the available water inside the plant for its growth, and (3) the plant size or amount of dry matter. From these phases and their interactions, a model based on a three-dimensional nonlinear dynamic system was proposed. The results obtained showed the existence of a single equilibrium point, global and exponentially stable. Additionally, considering the framework of the perturbation theory, this model was perturbed by incorporating irrigation to the available soil water, obtaining some stability results under different assumptions. Later through the control theory, it was demonstrated that the proposed system was controllable. Finally, a numerical simulation of the proposed model was carried out, to depict the soil water content and plant growth dynamic and its agreement with the results of the mathematical analysis. In addition, a specific calibration for field data from an experiment with wheat was considered, and these parameters were then used to test the proposed model, obtaining an error of about 6% in the soil water content estimation.

Combining cross-section images and modeling tools to create high-resolution root system hydraulic atlases in Zea mays

Root hydraulic properties play a central role in the global water cycle, in agricultural systems productivity, and in ecosystem survival as they impact the canopy water supply. However, the existing experimental methods to quantify root hydraulic conductivities, such as the root pressure probing, are particularly challenging, and their applicability to thin roots and small root segments is limited. Therefore, there is a gap in methods enabling easy estimations of root hydraulic conductivities in diverse root types. Here, we present a new pipeline to quickly estimate root hydraulic conductivities across different root types, at high resolution along root axes. Shortly, free-hand root cross-sections were used to extract a selected number of key anatomical traits. We used these traits to parametrize the Generator of Root Anatomy in R (GRANAR) model to simulate root anatomical networks. Finally, we used these generated anatomical networks within the Model of Explicit Cross-section Hydraulic Anatomy (MECHA) to compute an estimation of the root axial and radial hydraulic conductivities (k x and k r , respectively). Using this combination of anatomical data and computational models, we were able to create a root hydraulic conductivity atlas at the root system level, for 14-day-old pot-grown Zea mays (maize) plants of the var. B73. The altas highlights the significant functional variations along and between different root types. For instance, predicted variations of radial conductivity along the root axis were strongly dependent on the maturation stage of hydrophobic barriers. The same was also true for the maturation rates of the metaxylem vessels. Differences in anatomical traits along and across root types generated substantial variations in radial and axial conductivities estimated with our novel approach. Our methodological pipeline combines anatomical data and computational models to turn root cross-section images into a detailed hydraulic atlas. It is an inexpensive, fast, and easily applicable investigation tool for root hydraulics that complements existing complex experimental methods. It opens the way to high-throughput studies on the functional importance of root types in plant hydraulics, especially if combined with novel phenotyping techniques such as laser ablation tomography.

Overcoming the Challenges to Enhancing Experimental Plant Biology With Computational Modeling

The study of complex biological systems necessitates computational modeling approaches that are currently underutilized in plant biology. Many plant biologists have trouble identifying or adopting modeling methods to their research, particularly mechanistic mathematical modeling. Here we address challenges that limit the use of computational modeling methods, particularly mechanistic mathematical modeling. We divide computational modeling techniques into either pattern models (e.g., bioinformatics, machine learning, or morphology) or mechanistic mathematical models (e.g., biochemical reactions, biophysics, or population models), which both contribute to plant biology research at different scales to answer different research questions. We present arguments and recommendations for the increased adoption of modeling by plant biologists interested in incorporating more modeling into their research programs. As some researchers find math and quantitative methods to be an obstacle to modeling, we provide suggestions for easy-to-use tools for non-specialists and for collaboration with specialists. This may especially be the case for mechanistic mathematical modeling, and we spend some extra time discussing this. Through a more thorough appreciation and awareness of the power of different kinds of modeling in plant biology, we hope to facilitate interdisciplinary, transformative research.

Multiscale computational models can guide experimentation and targeted measurements for crop improvement

Computational models of plants have identified gaps in our understanding of biological systems, and have revealed ways to optimize cellular processes or organ-level architecture to increase productivity. Thus, computational models are learning tools that help direct experimentation and measurements. Models are simplifications of complex systems, and often simulate specific processes at single scales (e.g. temporal, spatial, organizational, etc.). Consequently, single-scale models are unable to capture the critical cross-scale interactions that result in emergent properties of the system. In this perspective article, we contend that to accurately predict how a plant will respond in an untested environment, it is necessary to integrate mathematical models across biological scales. Computationally mimicking the flow of biological information from the genome to the phenome is an important step in discovering new experimental strategies to improve crops. A key challenge is to connect models across biological, temporal and computational (e.g. CPU versus GPU) scales, and then to visualize and interpret integrated model outputs. We address this challenge by describing the efforts of the international Crops in silico consortium.

Call for Participation: Collaborative Benchmarking of Functional-Structural Root Architecture Models. The Case of Root Water Uptake

Three-dimensional models of root growth, architecture and function are becoming important tools that aid the design of agricultural management schemes and the selection of beneficial root traits. However, while benchmarking is common in many disciplines that use numerical models, such as natural and engineering sciences, functional-structural root architecture models have never been systematically compared. The following reasons might induce disagreement between the simulation results of different models: different representation of root growth, sink term of root water and solute uptake and representation of the rhizosphere. Presently, the extent of discrepancies is unknown, and a framework for quantitatively comparing functional-structural root architecture models is required. We propose, in a first step, to define benchmarking scenarios that test individual components of complex models: root architecture, water flow in soil and water flow in roots. While the latter two will focus mainly on comparing numerical aspects, the root architectural models have to be compared at a conceptual level as they generally differ in process representation. Therefore, defining common inputs that allow recreating reference root systems in all models will be a key challenge. In a second step, benchmarking scenarios for the coupled problems are defined. We expect that the results of step 1 will enable us to better interpret differences found in step 2. This benchmarking will result in a better understanding of the different models and contribute toward improving them. Improved models will allow us to simulate various scenarios with greater confidence and avoid bugs, numerical errors or conceptual misunderstandings. This work will set a standard for future model development.

Declining root water transport drives stomatal closure in olive under moderate water stress

Efficient water transport from soil to leaves sustains stomatal opening and steady-state photosynthesis. The aboveground portion of this pathway is well-described, yet the roots and their connection with the soil are still poorly understood due to technical limitations. Here we used a novel rehydration technique to investigate changes in the hydraulic pathway between roots and soil and within the plant body as individual olive plants were subjected to a range of water stresses. Whole root hydraulic resistance (including the radial pathway from xylem to the soil-root interface) constituted 81% of the whole-plant resistance in unstressed plants, increasing to > 95% under a moderate level of water stress. The decline in this whole root hydraulic conductance occurred in parallel with stomatal closure and contributed significantly to the reduction in canopy conductance according to a hydraulic model. Our results demonstrate that losses in root hydraulic conductance, mainly due to a disconnection from the soil during moderate water stress in olive plants, are profound and sufficient to induce stomatal closure before cavitation occurs. Future studies will determine whether this core regulatory role of root hydraulics exists more generally among diverse plant species.

Functional-structural root-system model validation using a soil MRI experiment

For the first time, a functional-structural root-system model is validated by combining a tracer experiment monitored with magnetic resonance imaging and three-dimensional modeling of water and solute transport.