Wind loads and competition for light sculpt trees into self-similar structures

Plant science in the age of simulation intelligence

Historically, plant and crop sciences have been quantitative fields that intensively use measurements and modeling. Traditionally, researchers choose between two dominant modeling approaches: mechanistic plant growth models or data-driven, statistical methodologies. At the intersection of both paradigms, a novel approach referred to as "simulation intelligence", has emerged as a powerful tool for comprehending and controlling complex systems, including plants and crops. This work explores the transformative potential for the plant science community of the nine simulation intelligence motifs, from understanding molecular plant processes to optimizing greenhouse control. Many of these concepts, such as surrogate models and agent-based modeling, have gained prominence in plant and crop sciences. In contrast, some motifs, such as open-ended optimization or program synthesis, still need to be explored further. The motifs of simulation intelligence can potentially revolutionize breeding and precision farming towards more sustainable food production.

Engineering Themes in Plant Forms and Functions

Living structures constantly interact with the biotic and abiotic environment by sensing and responding via specialized functional parts. In other words, biological bodies embody highly functional machines and actuators. What are the signatures of engineering mechanisms in biology? In this review, we connect the dots in the literature to seek engineering principles in plant structures. We identify three thematic motifs-bilayer actuator, slender-bodied functional surface, and self-similarity-and provide an overview of their structure-function relationships. Unlike human-engineered machines and actuators, biological counterparts may appear suboptimal in design, loosely complying with physical theories or engineering principles. We postulate what factors may influence the evolution of functional morphology and anatomy to dissect and comprehend better the why behind the biological forms.

Crown feature effect evaluation on wind load for evergreen species based on laser scanning and wind tunnel experiments

The wind load a tree withstood is mainly applied to its crown, whose morphology and structure directly affect the degree of wind load given a certain wind condition. Though the features of tree crown are relatively easy to measure, however, among them which is/are the determining factor and how they contribute to wind load remain unknown. In order to figure out how crown features of different tree species influence the wind load, the wind tunnel experiment was performed for 7 most used urban greening tree species, and laser scanning was used to measure the accurate crown features. The results derived by multiple linear model showed (1) Ficus concinna, Dracontomelon duperreanum, Ormosia pinnata and Bischofia javanica are recommended in urban greening for suffering the smaller wind load under the same conditions, whereas Schefflera macrostachya, Acacia confusa and Khaya senegalensis are inadequate towards the view of crown features; (2) crown features like crown horizontal ratio, windward side projection and porosity ratio are important in estimating wind load. Our study demonstrated that evaluating the wind load via crown features is feasible, and provided valuable suggestion for selecting idealized decorative trees in urban environment with a smaller wind load due to the crown features.

Stronger wind, smaller tree: Testing tree growth plasticity through a modeling approach

Plants exhibit plasticity in response to various external conditions, characterized by changes in physiological and morphological features. Although being non-negligible, compared to the other environmental factors, the effect of wind on plant growth is less extensively studied, either experimentally or computationally. This study aims to propose a modeling approach that can simulate the impact of wind on plant growth, which brings a biomechanical feedback to growth and biomass distribution into a functional-structural plant model (FSPM). Tree reaction to the wind is simulated based on the hypothesis that plants tend to fit in the environment best. This is interpreted as an optimization problem of finding the best growth-regulation sink parameter giving the maximal plant fitness (usually seed weight, but expressed as plant biomass and size). To test this hypothesis in silico, a functional-structural plant model, which simulates both the primary and secondary growth of stems, is coupled with a biomechanical model which computes forces, moments of forces, and breakage location in stems caused by both wind and self-weight increment during plant growth. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is adopted to maximize the multi-objective function (stem biomass and tree height) by determining the key parameter value controlling the biomass allocation to the secondary growth. The digital trees show considerable phenotypic plasticity under different wind speeds, whose behavior, as an emergent property, is in accordance with experimental results from works of literature: the height and leaf area of individual trees decreased with wind speed, and the diameter at the breast height (DBH) increased at low-speed wind but declined at higher-speed wind. Stronger wind results in a smaller tree. Such response of trees to the wind is realistically simulated, giving a deeper understanding of tree behavior. The result shows that the challenging task of modeling plant plasticity may be solved by optimizing the plant fitness function. Adding a biomechanical model enriches FSPMs and opens a wider application of plant models.

The shaping of plant axes and crowns through tropisms and elasticity: an example of morphogenetic plasticity beyond the shoot apical meristem

Shoot morphogenetic plasticity is crucial to the adaptation of plants to their fluctuating environments. Major insights into shoot morphogenesis have been compiled studying meristems, especially the shoot apical meristem (SAM), through a methodological effort in multiscale systems biology and biophysics. However, morphogenesis at the SAM is robust to environmental changes. Plasticity emerges later on during post-SAM development. The purpose of this review is to show that multiscale systems biology and biophysics is insightful for the shaping of the whole plant as well. More specifically, we review the shaping of axes and crowns through tropisms and elasticity, combining the recent advances in morphogenetic control using physical cues and by genes. We focus mostly on land angiosperms, but with growth habits ranging from small herbs to big trees. We show that generic (universal) morphogenetic processes have been identified, revealing feedforward and feedback effects of global shape on the local morphogenetic process. In parallel, major advances have been made in the analysis of the major genes involved in shaping axes and crowns, revealing conserved genic networks among angiosperms. Then, we show that these two approaches are now starting to converge, revealing exciting perspectives.

3D modeling and reconstruction of plants and trees: A cross-cutting review across computer graphics, vision, and plant phenotyping

This paper reviews the past and current trends of three-dimensional (3D) modeling and reconstruction of plants and trees. These topics have been studied in multiple research fields, including computer vision, graphics, plant phenotyping, and forestry. This paper, therefore, provides a cross-cutting review. Representations of plant shape and structure are first summarized, where every method for plant modeling and reconstruction is based on a shape/structure representation. The methods were then categorized into 1) creating non-existent plants (modeling) and 2) creating models from real-world plants (reconstruction). This paper also discusses the limitations of current methods and possible future directions.

Cancer as a Model System for Testing Metabolic Scaling Theory

Biological allometries, such as the scaling of metabolism to mass, are hypothesized to result from natural selection to maximize how vascular networks fill space yet minimize internal transport distances and resistance to blood flow. Metabolic scaling theory argues two guiding principles—conservation of fluid flow and space-filling fractal distributions—describe a diversity of biological networks and predict how the geometry of these networks influences organismal metabolism. Yet, mostly absent from past efforts are studies that directly, and independently, measure metabolic rate from respiration and vascular architecture for the same organ, organism, or tissue. Lack of these measures may lead to inconsistent results and conclusions about metabolism, growth, and allometric scaling. We present simultaneous and consistent measurements of metabolic scaling exponents from clinical images of lung cancer, serving as a first-of-its-kind test of metabolic scaling theory, and identifying potential quantitative imaging biomarkers indicative of tumor growth. We analyze data for 535 clinical PET-CT scans of patients with non-small cell lung carcinoma to establish the presence of metabolic scaling between tumor metabolism and tumor volume. Furthermore, we use computer vision and mathematical modeling to examine predictions of metabolic scaling based on the branching geometry of the tumor-supplying blood vessel networks in a subset of 56 patients diagnosed with stage II-IV lung cancer. Examination of the scaling of maximum standard uptake value with metabolic tumor volume, and metabolic tumor volume with gross tumor volume, yield metabolic scaling exponents of 0.64 (0.20) and 0.70 (0.17), respectively. We compare these to the value of 0.85 (0.06) derived from the geometric scaling of the tumor-supplying vasculature. These results: (1) inform energetic models of growth and development for tumor forecasting; (2) identify imaging biomarkers in vascular geometry related to blood volume and flow; and (3) highlight unique opportunities to develop and test the metabolic scaling theory of ecology in tumors transitioning from avascular to vascular geometries.

Role of the crown in tree resistance against high winds

Rather than using wooden sticks to simulate the breakage of trees in high winds as in most research, we employ fresh samples from camphor and Formosa gum with branches and leaves to certify the crucial role of the tree crown. By using a blowdown wind tunnel with a maximum wind speed of 50 m/s, we purposely reduce the number of leaves and show that the drag force will drop by as much as two thirds when half pruned. Based on real observations, we model the leaf by an open and full cone in the presence of light and strong winds, and calculate how their corresponding cross-sectional area A and drag force F vary with wind speed v. Different slopes before and after the formation of a full cone are predicted and confirmed when these two quantities are plotted in full-log scale. Compared to the empirical value, our simple model gave α=2/5 and 2/3 for A∝v^{-α} and β=4/5 and 2/3 for F∝v^{β} at low and high winds. Discrepancies can be accounted for by including further details, such as the reorientation of open cones and the movement of branches.

Measuring the Contribution of Leaves to the Structural Complexity of Urban Tree Crowns with Terrestrial Laser Scanning

Trees have a fractal-like branching architecture that determines their structural complexity. We used terrestrial laser scanning technology to study the role of foliage in the structural complexity of urban trees. Forty-five trees of three deciduous species, Gleditsia triacanthos, Quercus macrocarpa, Metasequoia glyptostroboides, were sampled on the Michigan State University campus. We studied their structural complexity by calculating the box-dimension (Db) metric from point clouds generated for the trees using terrestrial laser scanning, during the leaf-on and -off conditions. Furthermore, we artificially defoliated the leaf-on point clouds by applying an algorithm that separates the foliage from the woody material of the trees, and then recalculated the Db metric. The Db of the leaf-on tree point clouds was significantly greater than the Db of the leaf-off point clouds across all species. Additionally, the leaf removal algorithm introduced bias to the estimation of the leaf-removed Db of the G. triacanthos and M. glyptostroboides trees. The index capturing the contribution of leaves to the structural complexity of the study trees (the ratio of the Db of the leaf-on point clouds divided by the Db of the leaf-off point clouds minus one), was negatively correlated with branch surface area and different metrics of the length of paths through the branch network of the trees, indicating that the contribution of leaves decreases as branch network complexity increases. Underestimation of the Db of the G. triacanthos trees, after the artificial leaf removal, was related to maximum branch order. These results enhance our understanding of tree structural complexity by disentangling the contribution of leaves from that of the woody structures. The study also highlighted important methodological considerations for studying tree structure, with and without leaves, from laser-derived point clouds.

Fluctuations shape plants through proprioception

Plants constantly experience fluctuating internal and external mechanical cues, ranging from nanoscale deformation of wall components, cell growth variability, nutating stems, and fluttering leaves to stem flexion under tree weight and wind drag. Developing plants use such fluctuations to monitor and channel their own shape and growth through a form of proprioception. Fluctuations in mechanical cues may also be actively enhanced, producing oscillating behaviors in tissues. For example, proprioception through leaf nastic movements may promote organ flattening. We propose that fluctuation-enhanced proprioception allows plant organs to sense their own shapes and behave like active materials with adaptable outputs to face variable environments, whether internal or external. Because certain shapes are more amenable to fluctuations, proprioception may also help plant shapes to reach self-organized criticality to support such adaptability.

Branching principles of animal and plant networks identified by combining extensive data, machine learning and modelling

Branching in vascular networks and in overall organismic form is one of the most common and ancient features of multicellular plants, fungi and animals. By combining machine-learning techniques with new theory that relates vascular form to metabolic function, we enable novel classification of diverse branching networks—mouse lung, human head and torso, angiosperm and gymnosperm plants. We find that ratios of limb radii—which dictate essential biologic functions related to resource transport and supply—are best at distinguishing branching networks. We also show how variation in vascular and branching geometry persists despite observing a convergent relationship across organisms for how metabolic rate depends on body mass.

What is quantitative plant biology?

Quantitative plant biology is an interdisciplinary field that builds on a long history of biomathematics and biophysics. Today, thanks to high spatiotemporal resolution tools and computational modelling, it sets a new standard in plant science. Acquired data, whether molecular, geometric or mechanical, are quantified, statistically assessed and integrated at multiple scales and across fields. They feed testable predictions that, in turn, guide further experimental tests. Quantitative features such as variability, noise, robustness, delays or feedback loops are included to account for the inner dynamics of plants and their interactions with the environment. Here, we present the main features of this ongoing revolution, through new questions around signalling networks, tissue topology, shape plasticity, biomechanics, bioenergetics, ecology and engineering. In the end, quantitative plant biology allows us to question and better understand our interactions with plants. In turn, this field opens the door to transdisciplinary projects with the society, notably through citizen science.

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.

Tree crowns grow into self-similar shapes controlled by gravity and light sensing

Plants have developed different tropisms: in particular, they reorient the growth of their branches towards the light (phototropism) or upwards (gravitropism). How these tropisms affect the shape of a tree crown remains unanswered. We address this question by developing a propagating front model of tree growth. Being length-free, this model leads to self-similar solutions after a long period of time, which are independent of the initial conditions. Varying the intensities of each tropism, different self-similar shapes emerge, including singular ones. Interestingly, these shapes bear similarities to existing tree species. It is concluded that the core of specific crown shapes in trees relies on the balance between tropisms.

Posture control in land plants: growth, position sensing, proprioception, balance, and elasticity

The colonization of the atmosphere by land plants was a major evolutionary step. The mechanisms that allow for vertical growth through air and the establishment and control of a stable erect habit are just starting to be understood. A key mechanism was found to be continuous posture control to counterbalance the mechanical and developmental challenges of maintaining a growing upright structure. An interdisciplinary systems biology approach was invaluable in understanding the underlying principles and in designing pertinent experiments. Since this discovery previously held views of gravitropic perception had to be reexamined and this has led to the description of proprioception in plants. In this review, we take a purposefully pedagogical approach to present the dynamics involved from the cellular to whole-plant level. We show how the textbook model of how plants sense gravitational force has been replaced by a model of position sensing, a clinometer mechanism that involves both passive avalanches and active motion of statoliths, granular starch-filled plastids, in statocytes. Moreover, there is a transmission of information between statocytes and other specialized cells that sense the degree of organ curvature and reset asymmetric growth to straighten and realign the structure. We give an overview of how plants have used the interplay of active posture control and elastic sagging to generate a whole range of spatial displays during their life cycles. Finally, a position-integrating mechanism has been discovered that prevents directional plant growth from being disrupted by wind-induced oscillations.

Emergence of robust patterns from local rules during plant development

The formation of spatial and temporal patterns is an essential component of organismal development. Patterns can be observed on every level from subcellular to organismal and may emerge from local rules that correspond to the interactions between molecules, cells, or tissues. The emergence of robust patterns may seem in contradiction with the prominent heterogeneity at subcellular and cellular scales, however it has become increasingly clear that heterogeneity can be instrumental for pattern formation. Here we review recent examples in plant development, involving genetic regulation, cell arrangement, growth and signal gradient. We discuss how patterns emerge from local rules, whether heterogeneity is stochastic or can be patterned, and whether stochastic noise is amplified or requires filtering for robust patterns to be achieved. We also stress the importance of modelling in investigating such questions.