Modeling of Branching Patterns in Plants (original) (raw)
Understanding shoot branching by modelling form and function
Trends in Plant Science, 2011
Shoot branching plays a pivotal role in the development of the aboveground plant structure. Therefore, to understand branching in relation to the environment, it is not only necessary to integrate the knowledge on mechanisms that regulate branching at multiple levels of biological organisation, but also to include plant structure explicitly. To this end, we propose the application of an established methodology called functional-structural plant modelling.
Modeling of branching structures of plants
2001
Previous studies of branching structures generally focused on arteries. Four cost models minimizing total surface area, total volume, total drag and total power losses at a junction point have been proposed to study branching structures. In this paper, we highlight the branching structures of plants and examine which model fits data of branching structures of plants the best.
Patterns of external branching link form and function across diverse plants
The West, Brown, Enquist (WBE) model derives symmetrically self-similar branching to predict metabolic scaling from hydraulic conductance, K, (a metabolism proxy) and tree mass (or volume, V). The original prediction was K / V 0:75 . We ask whether trees differ from WBE symmetry and if it matters for plant function and scaling. We measure tree branching and model how architecture influences K, V, mechanical stability, light interception and metabolic scaling.
Computational models of plant development and form
The use of computational techniques increasingly permeates developmental biology, from the acquisition, processing and analysis of experimental data to the construction of models of organisms. Specifically, models help to untangle the non-intuitive relations between local morphogenetic processes and global patterns and forms. We survey the modeling techniques and selected models that are designed to elucidate plant development in mechanistic terms, with an emphasis on: the history of mathematical and computational approaches to developmental plant biology; the key objectives and methodological aspects of model construction; the diverse mathematical and computational methods related to plant modeling; and the essence of two classes of models, which approach plant morphogenesis from the geometric and molecular perspectives. In the geometric domain, we review models of cell division patterns, phyllotaxis, the form and vascular patterns of leaves, and branching patterns. In the molecular-level domain, we focus on the currently most extensively developed theme: the role of auxin in plant morphogenesis. The review is addressed to both biologists and computational modelers.
Theories of Optimization, Form and Function in Branching Architecture in Plants
Functional Ecology, 1995
Detecting suites of variation shaped as triangles and lines and evaluating statistical significance Here we present a statistical test of whether the data resembles a triangle, and whether the data falls on a line. Detection of triangles This requires a criterion for triangularity, and a null model in order to obtain a p-value. We use data from (13) on Darwin's finch body/beak measurements as an example. Criterion for triangularity We sought a criterion that fits the subjective notion that the data occupies a region which is triangular in shape. For this purpose, a reasonable criterion is the ratio of the areas of the convex hull of the data and the minimal triangle that encloses the data. First, we calculated the convex hull of the data (Figure S1A,B) using a standard algorithm (quickhull (22)). Then, we calculated the minimal area triangle that encloses the convex hull (Figure S1C), using the algorithm described in (23). The ratio between the area of the minimal enclosing triangle and the convex hull is a measure of the triangularity of the data. We denote this ratio by 't-ratio'. A t-ratio of one occurs when the convex hull is perfectly shaped as a triangle. The larger the t-ratio, the less the data is arranged in a triangle. In the Darwin's finch example, depicted in Figure S1, the t-ratio is 1.07. Analysis of triangular suites of variation presented in the main text Darwin's finches (Geospiza) Darwin's finches present one of the hallmarks for the study of evolution. The different species occupy niches that differ mostly in diet. Grant et al. (13) used five different measured parameters for multiple individuals in each of the different Darwin's finch species. Parameters measured are: wing length, tarsus length, bill length, bill depth, and bill width. Here we review their results regarding the six species of ground finches (see Table S1 for name abbreviations). Each data point is an average of a certain species in a given island. Data from (13), tables A1-A5. Species name Abbreviation English name Geospiza magnirostris MAG Large ground finch Geospiza fortis FORT Medium ground finch Geospiza fuliginosa FUL Small ground finch Geospiza dificilis DIFF Sharp beaked ground finch Geospiza scandens SCAN Cactus finch Geospiza conirostris CON Large cactus finch
Frontiers in Plant Science
Branching density (or the reciprocal: inter-branch distance) is an important trait which contributes to defining the number of roots in individual plants. The environmental and local variations in inter-branch distance have often been stressed, and simulations models have been put forward to take them into account within the dynamics of root system architecture (RSA). However, little is known about the interspecific and intraplant variations of inter-branch distance. In this paper, we present an analysis which draws on 40 samples of plants belonging to 36 species collected in homogeneous soils, to address how the variations in inter-branch distance are structured within individual plants, and how this structure varies from one species to another. Using measurements of inter-branch distance on various roots of the same species and our knowledge of the branching process, we defined a simple and generic model dedicated to the simulation of the observed variations. This model distinguishes between two sub-processes: i) the longitudinal location of potential branching sites and ii) the effective emergence of lateral roots at these sites. Thus, it represents the variations in distance between the potential sites (with two parameters), and the probability of emergence of a lateral root at each site (one parameter). We show the ability of this model to account for the main variations in inter-branch distances with a limited number of parameters, and we estimated them for the different species. These parameters can be considered as promising traits to characterize-in a comprehensive and simple way-the genetic and environmental variations in the whole branching process at plant level. Based on the results, we make recommendations for carrying out comparable measurements of the branching density in developed plants. Moreover, we suggest the integration of this new model as a module in future RSA simulators, to improve their capacity to account for this important and highly variable characteristic of plant species.
The Search for Geometrical Parameters That Represent the Dynamic Nature of Phyllotaxis in Plants
Symmetry
The shoot apical meristem (SAM) is the main growth centre that produces lateral organs such as leaves in specific and precise symmetrical patterns. The main goal of this commentary is to explore the link between phyllotactic parameters such as the plastochrone ratio (R) as well as Γ (relationship between the size of the SAM and the size of primordia) and growth processes involved in the expression of symmetrical patterns at the level of the SAM. It is also possible to deduce the values of these parameters from measures of the apical area and the radius of the SAM. A comparative analysis of phyllotactic parameters for three species (Begonia scabrida, Euterpe oleracea, and Anagallis arvensis) for which ‘dynamic’ data are available reveals that empirical and theoretical values of R and Γ can differ, indicating that characters defining these parameters are subject to developmental constraints that in turn determine the boundary conditions for the dynamic manifestation of phyllotactic pa...
Multiple pathways regulate shoot branching
Frontiers in Plant Science, 2015
Shoot branching patterns result from the spatio-temporal regulation of axillary bud outgrowth. Numerous endogenous, developmental and environmental factors are integrated at the bud and plant levels to determine numbers of growing shoots. Multiple pathways that converge to common integrators are most probably involved. We propose several pathways involving not only the classical hormones auxin, cytokinins and strigolactones, but also other signals with a strong influence on shoot branching such as gibberellins, sugars or molecular actors of plant phase transition. We also deal with recent findings about the molecular mechanisms and the pathway involved in the response to shade as an example of an environmental signal controlling branching. We propose the TEOSINTE BRANCHED1, CYCLOIDEA, PCF transcription factor TB1/BRC1 and the polar auxin transport stream in the stem as possible integrators of these pathways. We finally discuss how modeling can help to represent this highly dynamic system by articulating knowledges and hypothesis and calculating the phenotype properties they imply.
A Linear Model to Describe Branching and Allometry in Root Architecture
Plants, 2019
Root architecture is a complex structure that comprises multiple traits of the root phenotype. Novel platforms and models have been developed to better understand root architecture. In this methods paper, we introduce a novel allometric model, named rhizochron index (m), which describes lateral root (LR) branching and elongation patterns across the primary root (PR). To test our model, we obtained data from 16 natural accessions of Arabidopsis thaliana at three stages of early root development to measure conventional traits of root architecture (e.g., PR and LR length), and extracted the rhizochron index (m). In addition, we tested previously published datasets to assess the utility of the rhizochron index (m) to distinguish mutants and environmental effects on root architecture. Our results indicate that rhizochron index (m) is useful to distinguish the natural variations of root architecture between A. thaliana accessions, but not across early stages of root development. Correlati...
Modelling Branching Patterns on 1-year-old Trunks of Six Apple Cultivars
Annals of Botany, 2002
The structure resulting from branching on 1-year-old apple tree trunks was analysed in a set of apple cultivars with diverse branching and fruiting habits. Four different lateral types borne on successive nodes were observed when vegetative and¯owering fates, as well as sylleptic and proleptic branching, were taken into account. The location and grouping of lateral types along the trunk were analysed for all cultivars, but are detailed for one cultivar only. This cultivar showed a succession of zones, each zone being characterized by its composition of lateral types. Statistical modelsÐhidden semi-Markov chainsÐwere built to take this structure into account and to characterize the cultivar's speci®c branching pattern. The models showed that most of the branching zones had a similar location in the different cultivars, even though zone composition and zone length differed among cultivars. On a more detailed scale, the nodes bearing a lateral, regardless of its type, were frequently followed by latent buds. The validity of the models and their biological interpretation are discussed with respect to parent shoot dynamics, hormonal gradients and competition between neighbouring buds.
A New Model for the Structure of Leaves
Journal of Software, 2011
This paper proposes a new model for the shapes and details of simple and compound leaves in plants. The layout of leaf is modeled via branching structure generated using B-Splines. The proposed model controls the relationships that govern the shape through the marginal and venation of the considered simple leaf or leaflet. The developed algorithm starts by taking four points that represent the out boundary of a simple leaf or a leaflet of compound one. Then, the algorithm optimizes the value of these parameters in order to get the best representation of the considered leaf/leaflet. The proposed model is tested with acceptable results for various shapes of leaf and compound leaves.
Proceedings of the Fifteenth International Conference on Industrial & Engineering Application of Artificial Intelligence & Expert Systems, 2002
L-systems are widely used in the modelling of branching structures and the growth of biological objects such as plants, nerves and the airways in lungs. The derivation of such L-system models involves a lot of ha rd mental work and time-consuming manual procedures. A method based on genetic algorithms for automating the derivation of L -systems is presented here. The method involves representation of branching structure, translation of Lsystems to axial tree architectures, comparison of branching structure and the application of genetic algorithms. Branching structures are represented as axial trees and positional information is considered as an important attribute along with length and angle in the database configuration of branches. An algorithm is proposed for automatic L -system translation, in order to compare randomly generated branching structures with the target one. Edit distance, which is proposed for giving a measure of dissimilarity between rooted trees, is extended for the comparison of structures represented in axial trees and positional information is involved in the local cost function. Conventional genetic algorithms and repair mechanics are employed in the search for L -system models having the best fit to observational data.
Plant science modeling branching in cereals
2013
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.
Modeling Plant Growth and Development
Computational plant models or 'virtual plants' are increasingly seen as a useful tool for comprehending complex relationships between gene function, plant physiology, plant development, and the resulting plant form. The theory of L-systems, which was introduced by Lindemayer in 1968, has led to a wellestablished methodology for simulating the branching architecture of plants. Many current architectural models provide insights into the mechanisms of plant development by incorporating physiological processes, such as the transport and allocation of carbon. Other models aim at elucidating the geometry of plant organs, including flower petals and apical meristems, and are beginning to address the relationship between patterns of gene expression and the resulting plant form.
A model for leaf initiation: Determination of phyllotaxis by waves in the generative circle
Plant Signaling & Behavior, 2011
King et al. 8 and Newell et al. 9,10 The regular geometric order of these phyllotaxic patterns led to the major pattern classifications of a spiral, with distichous a special case, and a whorl, with decussate a special case. The generative spiral patterns of leaves wind along the stem with one leaf on each level. The distichous pattern has a single leaf at each level along the plant stem where the leaves rotate 180 degrees at the successive levels. The higher order spiral patterns have a fixed divergence (azimuthal) angle between successive leaves. When the spiral patterns are projected onto a plane perpendicular to the stem, a spiral pattern is seen on that plane also. In addition there are parastichy-associated spiral patterns on the projected plane with right and left twists. Many generative and parastichy spiral patterns can be identified with the Fibonacci series of numbers, 11 although not uncommon are other series such as the Lucas series which is actually a member of the general Fibonacci series. The fixed divergence (azimuthal) angle between successive emerging leaves gives a periodicity. There is in addition the repeat periodicity of the pattern along the stem. The whorl patterns have a number of leaves on each level evenly spaced with respect to angle. The decussate pattern of whorls has two leaves at each level with the leaves rotated 90 degrees at successive levels. The whorl patterns rotate at half the angle between the adjoining leaves at the next level.
Ecology Letters, 2013
Several theories predict whole-tree function on the basis of allometric scaling relationships assumed to emerge from traits of branching networks. To test this key assumption, and more generally, to explore patterns of external architecture within and across trees, we measure branch traits (radii/lengths) and calculate scaling exponents from five functionally divergent species. Consistent with leading theories, including metabolic scaling theory, branching is area preserving and statistically self-similar within trees. However, differences among scaling exponents calculated at node-and whole-tree levels challenge the assumption of an optimised, symmetrically branching tree. Furthermore, scaling exponents estimated for branch length change across branching orders, and exponents for scaling metabolic rate with plant size (or number of terminal tips) significantly differ from theoretical predictions. These findings, along with variability in the scaling of branch radii being less than for branch lengths, suggest extending current scaling theories to include asymmetrical branching and differential selective pressures in plant architectures.