T Sphere Box
2.2. Classification of Modelling Approaches
Based on individual backgrounds, preferences, and interests of the scientists and their teams several plant modelling ‘schools’ can be identified. The technical developments and new fields of research had also a huge impact on the development of new methods during the past decades.
The classification of plant modelling approaches can be done according to different criteria depending on, e.g., the focus on the method used to obtain or describe the structure (formalism / formal language used), or the research background.
2.2.1. The Triangle of Plant Models
According to the triangle of plant models, a systematisation of modelling approaches by Kurth (1994b), plant models can be classified into three main classes: aggregated models, morpholog-ical models, and process models. FSPMcombine morphology with physiology and therefore form their own class located between structural and functional models at the hierarchical level of the plant individual.
Another common classification distinguishes modelling approaches depending on the methods, aims, and processes employed. The three main classes are referred to asgeometrical models (GM)(Sec.2.2.1.1), process-based models (PBM)(Sec.2.2.1.2), andfunctional-structural plant models (FSPM)(Sec.2.2.1.3).
SinceGMs can be referred to as morphological models and PBMsare process models, both classifications can be combined to an extended triangle of plant models (Fig.2.33).
2.2.1.1. Geometrical Modelling
Geometrical models (GM), also known as morphological or structural models, are only con-cerned with the pure 3-d representation of plants and their development. Plant development is often defined by L-systems (cf. Sec.2.1.5.2) orturtle geometryin the static case. The main focus lies on the visual output of the model. While the overall plant size may be increased by rule application, the organ sizes are fixed and typically based on empirical observations on real plants. The same applies to morphological data like branching angles or phyllotaxy.
Structure
morphological models Function
process models Statistics
aggregated models
Kurth (1999) de Reffyeet al.(2008)
individual
scale
canopy
FSPM
GM PBM
Figure 2.33.: Extended model triangle of plant models based on Kurth (1994b). FSPMscan be located at the level of the plant individual, halfway between structural models and process oriented models.
Specialised tools, like the Xfrog (Deussen and Strothotte (2000), Sec.A.17) software, have been developed, that are able to produce nice 3-d mockups widely used in computer animated films, landscape planning, and games.
2.2.1.2. Process-Based Modelling
Process-based models (PBM)or process-based crop models are models based on primary pro-duction of biomass and centred around a generic implementation of photosynthesis. The major-ity of process-based crop models are designed to predict yield from the simulation of biomass production on a per-square-meter basis, under field or greenhouse conditions. They simu-late plant functioning according to endogenous plant properties and environmental conditions without any 3-d representation or spatial information (Fig.2.34). Plants are considered only at
a simplistic level of organ compartments typically leaf, stem, fruit, and root compartment -which renders fitting of models easy but poses at the same time a potential source for errors, since a very large number of plant architectures could correspond to a plant fitted with aPBM (de Reffyeet al. 2008). The calculation of photosynthesis is a typical case for such simplified models, which are purely concentrating on function, at the expense of structure. E.g., the ‘big leaf’ model (Thornleyet al.1992) represents the leaves of the whole canopy as one single (big) leaf.
Figure 2.34.: Organ source and sink principle inprocess-based models (PBM)and functional-structural plant models (FSPM). The organ compartments are usually limited to organ types inPBM, competing for a common biomass pool, while inFSPM, each organ is individualised.
The assimilates produced by local sources are transported in the direction of sinks according to their sink strength. (Drawing: de Reffye, CIRAD,http://greenlab.cirad.fr/GLUVED/
html/P1_Prelim/Model/Model_FSPM_001.html)
Most crop growth models have been based on a selection of general, primary processes de-scribing (process-based) the mechanisms of primary production. A typical flowchart of aPBM for plant modelling is given in Fig.2.35. They have been developed to enhance understanding
of the basic processes of crop growth and development. Generally, in these models factors determining potential, attainable and actual crop growth are distinguished, allowing the use of these models for a variety of crop species, given the availability of a standard set of crop parameters.
Radiation Temperature CO2 LAI
Module for biomass production
Common pool
Module for biomass partitioning
Roots Stems Fruits Leaves
Figure 2.35.: Simplified workflow of aPBMfor plant modelling. The ‘Module for biomass pro-duction’ covers processes like light interception, photosynthesis and respiration.
A number of the drawbacks ofPBMshave their origin in the total neglect or oversimplifica-tion of 3-d plant architecture and its plasticity, such as the interacoversimplifica-tions between growth and development. E.g., an accurate calculation of light interception is a very important input fac-tor for realistic plant modelling. Further simplifications are, e.g., the missing direct interaction between sources and sinks, the common pool of biomass, and the computation of both biomass production (dry matter) and biomass partitioning by single equations/models.
The leading school ofPBMwas founded in Wageningen UR and dates back to 1958, when de Wit implemented first crop models for agriculture, modelling linkage between transpiration and growth (de Wit1958). A first model for simulating photosynthesis in plant communities
was introduced by Duncanet al.(1967). Joneset al.(1974) introduced a first nitrogen balance for a cotton growth model.
Crop modelling is based on the assumption that the only ingredients necessary for yield pre-diction are organ number, biomass production and its partitioning among organs. Some of the successors of the school of ‘de Wit’ at Wageningen UR have acknowledged the importance of 3-d structure and FSPMforPBM, which is reflected in an increasing number of publications (Fourcaudet al.2008; Voset al.2010,2007).
2.2.1.3. Functional-Structural Plant Modelling
‘FSPM, refers to a paradigm for the description of a plant by creating a (usually object-oriented) computer model of its structure and selected physiological and physical processes, at differ-ent hierarchical levels: organ, plant individual, canopy (a stand of plants), and in which the processes are modulated by the local environment. Structure comprises the explicit topology (connection between organs) and geometry (orientation, inclination, and shape) of the organs and the plant. At the individual level, this is also referred to as plant architecture…’
Buck-Sorlin (2013)
FSPMs are integrated models as they combine plant function with structure. They are typ-ically organised in a modular way, where plant structure is described regarding basic units, e.g., organs,compartments,growth units, ormetamers. The models are often object-oriented, i.e. each plant organ is mapped/linked to a specific organ class in the model. Processes like transport take place between instances of these organ classes that are distributed in 3-d, while other processes like transpiration or photosynthesis take place only locally, e.g., in the leaf organs. A set of rules is used to describe the morphological development, with submodels for metabolic processes driving plant growth. Usually, the actual 3-d shape is directly linked to this organ class for rapid visualisation. Modern modelling languages like L-Py (Sec.A.13.1) or XL(Sec.A.9.1) support such mechanisms directly.
FSPMsare highly interdisciplinary and involve a wide range of disciplines of the natural sci-ences, including botany, plant physiology, plant anatomy, plant morphology, mathematics, computer science, cellular biology, ecophysiology, ecology and agronomy.
2.2.2. Research Background
The origins and influences of plant modelling are quite diverse. Researchers with various sci-entific backgrounds and objectives developed their approaches and provided input to the topic.
Figure2.36illustrates the main sources and influencing factors for plant modelling classified by the predominating research backgrounds.
Pillars of plant modelling
(classified according to scientific areas of origin)
French school Theoretical biology Theoretical
computer science Computer graphics Other
architectural meristem-oriented
rule-based L-systems
procedural fractals
IFS cellular automata
image-based CSG
forestry entomology bio-climatology
Figure 2.36.: Pillars of plant modelling classified by research background (non exhaustive).
2.2.2.1. French School
The so-called French school is mainly based on the work by Francis Hallé, a botanist who was professor of Botany at Montpellier university. Hallé investigated the diversity of crown ar-chitectures of tropical trees in the rainforest (Hallé1971; Hallé and Oldeman1970). In Hallé et al.(1978), he identified 23 different architectural patterns (Fig.2.37). With his work, Hallé established a new scientific discipline of architectural studies in trees to provide tools for ‘tax-onomists, valuable for diagnosis, and sometimes more successful than floral characters for species identification in the tropical trees’ (Hallé1974).
In the late 1980s, de Reffye established the AMAP (Sec. A.2) workgroup at the Centre de coopération internationale en recherche agronomique pour le développement (CIRAD), Mont-pellier. His approach uses the meristem, a tissue that contains stem cells that produce new tissue within a bud, as only growth region within his model. Based on this and other botanical
Figure 2.37.: 23 architectural tree patterns after Halléet al.(1978) (modified).
laws, de Reffyeet al.(1988) introduced a mathematical model which explains plant growth and architecture.
Shebell (1986) showed that principally all 23 tree architectures of Hallé could be simulated with L-systems. Prusinkiewicz and Remphrey (2000) propose a symbolic notation inspired by L-systems and a graphical representation based on Petri nets to formally describe architectural tree models introduced by Hallé and Oldeman.
2.2.2.2. Theoretical Computer Science
Most of the formalism used in FSPMsare based on mathematical concepts and formal lan-guages originally developed by mathematicians and computer scientists. The probably best-known formalism used for plant modelling are Lindenmayer-systems (or short L-systems). It is a formal language, developed 1968 by Aristid Lindenmayer at Utrecht University. Cellu-lar automataanditerated function systemsare further formalisms that have their origins in theoretical computer science.
2.2.2.3. Theoretical Biology
During his time as head of the Theoretical Biology Group at the Utrecht University, Linden-mayer investigated cell division in general. He studied growth patterns of various types of algae, yeast and filamentous fungi. Today, L-systems are widely used in many disciplines but mainly in plant modelling. A comprehensive overview is given in the de-facto standard book of plant modelling: ‘The Algorithmic Beauty of Plants’ by Prusinkiewicz and Lindenmayer (1990).
2.2.2.4. Computer Graphics
Since their beginnings in the early 1970s, the emphasis in the creation of computer-generated plants and trees in computer graphics was always put on the rapid and comfortable generation of plants, or more precisely on the production of images, than on biological accuracy. While first approaches were simple 2-d models, it did not take long before the first 3-d models were published, e.g., ‘virtual plants’ by Room et al. (1996). CAD programs used CSGtechniques and boundary representation to generate plant-like structures. Later, specialised software, like Xfrog (Deussen and Strothotte (2000) and Greenworks (2017), Sec.A.17) was developed as plu-gins for leading 3-d computer graphics software.
Today’s driving force in this area are the computer gaming industry and animation studios working for the movie industry. Both have a huge demand for computer-generated plants and virtual reality and are always interested in the latest developments.
2.2.2.5. Others
Researchers from other scientific areas also designed plant models based on different concepts and ideas.
Forest ecologists and foresters used yield tables for more than 100 years to estimate growth for several forest tree species. Based on this huge data base, several forest simulations have been
developed. Based on single-tree models complex forest simulators are developed. BWINPro1 (Nagelet al.2006) and SILVA2(Pretzsch2001) are two examples of current forest simulators.
Tree physicists investigated several aspects of tree morphology concerning mechanical prop-erties like effects of wind exposure. In hydraulic models water and nutrient transport was modelled to investigate, e.g., the effects of water-stress (Fishman and Génard1998).
Remote sensing is another area that had influence on plant modelling. Applications worth mentioning here are landscape planning through modelling and visualisation (Disney et al.
2006). Iovanet al.(2014) used remote sensing data to analyse and reconstruct urban vegetation using architectural tree models combined with model inputs estimated from aerial image anal-ysis. Côtéet al.(2009) used terrestriallight detection and ranging (LiDAR)data to reconstruct 3-d tree architectures, a method that promises to be robust and relatively insensitive to wind-and occlusion-induced artefacts.
2.2.3. Structure- and Space-Oriented Models
Other criteria for the classification of plant modelling approaches, apart from the scientific background and motivation of its protagonists, can be applied: Prusinkiewicz (1993) divided developmental biology models into structure- and space-oriented models (Fig.2.38). Structure-oriented models use components, e.g., plant organs, to constitute the structure and describe the development. Structure-oriented models are, therefore, mainly based on endogenous mecha-nisms to control the structure by internal growth and elongation. In contrast to structure-oriented models, space-structure-oriented models emphasise exogenous control. Space-structure-oriented models usually allow growth only on the system boundaries while they capture influences of the entire environment of a growing plant.
2.2.4. Procedural and Rule-Based Modelling
The difference between procedural and rule-based modelling is more fundamental (Fig.2.39).
Procedural models are parameterised algorithms that are usually designed for the simulation
1https://www.nw-fva.de/index.php?id=475
2http://www.wwk.forst.tu-muenchen.de/research/methods/modelling/silva
Modelling concept
Space-oriented Structure-oriented
Reaction-diffusion models
Cellular automata Voxel automata Particle systems L-systems
Map L-systems Procedural models
Figure 2.38.: Classification of modelling approaches into space- and structure-oriented models according to Prusinkiewicz (1993) and Prusinkiewiczet al.(1994) (non exhaustive).
of a plant type or a single species, respectively. They can be regarded as classical simulation programs, see Fig.2.40. Rule-based modelling approaches, on the other hand, are using a formal system to define the model in terms of rules that are applied to an initial state until a complex final state is reached. These sets of rules can be seen as program that is being executed by the formal system.
While procedural modelling is usually more intuitive, the rule-based approach is more flexible and powerful. The combination of both approaches lead to the so-called rule-based object production, which was implemented in the Xfrog modelling system (Deussen and Lintermann 1997; Lintermann and Deussen1999).
Modelling concept
Procedural Rule-based
Meristem-oriented Space colonisation
Fractal tree models Particle systems
L-systems
Iterated function system
Constructive solid geometry
Cellular automaton
Figure 2.39.: Classification of modelling approaches into procedural and rule-based models (non exhaustive).