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Functional structural plant models - case LIGNUM Risto Sievänen Finnish Forest Research Institute 01301 Vantaa, Finland [email protected] Jari Perttunen Finnish Forest Research Institute 01301 Vantaa, Finland [email protected] Eero Nikinmaa Department of Forest Ecology University of Helsinki 00014 University of Helsinki, Finland [email protected] Juan M. Posada Programa de Biologia Facultad de Ciencias Naturales y Matemáticas Universidad del Rosario, Bogotá, Colombia juan [email protected] Abstract The functional structural plant models (FSPMs) can be defined as models that combine descriptions of metabolic (physiological) processes with a presentation of the 3D structure of a plant. They contain usually the following components 1) Presentation of the plant structure in terms of basic units, 2) Rules of morphological development and 3) Models of metabolic processes that drive the plant growth. The main emphasis in these applications has been individual plants. It is understandable because, due to the detailed description of the plant structure, and consequently, of the local environment of each organ, the FSPMs tend to require a large number of parameters and/or input data. Owing to the large amount of information they contain about the plant to be modeled, they also tend to be computationally heavy. In the following we shortly describe how the three FSPM model components have been realized in the LIGNUM model. Three basic units (Tree segment, Branching point and Bud) are used. We are using the STL template library of C++ to define a blueprint of a tree that can be instantiated by actual representations of the species specific components. We are using four generic algorithms for traversing the data structure of the tree and to make calculations. L-systems are used for specifying the morphological development of the trees. We present three examples of applications made using LIGNUM: a calculation of optimal leaf traits in Sugar maple saplings, a system for storing and analyzing information on decay in city trees and simulation of growth of a tree stand. 1 Introduction The functional-structural plant models (FSPMs, [5, 4]) or architectural plant models or virtual plants have been around for a while. They usually combine descriptions of metabolic (physiological) pro- cesses with a detailed presentation of the 3D structure of a plant. The architectural structure of the model plant is usually presented on the basis of a small number of elementary units. The structural dynamics of the plant is based on the production, death and growth of the elementary units, and is affected by the metabolic processes. These models have been applied to a large variety to both theoretical and practical problems of plant development and growth (e.g. the recent proceeding in Functional Plant Biology vol 25, issue 9/10, 2008). The main emphasis in these applications has been individual plants. The FSPMs are realized with the aid of a computer program, within which the following functionalities are available: 1. Presentation of the plant structure in terms of basic units sic model components. LIGNUM has been implemented with C++ programming language [12]. Different applications of the model are realized with the aid combinations of program modules. However, mainly with the aid of generic programming [1] we have been able to achieve some degree of generality with LIGNUM. First, we have defined three basic units: Tree segment, Bud, and Branching point. A sequence of these basic units forms an Axis (Fig. 2). With these units we are dealing with an axial tree discussed in [16] as a link between graph-theoretic formalism and real plants. So far we have not dealt with either inflorescences or fruits; applications with them would evidently require introduction of new basic units. We implement the axial tree as two-way list, that allows us to use efficient algorithms designed for them. 2. Rules of morphological development 3. Growth engine, that is, models of metabolic processes that drive the plant growth In addition to dealing with plant growth the software usually contains modules for visual rendering of the simulated plants. There are a great number of approaches to these these components in the existing models. The most straightforward way is to use a computer language. On the other hand, there are formalisms and related software for constructing FSPMs. L-systems [16] with their extensions ([15, 9] and the related software for building applications [7, 8]) are one widely used group of methods. Other modeling systems are OpenAlea [14] and GREENLAB [2]. In the following we shortly describe how the three FSPM model components have been realized in the LIGNUM model with some examples. 2 2.1 The LIGNUM model Presentation of the plant structure in terms of basic units The main target of LIGNUM model have been the trees and it shows in the choice of the ba- Figure 2: Tree segment is a part of stem between two branching events in the stem and thus corresponds to the botanical term internode. The Tree segment may contain a layer of needles in conifers or carry leaves and buds in deciduous trees. If the buds in the Tree segment flush, it splits to several Tree segments. A sequence of Tree segments and Branching points ending with a Bud forms an Axis. Second, the STL template library of C++ [1] allows us to define a blueprint of a tree that can then be instantiated by actual representations of the concrete species specific components (Fig. 1). The �������������������� ���������������������������� ����������� ���������������������������� ����������������������������������� �� ��������������������� ���������������� ������������������������ ���������������������������� ������������������������� ����������� ���������������������������� ��������������������� ������������������������������������������������ ������������������������������ ���������������������������������������� ������������������������������������������������� �������������������������������������������� ����������������������������������� ������ ��� �� ��������������������������������� ���������������������������������������������� ������������������������������������������������������������������� Figure 1: The LIGNUM template library implements the tree topology as a list structure (1). TS and B denote type parameters for tree segment and bud respectively. The generic algorithms (2) can be used to apply user defined physiological processes (3) in the tree, collect data and pass information. User defined concrete datatypes (4) can be used to instantiate the blueprint for the tree for species specific implementions. components to be specified include the basic units (Fig. 2) with their necessary geometrical and physiological functions and data. Third, analogous to the STL library, the C++ template library for the blueprint of the tree makes a clear distinction between the abstract data types and the algorithms that operate on them. We have implemented four generic algorithms for traversing the data structure of the tree and to make calculations (Fig. 1): • ForEach that applies an operator to each tree compartment. • Accumulate that can collect data from the tree • AccumulateDown to collect data or pass infor- mation basipetally in the tree • PropagateUp to collect data or pass information acropetally in the tree These generic algorithms are the interface of an application programmer to the tree (data structure). For example, if one desires to experiment with different photosynthesis models, it is necessary to change only the operator or functor in the ForEach algorithm. Fourth, the L-systems [16] provide a powerful formal method to define the architectural development of the tree structure. LIGNUM utilizes Lsystems for specifying the morphological development of the trees (Fig. 3, [10]). This improves the applicability and and ease of use of the model. This way building computer program for simulation of plant is flexible. It may also be that metabolic processes may be best accounted for with general purpose programming language and its libraries. The difficult parts are programming of complicated models of physical and metabolical processes. It may not matter whether they are programmed with using a certain formal language or a general purpose programming language. The disadvantage of the approach is that it is not according to any formalism - it is an ad hoc collection software components. It is also true that using LIGNUM requires programming skills to implement species specific applications ���������������� ������������������ ������������ ����������������� ���������� Figure 4: A 2.1 m tall sapling in a forest gap with optimal leaf angles. 100 Figure 3: The two-way communication between Lsystem and LIGNUM. After each rewrite of the Lstring the LIGNUM model structure is updated and physiological processes can follow. The LIGNUM model can pass back to the L-string the results of the metabolic processes (e.g. lengths of the new tree segments, if a bud is living or dead, radiation regime in different parts of the tree crown etc.) that affect the architectural development of the tree. 3 3.1 90 80 Averagea leaf agle (degrees) ���������������� ������ 70 60 G 50 O 40 30 20 10 0 0 0.5 1 1.5 2 2.5 Tree height (m) Figure 5: Mean optimal leaf zenith angle as a function of sapling height (G = in a forest gap, O = growing in open). Small saplings tend tend to have horizontal leaves; leaves are more horizontal in in a gap than in open conditions. Some examples Optimal tree We used LIGNUM in a simulation study to understand how plants could maximize their net photosynthesis based on photosynthetic properties of leaves, leaf inclination and consequent radiation capture affected by self-shading [13] (Figs. 4, 5) We studied this general problem by simulations and used Acer sacharum (sugar maple) saplings as target. We used LIGNUM to generate saplings of different sizes and to make optimization calcula- tions. We set some simple functions that determined how photosynthetic properties of leaves and angle of leaves acclimated to their immediate light environment. Plants were studied in two light environments (in the open or in a forest gap) and with or without constrains regarding the maximum photosynthetic rate of leaves. The optimization took place outside LIGNUM (R program). In LIGNUM the properties and angles of leaves were set as a function of available radiation with the generic algorithms (especially AccumulateDown) and photo- synthetic rate was evaluated. 3.2 Decay in urban trees LIGNUM was used as a basis for software application into studies of the decay in trees growing in urban areas[6]. The application implements the storage of measurements of stem characteristics (related to decay) and visualization of the 3D structural model of tree stems and branches built using this material (Fig. 6). Photographs taken from discs cut from felled trees were used as the input for the application. The contours of healthy wood, decayed wood and cavity were marked manually in the photographs of stem or branch cross sections. The application then built a 3D structural model of stem and/or branches on the basis of the input. It makes possible to study visually the composition of the stem and/or branches of different types of wood. 3.3 Tree stand The FSPMs bring in a new level of interaction (within tree crown) into the simulation of tree stand growth, and instead of assuming a predetermined geometric crown shape, they allow for simulation of the actual process of space filling by the crowns. Our simulations show that stand dynamics follow from the shoot based definition of growth in LIGNUM (Fig. 7, [17]). In the simulation of Scots pine stands by LIGNUM, one important topic has been in the accurate evaluation of the radiation conditions. The radiation in Scots pine version of LIGNUM has been calculated on the basis of the mutual shading of the shoots (Tree segments that carry needles) [11]. When the stand or trees are large, the calculations of mutual shading become prohibitively slow. The calculations can be speeded up e.g. by using the voxel space approach (spatial discretization). However, information about the structure of the shading elements is always lost in the spatial averaging. Figures 8 and 9 indicate that self-shading may be quite important factor in radiation regime, since it is bigger than the effect of other trees. At short distances the effect of spa- Figure 6: A Tilia tree before felling and taking of the cross section photographs is pictured on the left and the finished visualized model of the tree on the right. The green healthy wood polygon mesh is translucent depending on the proportional surface area of damaged wood on the corresponding cross section pointing out the most damaged part of the tree. tial arrangement of shading elements is important. Hence, it may be that an optimal way to treat radiation conditions in FSPMs of tree stands would be to calculate self-shading in a tree more accurately than mutual shading of trees. 4 Conclusions Godin and Sinoquet [5] emphasize that the FSMPs face several aspects of complexity in modeling plants: • complexity of the biological system • complexity of various sources of knowledge • computer simulation complexity The present short summary of some features and applications of LIGNUM indicates how the com- Figure 7: Images of the simulated Scots pine tree at ages of 10, 20, 30, and 40 years (from left to right). The heights were 2.7, 5.7, 8.8, and 12.0 m, respectively. Figure 8: Transmission of photosynthetically active radiation through surrounding trees to Tree segments of the subject tree as a function of downward cumulative LAI. There were 36 trees on a 11 m x 11 m plot, all similar to the tree on the left in Fig. 7. LAI of the stand was 9.4. plexity matters have been tackled within it. By suitable choice of elementary units that make the plant and by the possibility to instantiate them (both data structures and functions) according to the needs of the application it is possible deal effectively with the biological systems. This flexibility also helps in integrating various sources of knowledge. As the FSPMs make possible to relax almost every assumption of homogeneity (e.g. of plant, environment), they tend to be computationally complex, as radiation calculations of mutual shading of Tree segments in LIGNUM. One way forward may be to simplify the calculations in the model, cf. [3]. References [1] U. Breymann. Designing Components with the C++ STL. A New Apporoach to Programming. Addison-Wesley, Harlow, England, 1998. [2] P.-H. Cournéde and P. De Reffye. Greenlab: A dynamical model of plant growth for environmental applications. ERCIM News, 61, 2005. [3] P.-H. Cournède, M.-Z. Kang, A. 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