Functional structural plant models - case LIGNUM

Risto SievanenFinnish Forest Research Institute

01301 Vantaa, Finlandristo.sievanen@metla.fi

Jari PerttunenFinnish Forest Research Institute

01301 Vantaa, Finlandjari.perttunen@metla.fi

Eero NikinmaaDepartment of Forest Ecology

University of Helsinki00014 University of Helsinki, Finland

eero.nikinmaa@helsinki.fi

Juan M. Posada Programa de BiologiaFacultad de Ciencias Naturales y MatematicasUniversidad del Rosario, Bogota, Colombia

juan posada@mac.com

Abstract

The functional structural plant models (FSPMs)can be defined as models that combine descriptionsof metabolic (physiological) processes with a pre-sentation of the 3D structure of a plant. They con-tain usually the following components 1) Presenta-tion of the plant structure in terms of basic units, 2)Rules of morphological development and 3) Modelsof metabolic processes that drive the plant growth.The main emphasis in these applications has beenindividual plants. It is understandable because,due to the detailed description of the plant struc-ture, and consequently, of the local environment ofeach organ, the FSPMs tend to require a large num-ber of parameters and/or input data. Owing to thelarge amount of information they contain about theplant to be modeled, they also tend to be computa-tionally heavy. In the following we shortly describehow the three FSPM model components have beenrealized in the LIGNUM model. Three basic units

(Tree segment, Branching point and Bud) are used.We are using the STL template library of C++ todefine a blueprint of a tree that can be instanti-ated by actual representations of the species spe-cific components. We are using four generic algo-rithms for traversing the data structure of the treeand to make calculations. L-systems are used forspecifying the morphological development of thetrees. We present three examples of applicationsmade using LIGNUM: a calculation of optimal leaftraits in Sugar maple saplings, a system for storingand analyzing information on decay in city treesand simulation of growth of a tree stand.

1 Introduction

The functional-structural plant models (FSPMs,[5, 4]) or architectural plant models or virtual plantshave been around for a while. They usually com-bine descriptions of metabolic (physiological) pro-

cesses with a detailed presentation of the 3D struc-ture of a plant. The architectural structure of themodel plant is usually presented on the basis of asmall number of elementary units. The structuraldynamics of the plant is based on the production,death and growth of the elementary units, and is af-fected by the metabolic processes. These modelshave been applied to a large variety to both theoret-ical and practical problems of plant developmentand growth (e.g. the recent proceeding in Func-tional Plant Biology vol 25, issue 9/10, 2008). Themain emphasis in these applications has been indi-vidual plants.

The FSPMs are realized with the aid of a com-puter program, within which the following func-tionalities are available:

1. Presentation of the plant structure in terms ofbasic units

2. Rules of morphological development

3. Growth engine, that is, models of metabolicprocesses that drive the plant growth

In addition to dealing with plant growth the soft-ware usually contains modules for visual renderingof the simulated plants. There are a great numberof approaches to these these components in the ex-isting models. The most straightforward way is touse a computer language. On the other hand, thereare formalisms and related software for construct-ing FSPMs. L-systems [16] with their extensions([15, 9] and the related software for building appli-cations [7, 8]) are one widely used group of meth-ods. Other modeling systems are OpenAlea [14]and GREENLAB [2].

In the following we shortly describe how thethree FSPM model components have been realizedin the LIGNUM model with some examples.

2 The LIGNUM model

2.1 Presentation of the plant struc-ture in terms of basic units

The main target of LIGNUM model have beenthe trees and it shows in the choice of the ba-

sic model components. LIGNUM has been im-plemented with C++ programming language [12].Different applications of the model are realizedwith the aid combinations of program modules.However, mainly with the aid of generic program-ming [1] we have been able to achieve some degreeof generality with LIGNUM.

First, we have defined three basic units: Treesegment, Bud, and Branching point. A sequence ofthese basic units forms an Axis (Fig. 2). With theseunits we are dealing with an axial tree discussed in[16] as a link between graph-theoretic formalismand real plants. So far we have not dealt with ei-ther inflorescences or fruits; applications with themwould evidently require introduction of new basicunits. We implement the axial tree as two-way list,that allows us to use efficient algorithms designedfor them.

Figure 2: Tree segment is a part of stem betweentwo branching events in the stem and thus corre-sponds to the botanical term internode. The Treesegment may contain a layer of needles in conifersor carry leaves and buds in deciduous trees. If thebuds in the Tree segment flush, it splits to severalTree segments. A sequence of Tree segments andBranching points ending with a Bud forms an Axis.

Second, the STL template library of C++ [1] al-lows us to define a blueprint of a tree that can thenbe instantiated by actual representations of the con-crete species specific components (Fig. 1). The

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Figure 1: The LIGNUM template library implements the tree topology as a list structure (1). TS and Bdenote type parameters for tree segment and bud respectively. The generic algorithms (2) can be used toapply user defined physiological processes (3) in the tree, collect data and pass information. User definedconcrete 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 phys-iological functions and data.

Third, analogous to the STL library, the C++template library for the blueprint of the tree makesa clear distinction between the abstract data typesand the algorithms that operate on them. We haveimplemented four generic algorithms for traversingthe data structure of the tree and to make calcula-tions (Fig. 1):

• ForEach that applies an operator to each treecompartment.

• 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 informa-tion acropetally in the tree

These generic algorithms are the interface ofan application programmer to the tree (data struc-ture). For example, if one desires to experimentwith different photosynthesis models, it is neces-sary to change only the operator or functor in theForEach algorithm.

Fourth, the L-systems [16] provide a powerfulformal method to define the architectural develop-ment of the tree structure. LIGNUM utilizes L-systems for specifying the morphological develop-ment of the trees (Fig. 3, [10]). This improves theapplicability and and ease of use of the model.

This way building computer program for sim-ulation of plant is flexible. It may also be thatmetabolic processes may be best accounted forwith general purpose programming language andits libraries. The difficult parts are programmingof complicated models of physical and metaboli-cal processes. It may not matter whether they areprogrammed with using a certain formal languageor a general purpose programming language. Thedisadvantage of the approach is that it is not ac-cording to any formalism - it is an ad hoc collec-tion software components. It is also true that us-ing LIGNUM requires programming skills to im-plement species specific applications

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Figure 3: The two-way communication between L-system and LIGNUM. After each rewrite of the L-string the LIGNUM model structure is updated andphysiological processes can follow. The LIGNUMmodel can pass back to the L-string the results ofthe metabolic processes (e.g. lengths of the newtree segments, if a bud is living or dead, radiationregime in different parts of the tree crown etc.) thataffect the architectural development of the tree.

3 Some examples

3.1 Optimal tree

We used LIGNUM in a simulation study to un-derstand how plants could maximize their net pho-tosynthesis based on photosynthetic properties ofleaves, leaf inclination and consequent radiationcapture affected by self-shading [13] (Figs. 4, 5)We studied this general problem by simulations andused Acer sacharum (sugar maple) saplings as tar-get. We used LIGNUM to generate saplings ofdifferent sizes and to make optimization calcula-

Figure 4: A 2.1 m tall sapling in a forest gap withoptimal leaf angles.

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Figure 5: Mean optimal leaf zenith angle as a func-tion of sapling height (G = in a forest gap, O =growing in open). Small saplings tend tend to havehorizontal leaves; leaves are more horizontal in ina gap than in open conditions.

tions. We set some simple functions that deter-mined how photosynthetic properties of leaves andangle of leaves acclimated to their immediate lightenvironment. Plants were studied in two light envi-ronments (in the open or in a forest gap) and withor without constrains regarding the maximum pho-tosynthetic rate of leaves. The optimization tookplace outside LIGNUM (R program). In LIGNUMthe properties and angles of leaves were set as afunction of available radiation with the generic al-gorithms (especially AccumulateDown) and photo-

synthetic rate was evaluated.

3.2 Decay in urban trees

LIGNUM was used as a basis for software ap-plication into studies of the decay in trees grow-ing in urban areas[6]. The application implementsthe storage of measurements of stem characteristics(related to decay) and visualization of the 3D struc-tural model of tree stems and branches built usingthis material (Fig. 6). Photographs taken fromdiscs cut from felled trees were used as the inputfor the application. The contours of healthy wood,decayed wood and cavity were marked manually inthe photographs of stem or branch cross sections.The application then built a 3D structural model ofstem and/or branches on the basis of the input. Itmakes possible to study visually the compositionof the stem and/or branches of different types ofwood.

3.3 Tree stand

The FSPMs bring in a new level of interac-tion (within tree crown) into the simulation of treestand growth, and instead of assuming a predeter-mined geometric crown shape, they allow for sim-ulation of the actual process of space filling by thecrowns. Our simulations show that stand dynamicsfollow from the shoot based definition of growthin LIGNUM (Fig. 7, [17]). In the simulation ofScots pine stands by LIGNUM, one important topichas been in the accurate evaluation of the radiationconditions. The radiation in Scots pine version ofLIGNUM has been calculated on the basis of themutual shading of the shoots (Tree segments thatcarry needles) [11]. When the stand or trees arelarge, the calculations of mutual shading becomeprohibitively slow. The calculations can be speededup e.g. by using the voxel space approach (spa-tial discretization). However, information about thestructure of the shading elements is always lost inthe spatial averaging. Figures 8 and 9 indicate thatself-shading may be quite important factor in radi-ation regime, since it is bigger than the effect ofother trees. At short distances the effect of spa-

Figure 6: A Tilia tree before felling and taking ofthe cross section photographs is pictured on the leftand the finished visualized model of the tree on theright. The green healthy wood polygon mesh istranslucent depending on the proportional surfacearea of damaged wood on the corresponding crosssection pointing out the most damaged part of thetree.

tial arrangement of shading elements is important.Hence, it may be that an optimal way to treat radi-ation conditions in FSPMs of tree stands would beto calculate self-shading in a tree more accuratelythan mutual shading of trees.

4 Conclusions

Godin and Sinoquet [5] emphasize that theFSMPs face several aspects of complexity in mod-eling plants:

• complexity of the biological system

• complexity of various sources of knowledge

• computer simulation complexity

The present short summary of some features andapplications of LIGNUM indicates how the com-

Figure 7: Images of the simulated Scots pine treeat ages of 10, 20, 30, and 40 years (from left toright). The heights were 2.7, 5.7, 8.8, and 12.0 m,respectively.

plexity matters have been tackled within it. By suit-able choice of elementary units that make the plantand by the possibility to instantiate them (both datastructures and functions) according to the needs ofthe application it is possible deal effectively withthe biological systems. This flexibility also helpsin integrating various sources of knowledge. Asthe FSPMs make possible to relax almost every as-sumption of homogeneity (e.g. of plant, environ-ment), they tend to be computationally complex,as radiation calculations of mutual shading of Treesegments in LIGNUM. One way forward may be tosimplify the calculations in the model, cf. [3].

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Figure 8: Transmission of photosynthetically activeradiation through surrounding trees to Tree seg-ments of the subject tree as a function of downwardcumulative LAI. There were 36 trees on a 11 m x11 m plot, all similar to the tree on the left in Fig.7. LAI of the stand was 9.4.

Figure 9: Transmission of photosynthetically activeradiation through own crown, that is, self-shadingof the tree on the left in Fig. 7 as a function ofdownward cumulative LAI (i.e. the tree is in theplot of Fig 8).

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