Download Functional structural plant models

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
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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
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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)
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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].
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