Jari Perttunen

LIGNUM: a model combining the structure and the functioning of trees

The model LIGNUM treats a tree as a collection of a large number of simple units that correspond to the organs of a tree. The model describes the three-dimensional structure of the tree crown and derives growth in terms of the metabolism taking place in these units. The time step is one year. The structural units are: tree segments, branching points and buds. Tree segments are separated by branching points. The buds produce new tree segments, branching points and buds. The tree segments contain wood, bark and foliage. A model tree consisting of simple elements translates conveniently to a list structure: the computer program implementing LIGNUM treats trees as a collection of lists. The annual growth of the tree is driven by the available photosynthetic products after accounting for respiration losses. The photosynthetic rate of foliage depends on the amount of intercepted light. The amount of photosynthates allocated to the growth of new tree segments is controlled by the light conditions and the amount of foliage of the mother tree segment. The biomass relationships of the tree parts follow, e.g. from a pipe model hypothesis. The orientation of new tree segments results from application of simple branching rules. LIGNUM has been parametrized for young Scots pines (Pinus sylvestris L.).

Modelling trees using an object-oriented scheme

Object-oriented modelling techniques are used to construct a conceptual framework which defines the hierarchical levels and structures of a tree and connects processes from the different levels. At the tree level, combining functions with structure is a logical step towards a better understanding of growth dynamics. A generic tree growth simulation system conforming to the conceptual object framework is constructed. The essential part of the system is a tree, which consists of a large number of relatively simple structural units corresponding to shoots, buds and branch whorls. The development of the tree is driven by basic ecophysiological processes such as photosynthesis and respiration and controlled by principles of functional balance and pipe model theory. The application interface allows changes to the parameter values and the forms of the basic functions. In principle, the system can thus model the development of different tree species and different circumstances. The present implementation models the growth of young Scots pine; it is programmed using the C++ language. The basic units of the tree are linked together using list structures. They also carry the topology of the tree, which is visible in the interface of the application. The available methodologies for object-oriented modelling are promising for ecological projects, but the present lack of integrated tools covering analysis, design, and programming prevents their straightforward adoption.

Crown architecture of grafted Stone pine (Pinus pinea L.): shoot growth and bud differentiation

The singular umbrella-like crown shape of Stone pine can be interpreted as a consequence of primary shoot-growth patterns and posterior axis differentiation due to differential secondary growth and down-bending of branches. This paper centres on the first aspect, analysing the growth, branching and flowering behaviour of about 5,000 individual shoots on 27 grafted Stone pines. The data measurement on standing trees allowed to study correlations of topologic and geometric variables in the shoot and their ancestors. The only significant correlations were found with parameters of the mother shoot formed the previous year and with the number of cones born 3 years before by the respective ancestor. The fitted relationships between geometric and topologic shoot and branch variables are the first step of a structural model construction that can be completed with functional components like a radiation and a carbon allocation submodel, stressing the importance of the heavy Stone pine cones as carbon sinks, with a total annual allocation similar to stem wood. In conclusion, the Stone pine crown shape emerges as consequence of the lack of initial vigour differentiation between stem and main-branch apical meristems that favour the generalized sylleptic reiteration in the open-grown trees.

Adaptation of the LIGNUM model for simulations of growth and light response in Jack pine

LIGNUM is a whole tree model, developed for Pinus sylvestris in Finland, that combines tree metabolism with a realistic spatial distribution of morphological parts. We hypothesize that its general concepts, which include the pipe model, functional balance, yearly carbon budget, and a set of architectural growth rules, are applicable to all trees. Adaptation of the model to Pinus banksiana, a widespread species of economic importance in North America, is demonstrated. Conversion of the model to Jack pine entailed finding new values for 16 physiological and morphological parameters, and three growth functions. Calibration of the LIGNUM Jack pine model for open grown trees up to 15 years of age was achieved by matching crown appearance and structural parameters (height, foliage biomass, aboveground biomass) with those of real trees. A sensitivity study indicated that uncertainty in the photosynthesis and respiration parameters will primarily cause changes to the net annual carbon gain, which can be corrected through calibration of the growth rate. The effect of a decrease in light level on height, biomass, total tree branch length, and productivity were simulated and compared with field data. Additional studies yielded insight into branch pruning, carbon allocation patterns, crown structure, and carbon stress. We discuss the value of the LIGNUM model as a tool for understanding tree growth and survival dynamics in natural and managed forests.

Contributions of leaf photosynthetic capacity, leaf angle and self-shading to the maximization of net photosynthesis in Acer saccharum: a modelling assessment

BACKGROUND AND AIMS Plants are expected to maximize their net photosynthetic gains and efficiently use available resources, but the fundamental principles governing trade-offs in suites of traits related to resource-use optimization remain uncertain. This study investigated whether Acer saccharum (sugar maple) saplings could maximize their net photosynthetic gains through a combination of crown structure and foliar characteristics that let all leaves maximize their photosynthetic light-use efficiency (ε). METHODS A functional-structural model, LIGNUM, was used to simulate individuals of different leaf area index (LAI(ind)) together with a genetic algorithm to find distributions of leaf angle (L(A)) and leaf photosynthetic capacity (A(max)) that maximized net carbon gain at the whole-plant level. Saplings grown in either the open or in a forest gap were simulated with A(max) either unconstrained or constrained to an upper value consistent with reported values for A(max) in A. saccharum. KEY RESULTS It was found that total net photosynthetic gain was highest when whole-plant PPFD absorption and leaf ε were simultaneously maximized. Maximization of ε required simultaneous adjustments in L(A) and A(max) along gradients of PPFD in the plants. When A(max) was constrained to a maximum, plants growing in the open maximized their PPFD absorption but not ε because PPFD incident on leaves was higher than the PPFD at which ε(max) was attainable. Average leaf ε in constrained plants nonetheless improved with increasing LAI(ind) because of an increase in self-shading. CONCLUSIONS It is concluded that there are selective pressures for plants to simultaneously maximize both PPFD absorption at the scale of the whole individual and ε at the scale of leaves, which requires a highly integrated response between L(A), A(max) and LAI(ind). The results also suggest that to maximize ε plants have evolved mechanisms that co-ordinate the L(A) and A(max) of individual leaves with PPFD availability.

Computational analysis of the effects of light gradients and neighbouring species on foliar nitrogen

Abstract Foliar nitrogen is one of the key traits determining the photosynthetic capacity of trees. It is influenced by many environmental factors that are often confounded with the photosynthetic photon flux density (PPFD), which alone strongly modifies the nitrogen content and other foliar traits. We combined field measurements and computational estimates of light transmittance in 3D stands with different combinations of Scots pine (Pinus sylvestris) and silver birch (Betula pendula) to decouple the effect of PPFD from other potential effects exerted by the species of neighbouring trees on the leaf nitrogen content per unit leaf area (Narea) and leaf mass per area (LMA). Independent of the level of PPFD, silver birch had a significantly lower Narea and LMA when Scots pine was abundant in its neighbourhood compared with the presence of conspecific neighbours. In Scots pine, Narea and LMA were only dependent on PPFD and the branching order of shoots. In both species, the relationships between PPFD and Narea or LMA were nonlinear, especially at intermediate levels of PPFD. The levels of PPFD did not show any dependence on the species of the neighbouring trees. The responses of silver birch suggest that the species composition of the surrounding stand can influence foliar nitrogen, independent of the level of PPFD within the canopy.

A study of crown development mechanisms using a shoot-based tree model and segmented terrestrial laser scanning data

Background and Aims Functional-structural plant models (FSPMs) allow simulation of tree crown development as the sum of modular (e.g. shoot-level) responses triggered by the local environmental conditions. The actual process of space filling by the crowns can be studied. Although the FSPM simulations are at organ scale, the data for their validation have usually been at more aggregated levels (whole-crown or whole-tree). Measurements made by terrestrial laser scanning (TLS) that have been segmented into elementary units (internodes) offer a phenotyping tool to validate the FSPM predictions at levels comparable with their detail. We demonstrate the testing of different formulations of crown development of Scots pine trees in the LIGNUM model using segmented TLS data. Methods We made TLS measurements from four sample trees growing in a forest on a relatively poor soil from sapling size to mature stage. The TLS data were segmented into internodes. The segmentation also produced information on whether needles were present in the internode. We applied different formulations of crown development (flushing of buds and length of growth of new internodes) in LIGNUM. We optimized the parameter values of each formulation using genetic algorithms to observe the best fit of LIGNUM simulations to the measured trees. The fitness function in the estimation combined both tree-level characteristics (e.g. tree height and crown length) and measures of crown shape (e.g. spatial distribution of needle area). Key Results Comparison of different formulations against the data indicates that the Extended Borchert-Honda model for shoot elongation works best within LIGNUM. Control of growth by local density in the crown was important for all shoot elongation formulations. Modifying the number of lateral buds as a function of local density in the crown was the best way to accomplish density control. Conclusions It was demonstrated how segmented TLS data can be used in the context of a shoot-based model to select model components.

Invited Talk: Functional Structural Plant Models - Case LIGNUM

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.

Plant Growth Modeling, Simulation, Visualization and Applications, Proceedings - PMA09

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.