Silva Fennica : Special issues : Functional-structural tree models
Functional-structural tree models
Papers selected from the Helsinki Workshop on Functional-Structural Tree Models, 12–13 December 1996
Published as Silva Fennica 31(3). 146 pages.
Computer models that treat plants as consisting of elementary units have become increasingly popular. The core of such a model is the description of what happens in a single plant element. Models can use various elements, such as bud, leaf, internode, stem segment, etc. A computer program takes care of all the elements and integrates their activities to the functioning of the whole plant. Both the 3-D architecture and the metabolic processes can be treated in the same model at the same time in a natural way. Increasing speed of computers, developing programming tools and available mathematical techniques have made the construction of such models increasingly feasible.
Modelling plants using computer models where the plant consists of elementary units can be viewed as an extension of the classical method of differential calculus. Traditionally, the analysis of an entity proceeds in three steps: First, the elemental processes are analysed in a small (differential) volume and/or time element. Second, a differential equation is derived on the basis of this analysis, and third, this differential equation is solved with adequate boundary conditions and assuming adequate geometry (if spatial aspects are involved). In the computer models, the program acts both as the “differential equation” and as the “means of solution”. The difference in comparison with analytical solutions of differential equations is the immensely greater capacity of the computer to deal with complex situations. There are no per se limitations to the 3-D architecture or interactions of elements which could be programmed into the code. These models can hence be viewed as an extension of the existing methods of describing plant growth and development.
The stimulus to organise the “Helsinki workshop on functional-structural tree models” grew from the persuasion that models dealing with the functioning and structure in terms of elementary units will constitute an important extension to the methods of plant modelling in the future, and that the construction of such models will be an intriguing challenge to scientists. We coined the name “functional-structural model” to emphasize that both functioning (processes producing material for growth) and structure (true 3-D structure) can be and are dealt with in the same model. The present volume collects the articles of this workshop held 12–13 December 1996 in Helsinki. The aim was to deal with functional-structural tree models and important factors affecting these models. The program consisted of invited lectures and voluntary papers. Speakers were asked to submit manuscripts expanding their presentations at the meeting for inclusion in a special issue of Silva Fennica, in which the normal reviewing procedure has been applied. Articles in this issue cover the major part of the presentations.
The articles fall in five categories: First, modelling the distribution of growth in a system consisting of many parts is focal in these models. The transport/conversion process framework developed by J.H.M Thornley is of key importance in this. It and distribution of growth in general is analysed in the articles by J.H.M. Thornley, and C. Deleuze and F. Houllier.
Second, there exist constraints to the structure of trees, among others the so-called pipe model theory. The article of H. Valentine considers the height growth of trees in the pipe model framework and A. Mäkelä et al. use the same concept to predict the branch distribution in a tree.
Third, mathematical description and measurement of 3-D tree structure is of key importance for functional-structural models. The article by C. Godin et al. presents a method for analysis and description of topology of plants and the article by H. Sinoquet et al. describes measuring 3-D structure of a tree. The article by T. Früh describes a method of solving water flow (in terms of a partial differential equation) in a complex tree architecture.
Fourth, L-systems offer an effective mathematical means for constructing models for detailed simulation of tree structure. The article by W. Kurth and B. Sloboda presents the possibilities of L-systems and explores possibilities to represent complex interactions in them.
Fifth, the articles by Ph. de Reffye et al., S. Le Dizés et al. and R. Sievänen et al. give examples of functional-structural models.
We hope that this collection of papers gives insights into the possibilities and problems in the field of functional-structural modelling of plants, as well as invites new scientists to construct new models and to solve research problems using them.
We gratefully acknowledge the support provided by the Academy of Finland, the Finnish Society of Forest Science and the Finnish Forest Research Institute for making the Helsinki workshop feasible. We would also like to thank the contributors to this special edition. The work provided by the reviewers of the manuscripts is highly appreciated.
Risto Sievänen, Annikki Mäkelä, Eero Nikinmaa, workshop organisers
Eeva Korpilahti, Editor
METLA Editorial Office – TSal –
Comments