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-We analyze functional-structural tree models (FMSs) that are an outgrowth of developments in process-based models (PBMs) on the one hand, and morphological models on the other. Existing morphological and functional-structural models are briefly reviewed. We introduce the idealized elementary unit (IEU) that can be used as the basic component of a FSM, and pinpoint the processes that have to be accounted for. The distribution of metabolites and growth is identified as one of the main focal points to be investigated in conjunction with FSMs, and the different approaches that can be applied in constructing the model component for this process are presented. Finally, we analyze the computational requirements of FSMs, discuss the challenges they pose, and assess their applicability in a number of different tasks. functional-structural model / process-based model / morphological model / tree structure / L-system Résumé -Les composants des modèles fonctionnels et structuraux des arbres. Cet article a pour objet de faire une synthèse des approches réalisées dans le cadre de la modélisation fonctionnelle et structurale des arbres (FSM). Ces modèles résultent du couplage entre la modélisation du fonctionnement écophysiologique d'arbres, d'une part, et la modélisation des processus morphologiques, d'autre part. Après une brève présentation des approches existantes, nous introduisons la notion « d'unité élémentaire idéale » (IEU) qui peut être considérée comme la composante fondamentale des FSM au regard de la souplesse qu'elle confère dans l'articulation des processus. La distribution des métabolites et la croissance sont ensuite abordées comme étant les processus à résoudre de façon prioritaire dans le développement des FSM, et les différentes approches pouvant être mises à contribution dans la construction de ces modèles sont discutées. Enfin nous analysons les besoins en programmation des FSM, discutons des avancées nécessaires et évaluons leur adéquation à la résolution d'objectifs divers. modèle fonctionnel-structural / modèle de fonctionnement / modèle morphologique / structure des arbres / L-system

Trees have been increasingly considered as modular organisms, with individual shoots forming autonomous units that respond semi-independently to their surrounding environment. However, there is evidence for fairly strict hormonal control of tree crown development. Studies on the hydraulic architecture of trees suggest a closer functional connection between shoots and crown development than is postulated by the theory of branch autonomy. We studied how shoot growth pattern influences growth and crown architecture in young Scots pine trees simulated by the LIGNUM model assuming that (a) the growth of a shoot mainly depends on its light climate and (b) the growth of a shoot is influenced by its position within the crown. We determined shoot position within the crown based on a recently developed vigor index. The vigor index compares the relative axis cross-sectional area from the base of the tree to each shoot and gives a value of 1 to the pathway of the greatest cross-sectional area. All other shoots attain values between 0 and 1 depending on their cross-sectional areas and the cross-sectional areas of the branches leading there from the main axis. The shoot light climate is characterized by annually intercepted photosynthetically active radiation. We compared the results from simulations (a) and (b) against an independent data set. The addition of a within-shoot position index (the vigor index) to our simulation (simulation b) resulted in a more realistic tree form than that obtained with simulation (a) alone. We discuss the functional significance of the results as well as the possibilities of using an index of shoot position in simulations of crown architecture.

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.

LIGNUM is a functional-structural model that represents a tree using four modelling units which closely resemble the real structure of trees: tree segments, tree axes, branching points and buds. Metabolic processes are explicitly related to the structural units in which they take place. Here we adapt earlier versions of LIGNUM designed to model growth of conifers for use with broad-leaved trees. Two primary changes are involved. First, the tree segment for broadleaved trees consists of enclosed cylinders of heartwood, sapwood and bark. Leaves consisting of petioles and blades are attached to the segments. Secondly, axillary buds and rules governing their dormancy are included in the model. This modi®ed version of LIGNUM is used to simulate the growth and form of sugar maple saplings in forest gaps. The annual growth of the model tree is driven by net production after respiration losses are taken into account. The production rate of each leaf depends on the amount of photosynthetically active radiation it receives. The radiation regime is tracked explicitly in dierent parts of the tree crown using a model of mutual shading of the leaves. Forest gaps are represented by changing the radiation intensity in dierent parts of the model sky. This version of LIGNUM modi®ed for use with broad-leaf, deciduous trees and parameterized for sugar maple, yields good simulations of growth and form in saplings from dierent forest gap environments.# 2001 Annals of Botany Company

Functional–structural plant growth models (FSPMs) combine the description of the structure of plants and the resource acquisition and partitioning at a detailed architectural level. They offer a means to study tree and stand development on the basis of a structurally accurate description that combines resource capture at the same level of detail. We describe here how a ‘shoot-based’ individual tree model, LIGNUM of Scots pine (Pinus sylvestris L.) has been applied to a group of identical trees (forest). The model has been applied to isolated trees and saplings growing in forest gaps. First, we present the LIGNUM model and the changes necessary for simulation of a forest instead of individual trees. LIGNUM derives tree growth on the basis of a process-based model of tree carbon balance and the architectural development of the 3-D tree crown. The time step is 1 year. We realised the forest as consisting of individual Scots pine trees on a plot 17 × 17 m, but simplified the stand description by simulating the growth of only one tree in the middle of the plot and assumed that the other trees were identical to it at all times. The model produced results that are comparable with observations made in real Scots pine trees and tree stands in Finland. The simulations with variable values of the parameters controlling the foliage–sapwood relationship, amount of sapwood required below a point in a branch or a stem, and the senescence of sapwood showed how growth declines when the sapwood requirement in the branches and stem was high. In this case, the proportion of resources allocated to the needles became small and the needle mass was low.

The interplay between plant structure and functioning determines vital plant characteristics, such as the efficiency of light capture by the foliage, and thus continuous efforts have attempted to include plant architecture in plant growth models. We constructed two crown structure models enabling the generation of 3D trees using simple tree measurements as input for Scots pine ( Pinus sylvestris L.) and silver birch ( Betula pendula Roth.), boreal species growing in mixed stands. The data for the models were obtained from sample-based digitizing of 3D crown architecture accompanied by characterizations of stem, branch, and foliage volumes and biomass. A set of equations was used to predict local crown characteristics on the basis of local predictors and tree-level input variables such as tree height, crown height, diameter at breast height, and the degree of competition. The 3D tree model was realized within the LIGNUM tree modelling framework. Comparison with data showed that the model adequately predicts the distribution of biomass into different crown components as well as the distribution of foliage within the tree crowns. The applicability of the simulations is at its best when examining Scots pine and silver birch trees growing on medium fertile mixed stands in Finland.