Application of the Functional-Structural Tree Model LIGNUM to Sugar Maple Saplings ( Acer saccharum Marsh) Growing in Forest Gaps JARI PERTTUNEN* {, EERO NIKINMAA {, MARTIN J. LECHOWICZ } , RISTO SIEVA È NEN { and CHRISTIAN MESSIERk {Finnish Forest Research Institute, Vantaa Research Station, P.O. Box 18, 01301 Vantaa, Finland, {Department of Forest Ecology, University of Helsinki, P.O. Box 24, 00014, Finland, }Department of Biology, McGill University, 1205 Avenue Dr. Pen®eld, Montreal, Canada, H3A 1B1 and k GREFi, Dep. des Sciences Biologiques, UQAM, C.P. 8888, Succ. Centre-Ville, Montreal, Canada, H3C 3P8 Received: 16 January 2001 Returned for revision: 28 February 2001 Accepted: 25 May 2001 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 broad- leaved 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 photosyntheticallyactive radiation it receives. The radiation regime istracked explicitly in dierent parts of the tree crown using a model of mutual shading of the leaves. Forest gaps are represented by changing the radiation intensity in dierent 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 dierent forest gap environments. # 2001 Annals of Botany Company Key words: LIGNUM, functional-structural tree model, tree architecture, sugar maple, modelling growth and form. INTRODUCTION Functional-structural models (FSM) combine two traditional perspectives on the organization of plant life, one emphasizing function and the other form. Functional or process-based models treat metabolic processes in considerable detail but simplify structure and structural dynamics to the level of caricature, while structural or morphological models describe plant architecture very realistically but pay little or no attention to growth processes. Examples of process-based models can be found in MaÈ kelaÈ and Hari (1986) and Landsberg (1986). The most striking models of form often use Lindenmayer or L-systems (Prusinkiewicz and Lindenmayer, 1990; Kurth, 1999), fractal geometry methods (Hearn and Baker, 1994) or other mathematical means to describe branching structures (Fisher, 1992; Jaeger and de Reye, 1992) visualized as computer graphics. LIGNUM is a functional-structural model which com- bines, in one modelling framework, a process-based model with a three-dimensional (3D) description of the tree crown. The initial implementations of LIGNUM were for Scots pine (Perttunen et al., 1996) and Jack pine (Lo et al., 2000). LIGNUM includes a detailed model of self-shading within the tree crown that is based on the geometry of mutual shading (Perttunen et al., 1998). Our ®rst objective in this study was to adapt the structural units of LIGNUM from coniferous to broad- leaved trees (i.e from gymnosperms to angiosperms; in this paper the terms broad-leaved and hardwood are used instead of the more-correct botanical term, angiosperm). Our second objective was to apply the modi®ed LIGNUM model to simulate the development of sugar maple saplings (Acer saccharum Marsh) growing in forest gaps. This involved parameterizing and implementing the functioning and the architectural development of LIGNUM to simulate the growth and survival of sugar maple saplings in dierent light regimes determined by openings of dierent sizes in the forest canopy. Measurements in four forest gaps, two at Duchesnay (46855 0 N, 71849 0 W) and two at Mont St. Hilaire (45831 0 N, 75808 0 W) in Quebec, Canada, provide the detailed data on gap light regimes used in our simulations. Our long-term goal is to use LIGNUM as a research tool to develop new cutting guidelines for managing the natural regeneration of sugar maple, especially key features determining the size of canopy openings created during harvest and harvest frequency. At this stage in our research, it is essential that the robustness of our hardwood version of LIGNUM be evaluated. Annals of Botany 88: 471±481, 2001 doi:10.1006/anbo.2001.1489, available online at http://www.idealibrary.com on 0305-7364/01/090471+11 $35.00/00 # 2001 Annals of Botany Company * For correspondence. E-mail jari.perttunen@metla.®