Current issue: 56(2)
A process-oriented tree and stand growth model is extended to be applicable to the analysis of timber quality, and how it is influenced by silvicultural treatments. The tree-level model is based on the carbon balance and it incorporates the dynamics of five biomass variables as well as tree height, crown base, and breast height diameter. Allocation of carbon is based on the conservation of structural relationships, in particular, the pipe model. The pipe-model relationships are extended to the whorl level, but in order to avoid a 3-dimensional model of entire crown structure, the branch module is largely stochastic and aggregated. In model construction, a top-down hierarchy is used where at each step down, the upper level sets constraints for the lower level. Some advantages of this approach are model consistency and efficiency of calculations, but probably at the cost of reduced flexibility. The detailed structure related with the branching module is preliminary and will be improved when more data becomes available. Model parameters are identified for Scots pine (Pinus sylvestris L.) in Southern Finland, and example simulations are carried out to compare the development of quality characteristics in different stocking densities.
In the last decades, architectural analysis has been used to understand and to model plant development. These studies have led us to reconsider the problem of measuring plants while taking into account their topological structure at several scales of detail. A computational platform, called AMAPmod, was created to work on such plant representations. This paper outlines the general methodology used in AMAPmod to represent plant topological structures and to explore these special types of databases. Plant structures are first encoded in order to build corresponding formal representations. Then, a dedicated language, AML, enables the user to extract various types of information from the plant databases and provides appropriate analysing tools.
A shoot-root carbon:nitrogen allocation model, based on the two processes of transport and chemical conversion, is described and explored. The view is proposed that all allocation models, whether built for the purposes of theoretical investigation or practical application, should start with this irreducible framework. In the present implementation, the processes operate according to: for substrate sources, dependence on shoot and root sizes, with possible product inhibition; for transport, movement down a substrate concentration gradient; for substrate sinks or utilization, linear bisubstrate kinetics. The dynamic and equilibrium properties of the model are explored. Failure of this approach to allocation will indicate to the modeller that additional mechanisms to control the processes are needed, and the mode of failure will indicate the type of mechanisms required. Additional mechanisms are discussed which may involve hormones or teleonomic (goal-seeking) controls, and may be added to the irreducible framework. However, these additions should not replace the irreducible framework of transport and chemical conversion, because they do not in reality. Modifications to the basic model to reflect some possibilities such as ontogenesis with the transition from exponential growth towards a steady state or with the scaling of within-plant transport resistances, the influence of hormones, and active transport, are described.
The effects of two alternative formulations of sapwood senescence on the behaviour of model LIGNUM (with parameter values adjusted for Scots pine (Pinus sylvestris L.) growing southern Finland) were studied. The two alternatives were autonomous sapwood senescence assuming a maximum age for the tree ring, and sapwood senescence that is controlled by the mortality of foliage. For the latter alternative two hypothetical further mechanisms were stipulated. All the formulations were implemented in LIGNUM. Simulations were made with all model variants for fertile and poor soil conditions using high, normal and low rates of foliage mortality. The simulation results were compared against of a data set consisting of 11 open grown Scots pine trees from southern Finland. Observations of heartwood proportion were used in this study. They show that heartwood starts to increase in trees from age of approximately 20 years onwards. The simulation results showed no differences between fertile and poor soil conditions as regards heartwood formation. Of the variants of foliage-controlled sapwood senescence the one where death of sapwood in a tree segment induces sapwood senescence in the tree parts below only slightly was the best. This and the autonomous sapwood senescence corresponded equally well to the observations. In order to make more refined conclusions additional data and simulations are necessary.
An ecophysiological growth process model, called INCA, for simulating the growth and development of a young walnut tree (Juglans regia L.) during three or four years, is presented. This tool, currently under development, aims at integrating architectural and physiological knowledge of the processes involved, in order to give a more rational understanding of the pruning operation. The model describes a simple three-dimensional representation of tree crown, solar radiation interception, photosynthesis, respiration, growth and partitioning of assimilates to leaves, stems, branches and roots. It supports the hypothesis that the tree grows as a collection of semiautonomous, interacting organs that compete for resources, based on daily sink strengths and proximity to sources. The actual growth rate of organs is not predetermined by empirical data, but reflects the pattern of available resources. The major driving variables are solar radiation, temperature, topological, geometrical and physiological factors. Outputs are hourly and daily photosynthate production and respiration, daily dimensional growth, starch storage, biomass production and total number of different types of organ. The user can interact or override any or all of the input variables to examine the effects of such changes on photosynthate production and growth. Within INCA, the tree entities and the surrounding environment are structured in a frame-based representation whereas the processes are coded in a rule-based language. The simulation mechanism is primarily based on the rule chaining capabilities of an inference engine.
A new approach for modelling plant growth using the software AMAPpara is presented. This software takes into consideration knowledge about plant architecture which has been accumulated at the Plant Modelling Unit of CIRAD for several years, and introduces physiological concepts in order to simulate the dynamic functioning of trees. The plant is considered as a serial connection of vegetative organs which conduct water from the roots to the leaves. Another simple description of the plant as a network of parallel pipes is also presented which allows an analytical formulation of growth to be written. This recurring formula is used for very simple architectures and is useful to understand the role of each organ in water transport and assimilate production. Growth simulations are presented which show the influence of modifications in architecture on plant development.
The rule-based formal language of "stochastic sensitive growth grammars" was designed to describe algorithmically the changing morphology of forest trees during their lifetime under the impact of endogenous and exogenous factors, and to generate 3-D simulations of tree structures in a systematic manner. The description in the form of grammars allows the precise specification of structural models with functional components. These grammars (extended L-systems) can be interpreted by the software GROGRA (Growth grammar interpreter) yielding time series of attributed 3-D structures representing plants. With some recent extensions of the growth-grammar language (sensitive functions, local variables) it is possible to model environmental control of shoot growth and some simple allocation strategies, and to obtain typical competition effects in tree stands qualitatively in the model.
The model HYDRA, which simulates water flow in the branched tree architecture, is characterized. Empirical studies of the last decades give strong evidence for a close structure-function linkage in the case of tree water flow. Like stomatal regulation, spatial patterns of leaf specific conductivity can be regarded as a strategy counteracting conductivity losses, which may arise under drought. Branching-oriented water flow simulation may help to understand how damaging and compensating mechanisms interact within the hydraulic network of trees. Furthermore, a coupling of hydraulic to morphological modelling is a prerequisite if water flow shall be linked to other processes. Basic assumptions of the tree water flow model HYDRA are mass conservation, Darcy's law and the spatial homogeneity of capacitance and axial conductivity. Soil water potential is given as a one-sided border condition. Water flow is driven by transpiration. For unbranched regions these principles are condensed to a nonlinear diffusion equation, which serves as a continuous reference for the discrete method tailored to the specific features of the hydraulic network. The mathematical derivation and model tests indicate that the realization of the basic assumptions is reproducible and sufficiently exact. Moreover, structure and function are coupled in a flexible and computationally efficient manner. Thus, HYDRA may serve as a tool for the comparative study of different tree architectures in terms of hydraulic function.
A method for the measurement of the three-dimensional (3D) architecture of trees was applied to describe two 20-year-old walnut trees, one of them is a timber tree while the other is a fruit tree. The method works at the shoot level and simultaneously describes the plant topology, the plant geometry and the shoot morphology. The method uses a 3D digitiser (3SPACE® FASTRAK®, Polhemus Inc.) associated with software DiplAmi designed for digitiser control and data acquisition management. Plant images may be reconstructed from the data set by using the ray tracing software POV-Ray. Visual comparison between photographs of the walnut trees and images synthesised from digitising was satisfactory. Distribution of basal shoot diameter, as well as leaf area and fruit distributions for both the timber and the fruit tree were non-uniformly distributed in the crown volume. Gradients were likely to be related to the light distribution within the tree. This is in agreement with previous experimental results on several tree species, and also with the predictions of tree architecture models based on light-vegetation interactions.
A metabolic model of height growth and site index is derived from a parametrization of the annual carbon balance of a tree. The parametrization is based on pipe-model theory. Four principal variants of the height-growth model correspond to four combinations of assumptions regarding carbon allocation: (a) the apical shoot is autonomous or (b) it is not; and (A) the specific rate of elongation of a shoot equals that of a woody root or (B) it does not. The bB model is the most general as it includes the aA, bA, and aB models as special cases. If the physiological parameters are constant, then the aA model reduces to the form of the Mitscherlich model and the bA model to the form of a Bertalanffy model. Responses of height growth to year-to-year variation in atmospheric conditions are rendered through adjustments of a subset of the model's parameters, namely, the specific rate of production of carbon substrate and three specific rates of maintenance respiration. As an example, the effect of the increasing atmospheric concentration of CO2 on the time-course of tree height of loblolly pine (Pinus taeda) is projected over 50-year span from 1986. Site index is predicted to increase and, more importantly, the shape of the site-index curve is predicted to change.
Process-based tree growth models are recognized to be flexible tools which are valuable for investigating tree growth in relation to changing environment or silvicultural treatments. In the context of forestry, we address two key modelling problems: allocation of growth which determines total wood production, and distribution of wood along the stem which determines stem form and wood quality. Growth allocation and distribution are the outcome of carbon translocation, which may be described by the Munch theory. We propose a simpler gradient process to describe the carbon distribution in the phloem of conifers. This model is a reformulation of a carbon diffusion-like process proposed by Thornley in 1972. By taking into account the continuity of the cambium along the stem, we obtain a one-dimensional reaction-diffusion model which describes both growth allocation between foliage, stem and roots, and growth distribution along the stem. Distribution of wood along the stem is then regarded as an allocation process at a smaller scale. A preliminary sensitivity analysis is presented. The model predicts a strong relationship between morphology and foliage-root allocation. It also suggests how empirical data, such as stem analysis, could be used to calibrate and validate allocation rules in process-based growth models.