Growth grammars simulating trees – an extension of L-systems incorporating local variables and sensitivity.

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

Sensitive Growth Grammars Specifying Models of Forest Structure, Competition and Plant-Herbivore Interaction

Abstract. Sensitive growth grammars are systems of rewriting rules (extended Lindenmayer systems) with graphical interpretation and with "sensitive functions" designed to allow a feedback from the created virtual 3-D structures to the subsequent rule-application process. Thus it is possible to combine morphological (genetically fixed) growth rules with environmental impact and with functions depending on the competitive situation of individuals in the framework of a precisely-specified model of plant growth. The dynamics of stand development in such models results from purely local rule application. Preliminary results are shown for three different applications in forest-ecosystem modelling: (a) Creation of irregular stand structures, (b) simulation of competitive effects on crown radius development and resulting stand dynamics, and (c) modelling the interaction between trees and herbivores, including the energy budgets of the individual plants and animals. The software system GROGRA, designed to interpret sensitive growth grammars, enables visualisation of the resulting spatial structures and provides analysis tools and data interfaces to other software.

Enhanced Possibilities for Analyzing Tree Structure as Provided by an Interface between Different Modelling Systems

In recent years, many different advanced mathematical models and simulation systems for tree and forest growth have been developed. We show a possibility to extend analysis tools for measured and simulated plants using a data interface between the simulation model LIGNUM and the multifunctional software system GROGRA. Both systems were developed by different teams. To demonstrate the enhanced possibilities for analyzing a LIGNUM tree, several examples are given. In these examples three different approaches for analysis are applied to measured and simulated trees: Fractal dimension, deduction of tapering laws, and water potential patterns obtained from simulation of waterflow by the specialized software HYDRA. Conclusions for the interfacing and comparison of different modelling tools are drawn