Modelling Growth Forms of Biological Objects using Fractals
Jaap A. Kaandorp

Abstract

The emergence of forms in the growth process of biological objects is one of the most fundamental problems in biology. Since a long time mathematical models of growth processes in biology have been developed with the purpose to gain understanding in the morphogenesis. Even for organisms with a relatively simple growth process, little insight is yet obtained in the morphogenesis and it is unknown how the genetical information is translated in the actual form. A growth process can be described as an iteration process. In such a process the output of an iteration step is used again as input for the next iteration step. In a growth process the form of a growing object in a certain growth stage is also determined by the form of the object in the preceding growth stage. In each growth stage material is added to this preceding growth stage. The most natural way to describe a growth process is a morphological model in which the addition of material during the growth process is simulated. Growing objects can be thought to be built of basic building elements (cells, spicules, corallites etc.). These basic elements are united into a structure during the growth process. The emergence of this structure cannot be deduced from these individual composing elements. Together these basic elements exhibit a new often highly complex behaviour. To obtain a deeper insight of these complex systems, simulation models are often the only available option.

As a case study in this thesis one type of growth process (radiate accretive growth) which can be found among marine sessile organisms from various taxonomic classes, is used. Radiate accretive growth is a relatively simple growth process where layers of material in each growth stage are deposited on top of the preceding growth form. The preceding form remains unchanged in this process. The relative simplicity of the growth process, when compared to for example the growth process in seed plants, makes this class of marine sessile organisms a very suitable case study in the development of a morphological growth simulation model. Another important reason for selecting this group of organisms as a research object is that the physical environment for marine sessile organisms is relatively uniform when compared to the terrestrial environment. For many of these organisms the environmental parameters influencing the growth form can often be reduced to two key parameters: exposure to water movement and light intensity. This makes it possible to introduce the effect of the physical environment in the simulation models.

In this thesis the assumptions which are made in the simulation models are verified using the results of experiments done on the actual objects. In these experiments the biological relevance of the models was tested by comparing growth forms, which emerged in an environment where one of the key parameters (exposure to water movement) was experimentally changed, to the forms predicted by the simulation models. It was demonstrated that it is possible to predict several changing aspects in the growth forms with a simulation model.

Simulation models with a well-tested biological relevance and a predictive value can be applied in ecology. The growth form of an organism can be considered as a continuous and integral registration of the governing environmental parameters. This makes growth forms, in combination with a simulation model, applicable for bio-monitoring purposes. It becomes possible to detect slowly progressing changes in the physical environment from these growth forms. In this thesis also an example is given how a sudden change in the environment (a toxic agent) may affect the growth form.

Last modified: Monday, 20-Feb-1995 16:02:14 CET

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