Morphogenesis in marine algae: L-systems and fractal dimensions

David J. Garbary (1) and Marlies Weber (2)

(1) Department of Biology, St. Francis Xavier University, Antigonish, Nova Scotia, Canada, B2G 2W5 (dgarbary@juliet.stfx.ca)

(2) Department of Biology, University of Victoria, Victoria, British Columbia, Canada

Multicellular marine algae typically have complex shapes and very specific developmental rules that allow them to grow from single cells to mature organisms. Traditional morphological studies have detailed these patterns; however, the approaches have been very descriptive and non-analytical. There has been no clear mechanism for evaluating these forms quantitatively, nor has there been a clear mechanism for quantifying complexity during ontogeny. In addition, there have been no procedures for linking complexity of shape (i.e. morphology) and the information required to generate the particular forms involved. Here we bring together two modelling approaches (Lindenmayer-systems or L-systems, and fractal dimensions): fractal dimensions are used as a metric for complexity of shape, while the L-system production rules are used as a metric for complexity of information. Using images of real seaweeds (i.e., species of Fucus and Ascophyllum) we show that complexity increases with ontogeny in a predictable manner. L-system models (either 0L or stochastic L-systems) based on various filamentous red algae, are then formed for a range of species in which the plants develop from single cells to well developed structures that correspond to the vegetative form of the respective species. Fractal dimension of these forms can then be determined throughout development and compared at an equivalent point in ontogeny. Here we use the L-system models at the point where all of the production rules have been expressed to represent a homologous developmental condition among all of the species. The models show a strong relationship between the complexity of form and the information, e.g., the number of production rules, required to generate these forms.