# The Application of Fractal Geometry to Ecology

Principles of Ecology 310L

Victoria Levin

7 December 1995

Abstract

New insights into the natural world are just a few of the results from the use of fractal geometry. Examples from population and landscape ecology are used to illustrate the usefulness of fractal geometry to the field of ecology. The advent of the computer age played an important role in the development and acceptance of fractal geometry as a valid new discipline. New insights gained from the application of fractal geometry to ecology include: understanding the importance of spatial and temporal scales; the relationship between landscape structure and movement pathways; an increased understanding of landscape structures; and the ability to more accurately model landscapes and ecosystems. Using fractal dimensions allows ecologists to map animal pathways without creating an unmanageable deluge of information. Computer simulations of landscapes provide useful models for gaining new insights into the coexistence of species. Although many ecologists have found fractal geometry to be an extremely useful tool, not all concur. With all the new insights gained through the appropriate application of fractal geometry to natural sciences, it is clear that fractal geometry a useful and valid tool.

New insight into the natural world is just one of the results of the increasing popularity and use of fractal geometry in the last decade. What are fractals and what are they good for? Scientists in a variety of disciplines have been trying to answer this question for the last two decades. Physicists, chemists, mathematicians, biologists, computer scientists, and medical researchers are just a few of the scientists that have found uses for fractals and fractal geometry.

Ecologists have found fractal geometry to be an extremely useful tool for describing ecological systems. Many population, community, ecosystem, and landscape ecologists use fractal geometry as a tool to help define and explain the systems in the world around us. As with any scientific field, there has been some dissension in ecology about the appropriate level of study. For example, some organism ecologists think that anything larger than a single organism obscures the reality with too much detail. On the other hand, some ecosystem ecologists believe that looking at anything less than an entire ecosystem will not give meaningful results. In reality, both perspectives are correct. Ecologists must take all levels of organization into account to get the most out of a study. Fractal geometry is a tool that bridges the "gap" between different fields of ecology and provides a common language.

Fractal geometry has provided new insight into many fields of ecology. Examples from population and landscape ecology will be used to illustrate the usefulness of fractal geometry to the field of ecology. Some population ecologists use fractal geometry to correlate the landscape structure with movement pathways of populations or organisms, which greatly influences population and community ecology. Landscape ecologists tend to use fractal geometry to define, describe, and model the scale-dependent heterogeneity of the landscape structure.

Before exploring applications of fractal geometry in ecology, we must first define fractal geometry. The exact definition of a fractal is difficult to pin down. Even the man who conceived of and developed fractals had a hard time defining them (Voss 1988). Mandelbrot's first published definition of a fractal was in 1977, when he wrote, "A fractal is a set for which the Hausdorff- Besicovitch dimension strictly exceeds the topographical dimension" (Mandelbrot 1977). He later expressed regret for having defined the word at all (Mandelbrot 1982). Other attempts to capture the essence of a fractal include the following quotes:

"Different people use the word fractal in different ways, but all agree that fractal objects contain...

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