The Fractal Dimension of Lichens and the Distribution of Arthropod Body Lengths

Abstract

A single study (Morse et al., 1985; Lawton, 1986) has demonstrated that transects across woody plant surfaces are fractal. An important feature of a fractal curve or surface is that its length or area respectively become disproportionately large as the unit of measurement is decreased (Sugihara & May, 1990). This implies that for woody plant surfaces, there should be more usable space for smaller animals (small unit of measurement) than for larger ones. There should consequently be more small animals than large animals, and the precise slope of this relationship should be predictable from the fractal dimension of the surface and individual rates of resource use (Lawton, 1986). However, if this explanation for the distribution of arthropod body sizes is correct, it should be scale independent. Here we show that transects across small-scale surfaces (lichens) are fractal, and that the bodysize distribution of the small arthropods found on them can similarly be predicted from the fractal dimension. Key-words: Arthropod body size, fractal dimension, lichens, Parmelia saxatilis