THE APPLICATION OF FRACTAL GEOMETRY TO THE ANALYSIS OF Mytilus edulis SPATIAL DISTRIBUTION IN A SOFT-BOTTOM SYSTEM

Abstract

The focus of recent research in the application of fractal geometry to ecology has been in measuring the complexity of habitats and relating it to the amount of habitat space available to inhabiting organisms. In this study, the fractal dimension of the outline of a dense assemblage of the marine bivalve Mytilus edulis in Maine, USA, was measured over a scale of 0.004 m - 0.25 m and compared to the assemblages' percent cover, density, and spatial dispersion. Four hypotheses regarding these relationships were tested. The first hypothesis was that the outline of M. edulis against the substrate is fractal. Fractal dimensions of the outline were between 1.36 - 1.86, supporting the first hypothesis. The second hypothesis was that the relationship between the fractal dimension of the outline and the percent cover of M. edulis is represented by a downward opening parabola. This hypothesis was supported by the data being fit to a second order regression curve in the form of a downward opening parabola, with r²=0.94. The third hypothesis was that the relationship between the fractal dimension of the outline and the density of M. edulis is also represented by a downward opening parabola. This hypothesis was also supported by a second order regression curve, with r²=0.92. The fourth hypothesis was that the relationship between fractal dimension and the degree of spatial aggregation of M. edulis is linear and negative. The results supported this hypothesis, showing a negative relationship between the fractal dimension of the outline and the spatial dispersion as measured by Morisita's index value, with r²=0.82. The strength of the correlations found between the fractal dimension of the outline of M. edulis and the three measurements of spatial distribution indicate the usefulness of fractal dimension as an additional measurement tool for ecological studies and as a predictor of spatial distribution.