Dynamics in European and North American Soft-Bottom Mussel Beds
45
(the fractal dimension, D) to be given to natural objects like mussel beds that
have complicated shapes. Indeed, Mandelbrot's (1982) computer-generated
fractal shapes bear such a strong resemblance to aerial maps of mussel beds
(such as the maps in Nehls and Thiel 1993 and Herlyn and Michaelis 1995)
that they can easily be confused for the real thing.
Snover and Commito (1998) analyzed the fractal geometry of a softbottom Mytilus edulis bed in Maine, USA. They discovered that the complex,
patchy, and seemingly disordered distribution of mussels within the bed was
spatially ordered. They predicted that the fractal dimension of patch outlines
would be low at low mussel density and percent cover values, high at
intermediate values, and drop again as density and percent cover increased so
that mussels essentially filled the horizontal plane. They found that D values
varied as predicted, with concave-downward parabolic second-order regression curves (density: r 2 =0.94; percent cover: r 2 =0.92). They were also able to
relate fractal dimension to Morisita's index, a parameter commonly used by
ecologists to quantify spatial pattern (negative-slope regression line, r 2 =0.82).
The application of the fractal dimension to mussel-bed surface topography
has also proven to have predictive value. Commito and Rusignuolo (2000)
made plaster casts of the same mussel bed and calculated D values for the
vertical profiles of cross-sections through the casts. They predicted that D
values for surface topography would be lower than D values in aerial view,
simply because the bed profile cannot have irregularities as large and complex as the horizontal gaps and projections in mussel patches extending great
distances. They also predicted that the fractal dimension would be similar to
that of the familiar Koch curve, which (in their view!) has a shape somewhat
like that of a mussel-bed surface. In fact, D was lower for every surface profile
than for every aerial view. Moreover, D for the plaster casts ranged up to mean
(1.24) and median (1.25) values quite close to the predicted Koch curve value
of 1.26. At sites in Maine with high rates of mussel recruitment and growth,
hummocking has been observed, leading to more complex bed surface
topography, which Commito and Rusignuolo predict would cause higher D
values. If so, then the fractal dimension could serve as a useful indicator of
rates of recruitment and growth. Similarly, the fractal dimension of the bed
surface could be valuable in analyzing many important shape-dependent
parameters, including flow regimes over the bottom, the provision of habitat
space within the three-dimensional matrix of mussel beds, and the ability of
predators and herbivores to negotiate the bed surface.
Although the two Maine studies were carried out over a two order of magnitude range in spatial scale, they were still at the very local scale of less than
25 cm. At larger scales, the fractal dimension might serve as a useful
monitoring tool for the progress of mussel-bed alteration and recovery.
Schwinghamer et al. (1996) used fractals to measure the impact of dredging
on seafloor habitat structure, so the practical application of fractal dimension
45
(the fractal dimension, D) to be given to natural objects like mussel beds that
have complicated shapes. Indeed, Mandelbrot's (1982) computer-generated
fractal shapes bear such a strong resemblance to aerial maps of mussel beds
(such as the maps in Nehls and Thiel 1993 and Herlyn and Michaelis 1995)
that they can easily be confused for the real thing.
Snover and Commito (1998) analyzed the fractal geometry of a softbottom Mytilus edulis bed in Maine, USA. They discovered that the complex,
patchy, and seemingly disordered distribution of mussels within the bed was
spatially ordered. They predicted that the fractal dimension of patch outlines
would be low at low mussel density and percent cover values, high at
intermediate values, and drop again as density and percent cover increased so
that mussels essentially filled the horizontal plane. They found that D values
varied as predicted, with concave-downward parabolic second-order regression curves (density: r 2 =0.94; percent cover: r 2 =0.92). They were also able to
relate fractal dimension to Morisita's index, a parameter commonly used by
ecologists to quantify spatial pattern (negative-slope regression line, r 2 =0.82).
The application of the fractal dimension to mussel-bed surface topography
has also proven to have predictive value. Commito and Rusignuolo (2000)
made plaster casts of the same mussel bed and calculated D values for the
vertical profiles of cross-sections through the casts. They predicted that D
values for surface topography would be lower than D values in aerial view,
simply because the bed profile cannot have irregularities as large and complex as the horizontal gaps and projections in mussel patches extending great
distances. They also predicted that the fractal dimension would be similar to
that of the familiar Koch curve, which (in their view!) has a shape somewhat
like that of a mussel-bed surface. In fact, D was lower for every surface profile
than for every aerial view. Moreover, D for the plaster casts ranged up to mean
(1.24) and median (1.25) values quite close to the predicted Koch curve value
of 1.26. At sites in Maine with high rates of mussel recruitment and growth,
hummocking has been observed, leading to more complex bed surface
topography, which Commito and Rusignuolo predict would cause higher D
values. If so, then the fractal dimension could serve as a useful indicator of
rates of recruitment and growth. Similarly, the fractal dimension of the bed
surface could be valuable in analyzing many important shape-dependent
parameters, including flow regimes over the bottom, the provision of habitat
space within the three-dimensional matrix of mussel beds, and the ability of
predators and herbivores to negotiate the bed surface.
Although the two Maine studies were carried out over a two order of magnitude range in spatial scale, they were still at the very local scale of less than
25 cm. At larger scales, the fractal dimension might serve as a useful
monitoring tool for the progress of mussel-bed alteration and recovery.
Schwinghamer et al. (1996) used fractals to measure the impact of dredging
on seafloor habitat structure, so the practical application of fractal dimension