44
J.A. Commito and N.M.J.A. Dankers
dense mussel patches. They also show that higher edge-dependent rates of
larval recruitment and growth might lead to rapid "in-fill" and the coalescence of individual patches into a more uniform whole.
In summary, it can be seen that stability of soft-bottom mussel beds is scale
dependent with respect to space and time. So far, investigations have been
conducted at large scales of entire seas over decades (Reise and Schubert
1987; Nehls and Thiel 1993; Dankers et aI., in press), and in descending order,
individual estuaries and embayments over 5 or 10 years (McGrorty et aI.1990;
Nehls et ai. 1997), kilometer-scale saltmarshes and stretches of shoreline over
several years (Bertness and Grosholz 1985; Stiven and Gardner 1992; Reusch
and Chapman 1997), meter-scale mussel patches from months to a few years
(Bertness and Grosholz 1985; Stiven and Gardner 1992; Reusch and Chapman
1997), and centimeter-scale within-patch position effects from minutes to a
few years (Bertness and Grosholz 1985; Okamura 1986; Frechette et ai. 1989;
Frechette and Lefaivre 1990; Svane and Ompi 1993; Frechette and Despland
1999). Studies at small spatial and temporal scales have been carried out at
field sites and in laboratories all over the world, whereas those conducted at
the largest scales in time and space tend to be from northern Europe. These
latter investigations provide the background that is needed to assess the impacts of long-term commercial harvesting, pollution, coastal development,
and global warming over entire geographic regions.
2.3 Quantifying Mussel-Bed Structure Using Fractal
Geometry
The persistence of mussel beds depends on the dynamic balance between
removal of mussels and the addition of new mussel biomass by recruitment
and growth. These processes are regulated at least in part by physical structure - the sizes, shapes, and surface topography of the bed components. How
can this complexity be characterized quantitatively? Attention has increasingly been focused on the use of fractal geometry to characterize the shapes
and distributions of plants and animals across spatial scales (e. g., Sugihara
and May 1990; Hastings and Sugihara 1993). The application of fractals has
recently found its way into marine benthic ecology investigations in Europe,
North America, and Australia (Le Tourneux and Bourget 1988; Kaandorp
1991, 1994, 1999; Gee and Warwick 1994a,b; Davenport et ai. 1996, 1999;
Schwinghamer et ai. 1996; Kostylev et ai. 1997; Beck 1998; Snover and Commito 1998; Commito and Rusignuolo, 2000).A fractal outline is a jagged, nondifferentiable curve, often associated with self-similar structure that is repeated at different scales. Fractal geometry allows a quantifiable dimension
J.A. Commito and N.M.J.A. Dankers
dense mussel patches. They also show that higher edge-dependent rates of
larval recruitment and growth might lead to rapid "in-fill" and the coalescence of individual patches into a more uniform whole.
In summary, it can be seen that stability of soft-bottom mussel beds is scale
dependent with respect to space and time. So far, investigations have been
conducted at large scales of entire seas over decades (Reise and Schubert
1987; Nehls and Thiel 1993; Dankers et aI., in press), and in descending order,
individual estuaries and embayments over 5 or 10 years (McGrorty et aI.1990;
Nehls et ai. 1997), kilometer-scale saltmarshes and stretches of shoreline over
several years (Bertness and Grosholz 1985; Stiven and Gardner 1992; Reusch
and Chapman 1997), meter-scale mussel patches from months to a few years
(Bertness and Grosholz 1985; Stiven and Gardner 1992; Reusch and Chapman
1997), and centimeter-scale within-patch position effects from minutes to a
few years (Bertness and Grosholz 1985; Okamura 1986; Frechette et ai. 1989;
Frechette and Lefaivre 1990; Svane and Ompi 1993; Frechette and Despland
1999). Studies at small spatial and temporal scales have been carried out at
field sites and in laboratories all over the world, whereas those conducted at
the largest scales in time and space tend to be from northern Europe. These
latter investigations provide the background that is needed to assess the impacts of long-term commercial harvesting, pollution, coastal development,
and global warming over entire geographic regions.
2.3 Quantifying Mussel-Bed Structure Using Fractal
Geometry
The persistence of mussel beds depends on the dynamic balance between
removal of mussels and the addition of new mussel biomass by recruitment
and growth. These processes are regulated at least in part by physical structure - the sizes, shapes, and surface topography of the bed components. How
can this complexity be characterized quantitatively? Attention has increasingly been focused on the use of fractal geometry to characterize the shapes
and distributions of plants and animals across spatial scales (e. g., Sugihara
and May 1990; Hastings and Sugihara 1993). The application of fractals has
recently found its way into marine benthic ecology investigations in Europe,
North America, and Australia (Le Tourneux and Bourget 1988; Kaandorp
1991, 1994, 1999; Gee and Warwick 1994a,b; Davenport et ai. 1996, 1999;
Schwinghamer et ai. 1996; Kostylev et ai. 1997; Beck 1998; Snover and Commito 1998; Commito and Rusignuolo, 2000).A fractal outline is a jagged, nondifferentiable curve, often associated with self-similar structure that is repeated at different scales. Fractal geometry allows a quantifiable dimension