J .A. Commito, B.R. Rusignuolo J. Exp. Mar. Biol. Ecol. 255 2000 133 –152
137
Fig. 1. Generation of the Koch curve, a self-similar shape with fractal dimension of D 51.26.
mud-mussel boundary in aerial view at the 25 3 25-cm scale ranged from 1.36 to 1.86. If
bed surface topography is less complex than the bed spatial pattern, then over distances of about 25 cm, surface profile fractal dimension values should be smaller than those
obtained in the horizontal plane by Snover and Commito 1998.
2. Methods
2.1. Study site The study site was at the eastern end of the Mytilus edulis bed at Bob’s Cove, an
intertidal flat of sandy mud in Jonesboro, Washington County, Maine, USA 44 8339N:
67 8359W, near the mussel bed locations used in earlier studies describing the soft-
bottom community inside and outside of the bed Commito, 1987; Commito and Boncavage, 1989 and the fractal geometry of the mussel spatial pattern Snover and
Commito, 1998. The bed extends across the mouth of the cove in the lower intertidal and shallow subtidal zones. Air temperature ranges from
2 35 to 358C, and water
138 J
.A. Commito, B.R. Rusignuolo J. Exp. Mar. Biol. Ecol. 255 2000 133 –152
temperature from 0 to 10 8C. In the summer, shallow water moving on to or off the flat
can reach 21 8C. Salinity is usually about 30‰.
2.2. Field and laboratory procedures To obtain background information on the density and size–class distribution of live
2
and dead mussels at the site, on 27 May 1994, eight 20 cm 3 0.02 m cores were taken
at uniform positions 5 m apart, along two parallel transects 4 m apart from each other and 4 m in from the upper margin of the mussel bed. Core contents were sieved in situ
on 0.5-mm mesh. The residue was placed in buffered formalin, stained with rose bengal, and sorted. The lengths of all live mussels and whole disarticulated valves were
measured to the nearest 0.1 mm with vernier calipers or an ocular micrometer.
Casts of the mussel bed surface were made 8–11 June 1994 approximately 30 m east of the site where cores had been taken. Casts were made of three surface types found in
a patchy mosaic within a 5 3 10-m area: zero percent cover no live mussels; empty,
disarticulated whole and broken valves covered the bottom; intermediate percent cover approximately 50 live mussel cover; and high percent cover approximately 85 live
mussel cover; in nearly 20 years of observations at soft-bottom mussel beds in eastern Maine, 100 cover has sometimes been observed at other sites, but not at Bob’s Cove.
Cast locations were spaced as far apart as possible to achieve overdispersion. Fifteen coffer dams of thin aluminum sheeting were constructed in a range of sizes with nominal
width
3 length 3 height dimensions up to 30 3 30 3 30 cm. Plaster of paris mixed in situ with seawater was poured to a thickness of approximately 10 cm into dams that had
been inserted several centimeters into the bed. Casts were made at low tide, so they did not capture the positions of mussels while feeding, nor was there any attempt to
determine the effects of the casting process on mussel behavior. Casts were left in place to harden until low tide the next day and then carefully retrieved with all live mussels
and other surface objects embedded within the plaster. Casts were immediately returned to the laboratory and placed in an oven for approximately 4 h at 150
8C to aid in the plaster curing process and kill any live organisms adhering to the plaster. Casts were
re-measured and did not change size or shape during curing. In test casts, surface objects removed from pre-cured casts fit exactly back into their same locations after the casts
had been cured.
To obtain the longest surface profiles possible, only the five largest casts were used in the analysis: two high, two intermediate, and one zero percent cover. The central area
2.5 cm in from the perimeter of each cast was utilized in order to avoid possible edge effects. To preserve cast topography, all mussels and whole and broken valves were left
embedded in the plaster. The surface of each cast was coated with black graphite. An electric bandsaw with a 1.6-mm thick blade was used to cut each cast into 1.3-cm thick
cross-sections. Each of the resulting 88 cross-sections was scanned into a computer. The black graphite and gray shells contrasted sharply with the white plaster exposed on the
sides of the cross-sections, allowing the bed surface profile to be readily determined.
2.3. Calculating fractal dimension The profile from one face of each cross-section was included in the analysis. The
J .A. Commito, B.R. Rusignuolo J. Exp. Mar. Biol. Ecol. 255 2000 133 –152
139
boundary-grid method Sugihara and May, 1990 was used to determine the fractal dimension of each profile. Eight grids i
5 1, 2, . . . , 8 were superimposed on the first 20-cm length of each cross-section. Each grid contained squares with a side length of n
i
pixels, where n 5 3 3 2 5 6, 12, 24, 48, 96, 192, 384, or 768, resulting in squares with
side lengths of 1.44–200 mm. The number of squares entered by each profile N was counted for each grid. Fractal dimension, D, was determined from the following
equation where k represents a constant:
2D
N 5 kn
1 where D equals the negative of the slope from the linear regression of log n against
2
log N.
2
2.4. Statistical analysis To gain some understanding of how fractal dimension varied at the within-cast spatial
scale, the nonparametric runs test was used to determine if the D values for consecutive surface profiles in each cast had random variability or, alternatively, were serially
correlated Zar, 1984. To test for differences in D among the five casts, the nonparametric Kruskal–Wallis test one-way ANOVA on ranks and Dunn’s a posteriori
multiple comparison test were used Zar, 1984.
3. Results
