A fractal approach for detecting spatial hierarchy and structure on mussel beds

Abstract.

Within beds of blue mussel (Mytilus edulis L.), individuals are aggregated into small patches, which in turn are incorporated into bigger patches, revealing a complex hierarchy of spatial structure. The present study was done to find the different scales of variation in the distribution of mussel biomass, and to describe the spatial heterogeneity on these scales. The three approaches compared for this purpose were fractal analysis, spatial autocorrelation and hierarchical (or nested) analysis of variances (ANOVA). The complexity (i.e. patchiness) of mussel aggregations was described with fractal dimension, calculated with the semivariogram method. Three intertidal mussel beds were studied on the west coast of Sweden. The distribution of wet biomass was studied along transects up to 128 m. The average biomasses of blue mussels on the three mussel beds were 1825±210, 179±21 and 576±66 g per0.1 m², respectively, and the fractal dimensions of the mussel distribution were 1.726±0.010, 1.842±0.014 and 1.939±0.029 on transects 1–3, respectively. Distributions of mussels revealed multiscaling behaviour. The fractal dimension significantly changed twice on different scales on the first bed (thus showing three scaling regions), the second and third beds revealed two and three scaling regions, respectively. High fractal dimension was followed by significant spatial autocorrelation on smaller scales. The fractal analysis detects the multiple scaling regions of spatial variance even when the spatial structure may not be distinguished significantly by conventional statistical inference. The study shows that the fractal analysis, the spatial autocorrelation analysis and the hierarchical ANOVA give complementary information about the spatial variability in mussel populations.