Synergy between fractal dimension and lacunarity index in design of artificial habitat for alternative SCUBA diving site

Abstract

Because dive tourism is now a major commercial use of marine protected areas worldwide, the impact and damage to natural reefs caused by intensive diving are now an important eco-environmental issue. Redistributing divers to substituted natural reefs area is one management strategy recently used to solve the crisis. Lan et al. proposed the first deterministic fractal-based model to address the optimal design problem of habitat patterns in marine environments. Their model not only considered a finite project budget, but also applied the fractal dimension (FD), a commonly used index in landscape ecology, to assess the spatial complexity of the habitat. However, a problem with lots of landscape indices is that different spatial patterns can be realized for any single value of the respective index. The FD is no exception. Specifically, different fractal sets may share the same FD values but have different appearances. To select simulated artificial habitats patterns that meet the needs of decision makers, the overriding objective in this study is to enhance the performance of conventional fractal-based habitat model. Therefore, we introduce the index, lacunarity, as second stage index to characterize different spatial patterns that have the same FD value, since lacunarity has been verified to solve the problem effectively. Its application by ecological engineers and managers as a quantification tool for evaluating fractal-based artificial habitats is also demonstrated.