Fractal dimension of Posidonia oceanica meadows for the assessment of their ecological condition

Ecological analyses are aimed at characterizing the complexity of the structure of natural objects, yet their heterogeneity is hardly described by the Euclidean concepts. For such purpose, the fractal geometry can be best suited due to its ability in describing, with mathematical rigor, the inherent irregularity of nature. Fractal dimension provides indeed a measurement of the complexity of the analyzed object in terms of space occupation. In this study, we applied the fractal geometry to Posidonia oceanica in order to characterize the structural complexity of its meadows, which are widely recognized as one of the most important coastal ecosystems in the Mediterranean basin. For achieving our aim, we developed an ad hoc implementation of the Box-Counting algorithm based on the Moore neighborhood analysis. Our approach allowed to render the structural complexity of P. oceanica meadows spatially explicit, thus expressing an intrinsic ecological property. The fractal analysis suggested that the complexity of meadows structure is intimately connected with the ecological conditions of P. oceanica. In fact, meadows in living and mixed conditions showed a higher fractal dimension, suggesting a largely uniform and smooth structure. While the fractal dimension associated to the regressed ecological condition of P. oceanica meadows exhibited lower values, highlighting a more jagged and rough structure. Therefore, the fractal theory may prove useful to both fundamental and applied ecological research focusing on P. oceanica and its interactions with Mediterranean coastal ecosystems. In fact, the fractal analysis we performed could result in an effective and straightforward approach for assessing the condition of P. oceanica at large spatial scale, enhancing an integrated maritime spatial planning over the whole Mediterranean basin