On the fractal modelling of biomass distributions: An application to size class in fisheries

Size structure is a fundamental property in an ecosystem. We explore the potential of fractal models to describe biomass distribution within a community across a range of body-weight size. We propose a consistent method selecting a self-similar cascade generating a fractal distribution that replicates field data within a range of scales. Admissible cascades constructed from biomass distribution data are filtered out using the non-parametric Kolmogorov–Smirnov test. A specific analysis is then performed to detect the biomass spreading across a suitable size scales. This is done by computing a parameter (the balanced entropy index) that evaluates evenness in mass splitting. This method is successfully applied to replicate the distribution of fish biomass obtained from a fisheries dataset. The proposed fractal description of the community size structure of the sampled marine ecosystem may prove useful when analyzing key ecological processes which involve all individuals in a community regardless of their species.