Using fractals to describe ecologically-relevant patterns in distributions of large rocks in streams

Measuring the physical complexity of habitats or ecological resources is often achieved using system-specific methods that make comparisons across ecosystems difficult. One measure that is applicable across multiple ecosystems and scales is the fractal dimension, which has the benefit of generality as well as potential scale independence. This study evaluated the use of box-counting and entropy fractal dimensions for characterising the complexity of emergent rock distributions in six streams across Scotland and Australia. Emergent rocks (ER) are important hydraulic features and ecological resources, including as oviposition sites for aquatic insects and cover for fish. We complete fractal analysis on counts of ER in 5-m segments along longitudinal stretches of the six streams. All six streams exhibited fractal behaviour (self-similarity), suggesting that fractals can be used to measure the complexity of longitudinal ER distributions in a way that is scale independent. Entropy was a superior measure due to its ability to differentiate among the six streams whereas box-counting could not. Together, field results and numerical simulations showed that fractal dimensions of emergent rock distributions were related to stream geomorphology. Well-developed bedforms, like alternating pools and riffles had better organised emergent rocks because large bed materials were more likely to be emergent in topographic highs. Streams with coarser bed materials had more chaotic arrangements of emergent rocks because this increased the general abundance of emergent rocks, making differentiation between topographic highs and lows less distinctive. Fractal dimensions, therefore, can measure the complexity of river systems in a way that is relevant to geomorphological and ecological processes.