Using Fractals to Describe Ecologically Relevant Patterns in Distributions of Large Rocks in Streams. Issue 7 (7th July 2021) - Dwyer, G. K.; Cummings, C. R.; Rice, S. P.; Lancaster, Jill; Downes, Barbara J.; Slater, L.; Lester, Rebecca E.
Abstract: 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 characterizing 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 completed fractal analysis on counts of ER in 5‐m segments along longitudinal stretches of the six streams. All six streams exhibited fractal behavior (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 organized 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. Plain Language Summary: Fractal dimensions are used to characterize the complexity of a wide range of patterns in nature, from single objects (e.g., branched twigs) to whole environments (rainforests), and learn where consistent patterns may occur. We measured the complexity of rock patterns (specifically rocks that emerge above the water's surface) in six rivers from Scotland and Australia using fractal dimensions. These rocks provide important habitat for plants, insects, and fish in rivers, and so are important to overall stream condition and functioning. Less complex, more highly structured rock patterns (lower fractal dimensions) occurred in streams with smaller rocks, which had areas where emergent rocks were concentrated (riffles) and many long pools without emergent rocks. These results suggest that fractal dimensions may be a promising measure of complexity that can help us understand relationships between physical characteristics of streams and their ecology. Fractal dimensions also allow comparison of rock patterns in rivers with other habitats, such as shrubs in grasslands for example. This may allow future research to explain patterns that are consistent across these different ecosystems and so advance general ecological theory. Key Points: Longitudinal patterns of emergent fluvial rocks in six streams in Scotland and Australia exhibited fractal behavior (self‐similarity) Fractal dimensions were related to development of bedform topography and the density and size of available bed materials in the streams Fractal dimensions are a promising measure of physical complexity that enable comparisons across ecosystems, scales and disciplines