Species diversity in a fractal world

Collaborators: Barbara Downes (lead investigator), Jill Lancaster, Rebecca Lester (Deakin Uni) & Steve Rice (Loughborough Uni, UK)

Funding: Australian Research Council Discovery Grant (2016-2018)


Segment of a coastline. Coastlines have fractal dimensions greater than 1, which captures their wiggly nature.

Understanding the connections between the number of species in a region (the “regional species pool”) and which species coexist in particular locales (“local species diversity”) is a key question in ecology. A known source of variation in local species diversity is the physical complexity of the environment. Increasing complexity creates a greater diversity of resources (living spaces and food), and results in higher species diversity, but quantifying physical complexity is difficult. An exciting means for capturing physical complexity is a measure called the fractal dimension. Fractal dimensions (FD, literally “fractional dimensions”) have values lying between the well-understood dimensions of 1, 2 or 3 (line, surface and volume). Thus a perfectly straight line has an FD of 1.0, whereas a wiggly line on a 2-dimensional plane has an FD between 1.0 and 2.0. One compelling aspect of fractal dimensions is that many environments have the same fractal dimension over a range of spatial scales, and are termed self-similar over those scales. Coastlines are a famous example, and river networks also exhibit self-similarity.Self-similar environments mean the FD measures variability in a way that is scale-independent, which is rare in ecology.


The coastline from within the red box (above, left) but magnified. Its appearance is very similar to the image above because coastlines look the same regardless of spatial scale (Pictures from Google Earth)

Our aim is to test – at landscape-scales – a new model (the spatial scaling model, SSM), which proposes that fractals successfully predict distributions of essential resources and hence species diversity, as long as species’ dispersal abilities are also taken into account.

The research will focus specifically on a guild of caddisflies with larvae that live in streams and terrestrially based adults that have the same specialised egg-laying (‘oviposition’) behaviour. They lay their eggs as discrete masses on the underside of objects in the river that protrude above the water surface, predominantly emergent rocks.

Our previous research demonstrates that emergent rocks are the most important resources for gravid females, and can have direct demographic consequences because they limit the supply of new individuals into the population (see for example Lancaster & Downes 2014).


Riffles – areas of fast-flowing water in streams – provide places with lots of emergent rocks, which are essential for many species of aquatic insects for ovipositing eggs. The distribution of emergent rocks can be measured using fractal dimensions and preliminary data suggest their distributions are self-similar along river channels.


Insect egg masses attached to a rock

The spatial arrangement of emergent rocks can be mapped accurately at multiple scales.Our preliminary data indicate the potential for fractal arrangements of emergent rocks in rivers as well as the distribution of egg masses on those rocks – thus highlighting the suitability of testing the spatial scaling model in this system.